From b1f291396d8ff56fffe7687b1162534e3673f89c Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 16 Apr 2025 19:26:15 +0200 Subject: [PATCH 01/49] Expose function to get the node values & improve corresponding test --- examples/cpp/get-subgrids.cpp | 93 ++++++++++++++++++++++++++++------- examples/cpp/output | 52 ++++++++++---------- pineappl_capi/src/lib.rs | 27 ++++++++-- 3 files changed, 125 insertions(+), 47 deletions(-) diff --git a/examples/cpp/get-subgrids.cpp b/examples/cpp/get-subgrids.cpp index b37f0db4b..445e75c87 100644 --- a/examples/cpp/get-subgrids.cpp +++ b/examples/cpp/get-subgrids.cpp @@ -5,11 +5,10 @@ #include #include #include +#include #include #include #include -#include - std::vector unravel_index(std::size_t flat_index, const std::vector& shape) { std::size_t ndim = shape.size(); @@ -23,13 +22,14 @@ std::vector unravel_index(std::size_t flat_index, const std::vector return coords; } -std::string coords_to_string(const std::vector& coords) { +template +std::string vector_to_string(const std::vector& coords) { std::ostringstream osstream; osstream << "("; for (std::size_t i = 0; i < coords.size(); ++i) { osstream << coords[i]; - if (i != coords.size() - 1) { + if (i != coords.size() - 1) { osstream << ", "; } } @@ -38,6 +38,41 @@ std::string coords_to_string(const std::vector& coords) { return osstream.str(); } +std::vector get_subgrid_array( + const pineappl_grid* grid, + std::vector subgrid_shape, + std::size_t bin, + std::size_t order, + std::size_t channel +) { + // Compute the length of the flattened shape by multiplying the entries + std::size_t flat_shape = std::accumulate(subgrid_shape.begin(), + subgrid_shape.end(), 1, std::multiplies()); + + // Extract the flattened subgrid values/weights + std::vector subgrid_array(flat_shape); + pineappl_grid_subgrid_array(grid, bin, order, channel, subgrid_array.data()); + + return subgrid_array; +} + +std::vector get_node_values( + const pineappl_grid* grid, + std::vector subgrid_shape, + std::size_t bin, + std::size_t order, + std::size_t channel +) { + // Compute the length of the flattend nodes + std::size_t nodes_size = std::accumulate(subgrid_shape.begin(), + subgrid_shape.end(), 0.0); + + // Extract the values of the nodes as a flattened array + std::vector node_values(nodes_size); + pineappl_grid_node_values(grid, bin, order, channel, node_values.data()); + + return node_values; +} int main() { std::string filename = "drell-yan-rap-ll.pineappl.lz4"; @@ -54,35 +89,57 @@ int main() { std::size_t subgrid_dim = pineappl_grid_kinematics_len(grid); std::cout << std::right << std::setw(10) << "bin" << std::setw(10) << "sg idx" - << std::setw(6 * subgrid_dim) << "sg coordinates" << std::setw(16) - << "sg value" << "\n"; + << std::setw(6 * subgrid_dim) << "sg coordinates" + << std::setw(12 * subgrid_dim) << "node values" << std::setw(16) + << "weight value" << "\n"; std::cout << std::right << std::setw(10) << "---" << std::setw(10) << "------" - << std::setw(6 * subgrid_dim) << "--------------" << std::setw(16) - << "------------" << "\n"; + << std::setw(6 * subgrid_dim) << "--------------" + << std::setw(12 * subgrid_dim) << "--------------------------------" + << std::setw(16) << "------------" << "\n"; for (std::size_t b = 0; b < n_bins; ++b) { + // Extract the shape of the subgrids std::vector subgrid_shape(subgrid_dim); pineappl_grid_subgrid_shape(grid, b, order, channel, subgrid_shape.data()); // Check if the subgrid is not empty if (subgrid_shape[0] != 0) { - std::size_t flat_shape = std::accumulate(subgrid_shape.begin(), - subgrid_shape.end(), 1, std::multiplies()); - std::vector subgrid_array(flat_shape); - - pineappl_grid_subgrid_array(grid, b, order, channel, subgrid_array.data()); + std::vector subgrid_array = get_subgrid_array(grid, subgrid_shape, b, order, channel); + std::vector node_values = get_node_values(grid, subgrid_shape, b, order, channel); for (std::size_t index = 0; index < subgrid_array.size(); ++index) { if (subgrid_array[index] != 0) { // Unravel the index to recover the standard coordinates std::vector coords = unravel_index(index, subgrid_shape); - std::cout << std::right << std::setw(10) << b << std::setw(10) - << index << std::setw(6 * subgrid_dim) << coords_to_string(coords) - << std::setw(16) << subgrid_array[index] << "\n"; + // Store the values of the nodes in a vector. The vector therefore + // contains as elements {Scale, x1, x2, ..., xn} + std::vector node_values_index(coords.size()); + std::size_t start_index = 0; + for (std::size_t nd = 0; nd < coords.size(); ++nd) { + if (nd != 0) { start_index += subgrid_shape[nd - 1]; } + node_values_index[nd] = node_values[start_index + coords[nd]]; + } - // Compare to some reference value - if (b==0 && index==41020) { + std::cout << std::right << std::setw(10) << b << std::setw(10) + << index << std::setw(6 * subgrid_dim) + << vector_to_string(coords) << std::setw(12 * subgrid_dim) + << vector_to_string(node_values_index) << std::setw(16) + << subgrid_array[index] << "\n"; + + // Compare to some reference value. + if (b == 0 && index == 41020) { + // Check the unravelled index + assert(coords[0] == 16); + assert(coords[1] == 20); + assert(coords[2] == 20); + + // Check the values of the node entries. + assert(node_values_index[0] == 5442.30542919352900); // PyAPI: `subgrid.node_values[0][16]` + assert(node_values_index[1] == 0.03052158400782889); // PyAPI: `subgrid.node_values[1][20]` + assert(node_values_index[2] == 0.03052158400782889); // PyAPI: `subgrid.node_values[2][20]` + + // PyAPI: `grid.subgrid(0, 0, 0).to_array(subgrid.shape)[16][20][20]` assert(subgrid_array[index] == -4.936156925096015e-07); } break; diff --git a/examples/cpp/output b/examples/cpp/output index d5ad2d4d7..2ce8b5c7f 100644 --- a/examples/cpp/output +++ b/examples/cpp/output @@ -146,32 +146,32 @@ idx left right dsig/dx dx 21 2.1 2.2 3.507294e-02 0.1 22 2.2 2.3 1.976542e-02 0.1 23 2.3 2.4 5.590552e-03 0.1 - bin sg idx sg coordinates sg value - --- ------ -------------- ------------ - 0 41020 (16, 20, 20) -4.93616e-07 - 1 41020 (16, 20, 20) -4.5499e-08 - 2 40971 (16, 19, 21) -4.10008e-08 - 3 40971 (16, 19, 21) -2.78597e-07 - 4 40971 (16, 19, 21) -2.01924e-07 - 5 40922 (16, 18, 22) -3.39322e-10 - 6 40922 (16, 18, 22) -8.43358e-08 - 7 40922 (16, 18, 22) -2.99247e-07 - 8 40922 (16, 18, 22) -1.5117e-07 - 9 40872 (16, 17, 22) -9.95013e-11 - 10 40873 (16, 17, 23) -1.30578e-07 - 11 40873 (16, 17, 23) -2.55869e-07 - 12 40823 (16, 16, 23) -1.0823e-09 - 13 40823 (16, 16, 23) -4.22686e-09 - 14 40824 (16, 16, 24) -1.68149e-07 - 15 40774 (16, 15, 24) -7.58702e-10 - 16 40774 (16, 15, 24) -2.41887e-08 - 17 40774 (16, 15, 24) -8.83139e-09 - 18 40725 (16, 14, 25) -1.14932e-09 - 19 40725 (16, 14, 25) -3.03857e-08 - 20 40725 (16, 14, 25) -2.66414e-08 - 21 40675 (16, 13, 25) -3.60243e-10 - 22 40676 (16, 13, 26) -1.22785e-08 - 23 40626 (16, 12, 26) -7.04493e-11 + bin sg idx sg coordinates node values weight value + --- ------ -------------- -------------------------------- ------------ + 0 41020 (16, 20, 20) (5442.31, 0.0305216, 0.0305216) -4.93616e-07 + 1 41020 (16, 20, 20) (5442.31, 0.0305216, 0.0305216) -4.5499e-08 + 2 40971 (16, 19, 21) (5442.31, 0.0434149, 0.0210892) -4.10008e-08 + 3 40971 (16, 19, 21) (5442.31, 0.0434149, 0.0210892) -2.78597e-07 + 4 40971 (16, 19, 21) (5442.31, 0.0434149, 0.0210892) -2.01924e-07 + 5 40922 (16, 18, 22) (5442.31, 0.06048, 0.0143751) -3.39322e-10 + 6 40922 (16, 18, 22) (5442.31, 0.06048, 0.0143751) -8.43358e-08 + 7 40922 (16, 18, 22) (5442.31, 0.06048, 0.0143751) -2.99247e-07 + 8 40922 (16, 18, 22) (5442.31, 0.06048, 0.0143751) -1.5117e-07 + 9 40872 (16, 17, 22) (5442.31, 0.0822812, 0.0143751) -9.95013e-11 + 10 40873 (16, 17, 23) (5442.31, 0.0822812, 0.00969916) -1.30578e-07 + 11 40873 (16, 17, 23) (5442.31, 0.0822812, 0.00969916) -2.55869e-07 + 12 40823 (16, 16, 23) (5442.31, 0.109144, 0.00969916) -1.0823e-09 + 13 40823 (16, 16, 23) (5442.31, 0.109144, 0.00969916) -4.22686e-09 + 14 40824 (16, 16, 24) (5442.31, 0.109144, 0.00649621) -1.68149e-07 + 15 40774 (16, 15, 24) (5442.31, 0.141121, 0.00649621) -7.58702e-10 + 16 40774 (16, 15, 24) (5442.31, 0.141121, 0.00649621) -2.41887e-08 + 17 40774 (16, 15, 24) (5442.31, 0.141121, 0.00649621) -8.83139e-09 + 18 40725 (16, 14, 25) (5442.31, 0.178026, 0.0043285) -1.14932e-09 + 19 40725 (16, 14, 25) (5442.31, 0.178026, 0.0043285) -3.03857e-08 + 20 40725 (16, 14, 25) (5442.31, 0.178026, 0.0043285) -2.66414e-08 + 21 40675 (16, 13, 25) (5442.31, 0.219504, 0.0043285) -3.60243e-10 + 22 40676 (16, 13, 26) (5442.31, 0.219504, 0.00287387) -1.22785e-08 + 23 40626 (16, 12, 26) (5442.31, 0.265114, 0.00287387) -7.04493e-11 idx p-p c#0 l#0 p-p~ c#0 l# p-d c#0 l#0 p-d dx --- ------------ ----------- ------------- ------------ ------ 0 5.263109e-01 5.263109e-01 5.263109e-01 5.263109e-01 0.1 diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index c28ee9616..ab9150cdc 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -1951,10 +1951,31 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_shape( }; let shape = unsafe { slice::from_raw_parts_mut(shape, grid.kinematics().len()) }; - shape.copy_from_slice(&subgrid_shape); + shape.copy_from_slice(subgrid_shape); } -/// Get the subgrid for a given bin, channel, and order +/// Get the nodes of the subgrid. +/// +/// # Safety +/// +#[no_mangle] +pub unsafe extern "C" fn pineappl_grid_node_values( + grid: *const Grid, + bin: usize, + order: usize, + channel: usize, + node_values: *mut f64, +) { + let grid = unsafe { &*grid }; + let subgrid = &grid.subgrids()[[order, bin, channel]]; + + let flatten_subgrid: Vec = subgrid.node_values().into_iter().flatten().collect(); + let node_values = unsafe { slice::from_raw_parts_mut(node_values, flatten_subgrid.len()) }; + + node_values.copy_from_slice(flatten_subgrid.as_slice()); +} + +/// Get the subgrid for a given bin, channel, and order. /// /// # Safety /// @@ -1980,7 +2001,7 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_array( unsafe { slice::from_raw_parts_mut(subgrid_array, shape.iter().product()) }; for (index, value) in subgrid.indexed_iter() { - let ravel_index = ravel_multi_index(index.as_slice(), &shape); + let ravel_index = ravel_multi_index(index.as_slice(), shape); subgrid_array[ravel_index] = value; } } From fa23e329510fcd08e9c213cb6b5a44284d1db540 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Thu, 17 Apr 2025 20:12:39 +0200 Subject: [PATCH 02/49] Fix function naming --- examples/cpp/get-subgrids.cpp | 2 +- pineappl_capi/src/lib.rs | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/cpp/get-subgrids.cpp b/examples/cpp/get-subgrids.cpp index 445e75c87..5cd1385de 100644 --- a/examples/cpp/get-subgrids.cpp +++ b/examples/cpp/get-subgrids.cpp @@ -69,7 +69,7 @@ std::vector get_node_values( // Extract the values of the nodes as a flattened array std::vector node_values(nodes_size); - pineappl_grid_node_values(grid, bin, order, channel, node_values.data()); + pineappl_grid_subgrid_node_values(grid, bin, order, channel, node_values.data()); return node_values; } diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index ab9150cdc..18d0f83d2 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -1959,7 +1959,7 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_shape( /// # Safety /// #[no_mangle] -pub unsafe extern "C" fn pineappl_grid_node_values( +pub unsafe extern "C" fn pineappl_grid_subgrid_node_values( grid: *const Grid, bin: usize, order: usize, From 42ebeaa63da38752b16b0a550b09dcacd33afe24 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Mon, 21 Apr 2025 10:21:26 +0200 Subject: [PATCH 03/49] Sort download list alphabetically --- maintainer/download-test-data.sh | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/maintainer/download-test-data.sh b/maintainer/download-test-data.sh index 0e696dd67..31c0c23ac 100755 --- a/maintainer/download-test-data.sh +++ b/maintainer/download-test-data.sh @@ -18,6 +18,8 @@ download() { fi } +download 'https://data.nnpdf.science/dy_high_mass/CMS_DY_14TEV_MLL_6000_COSTH.pineappl.lz4' +download 'https://data.nnpdf.science/dy_high_mass/NNPDF_DY_14TEV_BSM_AFB.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/ATLASWPT11-Wplus_tot.appl' download 'https://data.nnpdf.science/pineappl/test-data/CMS_TTB_8TEV_2D_TTM_TRAP_TOT-opt.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/CMS_TTB_8TEV_2D_TTM_TRAP_TOT.tar' @@ -29,24 +31,22 @@ download 'https://data.nnpdf.science/pineappl/test-data/LHC8-Mtt-HT4-173_3-bin1. download 'https://data.nnpdf.science/pineappl/test-data/LHCBWZMU7TEV_PI_part1.appl' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_DY_8TEV.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_DY_8TEV.tar' +download 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV.tar' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_old.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_opt.pineappl.lz4' -download 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV.tar' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_v2.tar' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_v2_xif_2.tar' download 'https://data.nnpdf.science/pineappl/test-data/NJetEvents_0-0-2.tab.gz' +download 'https://data.nnpdf.science/pineappl/test-data/NNPDF_POS_F2D_40.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/NUTEV_CC_NU_FE_SIGMARED.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/NUTEV_CC_NU_FE_SIGMARED.tar' -download 'https://data.nnpdf.science/dy_high_mass/CMS_DY_14TEV_MLL_6000_COSTH.pineappl.lz4' -download 'https://data.nnpdf.science/dy_high_mass/NNPDF_DY_14TEV_BSM_AFB.pineappl.lz4' -download 'https://ploughshare.web.cern.ch/ploughshare/db/applfast/applfast-atlas-dijets-fnlo-arxiv-1312.3524/grids/applfast-atlas-dijets-fnlo-arxiv-1312.3524-xsec000.tab.gz' -download 'https://ploughshare.web.cern.ch/ploughshare/db/applfast/applfast-h1-dijets-appl-arxiv-0010054/grids/applfast-h1-dijets-appl-arxiv-0010054-xsec000.appl' -download 'https://ploughshare.web.cern.ch/ploughshare/db/applfast/applfast-h1-incjets-fnlo-arxiv-0706.3722/grids/applfast-h1-incjets-fnlo-arxiv-0706.3722-xsec000.tab.gz' -download 'https://ploughshare.web.cern.ch/ploughshare/db/atlas/atlas-atlas-wpm-arxiv-1109.5141/grids/atlas-atlas-wpm-arxiv-1109.5141-xsec001.appl' +download 'https://data.nnpdf.science/pineappl/test-data/SIHP-PP-POLARIZED-STAR-NLO.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/STAR_WMWP_510GEV_WM-AL-POL.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/STAR_WMWP_510GEV_WM-AL-POL_PolPDF.tar' download 'https://data.nnpdf.science/pineappl/test-data/STAR_WMWP_510GEV_WM-AL-POL_UnpolPDF.tar' download 'https://data.nnpdf.science/pineappl/test-data/ZEUS_2JET_319GEV_374PB-1_DIF_ETQ2_BIN6.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/ZEUS_2JET_319GEV_374PB-1_DIF_ETQ2_BIN6.tar' -download 'https://data.nnpdf.science/pineappl/test-data/SIHP-PP-POLARIZED-STAR-NLO.pineappl.lz4' -download 'https://data.nnpdf.science/pineappl/test-data/NNPDF_POS_F2D_40.pineappl.lz4' +download 'https://ploughshare.web.cern.ch/ploughshare/db/applfast/applfast-atlas-dijets-fnlo-arxiv-1312.3524/grids/applfast-atlas-dijets-fnlo-arxiv-1312.3524-xsec000.tab.gz' +download 'https://ploughshare.web.cern.ch/ploughshare/db/applfast/applfast-h1-dijets-appl-arxiv-0010054/grids/applfast-h1-dijets-appl-arxiv-0010054-xsec000.appl' +download 'https://ploughshare.web.cern.ch/ploughshare/db/applfast/applfast-h1-incjets-fnlo-arxiv-0706.3722/grids/applfast-h1-incjets-fnlo-arxiv-0706.3722-xsec000.tab.gz' +download 'https://ploughshare.web.cern.ch/ploughshare/db/atlas/atlas-atlas-wpm-arxiv-1109.5141/grids/atlas-atlas-wpm-arxiv-1109.5141-xsec001.appl' From a1cc5320df50da8ee4c485cec19ffcb3f9728785 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Mon, 21 Apr 2025 10:43:14 +0200 Subject: [PATCH 04/49] Download test data for Python into central cache --- .github/workflows/python.yml | 13 +++++++++++++ .github/workflows/rust.yml | 2 +- maintainer/download-test-data.sh | 4 ++++ pineappl_py/tests/conftest.py | 25 +++---------------------- 4 files changed, 21 insertions(+), 23 deletions(-) diff --git a/.github/workflows/python.yml b/.github/workflows/python.yml index 84c6d9b05..5e4806c09 100644 --- a/.github/workflows/python.yml +++ b/.github/workflows/python.yml @@ -23,6 +23,19 @@ jobs: - name: Set up Rust run: | rustup component add llvm-tools + + - name: Get test data + id: cache-test-data + uses: actions/cache@v4 + with: + path: test-data + key: test-data-v20 + - name: Download test data + if: steps.cache-test-data.outputs.cache-hit != 'true' + run: | + cd maintainer + ./download-test-data.sh + - name: Test env: # `-C link-dead-code` is needed to prevent 'warning: XX functions have mismatched data' warnings diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml index a0ac35300..44953aa37 100644 --- a/.github/workflows/rust.yml +++ b/.github/workflows/rust.yml @@ -25,7 +25,7 @@ jobs: uses: actions/cache@v4 with: path: test-data - key: test-data-v19 + key: test-data-v20 - name: Download test data if: steps.cache-test-data.outputs.cache-hit != 'true' run: | diff --git a/maintainer/download-test-data.sh b/maintainer/download-test-data.sh index 31c0c23ac..4ba3eb61b 100755 --- a/maintainer/download-test-data.sh +++ b/maintainer/download-test-data.sh @@ -25,8 +25,12 @@ download 'https://data.nnpdf.science/pineappl/test-data/CMS_TTB_8TEV_2D_TTM_TRAP download 'https://data.nnpdf.science/pineappl/test-data/CMS_TTB_8TEV_2D_TTM_TRAP_TOT.tar' download 'https://data.nnpdf.science/pineappl/test-data/E906nlo_bin_00.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/E906nlo_bin_00.tar' +download 'https://data.nnpdf.science/pineappl/test-data/FKTABLE_CMSTTBARTOT8TEV-TOPDIFF8TEVTOT.pineappl.lz4' +download 'https://data.nnpdf.science/pineappl/test-data/FKTABLE_STAR_WMWP_510GEV_WM-AL-POL.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/FK_ATLASTTBARTOT13TEV.dat' download 'https://data.nnpdf.science/pineappl/test-data/FK_POSXDQ.dat' +download 'https://data.nnpdf.science/pineappl/test-data/GRID_DYE906R_D_bin_1.pineappl.lz4' +download 'https://data.nnpdf.science/pineappl/test-data/GRID_STAR_WMWP_510GEV_WP-AL-POL.pineappl.lz4' download 'https://data.nnpdf.science/pineappl/test-data/LHC8-Mtt-HT4-173_3-bin1.tab.gz' download 'https://data.nnpdf.science/pineappl/test-data/LHCBWZMU7TEV_PI_part1.appl' download 'https://data.nnpdf.science/pineappl/test-data/LHCB_DY_8TEV.pineappl.lz4' diff --git a/pineappl_py/tests/conftest.py b/pineappl_py/tests/conftest.py index adfacabad..c6e7d6213 100644 --- a/pineappl_py/tests/conftest.py +++ b/pineappl_py/tests/conftest.py @@ -198,27 +198,8 @@ def fake_grids(): @pytest.fixture def download_objects(tmp_path_factory): def _download_fk(objname: str) -> None: - download_dir = tmp_path_factory.mktemp("data") - file_path = download_dir / f"{objname}" - args = [ - "wget", - "--no-verbose", - "--no-clobber", - "-P", - f"{download_dir}", - f"https://data.nnpdf.science/pineappl/test-data/{objname}", - ] - - try: - _ = subprocess.run( - args, - stdout=subprocess.DEVNULL, - stderr=subprocess.DEVNULL, - timeout=15, - ) - return file_path - except OSError as error: - msg = f"Failed to execute the command {args}." - raise EnvironmentError(msg) from error + import os + path = os.path.abspath(f"../test-data/{objname}") + return path return _download_fk From 533e10d9aaffad7900e47f56dea42bfe0f5f2d07 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Thu, 24 Apr 2025 10:53:07 +0200 Subject: [PATCH 05/49] Non-optimised modifications --- Cargo.lock | 1 + examples/cpp/Makefile | 4 + pineappl/src/convolutions.rs | 2 +- pineappl_capi/Cargo.toml | 1 + pineappl_capi/cbindgen.toml | 1 + pineappl_capi/src/lib.rs | 217 +++++++++++++++++++++++++++++++++++ 6 files changed, 225 insertions(+), 1 deletion(-) diff --git a/Cargo.lock b/Cargo.lock index 88377028a..10379b9ca 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -996,6 +996,7 @@ name = "pineappl_capi" version = "1.0.0-alpha4" dependencies = [ "itertools", + "ndarray", "pineappl 1.0.0-alpha4", ] diff --git a/examples/cpp/Makefile b/examples/cpp/Makefile index aef4689b5..964e0748c 100644 --- a/examples/cpp/Makefile +++ b/examples/cpp/Makefile @@ -14,6 +14,7 @@ PROGRAMS = \ convolve-grid-deprecated \ convolve-grid \ get-subgrids \ + evolve-grid \ deprecated \ display-channels-deprecated \ display-channels \ @@ -51,6 +52,9 @@ deprecated: deprecated.cpp get-subgrids: get-subgrids.cpp $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ +evolve-grid: evolve-grid.cpp + $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ + display-channels-deprecated: display-channels-deprecated.cpp $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ diff --git a/pineappl/src/convolutions.rs b/pineappl/src/convolutions.rs index 331f76020..b3503ab64 100644 --- a/pineappl/src/convolutions.rs +++ b/pineappl/src/convolutions.rs @@ -282,7 +282,7 @@ impl GridConvCache<'_, '_> { /// TODO #[repr(C)] -#[derive(Clone, Copy, Debug, Deserialize, Eq, PartialEq, Serialize)] +#[derive(Clone, Copy, Debug, Deserialize, Eq, PartialEq, Serialize, Hash)] pub enum ConvType { /// Unpolarized parton distribution function. UnpolPDF, diff --git a/pineappl_capi/Cargo.toml b/pineappl_capi/Cargo.toml index 3ef783b52..71417317b 100644 --- a/pineappl_capi/Cargo.toml +++ b/pineappl_capi/Cargo.toml @@ -18,6 +18,7 @@ workspace = true [dependencies] pineappl = { path = "../pineappl", version = "=1.0.0-alpha4" } itertools = "0.10.1" +ndarray = "0.15.4" [features] capi = [] diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index 8a07de992..b192277e6 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -47,6 +47,7 @@ rename_variants = "ScreamingSnakeCase" "KeyVal" = "pineappl_keyval" "SubGrid" = "pineappl_subgrid" "GridOptFlags" = "pineappl_gof" +"OperatorSliceInfo" = "pineappl_operator_slice_info" ############## Options for How Your Rust library Should Be Parsed ############## diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 18d0f83d2..5c0000d6a 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -56,14 +56,18 @@ //! [translation tables]: https://github.com/eqrion/cbindgen/blob/master/docs.md#std-types use itertools::izip; +use ndarray::{Array4, CowArray, Ix4}; use pineappl::boc::{Bin, BinsWithFillLimits, Channel, Kinematics, Order, ScaleFuncForm, Scales}; use pineappl::convolutions::{Conv, ConvType, ConvolutionCache}; +use pineappl::evolution::{AlphasTable, OperatorSliceInfo}; +use pineappl::fk_table::FkTable; use pineappl::grid::{Grid, GridOptFlags}; use pineappl::interpolation::{Interp, InterpMeth, Map, ReweightMeth}; use pineappl::packed_array::ravel_multi_index; use pineappl::pids::PidBasis; use pineappl::subgrid::Subgrid; use std::collections::HashMap; +use std::collections::HashSet; use std::ffi::{CStr, CString}; use std::fs::File; use std::mem; @@ -1463,6 +1467,20 @@ fn construct_interpolation(interp: &InterpTuples) -> Interp { ) } +/// Type for defining the Operator info. +#[repr(C)] +pub struct OperatorInfo { + fac0: f64, + fac1: f64, + x0: *mut f64, + x1: *mut f64, + pids0: *mut i32, + pids1: *mut i32, + pid_basis: PidBasis, + conv_type: ConvType, + tensor_shape: *mut usize, +} + /// An exact duplicate of `pineappl_lumi_new` to make naming (lumi -> channel) consistent. /// should be deleted using `pineappl_channels_delete`. #[no_mangle] @@ -2006,3 +2024,202 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_array( } } } + +/// Get the shape of the objects represented in the evolve info. +/// +/// # Safety +/// +/// TODO +#[no_mangle] +pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( + grid: *const Grid, + order_mask: *const bool, + shape_info: *mut usize, +) { + let grid = unsafe { &*grid }; + + let order_mask = if order_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } + }; + let shape_info = unsafe { slice::from_raw_parts_mut(shape_info, 5) }; + + let evolve_info = grid.evolve_info(order_mask); + let evinfo_shapes = [ + evolve_info.fac1.len(), + evolve_info.frg1.len(), + evolve_info.pids1.len(), + evolve_info.x1.len(), + evolve_info.ren1.len(), + ]; + + shape_info.copy_from_slice(&evinfo_shapes); +} + +/// Get the values of the parameters contained in evolve info. +/// +/// # Safety +/// +/// TODO +#[no_mangle] +pub unsafe extern "C" fn pineappl_grid_evolve_info( + grid: *const Grid, + order_mask: *const bool, + fac1: *mut f64, + frg1: *mut f64, + pids1: *mut i32, + x1: *mut f64, + ren1: *mut f64, +) { + let grid = unsafe { &*grid }; + + let order_mask = if order_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } + }; + + let evolve_info = grid.evolve_info(order_mask); + let evinfo_shapes = [ + evolve_info.fac1.len(), + evolve_info.frg1.len(), + evolve_info.pids1.len(), + evolve_info.x1.len(), + evolve_info.ren1.len(), + ]; + + let fac1 = unsafe { slice::from_raw_parts_mut(fac1, evinfo_shapes[0]) }; + let frg1 = unsafe { slice::from_raw_parts_mut(frg1, evinfo_shapes[1]) }; + let pids1 = unsafe { slice::from_raw_parts_mut(pids1, evinfo_shapes[2]) }; + let x1 = unsafe { slice::from_raw_parts_mut(x1, evinfo_shapes[3]) }; + let ren1 = unsafe { slice::from_raw_parts_mut(ren1, evinfo_shapes[4]) }; + + fac1.copy_from_slice(&grid.evolve_info(order_mask).fac1); + frg1.copy_from_slice(&grid.evolve_info(order_mask).frg1); + pids1.copy_from_slice(&grid.evolve_info(order_mask).pids1); + x1.copy_from_slice(&grid.evolve_info(order_mask).x1); + ren1.copy_from_slice(&grid.evolve_info(order_mask).ren1); +} + +/// Evolve a grid and dump the resulting FK table +/// +/// # Safety +/// +/// TODO +/// +/// # Panics +/// +/// TODO +#[no_mangle] +pub unsafe extern "C" fn pineappl_grid_evolve( + grid: *mut Grid, + op_info: *mut OperatorInfo, + order_mask: *const bool, + operators: *mut f64, + xi: *mut f64, + ren1: *mut f64, + alphas: *mut f64, +) -> Box { + let grid = unsafe { &mut *grid }; + + // Determine the number of EKOs needed to evolve this Grid + let conv_types: HashSet<_> = grid + .convolutions() + .iter() + .map(pineappl::convolutions::Conv::conv_type) + .collect(); + + let order_mask = if order_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } + }; + + // Determine the number of q2 values which defines the slices + let evolve_info = grid.evolve_info(order_mask); + + // The length of the operator info is `N_conv * N_q2` + let op_info = + unsafe { slice::from_raw_parts(op_info, conv_types.len() * evolve_info.fac1.len()) }; + + // Determine the total length of the operators when flattened + let flattened_shapes: usize = op_info + .iter() + .map(|op| { + let shape = unsafe { slice::from_raw_parts(op.tensor_shape, 4) }; + shape.iter().product::() + }) + .sum(); + let operators = + unsafe { slice::from_raw_parts(operators, conv_types.len() * flattened_shapes) }; + + // Chunk the operators + let mut start_index = 0; + let op_chunk: Vec<_> = op_info + .iter() + .map(|op| { + let eko_shape = unsafe { slice::from_raw_parts(op.tensor_shape, 4) }; + let end_idx = start_index + eko_shape.iter().product::(); + let op_range = operators[start_index..end_idx].to_vec(); + start_index = end_idx + 1; + op_range + }) + .collect(); + let op_slice: &[Vec<_>] = &op_chunk; + + // Chunk the objects + let opinfo_chunk = op_info.chunks_exact(conv_types.len()); + let operator_chunk = op_slice.chunks_exact(conv_types.len()); + + let ren1_len = evolve_info.ren1.len(); + let ren1 = unsafe { Vec::from_raw_parts(ren1, ren1_len, ren1_len) }; + let alphas = unsafe { Vec::from_raw_parts(alphas, ren1_len, ren1_len) }; + let xi = unsafe { Vec::from_raw_parts(xi, 3, 3) }; + + // let mut start_idx = 0; + let slices = opinfo_chunk + .into_iter() + .zip(operator_chunk) + .map(|(op_chunk, op_range)| { + op_chunk.iter().zip(op_range).map(|(opinfo, op_values)| { + let eko_shape = unsafe { slice::from_raw_parts(opinfo.tensor_shape, 4) }; + + let op_pids0 = + unsafe { Vec::from_raw_parts(opinfo.pids0, eko_shape[0], eko_shape[0]) }; + let op_x0 = unsafe { Vec::from_raw_parts(opinfo.x0, eko_shape[1], eko_shape[1]) }; + let op_pids1 = + unsafe { Vec::from_raw_parts(opinfo.pids1, eko_shape[2], eko_shape[2]) }; + let op_x1 = unsafe { Vec::from_raw_parts(opinfo.x1, eko_shape[3], eko_shape[3]) }; + + let operator_slice_info = OperatorSliceInfo { + pid_basis: opinfo.pid_basis, + fac0: opinfo.fac0, + pids0: op_pids0, + x0: op_x0, + fac1: opinfo.fac1, + pids1: op_pids1, + x1: op_x1, + conv_type: opinfo.conv_type, + }; + + let array = Array4::from_shape_vec( + Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), + op_values.clone(), + ) + .expect("Shape mismatch or invalid input."); + + Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) + }) + }) + .collect(); + + let fk_table = grid.evolve( + slices, + order_mask, + (xi[0], xi[1], xi[2]), + &AlphasTable { ren1, alphas }, + ); + + Box::new(fk_table.unwrap()) +} From 363cfc1b798dbaace5855bfe682c20f45068ec9e Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Thu, 24 Apr 2025 11:29:34 +0200 Subject: [PATCH 06/49] Add the actual test --- examples/cpp/evolve-grid.cpp | 97 ++++++++++++++++++++++++++++++++++++ pineappl_capi/src/lib.rs | 21 ++++++-- 2 files changed, 113 insertions(+), 5 deletions(-) create mode 100644 examples/cpp/evolve-grid.cpp diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp new file mode 100644 index 000000000..aad76110a --- /dev/null +++ b/examples/cpp/evolve-grid.cpp @@ -0,0 +1,97 @@ +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +double FAC0 = 1.65; + +std::vector get_operator_info( + std::vector fac1, + std::vector pids1, + std::vector x1, + pineappl_pid_basis pid_basis, + pineappl_conv_type conv_type +) { + std::vector opinfo_slices(fac1.size()); + std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; + + for (std::size_t q2 = 0; q2 != fac1.size(); q2++) { + OperatorInfo opinfo = { + FAC0, // fac0 + fac1[q2], // fac1 + x1.data(), // x0 + x1.data(), // x1 + pids1.data(), // pids0 + pids1.data(), // pids1 + pid_basis, + conv_type, + tensor_shape.data() + }; + + opinfo_slices[q2] = opinfo; + } + + return opinfo_slices; +} + +int main() { + std::string filename = "drell-yan-rap-ll.pineappl.lz4"; + + // read the grid from a file + auto* grid = pineappl_grid_read(filename.c_str()); + + // Get the number of perturbative orders + std::size_t orders = pineappl_grid_order_count(grid); + + // Get the PID basis representation + pineappl_pid_basis pid_basis = pineappl_grid_pid_basis(grid); + + // Get the number of convolutions + std::size_t n_convs = pineappl_grid_convolutions_len(grid); + + // Fill the vector of unique convolution types + std::vector conv_types(n_convs); + for (std::size_t i = 0; i != n_convs; i++) { + pineappl_conv_type conv = pineappl_grid_conv_type(grid, i); + if (std::find(conv_types.begin(), conv_types.end(), conv) == conv_types.end()) { + conv_types.push_back(conv); + } + } + + // Get the shape of the evolve info objects + std::vector evinfo_shape(5); + std::unique_ptr order_mask(new bool[orders]()); + order_mask[orders - 1] = true; // Choose the highest order + pineappl_grid_evolve_info_shape(grid, order_mask.get(), evinfo_shape.data()); + + // Get the values of the evolve info parameters. These contain, for example, the + // information on the `x`-grid and `PID` used to interpolate the Grid. + // NOTE: These are used to construct the Evolution Operator + std::vector fac1(evinfo_shape[0]); + std::vector frg1(evinfo_shape[1]); + std::vector pids1(evinfo_shape[2]); + std::vector x1(evinfo_shape[3]); + std::vector ren1(evinfo_shape[4]); + pineappl_grid_evolve_info(grid, order_mask.get(), fac1.data(), + frg1.data(), pids1.data(), x1.data(), ren1.data()); + + // Construct the Operator Info + std::vector opinfo_slices(n_convs * fac1.size()); + for (std::size_t i = 0; i != n_convs; i++) { + std::vector opinfo = get_operator_info(fac1, pids1, x1, pid_basis, conv_types[i]); + for (std::size_t j = 0; j != fac1.size(); j++) { + opinfo_slices.push_back(opinfo[j]); + } + } + + pineappl_grid_delete(grid); +} diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 5c0000d6a..90174c0c9 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -1798,7 +1798,7 @@ pub unsafe extern "C" fn pineappl_channels_entry( let entry = channels.0[entry].entry(); // if the channel has no entries we assume no convolutions, which is OK we don't copy anything // in this case - let convolutions = entry.get(0).map_or(0, |x| x.0.len()); + let convolutions = entry.first().map_or(0, |x| x.0.len()); let pdg_ids = unsafe { slice::from_raw_parts_mut(pdg_ids, convolutions * entry.len()) }; let factors = unsafe { slice::from_raw_parts_mut(factors, entry.len()) }; @@ -1917,6 +1917,18 @@ pub unsafe extern "C" fn pineappl_grid_convolve( )); } +/// Get the type of convolutions for this Grid given an index. +/// +/// # Safety +/// +/// TODO +#[no_mangle] +pub unsafe extern "C" fn pineappl_grid_conv_type(grid: *const Grid, index: usize) -> ConvType { + let grid = unsafe { &*grid }; + + grid.convolutions()[index].conv_type() +} + /// Get the number of convolutions for a given Grid. /// /// # Safety @@ -2154,7 +2166,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let operators = unsafe { slice::from_raw_parts(operators, conv_types.len() * flattened_shapes) }; - // Chunk the operators + // Split the operators into vectors corresponding to the Q2 slices let mut start_index = 0; let op_chunk: Vec<_> = op_info .iter() @@ -2166,11 +2178,10 @@ pub unsafe extern "C" fn pineappl_grid_evolve( op_range }) .collect(); - let op_slice: &[Vec<_>] = &op_chunk; - // Chunk the objects + // Chunk the operators depending on the number of convolutions let opinfo_chunk = op_info.chunks_exact(conv_types.len()); - let operator_chunk = op_slice.chunks_exact(conv_types.len()); + let operator_chunk = op_chunk.chunks_exact(conv_types.len()); let ren1_len = evolve_info.ren1.len(); let ren1 = unsafe { Vec::from_raw_parts(ren1, ren1_len, ren1_len) }; From c083a405330bb637987b427252e781acc9bb22eb Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Thu, 24 Apr 2025 17:11:35 +0200 Subject: [PATCH 07/49] Fix some bugs --- examples/cpp/evolve-grid.cpp | 63 ++++++++++++++++++++++++++++++++---- pineappl_capi/cbindgen.toml | 1 + pineappl_capi/src/lib.rs | 46 +++++++++++--------------- 3 files changed, 77 insertions(+), 33 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index aad76110a..dd4b9a0ba 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -1,3 +1,4 @@ +#include #include #include @@ -11,6 +12,7 @@ #include #include #include +#include double FAC0 = 1.65; @@ -43,6 +45,33 @@ std::vector get_operator_info( return opinfo_slices; } +std::vector generate_fake_ekos( + double q2, + std::vector pids0, + std::vector x0, + std::vector pids1, + std::vector x1 +) { + std::random_device rd; + std::mt19937 gen(rd()); + std::uniform_real_distribution distrib(q2 / 1000, q2 / 100); + + std::size_t flat_len = x0.size() * x1.size() * pids0.size() * pids1.size(); + std::vector ops(flat_len); + + for (std::size_t i = 0; i != pids1.size(); i++) { + for (std::size_t j = 0; j != x1.size(); j++) { + for (std::size_t k = 0; k != pids0.size(); i++) { + for (std::size_t l = 0; l != x0.size(); i++) { + ops.push_back(distrib(gen)); + } + } + } + } + + return ops; +} + int main() { std::string filename = "drell-yan-rap-ll.pineappl.lz4"; @@ -69,9 +98,8 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::unique_ptr order_mask(new bool[orders]()); - order_mask[orders - 1] = true; // Choose the highest order - pineappl_grid_evolve_info_shape(grid, order_mask.get(), evinfo_shape.data()); + std::vector order_mask = {1, 2}; + pineappl_grid_evolve_info_shape(grid, order_mask.data(), evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the // information on the `x`-grid and `PID` used to interpolate the Grid. @@ -81,17 +109,40 @@ int main() { std::vector pids1(evinfo_shape[2]); std::vector x1(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); - pineappl_grid_evolve_info(grid, order_mask.get(), fac1.data(), + pineappl_grid_evolve_info(grid, order_mask.data(), fac1.data(), frg1.data(), pids1.data(), x1.data(), ren1.data()); - // Construct the Operator Info + // ------------------ Construct the Operator Info ------------------ + // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose + // elements are `OperatorInfo` objects. std::vector opinfo_slices(n_convs * fac1.size()); - for (std::size_t i = 0; i != n_convs; i++) { + for (std::size_t i = 0; i != conv_types.size(); i++) { std::vector opinfo = get_operator_info(fac1, pids1, x1, pid_basis, conv_types[i]); for (std::size_t j = 0; j != fac1.size(); j++) { opinfo_slices.push_back(opinfo[j]); } } + // ------------------ Construct the Evolution Operator ------------------ + // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` + std::size_t flat_len = x1.size() * x1.size() * pids1.size() * pids1.size(); + std::vector op_slices(flat_len); + for (std::size_t i = 0; i != conv_types.size(); i++) { + std::cout << conv_types[i] << "\n"; + for (std::size_t j = 0; j != fac1.size(); j++) { + std::vector eko = generate_fake_ekos(fac1[j], pids1, x1, pids1, x1); + for (std::size_t k = 0; k != flat_len; k++) { + op_slices.push_back(eko[k]); + } + } + } + + // Construct the values of alphas + std::vector alphas_table(ren1.size(), 0.118); + std::vector xi = {1.0, 1.0, 1.0}; + + pineappl_grid_evolve(grid, opinfo_slices.data(), order_mask.data(), + op_slices.data(), xi.data(), ren1.data(), alphas_table.data()); + pineappl_grid_delete(grid); } diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index b192277e6..b24d18d1d 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -35,6 +35,7 @@ rename_variants = "ScreamingSnakeCase" [export.rename] "Grid" = "pineappl_grid" +"FkTable" = "pineappl_fk_table" "Lumi" = "pineappl_lumi" "Channels" = "pineappl_channels" "PidBasis" = "pineappl_pid_basis" diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 90174c0c9..fcca09dea 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -1469,6 +1469,7 @@ fn construct_interpolation(interp: &InterpTuples) -> Interp { /// Type for defining the Operator info. #[repr(C)] +#[derive(Debug)] pub struct OperatorInfo { fac0: f64, fac1: f64, @@ -2045,19 +2046,16 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_array( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( grid: *const Grid, - order_mask: *const bool, + orders: *const u8, shape_info: *mut usize, ) { let grid = unsafe { &*grid }; - let order_mask = if order_mask.is_null() { - &[] - } else { - unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } - }; + let orders = unsafe { slice::from_raw_parts(orders, 2) }; + let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); let shape_info = unsafe { slice::from_raw_parts_mut(shape_info, 5) }; - let evolve_info = grid.evolve_info(order_mask); + let evolve_info = grid.evolve_info(&order_mask); let evinfo_shapes = [ evolve_info.fac1.len(), evolve_info.frg1.len(), @@ -2077,7 +2075,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve_info( grid: *const Grid, - order_mask: *const bool, + orders: *const u8, fac1: *mut f64, frg1: *mut f64, pids1: *mut i32, @@ -2086,13 +2084,10 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( ) { let grid = unsafe { &*grid }; - let order_mask = if order_mask.is_null() { - &[] - } else { - unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } - }; + let orders = unsafe { slice::from_raw_parts(orders, 2) }; + let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); - let evolve_info = grid.evolve_info(order_mask); + let evolve_info = grid.evolve_info(&order_mask); let evinfo_shapes = [ evolve_info.fac1.len(), evolve_info.frg1.len(), @@ -2107,11 +2102,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( let x1 = unsafe { slice::from_raw_parts_mut(x1, evinfo_shapes[3]) }; let ren1 = unsafe { slice::from_raw_parts_mut(ren1, evinfo_shapes[4]) }; - fac1.copy_from_slice(&grid.evolve_info(order_mask).fac1); - frg1.copy_from_slice(&grid.evolve_info(order_mask).frg1); - pids1.copy_from_slice(&grid.evolve_info(order_mask).pids1); - x1.copy_from_slice(&grid.evolve_info(order_mask).x1); - ren1.copy_from_slice(&grid.evolve_info(order_mask).ren1); + fac1.copy_from_slice(&grid.evolve_info(&order_mask).fac1); + frg1.copy_from_slice(&grid.evolve_info(&order_mask).frg1); + pids1.copy_from_slice(&grid.evolve_info(&order_mask).pids1); + x1.copy_from_slice(&grid.evolve_info(&order_mask).x1); + ren1.copy_from_slice(&grid.evolve_info(&order_mask).ren1); } /// Evolve a grid and dump the resulting FK table @@ -2127,7 +2122,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( pub unsafe extern "C" fn pineappl_grid_evolve( grid: *mut Grid, op_info: *mut OperatorInfo, - order_mask: *const bool, + orders: *const u8, operators: *mut f64, xi: *mut f64, ren1: *mut f64, @@ -2142,14 +2137,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .map(pineappl::convolutions::Conv::conv_type) .collect(); - let order_mask = if order_mask.is_null() { - &[] - } else { - unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } - }; + let orders = unsafe { slice::from_raw_parts(orders, 2) }; + let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); // Determine the number of q2 values which defines the slices - let evolve_info = grid.evolve_info(order_mask); + let evolve_info = grid.evolve_info(&order_mask); // The length of the operator info is `N_conv * N_q2` let op_info = @@ -2227,7 +2219,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let fk_table = grid.evolve( slices, - order_mask, + &order_mask, (xi[0], xi[1], xi[2]), &AlphasTable { ren1, alphas }, ); From 6de4972409ad4ee425d893bc88ad5dbfe69553a9 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Fri, 25 Apr 2025 15:06:49 +0200 Subject: [PATCH 08/49] Add further modifications --- examples/cpp/evolve-grid.cpp | 76 +++++++++++------------------------- pineappl_capi/src/lib.rs | 20 +++------- 2 files changed, 29 insertions(+), 67 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index dd4b9a0ba..f59c7a76e 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -1,50 +1,17 @@ #include +#include #include #include #include -#include -#include #include -#include -#include #include -#include #include #include #include double FAC0 = 1.65; -std::vector get_operator_info( - std::vector fac1, - std::vector pids1, - std::vector x1, - pineappl_pid_basis pid_basis, - pineappl_conv_type conv_type -) { - std::vector opinfo_slices(fac1.size()); - std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; - - for (std::size_t q2 = 0; q2 != fac1.size(); q2++) { - OperatorInfo opinfo = { - FAC0, // fac0 - fac1[q2], // fac1 - x1.data(), // x0 - x1.data(), // x1 - pids1.data(), // pids0 - pids1.data(), // pids1 - pid_basis, - conv_type, - tensor_shape.data() - }; - - opinfo_slices[q2] = opinfo; - } - - return opinfo_slices; -} - std::vector generate_fake_ekos( double q2, std::vector pids0, @@ -59,28 +26,19 @@ std::vector generate_fake_ekos( std::size_t flat_len = x0.size() * x1.size() * pids0.size() * pids1.size(); std::vector ops(flat_len); - for (std::size_t i = 0; i != pids1.size(); i++) { - for (std::size_t j = 0; j != x1.size(); j++) { - for (std::size_t k = 0; k != pids0.size(); i++) { - for (std::size_t l = 0; l != x0.size(); i++) { - ops.push_back(distrib(gen)); - } - } - } + for (std::size_t i = 0; i != flat_len; i++) { + ops.push_back(distrib(gen)); } return ops; } int main() { - std::string filename = "drell-yan-rap-ll.pineappl.lz4"; + std::string filename = "advanced-filling.pineappl.lz4"; // read the grid from a file auto* grid = pineappl_grid_read(filename.c_str()); - // Get the number of perturbative orders - std::size_t orders = pineappl_grid_order_count(grid); - // Get the PID basis representation pineappl_pid_basis pid_basis = pineappl_grid_pid_basis(grid); @@ -88,7 +46,7 @@ int main() { std::size_t n_convs = pineappl_grid_convolutions_len(grid); // Fill the vector of unique convolution types - std::vector conv_types(n_convs); + std::vector conv_types; for (std::size_t i = 0; i != n_convs; i++) { pineappl_conv_type conv = pineappl_grid_conv_type(grid, i); if (std::find(conv_types.begin(), conv_types.end(), conv) == conv_types.end()) { @@ -98,7 +56,7 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::vector order_mask = {1, 2}; + std::vector order_mask = {3, 0}; pineappl_grid_evolve_info_shape(grid, order_mask.data(), evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the @@ -115,20 +73,30 @@ int main() { // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose // elements are `OperatorInfo` objects. - std::vector opinfo_slices(n_convs * fac1.size()); + std::vector opinfo_slices(conv_types.size() * fac1.size()); + std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; for (std::size_t i = 0; i != conv_types.size(); i++) { - std::vector opinfo = get_operator_info(fac1, pids1, x1, pid_basis, conv_types[i]); for (std::size_t j = 0; j != fac1.size(); j++) { - opinfo_slices.push_back(opinfo[j]); + OperatorInfo opinfo = { + FAC0, // fac0 + fac1[j], // fac1 + x1.data(), // x0 + x1.data(), // x1 + pids1.data(), // pids0 + pids1.data(), // pids1 + pid_basis, + conv_types[i], + tensor_shape.data() + }; + opinfo_slices[i * fac1.size() + j] = opinfo; } } // ------------------ Construct the Evolution Operator ------------------ // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` + std::vector op_slices; std::size_t flat_len = x1.size() * x1.size() * pids1.size() * pids1.size(); - std::vector op_slices(flat_len); for (std::size_t i = 0; i != conv_types.size(); i++) { - std::cout << conv_types[i] << "\n"; for (std::size_t j = 0; j != fac1.size(); j++) { std::vector eko = generate_fake_ekos(fac1[j], pids1, x1, pids1, x1); for (std::size_t k = 0; k != flat_len; k++) { @@ -136,6 +104,7 @@ int main() { } } } + std::cout << "Arrived Here!" << "\n"; // Construct the values of alphas std::vector alphas_table(ren1.size(), 0.118); @@ -143,6 +112,7 @@ int main() { pineappl_grid_evolve(grid, opinfo_slices.data(), order_mask.data(), op_slices.data(), xi.data(), ren1.data(), alphas_table.data()); + std::cout << "Where does the double free happen!" << "\n"; pineappl_grid_delete(grid); } diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index fcca09dea..ba35104a4 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2088,19 +2088,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); let evolve_info = grid.evolve_info(&order_mask); - let evinfo_shapes = [ - evolve_info.fac1.len(), - evolve_info.frg1.len(), - evolve_info.pids1.len(), - evolve_info.x1.len(), - evolve_info.ren1.len(), - ]; - - let fac1 = unsafe { slice::from_raw_parts_mut(fac1, evinfo_shapes[0]) }; - let frg1 = unsafe { slice::from_raw_parts_mut(frg1, evinfo_shapes[1]) }; - let pids1 = unsafe { slice::from_raw_parts_mut(pids1, evinfo_shapes[2]) }; - let x1 = unsafe { slice::from_raw_parts_mut(x1, evinfo_shapes[3]) }; - let ren1 = unsafe { slice::from_raw_parts_mut(ren1, evinfo_shapes[4]) }; + let fac1 = unsafe { slice::from_raw_parts_mut(fac1, evolve_info.fac1.len()) }; + let frg1 = unsafe { slice::from_raw_parts_mut(frg1, evolve_info.frg1.len()) }; + let pids1 = unsafe { slice::from_raw_parts_mut(pids1, evolve_info.pids1.len()) }; + let x1 = unsafe { slice::from_raw_parts_mut(x1, evolve_info.x1.len()) }; + let ren1 = unsafe { slice::from_raw_parts_mut(ren1, evolve_info.ren1.len()) }; fac1.copy_from_slice(&grid.evolve_info(&order_mask).fac1); frg1.copy_from_slice(&grid.evolve_info(&order_mask).frg1); @@ -2166,7 +2158,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let eko_shape = unsafe { slice::from_raw_parts(op.tensor_shape, 4) }; let end_idx = start_index + eko_shape.iter().product::(); let op_range = operators[start_index..end_idx].to_vec(); - start_index = end_idx + 1; + start_index = end_idx; op_range }) .collect(); From e0964535a2eea7b0564e6cd48569ce546aa492e7 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Fri, 25 Apr 2025 16:44:49 +0200 Subject: [PATCH 09/49] Some clean up --- pineappl_capi/src/lib.rs | 88 ++++++++++++++++------------------------ 1 file changed, 36 insertions(+), 52 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index ba35104a4..e097efdeb 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -1473,13 +1473,8 @@ fn construct_interpolation(interp: &InterpTuples) -> Interp { pub struct OperatorInfo { fac0: f64, fac1: f64, - x0: *mut f64, - x1: *mut f64, - pids0: *mut i32, - pids1: *mut i32, pid_basis: PidBasis, conv_type: ConvType, - tensor_shape: *mut usize, } /// An exact duplicate of `pineappl_lumi_new` to make naming (lumi -> channel) consistent. @@ -2116,85 +2111,74 @@ pub unsafe extern "C" fn pineappl_grid_evolve( op_info: *mut OperatorInfo, orders: *const u8, operators: *mut f64, + x_grid: *mut f64, + x_fktable: *mut f64, + pids_grid: *mut i32, + pids_fktable: *mut i32, + eko_shape: *mut usize, xi: *mut f64, ren1: *mut f64, alphas: *mut f64, ) -> Box { let grid = unsafe { &mut *grid }; - // Determine the number of EKOs needed to evolve this Grid + let orders = unsafe { slice::from_raw_parts(orders, 2) }; + let eko_shape = unsafe { slice::from_raw_parts(eko_shape, 4) }; + let pids_fktable = unsafe { slice::from_raw_parts(pids_fktable, eko_shape[0]) }; + let x_fktable = unsafe { slice::from_raw_parts(x_fktable, eko_shape[1]) }; + let pids_grid = unsafe { slice::from_raw_parts(pids_grid, eko_shape[2]) }; + let x_grid = unsafe { slice::from_raw_parts(x_grid, eko_shape[3]) }; + + let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); + let evolve_info = grid.evolve_info(&order_mask); + + let ren1_len = evolve_info.ren1.len(); + let ren1 = unsafe { Vec::from_raw_parts(ren1, ren1_len, ren1_len) }; + let alphas = unsafe { Vec::from_raw_parts(alphas, ren1_len, ren1_len) }; + let xi = unsafe { Vec::from_raw_parts(xi, 3, 3) }; + let conv_types: HashSet<_> = grid .convolutions() .iter() .map(pineappl::convolutions::Conv::conv_type) .collect(); - let orders = unsafe { slice::from_raw_parts(orders, 2) }; - let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); - - // Determine the number of q2 values which defines the slices - let evolve_info = grid.evolve_info(&order_mask); - - // The length of the operator info is `N_conv * N_q2` let op_info = unsafe { slice::from_raw_parts(op_info, conv_types.len() * evolve_info.fac1.len()) }; + let opinfo_chunk = op_info.chunks_exact(conv_types.len()); - // Determine the total length of the operators when flattened let flattened_shapes: usize = op_info .iter() - .map(|op| { - let shape = unsafe { slice::from_raw_parts(op.tensor_shape, 4) }; - shape.iter().product::() - }) + .map(|_| eko_shape.iter().product::()) .sum(); let operators = unsafe { slice::from_raw_parts(operators, conv_types.len() * flattened_shapes) }; - // Split the operators into vectors corresponding to the Q2 slices - let mut start_index = 0; - let op_chunk: Vec<_> = op_info + let mut start_idx = 0; + let op_split: Vec<_> = op_info .iter() - .map(|op| { - let eko_shape = unsafe { slice::from_raw_parts(op.tensor_shape, 4) }; - let end_idx = start_index + eko_shape.iter().product::(); - let op_range = operators[start_index..end_idx].to_vec(); - start_index = end_idx; + .map(|_| { + let end_idx = start_idx + eko_shape.iter().product::(); + let op_range = operators[start_idx..end_idx].to_vec(); + start_idx = end_idx; op_range }) .collect(); + let ops_chunk = op_split.chunks_exact(conv_types.len()); - // Chunk the operators depending on the number of convolutions - let opinfo_chunk = op_info.chunks_exact(conv_types.len()); - let operator_chunk = op_chunk.chunks_exact(conv_types.len()); - - let ren1_len = evolve_info.ren1.len(); - let ren1 = unsafe { Vec::from_raw_parts(ren1, ren1_len, ren1_len) }; - let alphas = unsafe { Vec::from_raw_parts(alphas, ren1_len, ren1_len) }; - let xi = unsafe { Vec::from_raw_parts(xi, 3, 3) }; - - // let mut start_idx = 0; let slices = opinfo_chunk .into_iter() - .zip(operator_chunk) - .map(|(op_chunk, op_range)| { - op_chunk.iter().zip(op_range).map(|(opinfo, op_values)| { - let eko_shape = unsafe { slice::from_raw_parts(opinfo.tensor_shape, 4) }; - - let op_pids0 = - unsafe { Vec::from_raw_parts(opinfo.pids0, eko_shape[0], eko_shape[0]) }; - let op_x0 = unsafe { Vec::from_raw_parts(opinfo.x0, eko_shape[1], eko_shape[1]) }; - let op_pids1 = - unsafe { Vec::from_raw_parts(opinfo.pids1, eko_shape[2], eko_shape[2]) }; - let op_x1 = unsafe { Vec::from_raw_parts(opinfo.x1, eko_shape[3], eko_shape[3]) }; - + .zip(ops_chunk) + .map(|(op_subinfo, op_range)| { + op_subinfo.iter().zip(op_range).map(|(opinfo, op_values)| { let operator_slice_info = OperatorSliceInfo { pid_basis: opinfo.pid_basis, fac0: opinfo.fac0, - pids0: op_pids0, - x0: op_x0, + pids0: pids_fktable.to_vec(), + x0: x_fktable.to_vec(), fac1: opinfo.fac1, - pids1: op_pids1, - x1: op_x1, + pids1: pids_grid.to_vec(), + x1: x_grid.to_vec(), conv_type: opinfo.conv_type, }; From 869ec7060dc926d1746671f72fc21ce832cdfee5 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Fri, 25 Apr 2025 17:39:33 +0200 Subject: [PATCH 10/49] Add write and delete FK table objects --- pineappl_capi/cbindgen.toml | 2 +- pineappl_capi/src/lib.rs | 34 +++++++++++++++++++++++++++++++++- 2 files changed, 34 insertions(+), 2 deletions(-) diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index b24d18d1d..f20afba65 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -48,7 +48,7 @@ rename_variants = "ScreamingSnakeCase" "KeyVal" = "pineappl_keyval" "SubGrid" = "pineappl_subgrid" "GridOptFlags" = "pineappl_gof" -"OperatorSliceInfo" = "pineappl_operator_slice_info" +"OperatorInfo" = "pineappl_operator_info" ############## Options for How Your Rust library Should Be Parsed ############## diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index e097efdeb..6e8862694 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2096,7 +2096,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( ren1.copy_from_slice(&grid.evolve_info(&order_mask).ren1); } -/// Evolve a grid and dump the resulting FK table +/// Evolve a grid and dump the resulting FK table. /// /// # Safety /// @@ -2202,3 +2202,35 @@ pub unsafe extern "C" fn pineappl_grid_evolve( Box::new(fk_table.unwrap()) } + +/// Delete an FK table. +#[no_mangle] +#[allow(unused_variables)] +pub extern "C" fn pineappl_fk_table_delete(fktable: Option>) {} + +/// Write `fktable` to a file with name `filename`. If `filename` ends in `.lz4` the Fk table is +/// automatically LZ4 compressed. +/// +/// # Safety +/// +/// If `fktable` does not point to a valid `FkTable` object, for example when `fktable` is a null +/// pointer, this function is not safe to call. The parameter `filename` must be a non-`NULL`, +/// non-empty, and valid C string pointing to a non-existing, but writable file. +/// +/// # Panics +/// +/// TODO +#[no_mangle] +pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const FkTable, filename: *const c_char) { + let fktable = unsafe { &*fktable }; + let filename = unsafe { CStr::from_ptr(filename) }; + let filename = filename.to_string_lossy(); + let path = Path::new(filename.as_ref()); + let writer = File::create(path).unwrap(); + + if path.extension().is_some_and(|ext| ext == "lz4") { + fktable.grid().write_lz4(writer).unwrap(); + } else { + fktable.grid().write(writer).unwrap(); + } +} From 43b1619215418e24bec1bbb9d48367b892365a01 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Fri, 25 Apr 2025 17:54:58 +0200 Subject: [PATCH 11/49] Fix bug in example --- examples/cpp/evolve-grid.cpp | 33 +++++++++++++++------------------ 1 file changed, 15 insertions(+), 18 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index f59c7a76e..7f88ace53 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -1,10 +1,8 @@ +#include #include #include -#include - #include #include -#include #include #include #include @@ -27,14 +25,15 @@ std::vector generate_fake_ekos( std::vector ops(flat_len); for (std::size_t i = 0; i != flat_len; i++) { - ops.push_back(distrib(gen)); + ops[i] = distrib(gen); } return ops; } int main() { - std::string filename = "advanced-filling.pineappl.lz4"; + // TODO: How to get a Grid that can be evolved?? + std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; // read the grid from a file auto* grid = pineappl_grid_read(filename.c_str()); @@ -45,7 +44,8 @@ int main() { // Get the number of convolutions std::size_t n_convs = pineappl_grid_convolutions_len(grid); - // Fill the vector of unique convolution types + // Fill the vector of unique convolution types. If the EKOs required for the Grid + // are the same, then it suffices to only pass ONE single EKO. std::vector conv_types; for (std::size_t i = 0; i != n_convs; i++) { pineappl_conv_type conv = pineappl_grid_conv_type(grid, i); @@ -73,20 +73,14 @@ int main() { // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose // elements are `OperatorInfo` objects. - std::vector opinfo_slices(conv_types.size() * fac1.size()); - std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; + std::vector opinfo_slices(conv_types.size() * fac1.size()); for (std::size_t i = 0; i != conv_types.size(); i++) { for (std::size_t j = 0; j != fac1.size(); j++) { - OperatorInfo opinfo = { + pineappl_operator_info opinfo = { FAC0, // fac0 fac1[j], // fac1 - x1.data(), // x0 - x1.data(), // x1 - pids1.data(), // pids0 - pids1.data(), // pids1 pid_basis, conv_types[i], - tensor_shape.data() }; opinfo_slices[i * fac1.size() + j] = opinfo; } @@ -104,15 +98,18 @@ int main() { } } } - std::cout << "Arrived Here!" << "\n"; // Construct the values of alphas std::vector alphas_table(ren1.size(), 0.118); std::vector xi = {1.0, 1.0, 1.0}; + std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; + + pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), order_mask.data(), + op_slices.data(), x1.data(), x1.data(), pids1.data(), pids1.data(), + tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); - pineappl_grid_evolve(grid, opinfo_slices.data(), order_mask.data(), - op_slices.data(), xi.data(), ren1.data(), alphas_table.data()); - std::cout << "Where does the double free happen!" << "\n"; + pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); pineappl_grid_delete(grid); + pineappl_fk_table_delete(fktable); } From 2f5dbefb7dad2396554a753aa5cf04d37eb63d3b Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sat, 26 Apr 2025 01:19:26 +0200 Subject: [PATCH 12/49] Fix `alloc-dealloc-mismatch` by avoiding `Vec::from_raw_parts` --- examples/cpp/evolve-grid.cpp | 1 - pineappl_capi/src/lib.rs | 11 +++++++---- 2 files changed, 7 insertions(+), 5 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 7f88ace53..d984f922b 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -109,7 +109,6 @@ int main() { tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); - pineappl_grid_delete(grid); pineappl_fk_table_delete(fktable); } diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 6e8862694..281af7891 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2133,9 +2133,9 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let evolve_info = grid.evolve_info(&order_mask); let ren1_len = evolve_info.ren1.len(); - let ren1 = unsafe { Vec::from_raw_parts(ren1, ren1_len, ren1_len) }; - let alphas = unsafe { Vec::from_raw_parts(alphas, ren1_len, ren1_len) }; - let xi = unsafe { Vec::from_raw_parts(xi, 3, 3) }; + let ren1 = unsafe { slice::from_raw_parts(ren1, ren1_len) }; + let alphas = unsafe { slice::from_raw_parts(alphas, ren1_len) }; + let xi = unsafe { slice::from_raw_parts(xi, 3) }; let conv_types: HashSet<_> = grid .convolutions() @@ -2197,7 +2197,10 @@ pub unsafe extern "C" fn pineappl_grid_evolve( slices, &order_mask, (xi[0], xi[1], xi[2]), - &AlphasTable { ren1, alphas }, + &AlphasTable { + ren1: ren1.to_vec(), + alphas: alphas.to_vec(), + }, ); Box::new(fk_table.unwrap()) From 2bbac765243f1641f6bd50879d85dd861b5b796d Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sat, 26 Apr 2025 12:51:12 +0200 Subject: [PATCH 13/49] Clean up a bit `pineappl_grid_evolve` --- pineappl_capi/src/lib.rs | 85 ++++++++++++++++++---------------------- 1 file changed, 39 insertions(+), 46 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 281af7891..bfd7b116c 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2143,53 +2143,46 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .map(pineappl::convolutions::Conv::conv_type) .collect(); - let op_info = - unsafe { slice::from_raw_parts(op_info, conv_types.len() * evolve_info.fac1.len()) }; - let opinfo_chunk = op_info.chunks_exact(conv_types.len()); + let op_info = unsafe { + slice::from_raw_parts(op_info, conv_types.len() * evolve_info.fac1.len()) + .chunks_exact(conv_types.len()) + }; - let flattened_shapes: usize = op_info - .iter() - .map(|_| eko_shape.iter().product::()) - .sum(); - let operators = - unsafe { slice::from_raw_parts(operators, conv_types.len() * flattened_shapes) }; + let total_shape: usize = eko_shape.iter().product(); + let operators = unsafe { + slice::from_raw_parts( + operators, + conv_types.len() * evolve_info.fac1.len() * total_shape, + ) + .chunks_exact(total_shape) + }; - let mut start_idx = 0; - let op_split: Vec<_> = op_info - .iter() - .map(|_| { - let end_idx = start_idx + eko_shape.iter().product::(); - let op_range = operators[start_idx..end_idx].to_vec(); - start_idx = end_idx; - op_range - }) - .collect(); - let ops_chunk = op_split.chunks_exact(conv_types.len()); - - let slices = opinfo_chunk - .into_iter() - .zip(ops_chunk) - .map(|(op_subinfo, op_range)| { - op_subinfo.iter().zip(op_range).map(|(opinfo, op_values)| { - let operator_slice_info = OperatorSliceInfo { - pid_basis: opinfo.pid_basis, - fac0: opinfo.fac0, - pids0: pids_fktable.to_vec(), - x0: x_fktable.to_vec(), - fac1: opinfo.fac1, - pids1: pids_grid.to_vec(), - x1: x_grid.to_vec(), - conv_type: opinfo.conv_type, - }; - - let array = Array4::from_shape_vec( - Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), - op_values.clone(), - ) - .expect("Shape mismatch or invalid input."); - - Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) - }) + let slices = op_info + .zip(operators) + .map(|(op_infos, op_vals)| { + op_infos + .iter() + .zip(std::iter::once(op_vals)) + .map(|(op_info, values)| { + let operator_slice_info = OperatorSliceInfo { + pid_basis: op_info.pid_basis, + fac0: op_info.fac0, + pids0: pids_fktable.to_vec(), + x0: x_fktable.to_vec(), + fac1: op_info.fac1, + pids1: pids_grid.to_vec(), + x1: x_grid.to_vec(), + conv_type: op_info.conv_type, + }; + + let array = Array4::from_shape_vec( + Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), + values.to_vec(), + ) + .expect("Shape mismatch or invalid input."); + + Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) + }) }) .collect(); @@ -2203,7 +2196,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( }, ); - Box::new(fk_table.unwrap()) + Box::new(fk_table.expect("Evolving grid failed")) } /// Delete an FK table. From e1d414ed3beb4f10bc9618e24e7009d81f79ef0d Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sun, 27 Apr 2025 16:05:49 +0200 Subject: [PATCH 14/49] Add an interface to convolve FK tables --- pineappl_capi/src/lib.rs | 59 +++++++++++++++++++++++++++++++++++++++- 1 file changed, 58 insertions(+), 1 deletion(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index bfd7b116c..b4b1fa941 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -1833,7 +1833,7 @@ pub unsafe extern "C" fn pineappl_grid_order_params2(grid: *const Grid, order_pa } } -/// A generalization of the convolution function. +/// A generalization of the convolution function for Grids. /// /// # Safety /// @@ -2230,3 +2230,60 @@ pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const FkTable, filenam fktable.grid().write(writer).unwrap(); } } + +/// A generalization of the convolution function for FK tables. +/// +/// # Safety +/// +/// If `fktable` does not point to a valid `FkTable` object, for example when `fktable` is +/// a null pointer, this function is not safe to call. The function pointer `xfx` must not +/// be null pointers and point to valid functions. The parameter `channel_mask` must either +/// be null pointers or point to arrays that are as long as `fktable` has channels, respectively. +/// Finally, `results` must be as long as `FkTable` has bins. +#[no_mangle] +pub unsafe extern "C" fn pineappl_fk_table_convolve( + fktable: *const FkTable, + xfx: extern "C" fn(pdg_id: i32, x: f64, q2: f64, state: *mut c_void) -> f64, + pdfs_state: *mut *mut c_void, + channel_mask: *const bool, + bin_indices: *const usize, + results: *mut f64, +) { + let fktable = unsafe { &*fktable }; + + let channel_mask = if channel_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(channel_mask, fktable.channels().len()) } + }; + + let bin_indices = if bin_indices.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(bin_indices, fktable.grid().bwfl().len()) } + }; + + // TODO: Better way to do this? + let mut als = |_| 1.0; + + let pdfs_slices = + unsafe { slice::from_raw_parts(pdfs_state, fktable.grid().convolutions().len()) }; + let mut xfx_funcs: Vec<_> = pdfs_slices + .iter() + .map(|&state| move |id, x, q2| xfx(id, x, q2, state)) + .collect(); + + // Construct the Convolution cache + let mut convolution_cache = ConvolutionCache::new( + fktable.grid().convolutions().to_vec(), + xfx_funcs + .iter_mut() + .map(|fx| fx as &mut dyn FnMut(i32, f64, f64) -> f64) + .collect(), + &mut als, + ); + + let results = unsafe { slice::from_raw_parts_mut(results, fktable.grid().bwfl().len()) }; + + results.copy_from_slice(&fktable.convolve(&mut convolution_cache, bin_indices, channel_mask)); +} From 1b63579cd4598bf37971f1f25d7d2c5f0441a3e3 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sun, 27 Apr 2025 16:15:12 +0200 Subject: [PATCH 15/49] Finalize `evolve-grid.cpp` example --- examples/cpp/Makefile | 2 +- examples/cpp/evolve-grid.cpp | 108 +++++++++++++++++++++++++++++------ examples/cpp/output | 10 ++++ 3 files changed, 103 insertions(+), 17 deletions(-) diff --git a/examples/cpp/Makefile b/examples/cpp/Makefile index 964e0748c..2d5218259 100644 --- a/examples/cpp/Makefile +++ b/examples/cpp/Makefile @@ -53,7 +53,7 @@ get-subgrids: get-subgrids.cpp $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ evolve-grid: evolve-grid.cpp - $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ + $(CXX) $(CXXFLAGS) $< $(LHAPDF_DEPS) $(PINEAPPL_DEPS) -o $@ display-channels-deprecated: display-channels-deprecated.cpp $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index d984f922b..31f35c13d 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -1,31 +1,46 @@ +#include #include + +#include #include #include #include #include #include -#include #include -#include -double FAC0 = 1.65; +// NOTE: Uses the scale of the Grid as the starting scale such that we can use an IDENTITY EKO. +double FAC0 = 6456.44; + +std::vector unravel_index(std::size_t flat_index, const std::vector& shape) { + std::size_t ndim = shape.size(); + std::vector coords(ndim); + + for (int i = ndim - 1; i >= 0; --i) { + coords[i] = flat_index % shape[i]; + flat_index /= shape[i]; + } + + return coords; +} std::vector generate_fake_ekos( - double q2, std::vector pids0, std::vector x0, std::vector pids1, std::vector x1 ) { - std::random_device rd; - std::mt19937 gen(rd()); - std::uniform_real_distribution distrib(q2 / 1000, q2 / 100); - std::size_t flat_len = x0.size() * x1.size() * pids0.size() * pids1.size(); std::vector ops(flat_len); + std::vector shape = {pids0.size(), x0.size(), pids1.size(), x1.size()}; for (std::size_t i = 0; i != flat_len; i++) { - ops[i] = distrib(gen); + std::vector coords = unravel_index(i, shape); + + double delta_ik = (coords[0] == coords[2]) ? 1.0 : 0.0; + double delta_jl = (coords[1] == coords[3]) ? 1.0 : 0.0; + + ops[i] = delta_ik * delta_jl; } return ops; @@ -56,8 +71,8 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::vector order_mask = {3, 0}; - pineappl_grid_evolve_info_shape(grid, order_mask.data(), evinfo_shape.data()); + std::vector apply_order = {3, 0}; + pineappl_grid_evolve_info_shape(grid, apply_order.data(), evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the // information on the `x`-grid and `PID` used to interpolate the Grid. @@ -67,7 +82,7 @@ int main() { std::vector pids1(evinfo_shape[2]); std::vector x1(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); - pineappl_grid_evolve_info(grid, order_mask.data(), fac1.data(), + pineappl_grid_evolve_info(grid, apply_order.data(), fac1.data(), frg1.data(), pids1.data(), x1.data(), ren1.data()); // ------------------ Construct the Operator Info ------------------ @@ -90,9 +105,9 @@ int main() { // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` std::vector op_slices; std::size_t flat_len = x1.size() * x1.size() * pids1.size() * pids1.size(); - for (std::size_t i = 0; i != conv_types.size(); i++) { + for (std::size_t _i = 0; _i != conv_types.size(); _i++) { for (std::size_t j = 0; j != fac1.size(); j++) { - std::vector eko = generate_fake_ekos(fac1[j], pids1, x1, pids1, x1); + std::vector eko = generate_fake_ekos(pids1, x1, pids1, x1); for (std::size_t k = 0; k != flat_len; k++) { op_slices.push_back(eko[k]); } @@ -104,11 +119,72 @@ int main() { std::vector xi = {1.0, 1.0, 1.0}; std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; - pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), order_mask.data(), - op_slices.data(), x1.data(), x1.data(), pids1.data(), pids1.data(), + pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), + apply_order.data(), op_slices.data(), x1.data(), + x1.data(), pids1.data(), pids1.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); + // ------------------ Compare Grid & FK after convolution ------------------ + // disable LHAPDF banners to guarantee deterministic output + LHAPDF::setVerbosity(0); + std::string pdfset = "NNPDF31_nlo_as_0118_luxqed"; + auto pdf = std::unique_ptr(LHAPDF::mkPDF(pdfset, 0)); + + auto xfx = [](int32_t id, double x, double q2, void* pdf) { + return static_cast (pdf)->xfxQ2(id, x, q2); + }; + auto alphas = [](double q2, void* pdf) { + return static_cast (pdf)->alphasQ2(q2); + }; + + std::vector pdfs = {pdf.get(), pdf.get()}; + void** pdf_states = reinterpret_cast(pdfs.data()); + + // how many bins does this grid have? + std::size_t bins = pineappl_grid_bin_count(grid); + + // [ convolve the Grid ] + std::vector mu_scales = { 1.0, 1.0, 1.0 }; + std::vector dxsec_grid(bins); + pineappl_grid_convolve(grid, xfx, alphas, pdf_states, pdf.get(), + nullptr, nullptr, nullptr, 1, + mu_scales.data(), dxsec_grid.data()); + + // [ convolve the FK Table ] + std::vector dxsec_fktable(bins); + pineappl_fk_table_convolve(fktable, xfx, pdf_states, nullptr, + nullptr, dxsec_fktable.data()); + + // Print the results + const int idx_width = 6; + const int num_width = 15; + const int dif_width = 15; + + // Print headers + std::cout << std::setw(idx_width) << "Bin" + << std::setw(num_width) << "Grid" + << std::setw(num_width) << "FkTable" + << std::setw(dif_width) << "reldiff" << std::endl; + + // Print dashed lines + std::cout << std::setw(idx_width) << std::string(idx_width - 2, '-') + << std::setw(num_width) << std::string(num_width - 2, '-') + << std::setw(num_width) << std::string(num_width - 2, '-') + << std::setw(dif_width) << std::string(dif_width - 2, '-') << std::endl; + + // Print the data + std::cout << std::scientific << std::setprecision(6); + for (size_t i = 0; i < dxsec_grid.size(); ++i) { + double reldiff = std::abs(dxsec_grid[i] - dxsec_fktable[i]) / (std::abs(dxsec_grid[i])); + std::cout << std::setw(idx_width) << i + << std::setw(num_width) << dxsec_grid[i] + << std::setw(num_width) << dxsec_fktable[i] + << std::setw(dif_width) << reldiff + << std::endl; + } + pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); + pineappl_grid_delete(grid); pineappl_fk_table_delete(fktable); } diff --git a/examples/cpp/output b/examples/cpp/output index 2ce8b5c7f..bdeb022ae 100644 --- a/examples/cpp/output +++ b/examples/cpp/output @@ -172,6 +172,16 @@ idx left right dsig/dx dx 21 40675 (16, 13, 25) (5442.31, 0.219504, 0.0043285) -3.60243e-10 22 40676 (16, 13, 26) (5442.31, 0.219504, 0.00287387) -1.22785e-08 23 40626 (16, 12, 26) (5442.31, 0.265114, 0.00287387) -7.04493e-11 + Bin Grid FkTable reldiff + ---- ------------- ------------- ------------- + 0 7.545911e+02 7.603251e+02 7.598823e-03 + 1 6.902834e+02 6.949192e+02 6.715820e-03 + 2 6.002520e+02 6.037697e+02 5.860343e-03 + 3 4.855224e+02 4.878688e+02 4.832807e-03 + 4 3.619546e+02 3.634639e+02 4.169948e-03 + 5 2.458669e+02 2.467891e+02 3.750676e-03 + 6 1.158685e+02 1.163001e+02 3.724532e-03 + 7 2.751727e+01 2.763520e+01 4.285840e-03 idx p-p c#0 l#0 p-p~ c#0 l# p-d c#0 l#0 p-d dx --- ------------ ----------- ------------- ------------ ------ 0 5.263109e-01 5.263109e-01 5.263109e-01 5.263109e-01 0.1 From 47f7044fbe4f5e284d835ad70a6759459426de20 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sun, 27 Apr 2025 17:19:02 +0200 Subject: [PATCH 16/49] Clean up a bit and add documentation --- pineappl_capi/src/lib.rs | 64 +++++++++++++++++++++++++++------------- 1 file changed, 44 insertions(+), 20 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index b4b1fa941..9ab4049bb 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2037,7 +2037,8 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_array( /// /// # Safety /// -/// TODO +/// If `grid` does not point to a valid `Grid` object, for example when `grid` is the null pointer, +/// this function is not safe to call. #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( grid: *const Grid, @@ -2066,7 +2067,8 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( /// /// # Safety /// -/// TODO +/// If `grid` does not point to a valid `Grid` object, for example when `grid` is the null pointer, +/// this function is not safe to call. #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve_info( grid: *const Grid, @@ -2096,25 +2098,47 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( ren1.copy_from_slice(&grid.evolve_info(&order_mask).ren1); } -/// Evolve a grid and dump the resulting FK table. +/// Evolve a grid with an evolution operator and dump the resulting FK table. +/// +/// # Arguments +/// +/// * `grid` - A `Grid` object +/// * `op_info` - An array of `OperatorInfo` objects containing the information about the evolution. +/// Its length must be `(N_{conv} * N_{Q2_slices})`. +/// * `orders` - The maximum QCD and EW orders `(αs, α)` +/// * `operators` - An array of evolution operators. Each operator is a flattend version of a rank-4 +/// tensor whose shape is defined by: `pids_out`, `x_out`, `pids_in`, `x_in`, in that +/// order. The size of `operators` must be `(N_{conv} * N_{Q2_slices} * len_flat_op)`. +/// * `x_in` - The x-grid that defines the Grid +/// * `x_out` - The x-grid that will define the evolved Grid +/// * `pids_in` - The list of PID values that defines the Grid +/// * `pids_out` - The list of PID values that will define the evolved Grid +/// * `eko_shape` - The shape of the evolution operator +/// * `xi` - The values that defines that scale variations +/// * `ren` - An array containing the values of the renormalization scale variation +/// * `alphas` - An array containing the values of `αs`. It must have the same size as `ren1`. /// /// # Safety /// -/// TODO +/// This function is not safe to call if: (a) the `grid` does not point to a valid `Grid` object or +/// is a null pointer; (b) the `op_info` and `operators` objects do not have the expected lengths, +/// (c) the shape of `eko_shape` is different from the actual size of `pids_out`, `x_out`, `pids_in`, +/// `x_in`. /// /// # Panics /// -/// TODO +/// This function might panic if the either the `op_info` and/or `operators` are/is incompatible +/// with the `Grid`. #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve( grid: *mut Grid, op_info: *mut OperatorInfo, - orders: *const u8, + max_orders: *const u8, operators: *mut f64, - x_grid: *mut f64, - x_fktable: *mut f64, - pids_grid: *mut i32, - pids_fktable: *mut i32, + x_in: *mut f64, + x_out: *mut f64, + pids_in: *mut i32, + pids_out: *mut i32, eko_shape: *mut usize, xi: *mut f64, ren1: *mut f64, @@ -2122,14 +2146,14 @@ pub unsafe extern "C" fn pineappl_grid_evolve( ) -> Box { let grid = unsafe { &mut *grid }; - let orders = unsafe { slice::from_raw_parts(orders, 2) }; + let max_orders = unsafe { slice::from_raw_parts(max_orders, 2) }; let eko_shape = unsafe { slice::from_raw_parts(eko_shape, 4) }; - let pids_fktable = unsafe { slice::from_raw_parts(pids_fktable, eko_shape[0]) }; - let x_fktable = unsafe { slice::from_raw_parts(x_fktable, eko_shape[1]) }; - let pids_grid = unsafe { slice::from_raw_parts(pids_grid, eko_shape[2]) }; - let x_grid = unsafe { slice::from_raw_parts(x_grid, eko_shape[3]) }; + let pids_out = unsafe { slice::from_raw_parts(pids_out, eko_shape[0]) }; + let x_out = unsafe { slice::from_raw_parts(x_out, eko_shape[1]) }; + let pids_in = unsafe { slice::from_raw_parts(pids_in, eko_shape[2]) }; + let x_in = unsafe { slice::from_raw_parts(x_in, eko_shape[3]) }; - let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); + let order_mask = Order::create_mask(grid.orders(), max_orders[0], max_orders[1], true); let evolve_info = grid.evolve_info(&order_mask); let ren1_len = evolve_info.ren1.len(); @@ -2167,11 +2191,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let operator_slice_info = OperatorSliceInfo { pid_basis: op_info.pid_basis, fac0: op_info.fac0, - pids0: pids_fktable.to_vec(), - x0: x_fktable.to_vec(), + pids0: pids_out.to_vec(), + x0: x_out.to_vec(), fac1: op_info.fac1, - pids1: pids_grid.to_vec(), - x1: x_grid.to_vec(), + pids1: pids_in.to_vec(), + x1: x_in.to_vec(), conv_type: op_info.conv_type, }; From b2bf81b3dc064b9273a1c95a8a20ed2d36eb4961 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 29 Apr 2025 12:17:51 +0200 Subject: [PATCH 17/49] Fix bug in order masking --- examples/cpp/evolve-grid.cpp | 49 ++++++++++++++++++++---------------- examples/cpp/output | 16 ++++++------ 2 files changed, 35 insertions(+), 30 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 31f35c13d..678f42e27 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -50,6 +50,21 @@ int main() { // TODO: How to get a Grid that can be evolved?? std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; + // disable LHAPDF banners to guarantee deterministic output + LHAPDF::setVerbosity(0); + std::string pdfset = "NNPDF31_nlo_as_0118_luxqed"; + auto pdf = std::unique_ptr(LHAPDF::mkPDF(pdfset, 0)); + + auto xfx = [](int32_t id, double x, double q2, void* pdf) { + return static_cast (pdf)->xfxQ2(id, x, q2); + }; + auto alphas = [](double q2, void* pdf) { + return static_cast (pdf)->alphasQ2(q2); + }; + + std::vector pdfs = {pdf.get(), pdf.get()}; + void** pdf_states = reinterpret_cast(pdfs.data()); + // read the grid from a file auto* grid = pineappl_grid_read(filename.c_str()); @@ -71,8 +86,8 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::vector apply_order = {3, 0}; - pineappl_grid_evolve_info_shape(grid, apply_order.data(), evinfo_shape.data()); + std::vector max_orders = {3, 2}; + pineappl_grid_evolve_info_shape(grid, max_orders.data(), evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the // information on the `x`-grid and `PID` used to interpolate the Grid. @@ -82,7 +97,7 @@ int main() { std::vector pids1(evinfo_shape[2]); std::vector x1(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); - pineappl_grid_evolve_info(grid, apply_order.data(), fac1.data(), + pineappl_grid_evolve_info(grid, max_orders.data(), fac1.data(), frg1.data(), pids1.data(), x1.data(), ren1.data()); // ------------------ Construct the Operator Info ------------------ @@ -114,32 +129,22 @@ int main() { } } - // Construct the values of alphas - std::vector alphas_table(ren1.size(), 0.118); + // Construct the values of alphas table + std::vector alphas_table; + for (double q2 : ren1) { + double alpha = alphas(q2, pdf.get()); + alphas_table.push_back(alpha); + } + std::vector xi = {1.0, 1.0, 1.0}; std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - apply_order.data(), op_slices.data(), x1.data(), + max_orders.data(), op_slices.data(), x1.data(), x1.data(), pids1.data(), pids1.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); // ------------------ Compare Grid & FK after convolution ------------------ - // disable LHAPDF banners to guarantee deterministic output - LHAPDF::setVerbosity(0); - std::string pdfset = "NNPDF31_nlo_as_0118_luxqed"; - auto pdf = std::unique_ptr(LHAPDF::mkPDF(pdfset, 0)); - - auto xfx = [](int32_t id, double x, double q2, void* pdf) { - return static_cast (pdf)->xfxQ2(id, x, q2); - }; - auto alphas = [](double q2, void* pdf) { - return static_cast (pdf)->alphasQ2(q2); - }; - - std::vector pdfs = {pdf.get(), pdf.get()}; - void** pdf_states = reinterpret_cast(pdfs.data()); - // how many bins does this grid have? std::size_t bins = pineappl_grid_bin_count(grid); @@ -175,7 +180,7 @@ int main() { // Print the data std::cout << std::scientific << std::setprecision(6); for (size_t i = 0; i < dxsec_grid.size(); ++i) { - double reldiff = std::abs(dxsec_grid[i] - dxsec_fktable[i]) / (std::abs(dxsec_grid[i])); + double reldiff = (dxsec_fktable[i] - dxsec_grid[i]) / dxsec_grid[i]; std::cout << std::setw(idx_width) << i << std::setw(num_width) << dxsec_grid[i] << std::setw(num_width) << dxsec_fktable[i] diff --git a/examples/cpp/output b/examples/cpp/output index bdeb022ae..aee77c2cb 100644 --- a/examples/cpp/output +++ b/examples/cpp/output @@ -174,14 +174,14 @@ idx left right dsig/dx dx 23 40626 (16, 12, 26) (5442.31, 0.265114, 0.00287387) -7.04493e-11 Bin Grid FkTable reldiff ---- ------------- ------------- ------------- - 0 7.545911e+02 7.603251e+02 7.598823e-03 - 1 6.902834e+02 6.949192e+02 6.715820e-03 - 2 6.002520e+02 6.037697e+02 5.860343e-03 - 3 4.855224e+02 4.878688e+02 4.832807e-03 - 4 3.619546e+02 3.634639e+02 4.169948e-03 - 5 2.458669e+02 2.467891e+02 3.750676e-03 - 6 1.158685e+02 1.163001e+02 3.724532e-03 - 7 2.751727e+01 2.763520e+01 4.285840e-03 + 0 7.545911e+02 7.545911e+02 -3.762829e-08 + 1 6.902834e+02 6.902834e+02 -3.537025e-08 + 2 6.002520e+02 6.002520e+02 -3.293028e-08 + 3 4.855224e+02 4.855223e+02 -3.037598e-08 + 4 3.619546e+02 3.619545e+02 -2.782860e-08 + 5 2.458669e+02 2.458669e+02 -2.526536e-08 + 6 1.158685e+02 1.158685e+02 -2.182740e-08 + 7 2.751727e+01 2.751727e+01 -1.732084e-08 idx p-p c#0 l#0 p-p~ c#0 l# p-d c#0 l#0 p-d dx --- ------------ ----------- ------------- ------------ ------ 0 5.263109e-01 5.263109e-01 5.263109e-01 5.263109e-01 0.1 From 17cf36303865170dda75ade80b72103b13ea9e4e Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 30 Apr 2025 11:19:31 +0200 Subject: [PATCH 18/49] Clarify a bit the example --- examples/cpp/evolve-grid.cpp | 108 +++++++++++++++++++++-------------- pineappl_capi/src/lib.rs | 8 +-- 2 files changed, 70 insertions(+), 46 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 678f42e27..0b21d0e20 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -25,15 +25,16 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } std::vector generate_fake_ekos( - std::vector pids0, - std::vector x0, - std::vector pids1, - std::vector x1 + std::vector pids_in, + std::vector x_in, + std::vector pids_out, + std::vector x_out ) { - std::size_t flat_len = x0.size() * x1.size() * pids0.size() * pids1.size(); + std::size_t flat_len = x_out.size() * x_in.size() * pids_out.size() * pids_in.size(); std::vector ops(flat_len); - std::vector shape = {pids0.size(), x0.size(), pids1.size(), x1.size()}; + // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) + std::vector shape = {pids_in.size(), x_in.size(), pids_out.size(), x_out.size()}; for (std::size_t i = 0; i != flat_len; i++) { std::vector coords = unravel_index(i, shape); @@ -46,6 +47,35 @@ std::vector generate_fake_ekos( return ops; } +void print_results(std::vector dxsec_grid, std::vector dxsec_fktable) { + const int idx_width = 6; + const int num_width = 15; + const int dif_width = 15; + + // Print headers + std::cout << std::setw(idx_width) << "Bin" + << std::setw(num_width) << "Grid" + << std::setw(num_width) << "FkTable" + << std::setw(dif_width) << "reldiff" << std::endl; + + // Print dashed lines + std::cout << std::setw(idx_width) << std::string(idx_width - 2, '-') + << std::setw(num_width) << std::string(num_width - 2, '-') + << std::setw(num_width) << std::string(num_width - 2, '-') + << std::setw(dif_width) << std::string(dif_width - 2, '-') << std::endl; + + // Print the data + std::cout << std::scientific << std::setprecision(6); + for (size_t i = 0; i < dxsec_grid.size(); ++i) { + double reldiff = (dxsec_fktable[i] - dxsec_grid[i]) / dxsec_grid[i]; + std::cout << std::setw(idx_width) << i + << std::setw(num_width) << dxsec_grid[i] + << std::setw(num_width) << dxsec_fktable[i] + << std::setw(dif_width) << reldiff + << std::endl; + } +} + int main() { // TODO: How to get a Grid that can be evolved?? std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; @@ -70,6 +100,7 @@ int main() { // Get the PID basis representation pineappl_pid_basis pid_basis = pineappl_grid_pid_basis(grid); + assert(pid_basis == PINEAPPL_PID_BASIS_PDG); // Get the number of convolutions std::size_t n_convs = pineappl_grid_convolutions_len(grid); @@ -86,7 +117,7 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::vector max_orders = {3, 2}; + std::vector max_orders = {2, 3}; pineappl_grid_evolve_info_shape(grid, max_orders.data(), evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the @@ -94,11 +125,11 @@ int main() { // NOTE: These are used to construct the Evolution Operator std::vector fac1(evinfo_shape[0]); std::vector frg1(evinfo_shape[1]); - std::vector pids1(evinfo_shape[2]); - std::vector x1(evinfo_shape[3]); + std::vector pids_in(evinfo_shape[2]); + std::vector x_in(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); pineappl_grid_evolve_info(grid, max_orders.data(), fac1.data(), - frg1.data(), pids1.data(), x1.data(), ren1.data()); + frg1.data(), pids_in.data(), x_in.data(), ren1.data()); // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose @@ -117,12 +148,16 @@ int main() { } // ------------------ Construct the Evolution Operator ------------------ + // Choose a different PID basis for the FK table + // std::vector pids_out = {-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 21, 22}; + std::vector pids_out = pids_in; + // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` std::vector op_slices; - std::size_t flat_len = x1.size() * x1.size() * pids1.size() * pids1.size(); + std::size_t flat_len = x_in.size() * x_in.size() * pids_in.size() * pids_out.size(); for (std::size_t _i = 0; _i != conv_types.size(); _i++) { for (std::size_t j = 0; j != fac1.size(); j++) { - std::vector eko = generate_fake_ekos(pids1, x1, pids1, x1); + std::vector eko = generate_fake_ekos(pids_in, x_in, pids_out, x_in); for (std::size_t k = 0; k != flat_len; k++) { op_slices.push_back(eko[k]); } @@ -137,11 +172,25 @@ int main() { } std::vector xi = {1.0, 1.0, 1.0}; - std::vector tensor_shape = {pids1.size(), x1.size(), pids1.size(), x1.size()}; - + // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) + std::vector tensor_shape = {pids_in.size(), x_in.size(), pids_out.size(), x_in.size()}; + + // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: + // - `grid`: PineAPPL Grid + // - `op_info`: operator info + // - `max_orders`: max orders to apply the evolution + // - `operators`: evolution operator + // - `x_in`: x-grid of the Grid + // - `x_out`: x-grid of the FK table + // - `pids_in`: PIDs basis representation of the Grid + // - `pids_out`: PIDs basis representation of the FK table + // - `eko_shape`: shape of the evolution operators + // - `xi`: scale variation + // - `ren1`: values of the renormalization scales + // - `alphas_table`: values of alphas for each renormalization scales pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - max_orders.data(), op_slices.data(), x1.data(), - x1.data(), pids1.data(), pids1.data(), + max_orders.data(), op_slices.data(), x_in.data(), + x_in.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); // ------------------ Compare Grid & FK after convolution ------------------ @@ -161,32 +210,7 @@ int main() { nullptr, dxsec_fktable.data()); // Print the results - const int idx_width = 6; - const int num_width = 15; - const int dif_width = 15; - - // Print headers - std::cout << std::setw(idx_width) << "Bin" - << std::setw(num_width) << "Grid" - << std::setw(num_width) << "FkTable" - << std::setw(dif_width) << "reldiff" << std::endl; - - // Print dashed lines - std::cout << std::setw(idx_width) << std::string(idx_width - 2, '-') - << std::setw(num_width) << std::string(num_width - 2, '-') - << std::setw(num_width) << std::string(num_width - 2, '-') - << std::setw(dif_width) << std::string(dif_width - 2, '-') << std::endl; - - // Print the data - std::cout << std::scientific << std::setprecision(6); - for (size_t i = 0; i < dxsec_grid.size(); ++i) { - double reldiff = (dxsec_fktable[i] - dxsec_grid[i]) / dxsec_grid[i]; - std::cout << std::setw(idx_width) << i - << std::setw(num_width) << dxsec_grid[i] - << std::setw(num_width) << dxsec_fktable[i] - << std::setw(dif_width) << reldiff - << std::endl; - } + print_results(dxsec_grid, dxsec_fktable); pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 9ab4049bb..796d67bf4 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2148,10 +2148,10 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let max_orders = unsafe { slice::from_raw_parts(max_orders, 2) }; let eko_shape = unsafe { slice::from_raw_parts(eko_shape, 4) }; - let pids_out = unsafe { slice::from_raw_parts(pids_out, eko_shape[0]) }; - let x_out = unsafe { slice::from_raw_parts(x_out, eko_shape[1]) }; - let pids_in = unsafe { slice::from_raw_parts(pids_in, eko_shape[2]) }; - let x_in = unsafe { slice::from_raw_parts(x_in, eko_shape[3]) }; + let pids_in = unsafe { slice::from_raw_parts(pids_in, eko_shape[0]) }; + let x_in = unsafe { slice::from_raw_parts(x_in, eko_shape[1]) }; + let pids_out = unsafe { slice::from_raw_parts(pids_out, eko_shape[2]) }; + let x_out = unsafe { slice::from_raw_parts(x_out, eko_shape[3]) }; let order_mask = Order::create_mask(grid.orders(), max_orders[0], max_orders[1], true); let evolve_info = grid.evolve_info(&order_mask); From 6e77212b0770288dfa24f3da01254ad5ddea89a3 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 30 Apr 2025 13:29:59 +0200 Subject: [PATCH 19/49] Change the way in which data are cached --- .github/workflows/capi.yaml | 3 +++ .github/workflows/download-test-data.yml | 27 ++++++++++++++++++++++++ .github/workflows/python.yml | 13 ++---------- .github/workflows/rust.yml | 13 ++---------- examples/cpp/evolve-grid.cpp | 2 +- 5 files changed, 35 insertions(+), 23 deletions(-) create mode 100644 .github/workflows/download-test-data.yml diff --git a/.github/workflows/capi.yaml b/.github/workflows/capi.yaml index 65f35070c..a4f3854bc 100644 --- a/.github/workflows/capi.yaml +++ b/.github/workflows/capi.yaml @@ -23,6 +23,9 @@ jobs: cargo cinstall --verbose --prefix=/usr/local/ --libdir=/usr/local/lib ldconfig + - name: Download test data if not cached + uses: ./.github/workflows/download-test-data.yml + - name: Test C++ examples run: | cd examples/cpp diff --git a/.github/workflows/download-test-data.yml b/.github/workflows/download-test-data.yml new file mode 100644 index 000000000..117f372b1 --- /dev/null +++ b/.github/workflows/download-test-data.yml @@ -0,0 +1,27 @@ +name: Download/Cache Test Data +on: + workflow_call: + # If needed downstream + outputs: + cache-hit: + description: "Whether cache was hit" + value: ${{ jobs.cache-test.outputs.cache-hit }} + +jobs: + cache-test: + runs-on: ubuntu-latest + outputs: + cache-hit: ${{ steps.cache-test-data.outputs.cache-hit }} + steps: + - name: Cache test data + id: cache-test-data + uses: actions/cache@v4 + with: + path: test-data + key: test-data-v20 + + - name: Download test data if cache miss + if: steps.cache-test-data.outputs.cache-hit != 'true' + run: | + cd maintainer + ./download-test-data.sh diff --git a/.github/workflows/python.yml b/.github/workflows/python.yml index 5e4806c09..398cc7c3e 100644 --- a/.github/workflows/python.yml +++ b/.github/workflows/python.yml @@ -24,17 +24,8 @@ jobs: run: | rustup component add llvm-tools - - name: Get test data - id: cache-test-data - uses: actions/cache@v4 - with: - path: test-data - key: test-data-v20 - - name: Download test data - if: steps.cache-test-data.outputs.cache-hit != 'true' - run: | - cd maintainer - ./download-test-data.sh + - name: Download test data if not cached + uses: ./.github/workflows/download-test-data.yml - name: Test env: diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml index 44953aa37..bf63fe199 100644 --- a/.github/workflows/rust.yml +++ b/.github/workflows/rust.yml @@ -20,17 +20,8 @@ jobs: steps: - uses: actions/checkout@v4 - - name: Get test data - id: cache-test-data - uses: actions/cache@v4 - with: - path: test-data - key: test-data-v20 - - name: Download test data - if: steps.cache-test-data.outputs.cache-hit != 'true' - run: | - cd maintainer - ./download-test-data.sh + - name: Download test data if not cached + uses: ./.github/workflows/download-test-data.yml - name: Set RUSTDOCFLAGS run: | diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 0b21d0e20..aff78ecb7 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -78,7 +78,7 @@ void print_results(std::vector dxsec_grid, std::vector dxsec_fkt int main() { // TODO: How to get a Grid that can be evolved?? - std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; + std::string filename = "../../test-data/LHCB_WP_7TEV_opt.pineappl.lz4"; // disable LHAPDF banners to guarantee deterministic output LHAPDF::setVerbosity(0); From 6d23a0b3ea73d20cbbdc47ad285c7cbaf7384f9b Mon Sep 17 00:00:00 2001 From: Tanjona Rabemananjara Date: Wed, 30 Apr 2025 13:34:24 +0200 Subject: [PATCH 20/49] Revert "Change the way in which data are cached" This reverts commit 6e77212b0770288dfa24f3da01254ad5ddea89a3. --- .github/workflows/capi.yaml | 3 --- .github/workflows/download-test-data.yml | 27 ------------------------ .github/workflows/python.yml | 13 ++++++++++-- .github/workflows/rust.yml | 13 ++++++++++-- examples/cpp/evolve-grid.cpp | 2 +- 5 files changed, 23 insertions(+), 35 deletions(-) delete mode 100644 .github/workflows/download-test-data.yml diff --git a/.github/workflows/capi.yaml b/.github/workflows/capi.yaml index a4f3854bc..65f35070c 100644 --- a/.github/workflows/capi.yaml +++ b/.github/workflows/capi.yaml @@ -23,9 +23,6 @@ jobs: cargo cinstall --verbose --prefix=/usr/local/ --libdir=/usr/local/lib ldconfig - - name: Download test data if not cached - uses: ./.github/workflows/download-test-data.yml - - name: Test C++ examples run: | cd examples/cpp diff --git a/.github/workflows/download-test-data.yml b/.github/workflows/download-test-data.yml deleted file mode 100644 index 117f372b1..000000000 --- a/.github/workflows/download-test-data.yml +++ /dev/null @@ -1,27 +0,0 @@ -name: Download/Cache Test Data -on: - workflow_call: - # If needed downstream - outputs: - cache-hit: - description: "Whether cache was hit" - value: ${{ jobs.cache-test.outputs.cache-hit }} - -jobs: - cache-test: - runs-on: ubuntu-latest - outputs: - cache-hit: ${{ steps.cache-test-data.outputs.cache-hit }} - steps: - - name: Cache test data - id: cache-test-data - uses: actions/cache@v4 - with: - path: test-data - key: test-data-v20 - - - name: Download test data if cache miss - if: steps.cache-test-data.outputs.cache-hit != 'true' - run: | - cd maintainer - ./download-test-data.sh diff --git a/.github/workflows/python.yml b/.github/workflows/python.yml index 398cc7c3e..5e4806c09 100644 --- a/.github/workflows/python.yml +++ b/.github/workflows/python.yml @@ -24,8 +24,17 @@ jobs: run: | rustup component add llvm-tools - - name: Download test data if not cached - uses: ./.github/workflows/download-test-data.yml + - name: Get test data + id: cache-test-data + uses: actions/cache@v4 + with: + path: test-data + key: test-data-v20 + - name: Download test data + if: steps.cache-test-data.outputs.cache-hit != 'true' + run: | + cd maintainer + ./download-test-data.sh - name: Test env: diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml index bf63fe199..44953aa37 100644 --- a/.github/workflows/rust.yml +++ b/.github/workflows/rust.yml @@ -20,8 +20,17 @@ jobs: steps: - uses: actions/checkout@v4 - - name: Download test data if not cached - uses: ./.github/workflows/download-test-data.yml + - name: Get test data + id: cache-test-data + uses: actions/cache@v4 + with: + path: test-data + key: test-data-v20 + - name: Download test data + if: steps.cache-test-data.outputs.cache-hit != 'true' + run: | + cd maintainer + ./download-test-data.sh - name: Set RUSTDOCFLAGS run: | diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index aff78ecb7..0b21d0e20 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -78,7 +78,7 @@ void print_results(std::vector dxsec_grid, std::vector dxsec_fkt int main() { // TODO: How to get a Grid that can be evolved?? - std::string filename = "../../test-data/LHCB_WP_7TEV_opt.pineappl.lz4"; + std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; // disable LHAPDF banners to guarantee deterministic output LHAPDF::setVerbosity(0); From 4c833815cab8696bf01f989d7512cf3a8969d295 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 13 May 2025 10:25:07 +0200 Subject: [PATCH 21/49] Add actual example using actual EKO --- examples/cpp/EKO_LHCB_WP_7TEV.txt | 490000 +++++++++++++++++++++++ examples/cpp/Makefile | 4 + examples/cpp/evolve-grid-identity.cpp | 219 + examples/cpp/evolve-grid.cpp | 105 +- examples/cpp/output | 10 + 5 files changed, 490309 insertions(+), 29 deletions(-) create mode 100644 examples/cpp/EKO_LHCB_WP_7TEV.txt create mode 100644 examples/cpp/evolve-grid-identity.cpp diff 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display-channels-deprecated: display-channels-deprecated.cpp $(CXX) $(CXXFLAGS) $< $(PINEAPPL_DEPS) -o $@ diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp new file mode 100644 index 000000000..0b21d0e20 --- /dev/null +++ b/examples/cpp/evolve-grid-identity.cpp @@ -0,0 +1,219 @@ +#include +#include + +#include +#include +#include +#include +#include +#include +#include + +// NOTE: Uses the scale of the Grid as the starting scale such that we can use an IDENTITY EKO. +double FAC0 = 6456.44; + +std::vector unravel_index(std::size_t flat_index, const std::vector& shape) { + std::size_t ndim = shape.size(); + std::vector coords(ndim); + + for (int i = ndim - 1; i >= 0; --i) { + coords[i] = flat_index % shape[i]; + flat_index /= shape[i]; + } + + return coords; +} + +std::vector generate_fake_ekos( + std::vector pids_in, + std::vector x_in, + std::vector pids_out, + std::vector x_out +) { + std::size_t flat_len = x_out.size() * x_in.size() * pids_out.size() * pids_in.size(); + std::vector ops(flat_len); + + // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) + std::vector shape = {pids_in.size(), x_in.size(), pids_out.size(), x_out.size()}; + for (std::size_t i = 0; i != flat_len; i++) { + std::vector coords = unravel_index(i, shape); + + double delta_ik = (coords[0] == coords[2]) ? 1.0 : 0.0; + double delta_jl = (coords[1] == coords[3]) ? 1.0 : 0.0; + + ops[i] = delta_ik * delta_jl; + } + + return ops; +} + +void print_results(std::vector dxsec_grid, std::vector dxsec_fktable) { + const int idx_width = 6; + const int num_width = 15; + const int dif_width = 15; + + // Print headers + std::cout << std::setw(idx_width) << "Bin" + << std::setw(num_width) << "Grid" + << std::setw(num_width) << "FkTable" + << std::setw(dif_width) << "reldiff" << std::endl; + + // Print dashed lines + std::cout << std::setw(idx_width) << std::string(idx_width - 2, '-') + << std::setw(num_width) << std::string(num_width - 2, '-') + << std::setw(num_width) << std::string(num_width - 2, '-') + << std::setw(dif_width) << std::string(dif_width - 2, '-') << std::endl; + + // Print the data + std::cout << std::scientific << std::setprecision(6); + for (size_t i = 0; i < dxsec_grid.size(); ++i) { + double reldiff = (dxsec_fktable[i] - dxsec_grid[i]) / dxsec_grid[i]; + std::cout << std::setw(idx_width) << i + << std::setw(num_width) << dxsec_grid[i] + << std::setw(num_width) << dxsec_fktable[i] + << std::setw(dif_width) << reldiff + << std::endl; + } +} + +int main() { + // TODO: How to get a Grid that can be evolved?? + std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; + + // disable LHAPDF banners to guarantee deterministic output + LHAPDF::setVerbosity(0); + std::string pdfset = "NNPDF31_nlo_as_0118_luxqed"; + auto pdf = std::unique_ptr(LHAPDF::mkPDF(pdfset, 0)); + + auto xfx = [](int32_t id, double x, double q2, void* pdf) { + return static_cast (pdf)->xfxQ2(id, x, q2); + }; + auto alphas = [](double q2, void* pdf) { + return static_cast (pdf)->alphasQ2(q2); + }; + + std::vector pdfs = {pdf.get(), pdf.get()}; + void** pdf_states = reinterpret_cast(pdfs.data()); + + // read the grid from a file + auto* grid = pineappl_grid_read(filename.c_str()); + + // Get the PID basis representation + pineappl_pid_basis pid_basis = pineappl_grid_pid_basis(grid); + assert(pid_basis == PINEAPPL_PID_BASIS_PDG); + + // Get the number of convolutions + std::size_t n_convs = pineappl_grid_convolutions_len(grid); + + // Fill the vector of unique convolution types. If the EKOs required for the Grid + // are the same, then it suffices to only pass ONE single EKO. + std::vector conv_types; + for (std::size_t i = 0; i != n_convs; i++) { + pineappl_conv_type conv = pineappl_grid_conv_type(grid, i); + if (std::find(conv_types.begin(), conv_types.end(), conv) == conv_types.end()) { + conv_types.push_back(conv); + } + } + + // Get the shape of the evolve info objects + std::vector evinfo_shape(5); + std::vector max_orders = {2, 3}; + pineappl_grid_evolve_info_shape(grid, max_orders.data(), evinfo_shape.data()); + + // Get the values of the evolve info parameters. These contain, for example, the + // information on the `x`-grid and `PID` used to interpolate the Grid. + // NOTE: These are used to construct the Evolution Operator + std::vector fac1(evinfo_shape[0]); + std::vector frg1(evinfo_shape[1]); + std::vector pids_in(evinfo_shape[2]); + std::vector x_in(evinfo_shape[3]); + std::vector ren1(evinfo_shape[4]); + pineappl_grid_evolve_info(grid, max_orders.data(), fac1.data(), + frg1.data(), pids_in.data(), x_in.data(), ren1.data()); + + // ------------------ Construct the Operator Info ------------------ + // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose + // elements are `OperatorInfo` objects. + std::vector opinfo_slices(conv_types.size() * fac1.size()); + for (std::size_t i = 0; i != conv_types.size(); i++) { + for (std::size_t j = 0; j != fac1.size(); j++) { + pineappl_operator_info opinfo = { + FAC0, // fac0 + fac1[j], // fac1 + pid_basis, + conv_types[i], + }; + opinfo_slices[i * fac1.size() + j] = opinfo; + } + } + + // ------------------ Construct the Evolution Operator ------------------ + // Choose a different PID basis for the FK table + // std::vector pids_out = {-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 21, 22}; + std::vector pids_out = pids_in; + + // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` + std::vector op_slices; + std::size_t flat_len = x_in.size() * x_in.size() * pids_in.size() * pids_out.size(); + for (std::size_t _i = 0; _i != conv_types.size(); _i++) { + for (std::size_t j = 0; j != fac1.size(); j++) { + std::vector eko = generate_fake_ekos(pids_in, x_in, pids_out, x_in); + for (std::size_t k = 0; k != flat_len; k++) { + op_slices.push_back(eko[k]); + } + } + } + + // Construct the values of alphas table + std::vector alphas_table; + for (double q2 : ren1) { + double alpha = alphas(q2, pdf.get()); + alphas_table.push_back(alpha); + } + + std::vector xi = {1.0, 1.0, 1.0}; + // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) + std::vector tensor_shape = {pids_in.size(), x_in.size(), pids_out.size(), x_in.size()}; + + // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: + // - `grid`: PineAPPL Grid + // - `op_info`: operator info + // - `max_orders`: max orders to apply the evolution + // - `operators`: evolution operator + // - `x_in`: x-grid of the Grid + // - `x_out`: x-grid of the FK table + // - `pids_in`: PIDs basis representation of the Grid + // - `pids_out`: PIDs basis representation of the FK table + // - `eko_shape`: shape of the evolution operators + // - `xi`: scale variation + // - `ren1`: values of the renormalization scales + // - `alphas_table`: values of alphas for each renormalization scales + pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), + max_orders.data(), op_slices.data(), x_in.data(), + x_in.data(), pids_in.data(), pids_out.data(), + tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); + + // ------------------ Compare Grid & FK after convolution ------------------ + // how many bins does this grid have? + std::size_t bins = pineappl_grid_bin_count(grid); + + // [ convolve the Grid ] + std::vector mu_scales = { 1.0, 1.0, 1.0 }; + std::vector dxsec_grid(bins); + pineappl_grid_convolve(grid, xfx, alphas, pdf_states, pdf.get(), + nullptr, nullptr, nullptr, 1, + mu_scales.data(), dxsec_grid.data()); + + // [ convolve the FK Table ] + std::vector dxsec_fktable(bins); + pineappl_fk_table_convolve(fktable, xfx, pdf_states, nullptr, + nullptr, dxsec_fktable.data()); + + // Print the results + print_results(dxsec_grid, dxsec_fktable); + + pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); + + pineappl_grid_delete(grid); + pineappl_fk_table_delete(fktable); +} diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 0b21d0e20..f1f075670 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -1,6 +1,7 @@ #include #include +#include #include #include #include @@ -10,7 +11,64 @@ #include // NOTE: Uses the scale of the Grid as the starting scale such that we can use an IDENTITY EKO. -double FAC0 = 6456.44; +double FAC0 = 2.7224999999999997; + +// x-grid nodes definition for the `in` and `out` +std::vector XGRID = { + 2.00000000000000e-07, + 3.03430476586795e-07, + 4.60350147489639e-07, + 6.98420853070036e-07, + 1.05960949591010e-06, + 1.60758549847081e-06, + 2.43894329289168e-06, + 3.70022720698550e-06, + 5.61375771693015e-06, + 8.51680667757335e-06, + 1.29210156907473e-05, + 1.96025050023917e-05, + 2.97384953722449e-05, + 4.51143839496404e-05, + 6.84374491896790e-05, + 1.03811729865769e-04, + 1.57456056008414e-04, + 2.38787829185619e-04, + 3.62054496381397e-04, + 5.48779532367080e-04, + 8.31406883648814e-04, + 1.25867971442728e-03, + 1.90346340228674e-03, + 2.87386758128175e-03, + 4.32850063882081e-03, + 6.49620619463380e-03, + 9.69915957404340e-03, + 1.43750685810901e-02, + 2.10891866837872e-02, + 3.05215840078289e-02, + 4.34149174170227e-02, + 6.04800287544474e-02, + 8.22812212620489e-02, + 1.09143757463307e-01, + 1.41120806444403e-01, + 1.78025660425694e-01, + 2.19504126500389e-01, + 2.65113704158282e-01, + 3.14387400769276e-01, + 3.66875318648224e-01, + 4.22166775358965e-01, + 4.79898902961025e-01, + 5.39757233788045e-01, + 6.01472197967335e-01, + 6.64813948247382e-01, + 7.29586844241431e-01, + 7.95624252292276e-01, + 8.62783932390611e-01, + 9.30944080871754e-01, + 1.00000000000000e+00 +}; + +// Particle PIDs for both `in` and `out` +std::vector PIDS = {- 22 , -6 , -5 , -4 , -3 , -2 , -1 , 21 , 1 , 2 , 3 , 4 , 5 , 6}; std::vector unravel_index(std::size_t flat_index, const std::vector& shape) { std::size_t ndim = shape.size(); @@ -24,24 +82,13 @@ std::vector unravel_index(std::size_t flat_index, const std::vector return coords; } -std::vector generate_fake_ekos( - std::vector pids_in, - std::vector x_in, - std::vector pids_out, - std::vector x_out -) { - std::size_t flat_len = x_out.size() * x_in.size() * pids_out.size() * pids_in.size(); - std::vector ops(flat_len); +std::vector generate_fake_ekos(std::string filename) { + std::ifstream input_file(filename); + std::vector ops; + double weight_value; - // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) - std::vector shape = {pids_in.size(), x_in.size(), pids_out.size(), x_out.size()}; - for (std::size_t i = 0; i != flat_len; i++) { - std::vector coords = unravel_index(i, shape); - - double delta_ik = (coords[0] == coords[2]) ? 1.0 : 0.0; - double delta_jl = (coords[1] == coords[3]) ? 1.0 : 0.0; - - ops[i] = delta_ik * delta_jl; + while (input_file >> weight_value) { + ops.push_back(weight_value); } return ops; @@ -125,11 +172,11 @@ int main() { // NOTE: These are used to construct the Evolution Operator std::vector fac1(evinfo_shape[0]); std::vector frg1(evinfo_shape[1]); - std::vector pids_in(evinfo_shape[2]); - std::vector x_in(evinfo_shape[3]); + std::vector _pids_in(evinfo_shape[2]); + std::vector _x_in(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); pineappl_grid_evolve_info(grid, max_orders.data(), fac1.data(), - frg1.data(), pids_in.data(), x_in.data(), ren1.data()); + frg1.data(), _pids_in.data(), _x_in.data(), ren1.data()); // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose @@ -148,16 +195,16 @@ int main() { } // ------------------ Construct the Evolution Operator ------------------ - // Choose a different PID basis for the FK table - // std::vector pids_out = {-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 21, 22}; - std::vector pids_out = pids_in; + // Define the same PIDs for both `in` and `out` according to the EKO + std::vector pids_in = PIDS; + std::vector pids_out = PIDS; // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` std::vector op_slices; - std::size_t flat_len = x_in.size() * x_in.size() * pids_in.size() * pids_out.size(); + std::size_t flat_len = XGRID.size() * XGRID.size() * pids_in.size() * pids_out.size(); for (std::size_t _i = 0; _i != conv_types.size(); _i++) { for (std::size_t j = 0; j != fac1.size(); j++) { - std::vector eko = generate_fake_ekos(pids_in, x_in, pids_out, x_in); + std::vector eko = generate_fake_ekos("EKO_LHCB_WP_7TEV.txt"); for (std::size_t k = 0; k != flat_len; k++) { op_slices.push_back(eko[k]); } @@ -173,7 +220,7 @@ int main() { std::vector xi = {1.0, 1.0, 1.0}; // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) - std::vector tensor_shape = {pids_in.size(), x_in.size(), pids_out.size(), x_in.size()}; + std::vector tensor_shape = {pids_in.size(), XGRID.size(), pids_out.size(), XGRID.size()}; // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: // - `grid`: PineAPPL Grid @@ -189,8 +236,8 @@ int main() { // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - max_orders.data(), op_slices.data(), x_in.data(), - x_in.data(), pids_in.data(), pids_out.data(), + max_orders.data(), op_slices.data(), XGRID.data(), + XGRID.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); // ------------------ Compare Grid & FK after convolution ------------------ diff --git a/examples/cpp/output b/examples/cpp/output index aee77c2cb..5dfc41761 100644 --- a/examples/cpp/output +++ b/examples/cpp/output @@ -173,6 +173,16 @@ idx left right dsig/dx dx 22 40676 (16, 13, 26) (5442.31, 0.219504, 0.00287387) -1.22785e-08 23 40626 (16, 12, 26) (5442.31, 0.265114, 0.00287387) -7.04493e-11 Bin Grid FkTable reldiff + ---- ------------- ------------- ------------- + 0 7.545911e+02 7.559965e+02 1.862504e-03 + 1 6.902834e+02 6.921603e+02 2.718991e-03 + 2 6.002520e+02 6.024318e+02 3.631522e-03 + 3 4.855224e+02 4.877053e+02 4.496133e-03 + 4 3.619546e+02 3.638695e+02 5.290429e-03 + 5 2.458669e+02 2.473256e+02 5.933028e-03 + 6 1.158685e+02 1.166059e+02 6.363742e-03 + 7 2.751727e+01 2.765255e+01 4.916187e-03 + Bin Grid FkTable reldiff ---- ------------- ------------- ------------- 0 7.545911e+02 7.545911e+02 -3.762829e-08 1 6.902834e+02 6.902834e+02 -3.537025e-08 From 6d0d5514085e38ca7af7b1a0c4e0eb15a160b917 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 14 May 2025 10:41:36 +0200 Subject: [PATCH 22/49] Rely on re-usable step to download/cache data --- .github/actions/cache-test-data/action.yml | 19 +++++++++++++++++++ .github/workflows/python.yml | 13 +------------ .github/workflows/rust.yml | 11 +---------- 3 files changed, 21 insertions(+), 22 deletions(-) create mode 100644 .github/actions/cache-test-data/action.yml diff --git a/.github/actions/cache-test-data/action.yml b/.github/actions/cache-test-data/action.yml new file mode 100644 index 000000000..e68fe86dc --- /dev/null +++ b/.github/actions/cache-test-data/action.yml @@ -0,0 +1,19 @@ +# .github/actions/cache-test-data/action.yml + +name: Cache Test Data +description: Caches and downloads test data +runs: + using: "composite" + steps: + - name: Cache test data + id: cache + uses: actions/cache@v4 + with: + path: test-data + key: test-data-v20 + - name: Download test data if cache miss + if: steps.cache.outputs.cache-hit != 'true' + run: | + cd maintainer + ./download-test-data.sh + shell: bash diff --git a/.github/workflows/python.yml b/.github/workflows/python.yml index 5e4806c09..6df4bfc8e 100644 --- a/.github/workflows/python.yml +++ b/.github/workflows/python.yml @@ -23,19 +23,8 @@ jobs: - name: Set up Rust run: | rustup component add llvm-tools - - name: Get test data - id: cache-test-data - uses: actions/cache@v4 - with: - path: test-data - key: test-data-v20 - - name: Download test data - if: steps.cache-test-data.outputs.cache-hit != 'true' - run: | - cd maintainer - ./download-test-data.sh - + uses: ./.github/actions/cache-test-data - name: Test env: # `-C link-dead-code` is needed to prevent 'warning: XX functions have mismatched data' warnings diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml index 44953aa37..0f9e75287 100644 --- a/.github/workflows/rust.yml +++ b/.github/workflows/rust.yml @@ -21,16 +21,7 @@ jobs: - uses: actions/checkout@v4 - name: Get test data - id: cache-test-data - uses: actions/cache@v4 - with: - path: test-data - key: test-data-v20 - - name: Download test data - if: steps.cache-test-data.outputs.cache-hit != 'true' - run: | - cd maintainer - ./download-test-data.sh + uses: ./.github/actions/cache-test-data - name: Set RUSTDOCFLAGS run: | From 8519c7351e0567ee87dbecb689c303bc20dd089f Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 14 May 2025 10:51:52 +0200 Subject: [PATCH 23/49] Move all files to `test-data` and increment cache --- .github/actions/cache-test-data/action.yml | 2 +- examples/cpp/evolve-grid-identity.cpp | 2 +- examples/cpp/evolve-grid.cpp | 5 +++-- maintainer/download-test-data.sh | 1 + 4 files changed, 6 insertions(+), 4 deletions(-) diff --git a/.github/actions/cache-test-data/action.yml b/.github/actions/cache-test-data/action.yml index e68fe86dc..be1504ca3 100644 --- a/.github/actions/cache-test-data/action.yml +++ b/.github/actions/cache-test-data/action.yml @@ -10,7 +10,7 @@ runs: uses: actions/cache@v4 with: path: test-data - key: test-data-v20 + key: test-data-v21 - name: Download test data if cache miss if: steps.cache.outputs.cache-hit != 'true' run: | diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 0b21d0e20..aff78ecb7 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -78,7 +78,7 @@ void print_results(std::vector dxsec_grid, std::vector dxsec_fkt int main() { // TODO: How to get a Grid that can be evolved?? - std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; + std::string filename = "../../test-data/LHCB_WP_7TEV_opt.pineappl.lz4"; // disable LHAPDF banners to guarantee deterministic output LHAPDF::setVerbosity(0); diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index f1f075670..6e504bb15 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -125,7 +125,8 @@ void print_results(std::vector dxsec_grid, std::vector dxsec_fkt int main() { // TODO: How to get a Grid that can be evolved?? - std::string filename = "LHCB_WP_7TEV_opt.pineappl.lz4"; + std::string filename = "../../test-data/LHCB_WP_7TEV_opt.pineappl.lz4"; + std::string ekoname = "../../test-data/EKO_LHCB_WP_7TEV.txt"; // disable LHAPDF banners to guarantee deterministic output LHAPDF::setVerbosity(0); @@ -204,7 +205,7 @@ int main() { std::size_t flat_len = XGRID.size() * XGRID.size() * pids_in.size() * pids_out.size(); for (std::size_t _i = 0; _i != conv_types.size(); _i++) { for (std::size_t j = 0; j != fac1.size(); j++) { - std::vector eko = generate_fake_ekos("EKO_LHCB_WP_7TEV.txt"); + std::vector eko = generate_fake_ekos(ekoname); for (std::size_t k = 0; k != flat_len; k++) { op_slices.push_back(eko[k]); } diff --git a/maintainer/download-test-data.sh b/maintainer/download-test-data.sh index 62c693482..fc036db10 100755 --- a/maintainer/download-test-data.sh +++ b/maintainer/download-test-data.sh @@ -35,6 +35,7 @@ files=( 'https://data.nnpdf.science/pineappl/test-data/LHCB_DY_8TEV.pineappl.lz4' 'https://data.nnpdf.science/pineappl/test-data/LHCB_DY_8TEV.tar' 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV.tar' + 'https://data.nnpdf.science/pineappl/test-data/EKO_LHCB_WP_7TEV.txt' 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_old.pineappl.lz4' 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_opt.pineappl.lz4' 'https://data.nnpdf.science/pineappl/test-data/LHCB_WP_7TEV_v2.tar' From 0d1f71b4e908c84560c9391b2831506f00eb8fc8 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 14 May 2025 11:01:16 +0200 Subject: [PATCH 24/49] Add download of data in C workflow --- .github/workflows/capi.yaml | 3 +++ 1 file changed, 3 insertions(+) diff --git a/.github/workflows/capi.yaml b/.github/workflows/capi.yaml index 65f35070c..daa60ecfd 100644 --- a/.github/workflows/capi.yaml +++ b/.github/workflows/capi.yaml @@ -23,6 +23,9 @@ jobs: cargo cinstall --verbose --prefix=/usr/local/ --libdir=/usr/local/lib ldconfig + - name: Get test data + uses: ./.github/actions/cache-test-data + - name: Test C++ examples run: | cd examples/cpp From c9c718792af8de4bbc1ac1c42d5e4d2c157f72cf Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 14 May 2025 11:22:35 +0200 Subject: [PATCH 25/49] Remove no longer needed EKO file --- examples/cpp/EKO_LHCB_WP_7TEV.txt | 490000 --------------------------- 1 file changed, 490000 deletions(-) delete mode 100644 examples/cpp/EKO_LHCB_WP_7TEV.txt diff --git a/examples/cpp/EKO_LHCB_WP_7TEV.txt 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-9.22965639e-03 -2.17499449e-02 -4.63831077e-02 -9.27936122e-02 -1.78295226e-01 -3.33267563e-01 -6.11007024e-01 -1.10460179e+00 -1.97596381e+00 -3.50550868e+00 -6.17666561e+00 -1.08185453e+01 -1.88443192e+01 -3.26437497e+01 -5.62158149e+01 -9.61554493e+01 -1.63114960e+02 -2.73789393e+02 -4.53216531e+02 -7.36595907e+02 -1.16891446e+03 -1.79995065e+03 -2.67307017e+03 -3.80989855e+03 -5.19803813e+03 -6.79022090e+03 -8.51680892e+03 -1.03043081e+04 -1.20900497e+04 -1.38286199e+04 -1.54916226e+04 -1.70642580e+04 -1.85412697e+04 -1.99234635e+04 -2.12151355e+04 -2.24223433e+04 -2.35520994e+04 -2.44272569e+04 -2.69653956e+04 -2.23711225e+04 -3.47970779e+04 -1.10851640e+04 -0.00000000e+00 -0.00000000e+00 --3.77599466e-14 -1.08599276e-06 --4.89476191e-05 -1.73330373e-04 -4.21623608e-04 -3.42419404e-03 -9.22965639e-03 -2.17499449e-02 -4.63831077e-02 -9.27936122e-02 -1.78295226e-01 -3.33267563e-01 -6.11007024e-01 -1.10460179e+00 -1.97596381e+00 -3.50550868e+00 -6.17666561e+00 -1.08185453e+01 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-4.30365745e+03 -1.38984589e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.65785580e-15 -4.70427204e-07 --1.76671497e-05 -4.28794703e-05 -6.31543429e-04 -3.28187520e-03 -9.24108130e-03 -2.17644111e-02 -4.63448050e-02 -9.26981775e-02 -1.78021236e-01 -3.32498671e-01 -6.08887395e-01 -1.09883655e+00 -1.96044857e+00 -3.46413361e+00 -6.06727785e+00 -1.05319609e+01 -1.81013735e+01 -3.07429980e+01 -5.14366140e+01 -8.44148573e+01 -1.35150727e+02 -2.09791442e+02 -3.13826224e+02 -4.50211975e+02 -6.17811275e+02 -8.11185569e+02 -1.02203234e+03 -1.24141769e+03 -1.46160100e+03 -1.67687669e+03 -1.88359521e+03 -2.07977669e+03 -2.26463114e+03 -2.43813747e+03 -2.60072775e+03 -2.75307202e+03 -2.89597984e+03 -3.00724882e+03 -3.32605376e+03 -2.75674746e+03 -4.30365745e+03 -1.38984589e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.65785580e-15 -4.70427204e-07 --1.76671497e-05 -4.28794703e-05 -6.31543429e-04 -3.28187520e-03 -9.24108130e-03 -2.17644111e-02 -4.63448050e-02 -9.26981775e-02 -1.78021236e-01 -3.32498671e-01 -6.08887395e-01 -1.09883655e+00 -1.96044857e+00 -3.46413361e+00 -6.06727785e+00 -1.05319609e+01 -1.81013735e+01 -3.07429980e+01 -5.14366140e+01 -8.44148573e+01 -1.35150727e+02 -2.09791442e+02 -3.13826224e+02 -4.50211975e+02 -6.17811275e+02 -8.11185569e+02 -1.02203234e+03 -1.24141769e+03 -1.46160100e+03 -1.67687669e+03 -1.88359521e+03 -2.07977669e+03 -2.26463114e+03 -2.43813747e+03 -2.60072775e+03 -2.75307202e+03 -2.89597984e+03 -3.00724882e+03 -3.32605376e+03 -2.75674746e+03 -4.30365745e+03 -1.38984589e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.65785580e-15 -4.70427204e-07 --1.76671497e-05 -4.28794703e-05 -6.31543429e-04 -3.28187520e-03 -9.24108130e-03 -2.17644111e-02 -4.63448050e-02 -9.26981775e-02 -1.78021236e-01 -3.32498671e-01 -6.08887395e-01 -1.09883655e+00 -1.96044857e+00 -3.46413361e+00 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--1.76671497e-05 -4.28794703e-05 -6.31543429e-04 -3.28187520e-03 -9.24108130e-03 -2.17644111e-02 -4.63448050e-02 -9.26981775e-02 -1.78021236e-01 -3.32498671e-01 -6.08887395e-01 -1.09883655e+00 -1.96044857e+00 -3.46413361e+00 -6.06727785e+00 -1.05319609e+01 -1.81013735e+01 -3.07429980e+01 -5.14366140e+01 -8.44148573e+01 -1.35150727e+02 -2.09791442e+02 -3.13826224e+02 -4.50211975e+02 -6.17811275e+02 -8.11185569e+02 -1.02203234e+03 -1.24141769e+03 -1.46160100e+03 -1.67687669e+03 -1.88359521e+03 -2.07977669e+03 -2.26463114e+03 -2.43813747e+03 -2.60072775e+03 -2.75307202e+03 -2.89597984e+03 -3.00724882e+03 -3.32605376e+03 -2.75674746e+03 -4.30365745e+03 -1.38984589e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.65785580e-15 -4.70427204e-07 --1.76671497e-05 -4.28794703e-05 -6.31543429e-04 -3.28187520e-03 -9.24108130e-03 -2.17644111e-02 -4.63448050e-02 -9.26981775e-02 -1.78021236e-01 -3.32498671e-01 -6.08887395e-01 -1.09883655e+00 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-1.93102777e-01 -3.51561013e-01 -6.36557480e-01 -1.14541927e+00 -2.04723017e+00 -3.63302677e+00 -6.39796480e+00 -1.11715427e+01 -1.93138737e+01 -3.29880750e+01 -5.54860827e+01 -9.15071505e+01 -1.47160828e+02 -2.29356199e+02 -3.44330480e+02 -4.95551708e+02 -6.81939944e+02 -8.97582529e+02 -1.13329576e+03 -1.37910820e+03 -1.62631826e+03 -1.86846442e+03 -2.10137381e+03 -2.32274595e+03 -2.53162353e+03 -2.72792352e+03 -2.91208319e+03 -3.08481736e+03 -3.24699527e+03 -3.37419638e+03 -3.73007117e+03 -3.10544338e+03 -4.82071483e+03 -1.67198286e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.82504951e-15 -4.11285620e-07 --1.45537126e-05 -2.97830912e-05 -6.52841139e-04 -3.26672004e-03 -9.24099651e-03 -2.17606970e-02 -4.63237743e-02 -9.26377078e-02 -1.77847070e-01 -3.32010231e-01 -6.07543176e-01 -1.09519004e+00 -1.95067477e+00 -3.43822915e+00 -5.99942734e+00 -1.03566921e+01 -1.76565536e+01 -2.96403446e+01 -4.87888240e+01 -7.83202851e+01 -1.21864543e+02 -1.82684695e+02 -2.62573425e+02 -3.60923345e+02 -4.74588189e+02 -5.98714019e+02 -7.28048705e+02 -8.58021237e+02 -9.85246576e+02 -1.10754623e+03 -1.22372614e+03 -1.33329668e+03 -1.43622557e+03 -1.53275176e+03 -1.62325807e+03 -1.70821326e+03 -1.77445065e+03 -1.96361691e+03 -1.62706588e+03 -2.54269304e+03 -8.24318074e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.82504951e-15 -4.11285620e-07 --1.45537126e-05 -2.97830912e-05 -6.52841139e-04 -3.26672004e-03 -9.24099651e-03 -2.17606970e-02 -4.63237743e-02 -9.26377078e-02 -1.77847070e-01 -3.32010231e-01 -6.07543176e-01 -1.09519004e+00 -1.95067477e+00 -3.43822915e+00 -5.99942734e+00 -1.03566921e+01 -1.76565536e+01 -2.96403446e+01 -4.87888240e+01 -7.83202851e+01 -1.21864543e+02 -1.82684695e+02 -2.62573425e+02 -3.60923345e+02 -4.74588189e+02 -5.98714019e+02 -7.28048705e+02 -8.58021237e+02 -9.85246576e+02 -1.10754623e+03 -1.22372614e+03 -1.33329668e+03 -1.43622557e+03 -1.53275176e+03 -1.62325807e+03 -1.70821326e+03 -1.77445065e+03 -1.96361691e+03 -1.62706588e+03 -2.54269304e+03 -8.24318074e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.82504951e-15 -4.11285620e-07 --1.45537126e-05 -2.97830912e-05 -6.52841139e-04 -3.26672004e-03 -9.24099651e-03 -2.17606970e-02 -4.63237743e-02 -9.26377078e-02 -1.77847070e-01 -3.32010231e-01 -6.07543176e-01 -1.09519004e+00 -1.95067477e+00 -3.43822915e+00 -5.99942734e+00 -1.03566921e+01 -1.76565536e+01 -2.96403446e+01 -4.87888240e+01 -7.83202851e+01 -1.21864543e+02 -1.82684695e+02 -2.62573425e+02 -3.60923345e+02 -4.74588189e+02 -5.98714019e+02 -7.28048705e+02 -8.58021237e+02 -9.85246576e+02 -1.10754623e+03 -1.22372614e+03 -1.33329668e+03 -1.43622557e+03 -1.53275176e+03 -1.62325807e+03 -1.70821326e+03 -1.77445065e+03 -1.96361691e+03 -1.62706588e+03 -2.54269304e+03 -8.24318074e+02 -0.00000000e+00 -0.00000000e+00 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-6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 -5.02704471e+02 -5.77770742e+02 -6.50011987e+02 -7.18708908e+02 -7.83558595e+02 -8.44529784e+02 -9.01753324e+02 -9.55446955e+02 -1.00588128e+03 -1.04525925e+03 -1.15734282e+03 -9.58701647e+02 -1.49983902e+03 -4.88208782e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.74479819e-15 -3.71686753e-07 --1.24598371e-05 -2.09617475e-05 -6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 -5.02704471e+02 -5.77770742e+02 -6.50011987e+02 -7.18708908e+02 -7.83558595e+02 -8.44529784e+02 -9.01753324e+02 -9.55446955e+02 -1.00588128e+03 -1.04525925e+03 -1.15734282e+03 -9.58701647e+02 -1.49983902e+03 -4.88208782e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.74479819e-15 -3.71686753e-07 --1.24598371e-05 -2.09617475e-05 -6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 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-1.49983902e+03 -4.88208782e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.69890090e-14 -3.61302019e-06 --1.29593583e-04 -6.53071562e-04 -6.51207412e-03 -1.64685895e-02 -3.11965443e-02 -5.75197943e-02 -1.05540223e-01 -1.92923416e-01 -3.51059345e-01 -6.35172630e-01 -1.14164056e+00 -2.03703112e+00 -3.60579837e+00 -6.32613871e+00 -1.09847540e+01 -1.88368452e+01 -3.17987571e+01 -5.26151515e+01 -8.48675061e+01 -1.32624635e+02 -1.99586546e+02 -2.87853112e+02 -3.96867513e+02 -5.23227986e+02 -6.61586013e+02 -8.06097872e+02 -9.51638679e+02 -1.09438339e+03 -1.23184554e+03 -1.36263946e+03 -1.48617278e+03 -1.60237209e+03 -1.71147492e+03 -1.81388638e+03 -1.91010665e+03 -1.98569703e+03 -2.19632758e+03 -1.82829073e+03 -2.84067091e+03 -9.91018964e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.74479819e-15 -3.71686753e-07 --1.24598371e-05 -2.09617475e-05 -6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 -5.02704471e+02 -5.77770742e+02 -6.50011987e+02 -7.18708908e+02 -7.83558595e+02 -8.44529784e+02 -9.01753324e+02 -9.55446955e+02 -1.00588128e+03 -1.04525925e+03 -1.15734282e+03 -9.58701647e+02 -1.49983902e+03 -4.88208782e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.74479819e-15 -3.71686753e-07 --1.24598371e-05 -2.09617475e-05 -6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 -5.02704471e+02 -5.77770742e+02 -6.50011987e+02 -7.18708908e+02 -7.83558595e+02 -8.44529784e+02 -9.01753324e+02 -9.55446955e+02 -1.00588128e+03 -1.04525925e+03 -1.15734282e+03 -9.58701647e+02 -1.49983902e+03 -4.88208782e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.74479819e-15 -3.71686753e-07 --1.24598371e-05 -2.09617475e-05 -6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 -5.02704471e+02 -5.77770742e+02 -6.50011987e+02 -7.18708908e+02 -7.83558595e+02 -8.44529784e+02 -9.01753324e+02 -9.55446955e+02 -1.00588128e+03 -1.04525925e+03 -1.15734282e+03 -9.58701647e+02 -1.49983902e+03 -4.88208782e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.74479819e-15 -3.71686753e-07 --1.24598371e-05 -2.09617475e-05 -6.67199819e-04 -3.25603746e-03 -9.23952921e-03 -2.17528697e-02 -4.62925862e-02 -9.25461084e-02 -1.77583416e-01 -3.31271652e-01 -6.05514056e-01 -1.08969997e+00 -1.93601795e+00 -3.39961566e+00 -5.89920248e+00 -1.01012870e+01 -1.70211813e+01 -2.81098326e+01 -4.52560791e+01 -7.05995737e+01 -1.06077222e+02 -1.52774483e+02 -2.10372864e+02 -2.77057832e+02 -3.49998049e+02 -4.26111821e+02 -5.02704471e+02 -5.77770742e+02 -6.50011987e+02 -7.18708908e+02 -7.83558595e+02 -8.44529784e+02 -9.01753324e+02 -9.55446955e+02 -1.00588128e+03 -1.04525925e+03 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.07564077e-15 -3.46104899e-07 --1.11053279e-05 -1.52577852e-05 -6.76441964e-04 -3.24852143e-03 -9.23628037e-03 -2.17394702e-02 -4.62458473e-02 -9.24074382e-02 -1.77184743e-01 -3.30156753e-01 -6.02459080e-01 -1.08146707e+00 -1.91417055e+00 -3.34257908e+00 -5.75315729e+00 -9.73649009e+00 -1.61393434e+01 -2.60680620e+01 -4.07816289e+01 -6.14279805e+01 -8.86634811e+01 -1.22325063e+02 -1.61369723e+02 -2.04149891e+02 -2.48861059e+02 -2.93917518e+02 -3.38133253e+02 -3.80735182e+02 -4.21290533e+02 -4.59612249e+02 -4.95674373e+02 -5.29547725e+02 -5.61355529e+02 -5.91253485e+02 -6.14631221e+02 -6.80943617e+02 -5.63893906e+02 -8.83196755e+02 -2.88718035e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.07564077e-15 -3.46104899e-07 --1.11053279e-05 -1.52577852e-05 -6.76441964e-04 -3.24852143e-03 -9.23628037e-03 -2.17394702e-02 -4.62458473e-02 -9.24074382e-02 -1.77184743e-01 -3.30156753e-01 -6.02459080e-01 -1.08146707e+00 -1.91417055e+00 -3.34257908e+00 -5.75315729e+00 -9.73649009e+00 -1.61393434e+01 -2.60680620e+01 -4.07816289e+01 -6.14279805e+01 -8.86634811e+01 -1.22325063e+02 -1.61369723e+02 -2.04149891e+02 -2.48861059e+02 -2.93917518e+02 -3.38133253e+02 -3.80735182e+02 -4.21290533e+02 -4.59612249e+02 -4.95674373e+02 -5.29547725e+02 -5.61355529e+02 -5.91253485e+02 -6.14631221e+02 -6.80943617e+02 -5.63893906e+02 -8.83196755e+02 -2.88718035e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.07564077e-15 -3.46104899e-07 --1.11053279e-05 -1.52577852e-05 -6.76441964e-04 -3.24852143e-03 -9.23628037e-03 -2.17394702e-02 -4.62458473e-02 -9.24074382e-02 -1.77184743e-01 -3.30156753e-01 -6.02459080e-01 -1.08146707e+00 -1.91417055e+00 -3.34257908e+00 -5.75315729e+00 -9.73649009e+00 -1.61393434e+01 -2.60680620e+01 -4.07816289e+01 -6.14279805e+01 -8.86634811e+01 -1.22325063e+02 -1.61369723e+02 -2.04149891e+02 -2.48861059e+02 -2.93917518e+02 -3.38133253e+02 -3.80735182e+02 -4.21290533e+02 -4.59612249e+02 -4.95674373e+02 -5.29547725e+02 -5.61355529e+02 -5.91253485e+02 -6.14631221e+02 -6.80943617e+02 -5.63893906e+02 -8.83196755e+02 -2.88718035e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.12366801e-14 -3.61149767e-06 --1.29679888e-04 -6.53595315e-04 -6.50994387e-03 -1.64658672e-02 -3.11853993e-02 -5.74864778e-02 -1.05444677e-01 -1.92651881e-01 -3.50300721e-01 -6.33082087e-01 -1.13595126e+00 -2.02173608e+00 -3.56520985e+00 -6.22003792e+00 -1.07125574e+01 -1.81554793e+01 -3.01480908e+01 -4.87854002e+01 -7.64590035e+01 -1.15360258e+02 -1.66758878e+02 -2.30376372e+02 -3.04262711e+02 -3.85311011e+02 -4.70104008e+02 -5.55629069e+02 -6.39625639e+02 -7.20614258e+02 -7.97761349e+02 -8.70701033e+02 -9.39375030e+02 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.07564077e-15 -3.46104899e-07 --1.11053279e-05 -1.52577852e-05 -6.76441964e-04 -3.24852143e-03 -9.23628037e-03 -2.17394702e-02 -4.62458473e-02 -9.24074382e-02 -1.77184743e-01 -3.30156753e-01 -6.02459080e-01 -1.08146707e+00 -1.91417055e+00 -3.34257908e+00 -5.75315729e+00 -9.73649009e+00 -1.61393434e+01 -2.60680620e+01 -4.07816289e+01 -6.14279805e+01 -8.86634811e+01 -1.22325063e+02 -1.61369723e+02 -2.04149891e+02 -2.48861059e+02 -2.93917518e+02 -3.38133253e+02 -3.80735182e+02 -4.21290533e+02 -4.59612249e+02 -4.95674373e+02 -5.29547725e+02 -5.61355529e+02 -5.91253485e+02 -6.14631221e+02 -6.80943617e+02 -5.63893906e+02 -8.83196755e+02 -2.88718035e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.07564077e-15 -3.46104899e-07 --1.11053279e-05 -1.52577852e-05 -6.76441964e-04 -3.24852143e-03 -9.23628037e-03 -2.17394702e-02 -4.62458473e-02 -9.24074382e-02 -1.77184743e-01 -3.30156753e-01 -6.02459080e-01 -1.08146707e+00 -1.91417055e+00 -3.34257908e+00 -5.75315729e+00 -9.73649009e+00 -1.61393434e+01 -2.60680620e+01 -4.07816289e+01 -6.14279805e+01 -8.86634811e+01 -1.22325063e+02 -1.61369723e+02 -2.04149891e+02 -2.48861059e+02 -2.93917518e+02 -3.38133253e+02 -3.80735182e+02 -4.21290533e+02 -4.59612249e+02 -4.95674373e+02 -5.29547725e+02 -5.61355529e+02 -5.91253485e+02 -6.14631221e+02 -6.80943617e+02 -5.63893906e+02 -8.83196755e+02 -2.88718035e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.07564077e-15 -3.46104899e-07 --1.11053279e-05 -1.52577852e-05 -6.76441964e-04 -3.24852143e-03 -9.23628037e-03 -2.17394702e-02 -4.62458473e-02 -9.24074382e-02 -1.77184743e-01 -3.30156753e-01 -6.02459080e-01 -1.08146707e+00 -1.91417055e+00 -3.34257908e+00 -5.75315729e+00 -9.73649009e+00 -1.61393434e+01 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--1.02728822e-05 -1.17695027e-05 -6.81988510e-04 -3.24305177e-03 -9.23059912e-03 -2.17181397e-02 -4.61754529e-02 -9.21977433e-02 -1.76582942e-01 -3.28478215e-01 -5.97877887e-01 -1.06919531e+00 -1.88190010e+00 -3.25946975e+00 -5.54457228e+00 -9.23023407e+00 -1.49631063e+01 -2.34825872e+01 -3.54679274e+01 -5.13154764e+01 -7.09444359e+01 -9.37574402e+01 -1.18798205e+02 -1.45012347e+02 -1.71468485e+02 -1.97466305e+02 -2.22546249e+02 -2.46448270e+02 -2.69057059e+02 -2.90352706e+02 -3.10372990e+02 -3.29187257e+02 -3.46884772e+02 -3.60743669e+02 -3.99915709e+02 -3.31062848e+02 -5.19156670e+02 -1.70480217e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --7.26299226e-15 -3.60916300e-06 --1.29689638e-04 -6.53767520e-04 -6.50790182e-03 -1.64608318e-02 -3.11685316e-02 -5.74363122e-02 -1.05299919e-01 -1.92241257e-01 -3.49155503e-01 -6.29934502e-01 -1.12741927e+00 -1.99893634e+00 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--9.55011875e-06 -8.84201057e-06 -6.86054782e-04 -3.23426114e-03 -9.20729888e-03 -2.16349738e-02 -4.59090794e-02 -9.14046171e-02 -1.74318247e-01 -3.22209352e-01 -5.80963715e-01 -1.02466011e+00 -1.76773490e+00 -2.97610125e+00 -4.86920194e+00 -7.70055679e+00 -1.17067938e+01 -1.70318190e+01 -2.36589733e+01 -3.13946514e+01 -3.99193430e+01 -4.88755234e+01 -5.79437765e+01 -6.68811889e+01 -7.55260975e+01 -8.37849758e+01 -9.16142462e+01 -9.90036172e+01 -1.05963210e+02 -1.12514555e+02 -1.18686643e+02 -1.23535418e+02 -1.37138070e+02 -1.13443805e+02 -1.78370778e+02 -5.91514407e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.38375767e-16 -3.16370015e-07 --9.55011875e-06 -8.84201057e-06 -6.86054782e-04 -3.23426114e-03 -9.20729888e-03 -2.16349738e-02 -4.59090794e-02 -9.14046171e-02 -1.74318247e-01 -3.22209352e-01 -5.80963715e-01 -1.02466011e+00 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--2.38375767e-16 -3.16370015e-07 --9.55011875e-06 -8.84201057e-06 -6.86054782e-04 -3.23426114e-03 -9.20729888e-03 -2.16349738e-02 -4.59090794e-02 -9.14046171e-02 -1.74318247e-01 -3.22209352e-01 -5.80963715e-01 -1.02466011e+00 -1.76773490e+00 -2.97610125e+00 -4.86920194e+00 -7.70055679e+00 -1.17067938e+01 -1.70318190e+01 -2.36589733e+01 -3.13946514e+01 -3.99193430e+01 -4.88755234e+01 -5.79437765e+01 -6.68811889e+01 -7.55260975e+01 -8.37849758e+01 -9.16142462e+01 -9.90036172e+01 -1.05963210e+02 -1.12514555e+02 -1.18686643e+02 -1.23535418e+02 -1.37138070e+02 -1.13443805e+02 -1.78370778e+02 -5.91514407e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.38375767e-16 -3.16370015e-07 --9.55011875e-06 -8.84201057e-06 -6.86054782e-04 -3.23426114e-03 -9.20729888e-03 -2.16349738e-02 -4.59090794e-02 -9.14046171e-02 -1.74318247e-01 -3.22209352e-01 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--1.81679800e-17 -3.10416232e-07 --9.35760660e-06 -8.85520605e-06 -6.80585248e-04 -3.19329390e-03 -9.03018185e-03 -2.10165243e-02 -4.39724028e-02 -8.57610111e-02 -1.58729045e-01 -2.81099320e-01 -4.77456868e-01 -7.76897388e-01 -1.20757204e+00 -1.78814096e+00 -2.51966527e+00 -3.38296215e+00 -4.34364778e+00 -5.36179996e+00 -6.40076901e+00 -7.43194143e+00 -8.43566726e+00 -9.40003533e+00 -1.03189475e+01 -1.11902779e+01 -1.20144129e+01 -1.27932060e+01 -1.35295387e+01 -1.41122080e+01 -1.57189258e+01 -1.29794502e+01 -2.05409830e+01 -6.97431563e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.81679800e-17 -3.10416232e-07 --9.35760660e-06 -8.85520605e-06 -6.80585248e-04 -3.19329390e-03 -9.03018185e-03 -2.10165243e-02 -4.39724028e-02 -8.57610111e-02 -1.58729045e-01 -2.81099320e-01 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--3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 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-1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 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-9.58610808e-06 -6.63473992e-04 -3.07206449e-03 -8.52256850e-03 -1.93029444e-02 -3.88749561e-02 -7.19480913e-02 -1.24203508e-01 -2.01306479e-01 -3.07278017e-01 -4.42865326e-01 -6.04893876e-01 -7.87102355e-01 -9.81943266e-01 -1.18230668e+00 -1.38250846e+00 -1.57853837e+00 -1.76787240e+00 -1.94912805e+00 -2.12172038e+00 -2.28558183e+00 -2.44095783e+00 -2.58832406e+00 -2.70572532e+00 -3.02402277e+00 -2.49269305e+00 -3.97021115e+00 -1.37811699e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.48153188e-18 -2.98136068e-07 --9.03494381e-06 -9.58610808e-06 -6.63473992e-04 -3.07206449e-03 -8.52256850e-03 -1.93029444e-02 -3.88749561e-02 -7.19480913e-02 -1.24203508e-01 -2.01306479e-01 -3.07278017e-01 -4.42865326e-01 -6.04893876e-01 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-2.86995215e-03 -7.72169092e-03 -1.67783036e-02 -3.20247292e-02 -5.54611146e-02 -8.85749492e-02 -1.31777944e-01 -1.84154882e-01 -2.43708800e-01 -3.07949951e-01 -3.74482020e-01 -4.41353098e-01 -5.07157769e-01 -5.70987221e-01 -6.32320829e-01 -6.90913752e-01 -7.46703482e-01 -7.99740514e-01 -8.50160952e-01 -8.90561868e-01 -9.98355712e-01 -8.21871892e-01 -1.31618661e+00 -4.64823558e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.94781380e-20 -2.77527894e-07 --8.47138628e-06 -1.04387773e-05 -6.34111678e-04 -2.86995215e-03 -7.72169092e-03 -1.67783036e-02 -3.20247292e-02 -5.54611146e-02 -8.85749492e-02 -1.31777944e-01 -1.84154882e-01 -2.43708800e-01 -3.07949951e-01 -3.74482020e-01 -4.41353098e-01 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-1.04387773e-05 -6.34111678e-04 -2.86995215e-03 -7.72169092e-03 -1.67783036e-02 -3.20247292e-02 -5.54611146e-02 -8.85749492e-02 -1.31777944e-01 -1.84154882e-01 -2.43708800e-01 -3.07949951e-01 -3.74482020e-01 -4.41353098e-01 -5.07157769e-01 -5.70987221e-01 -6.32320829e-01 -6.90913752e-01 -7.46703482e-01 -7.99740514e-01 -8.50160952e-01 -8.90561868e-01 -9.98355712e-01 -8.21871892e-01 -1.31618661e+00 -4.64823558e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.94781380e-20 -2.77527894e-07 --8.47138628e-06 -1.04387773e-05 -6.34111678e-04 -2.86995215e-03 -7.72169092e-03 -1.67783036e-02 -3.20247292e-02 -5.54611146e-02 -8.85749492e-02 -1.31777944e-01 -1.84154882e-01 -2.43708800e-01 -3.07949951e-01 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-5.83173171e-03 -6.18102865e-03 -7.04726932e-03 -5.76251751e-03 -9.46833498e-03 -4.93999579e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.27973078e-22 -1.51766537e-08 --5.97950469e-07 -2.00925531e-06 -5.60859722e-05 -1.97331045e-04 -3.84695084e-04 -5.96017408e-04 -8.23442337e-04 -1.05985973e-03 -1.30058702e-03 -1.54239729e-03 -1.76073804e-03 -2.17455929e-03 -1.80110702e-03 -3.24564825e-03 -1.30523066e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-4.10306918e-05 -1.45134078e-04 -2.83436150e-04 -4.39000190e-04 -6.06028151e-04 -7.79468412e-04 -9.56156920e-04 -1.11853095e-03 -1.41643612e-03 -1.17718596e-03 -2.17689003e-03 -8.86063746e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.53164271e-22 -1.09397034e-08 --4.32526362e-07 -1.39005812e-06 -4.10306918e-05 -1.45134078e-04 -2.83436150e-04 -4.39000190e-04 -6.06028151e-04 -7.79468412e-04 -9.56156920e-04 -1.11853095e-03 -1.41643612e-03 -1.17718596e-03 -2.17689003e-03 -8.86063746e-04 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--1.32365229e-07 -3.11351747e-07 -1.30988882e-05 -4.81802772e-05 -9.65083808e-05 -1.47901059e-04 -2.36744271e-04 -2.01835576e-04 -4.55235691e-04 -1.98913073e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.80863069e-23 -3.41554295e-09 --1.32365229e-07 -3.11351747e-07 -1.30988882e-05 -4.81802772e-05 -9.65083808e-05 -1.47901059e-04 -2.36744271e-04 -2.01835576e-04 -4.55235691e-04 -1.98913073e-04 -0.00000000e+00 -0.00000000e+00 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-2.99108969e-04 -1.34748741e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.75131390e-22 -7.96379546e-08 --3.14274831e-06 -1.04540618e-05 -2.50506151e-04 -6.67872122e-04 -9.95318226e-04 -1.39633106e-03 -1.17524329e-03 -2.23304448e-03 -1.55902123e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--4.28331984e-08 --7.55513610e-07 -1.01767986e-05 -6.11821324e-06 -6.06747923e-05 -3.31116711e-05 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.26481033e-23 -1.28949872e-09 --4.28331984e-08 --7.55513610e-07 -1.01767986e-05 -6.11821324e-06 -6.06747923e-05 -3.31116711e-05 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 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-8.19670563e+00 -1.41992207e+01 -2.44596923e+01 -4.18559735e+01 -7.10398701e+01 -1.19307901e+02 -1.97612477e+02 -3.21366605e+02 -5.10292812e+02 -7.86250367e+02 -1.16833794e+03 -1.66617291e+03 -2.27447922e+03 -2.97267040e+03 -3.73029162e+03 -4.51512661e+03 -5.29965034e+03 -6.06387336e+03 -6.79525981e+03 -7.48724087e+03 -8.13744396e+03 -8.74616792e+03 -9.31525431e+03 -9.84732748e+03 -1.03454043e+04 -1.07333943e+04 -1.18377642e+04 -9.86215631e+03 -1.52498746e+04 -5.14472959e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76199288e-13 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-4.55125308e+00 -7.48175969e+00 -1.22546650e+01 -1.98344233e+01 -3.14674044e+01 -4.85527801e+01 -7.23391346e+01 -1.03497893e+02 -1.41768101e+02 -1.85909786e+02 -2.34031408e+02 -2.84098091e+02 -3.34346865e+02 -3.83478193e+02 -4.30660706e+02 -4.75443260e+02 -5.17645680e+02 -5.57262922e+02 -5.94393174e+02 -6.29188864e+02 -6.61834130e+02 -6.87260609e+02 -7.60073380e+02 -6.30089607e+02 -9.83424725e+02 -3.17029038e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.05708775e-14 -6.62584844e-06 --2.66795827e-04 -1.48777256e-03 -1.35319354e-02 -3.02846115e-02 -5.25393932e-02 -9.08588967e-02 -1.58596370e-01 -2.78621205e-01 -4.90808962e-01 -8.63933537e-01 -1.51567207e+00 -2.64513976e+00 -4.58422329e+00 -7.87458712e+00 -1.33739585e+01 -2.23822560e+01 -3.67474504e+01 -5.88614811e+01 -9.14147497e+01 -1.36815618e+02 -1.96371333e+02 -2.69602556e+02 -3.54147915e+02 -4.46387720e+02 -5.42418383e+02 -6.38851528e+02 -7.33184697e+02 -8.23813005e+02 -9.09861923e+02 -9.90978280e+02 -1.06714647e+03 -1.13855034e+03 -1.20547898e+03 -1.26827851e+03 -1.31747164e+03 -1.45554900e+03 -1.21220037e+03 -1.87966163e+03 -6.45467318e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 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-4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00926872e-15 -3.91248754e-07 --1.23317538e-05 -1.23708363e-05 -8.67697969e-04 -4.16527813e-03 -1.19581830e-02 -2.81559749e-02 -5.95306031e-02 -1.17597217e-01 -2.21792169e-01 -4.04206919e-01 -7.16217081e-01 -1.23650751e+00 -2.07814405e+00 -3.38922500e+00 -5.33884002e+00 -8.08201402e+00 -1.17087789e+01 -1.61999095e+01 -2.14181509e+01 -2.71444552e+01 -3.31376609e+01 -3.91849654e+01 -4.51265159e+01 -5.08575334e+01 -5.63188252e+01 -6.14842413e+01 -6.63493888e+01 -7.09230172e+01 -7.52210565e+01 -7.92639316e+01 -8.24313431e+01 -9.13708613e+01 -7.56680597e+01 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-1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54487233e-15 -6.60538435e-06 --2.66011822e-04 -1.48538862e-03 -1.34899069e-02 -3.01588468e-02 -5.21775286e-02 -8.98434766e-02 -1.55791233e-01 -2.70983777e-01 -4.70331785e-01 -8.09968251e-01 -1.37632505e+00 -2.29428594e+00 -3.72841932e+00 -5.86802095e+00 -8.88864733e+00 -1.28953888e+01 -1.78726323e+01 -2.36726792e+01 -3.00547026e+01 -3.67507677e+01 -4.35225351e+01 -5.01895186e+01 -5.66322235e+01 -6.27820701e+01 -6.86076566e+01 -7.41022532e+01 -7.92741817e+01 -8.41401134e+01 -8.87216742e+01 -9.23395157e+01 -1.02291771e+02 -8.51410262e+01 -1.32593519e+02 -4.67804001e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69006833e-15 -3.85368563e-07 --1.21603022e-05 -1.19076661e-05 -8.67060090e-04 -4.15519393e-03 -1.19153534e-02 -2.80061643e-02 -5.90603728e-02 -1.16222579e-01 -2.17967902e-01 -3.93986052e-01 -6.89922563e-01 -1.17161155e+00 -1.92562478e+00 -3.05127905e+00 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-7.81104303e-01 -1.30534496e+00 -2.12753947e+00 -3.35847915e+00 -5.10174720e+00 -7.42064560e+00 -1.03085257e+01 -1.36814944e+01 -1.74005389e+01 -2.13098116e+01 -2.52698726e+01 -2.91745201e+01 -3.29529421e+01 -3.65640517e+01 -3.99885809e+01 -4.32218220e+01 -4.62680127e+01 -4.91364042e+01 -5.18392755e+01 -5.39774288e+01 -5.98328271e+01 -4.97941779e+01 -7.76251071e+01 -2.75581214e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.35016854e-15 -3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 -5.40368887e+00 -7.17824752e+00 -9.13288104e+00 -1.11854997e+01 -1.32629160e+01 -1.53095799e+01 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-8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.67336398e-17 -6.45441490e-06 --2.60568022e-04 -1.46715589e-03 -1.32973430e-02 -2.95520362e-02 -5.04791244e-02 -8.51885949e-02 -1.43379168e-01 -2.38901337e-01 -3.90481262e-01 -6.20153387e-01 -9.49107975e-01 -1.39120083e+00 -1.94686785e+00 -2.60123595e+00 -3.32805218e+00 -4.09704543e+00 -4.88057024e+00 -5.65715223e+00 -6.41213324e+00 -7.13670604e+00 -7.82643682e+00 -8.47986515e+00 -9.09739938e+00 -9.68053037e+00 -1.02314370e+01 -1.06698043e+01 -1.18526958e+01 -9.85953928e+00 -1.54231670e+01 -5.59016557e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.15162223e-05 -1.14771245e-05 -8.51821143e-04 -4.03440295e-03 -1.13980720e-02 -2.62323319e-02 -5.36693198e-02 -1.01175860e-01 -1.78763829e-01 -2.98195829e-01 -4.70733791e-01 -7.03666211e-01 -9.97080122e-01 -1.34289871e+00 -1.72702330e+00 -2.13328060e+00 -2.54695754e+00 -2.95666838e+00 -3.35467505e+00 -3.73635627e+00 -4.09941162e+00 -4.44311275e+00 -4.76771504e+00 -5.07404036e+00 -5.36329434e+00 -5.59201489e+00 -6.22219281e+00 -5.14478023e+00 -8.11970397e+00 -2.71927774e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-5.09205088e-01 -6.41792396e-01 -8.06479505e-01 -9.98993094e-01 -1.21198014e+00 -1.43697784e+00 -1.66622760e+00 -1.89366330e+00 -2.11510797e+00 -2.32802094e+00 -2.53109494e+00 -2.72386857e+00 -2.90641734e+00 -3.07913190e+00 -3.24262780e+00 -3.37075189e+00 -3.74018850e+00 -3.08741443e+00 -4.86236550e+00 -1.63826261e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79102126e-17 -3.55816408e-07 --1.12147653e-05 -1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 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-8.27543860e-04 -3.85644923e-03 -1.06869693e-02 -2.39273659e-02 -4.71048022e-02 -8.43428308e-02 -1.39641106e-01 -2.15692503e-01 -3.12754444e-01 -4.28266356e-01 -5.57533767e-01 -6.95061820e-01 -8.35780708e-01 -9.75714857e-01 -1.11211997e+00 -1.24331940e+00 -1.36844110e+00 -1.48716474e+00 -1.59952037e+00 -1.70574410e+00 -1.80621542e+00 -1.88603707e+00 -2.10297910e+00 -1.73760517e+00 -2.75228409e+00 -9.32063037e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.88226374e-17 -3.43371509e-07 --1.08309351e-05 -1.14853708e-05 -8.27543860e-04 -3.85644923e-03 -1.06869693e-02 -2.39273659e-02 -4.71048022e-02 -8.43428308e-02 -1.39641106e-01 -2.15692503e-01 -3.12754444e-01 -4.28266356e-01 -5.57533767e-01 -6.95061820e-01 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-4.73790100e-02 -6.90781492e-02 -9.40329517e-02 -1.21110276e-01 -1.49224691e-01 -1.77497663e-01 -2.05301419e-01 -2.32233805e-01 -2.58067472e-01 -2.82698184e-01 -3.06102355e-01 -3.28305836e-01 -3.49370022e-01 -3.66302526e-01 -4.10571530e-01 -3.38985412e-01 -5.41210726e-01 -1.86791937e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.58756235e-19 -2.80083925e-07 --8.99192520e-06 -1.30349499e-05 -7.29022712e-04 -3.20519246e-03 -8.25926999e-03 -1.68805806e-02 -2.98449550e-02 -4.73790100e-02 -6.90781492e-02 -9.40329517e-02 -1.21110276e-01 -1.49224691e-01 -1.77497663e-01 -2.05301419e-01 -2.32233805e-01 -2.58067472e-01 -2.82698184e-01 -3.06102355e-01 -3.28305836e-01 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.58756235e-19 -2.80083925e-07 --8.99192520e-06 -1.30349499e-05 -7.29022712e-04 -3.20519246e-03 -8.25926999e-03 -1.68805806e-02 -2.98449550e-02 -4.73790100e-02 -6.90781492e-02 -9.40329517e-02 -1.21110276e-01 -1.49224691e-01 -1.77497663e-01 -2.05301419e-01 -2.32233805e-01 -2.58067472e-01 -2.82698184e-01 -3.06102355e-01 -3.28305836e-01 -3.49370022e-01 -3.66302526e-01 -4.10571530e-01 -3.38985412e-01 -5.41210726e-01 -1.86791937e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.58756235e-19 -2.80083925e-07 --8.99192520e-06 -1.30349499e-05 -7.29022712e-04 -3.20519246e-03 -8.25926999e-03 -1.68805806e-02 -2.98449550e-02 -4.73790100e-02 -6.90781492e-02 -9.40329517e-02 -1.21110276e-01 -1.49224691e-01 -1.77497663e-01 -2.05301419e-01 -2.32233805e-01 -2.58067472e-01 -2.82698184e-01 -3.06102355e-01 -3.28305836e-01 -3.49370022e-01 -3.66302526e-01 -4.10571530e-01 -3.38985412e-01 -5.41210726e-01 -1.86791937e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.58756235e-19 -2.80083925e-07 --8.99192520e-06 -1.30349499e-05 -7.29022712e-04 -3.20519246e-03 -8.25926999e-03 -1.68805806e-02 -2.98449550e-02 -4.73790100e-02 -6.90781492e-02 -9.40329517e-02 -1.21110276e-01 -1.49224691e-01 -1.77497663e-01 -2.05301419e-01 -2.32233805e-01 -2.58067472e-01 -2.82698184e-01 -3.06102355e-01 -3.28305836e-01 -3.49370022e-01 -3.66302526e-01 -4.10571530e-01 -3.38985412e-01 -5.41210726e-01 -1.86791937e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.58756032e-19 -2.80079507e-07 --8.99238287e-06 -1.30612084e-05 -7.29038830e-04 -3.20151838e-03 -8.23377464e-03 -1.67924497e-02 -2.96373459e-02 -4.69970367e-02 -6.84853797e-02 -9.32178695e-02 -1.20082938e-01 -1.48008804e-01 -1.76122863e-01 -2.03797863e-01 -2.30629159e-01 -2.56385641e-01 -2.80959077e-01 -3.04322168e-01 -3.26497555e-01 -3.47543918e-01 -3.64479097e-01 -4.08641279e-01 -3.37427484e-01 -5.38887978e-01 -1.85956883e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715068e-18 -1.34311817e-07 --4.68423286e-06 -1.23632430e-05 -4.15039750e-04 -1.59092187e-03 -3.47982778e-03 -5.99994411e-03 -9.03145453e-03 -1.24095798e-02 -1.59819551e-02 -1.96266393e-02 -2.32558210e-02 -2.68113136e-02 -3.02576638e-02 -3.35755792e-02 -3.67566493e-02 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--1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.29901207e-19 -2.45459346e-06 --1.09130239e-04 -7.12372434e-04 -6.82866804e-03 -1.35543550e-02 -1.80120269e-02 -2.21860869e-02 -2.63739608e-02 -3.04882291e-02 -3.45341580e-02 -3.84811472e-02 -4.23065617e-02 -4.59964010e-02 -4.95442094e-02 -5.29490926e-02 -5.62149447e-02 -5.88624532e-02 -6.58655493e-02 -5.45849600e-02 -8.65825800e-02 -3.47076113e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 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-2.45285174e-02 -8.87141922e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -5.36629422e-19 -7.22695127e-08 --2.67743646e-06 -8.42126740e-06 -2.48493362e-04 -9.01581957e-04 -1.84932671e-03 -3.00966082e-03 -4.32610753e-03 -5.73720032e-03 -7.19402773e-03 -8.66017822e-03 -1.01104376e-02 -1.15284293e-02 -1.29042690e-02 -1.42330463e-02 -1.53646392e-02 -1.77990405e-02 -1.47488565e-02 -2.45285174e-02 -8.87141922e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-2.29039866e-06 -7.10924686e-05 -2.50443153e-04 -4.90702711e-04 -7.64152313e-04 -1.06072453e-03 -1.37094688e-03 -1.68827461e-03 -2.00800655e-03 -2.29896677e-03 -2.83626952e-03 -2.37556563e-03 -4.23462129e-03 -1.59274377e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.98362206e-20 -1.80254316e-08 --7.18269625e-07 -2.29039866e-06 -7.10924686e-05 -2.50443153e-04 -4.90702711e-04 -7.64152313e-04 -1.06072453e-03 -1.37094688e-03 -1.68827461e-03 -2.00800655e-03 -2.29896677e-03 -2.83626952e-03 -2.37556563e-03 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76199288e-13 -1.12225206e-06 --3.90710828e-05 -1.22032262e-04 -6.92477130e-04 -4.30630839e-03 -1.20233205e-02 -2.84190609e-02 -6.04317057e-02 -1.20240866e-01 -2.29264207e-01 -4.24659715e-01 -7.70742032e-01 -1.37828105e+00 -2.43707070e+00 -4.27032699e+00 -7.42424272e+00 -1.28123016e+01 -2.19403675e+01 -3.72400836e+01 -6.25219062e+01 -1.03500196e+02 -1.68209119e+02 -2.66918889e+02 -4.10998127e+02 -6.10359136e+02 -8.69959928e+02 -1.18699712e+03 -1.55070557e+03 -1.94520453e+03 -2.35372037e+03 -2.76193924e+03 -3.15947918e+03 -3.53984030e+03 -3.89962680e+03 -4.23762340e+03 -4.55400126e+03 -4.84973088e+03 -5.12618715e+03 -5.38496456e+03 -5.58555088e+03 -6.16642570e+03 -5.11631035e+03 -7.95846741e+03 -2.53365411e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 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-3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.52470701e-12 -2.33397863e-04 --1.93226257e-02 -3.80054407e-01 -4.47573812e-01 -2.86953057e-01 -2.62298667e-01 -2.81844936e-01 -3.19615822e-01 -3.94090319e-01 -5.22856785e-01 -7.42322713e-01 -1.11626243e+00 -1.75471131e+00 -2.84565413e+00 -4.70746309e+00 -7.87365754e+00 -1.32254477e+01 -2.21885829e+01 -3.70017070e+01 -6.10289450e+01 -9.90106184e+01 -1.57021790e+02 -2.41809516e+02 -3.59289192e+02 -5.12472973e+02 -6.99792638e+02 -9.14955639e+02 -1.14860832e+03 -1.39082903e+03 -1.63312099e+03 -1.86929772e+03 -2.09546587e+03 -2.30957233e+03 -2.51086112e+03 -2.69940423e+03 -2.87575359e+03 -3.04070618e+03 -3.19519466e+03 -3.31508064e+03 -3.66133913e+03 -3.03721548e+03 -4.72813587e+03 -1.50967720e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 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-7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.60323799e-14 -2.31873669e-04 --1.92529019e-02 -3.79568872e-01 -4.47313505e-01 -2.86282269e-01 -2.61207698e-01 -2.79898029e-01 -3.15694268e-01 -3.85861514e-01 -5.04685680e-01 -7.00559721e-01 -1.01790621e+00 -1.52119628e+00 -2.29533924e+00 -3.43774180e+00 -5.03826866e+00 -7.14989713e+00 -9.76293455e+00 -1.27994874e+01 -1.61339282e+01 -1.96271559e+01 -2.31558395e+01 -2.66268690e+01 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-1.47466925e-03 -1.33778174e-02 -2.98032544e-02 -5.11775078e-02 -8.70798698e-02 -1.48333373e-01 -2.51377219e-01 -4.20392706e-01 -6.87670003e-01 -1.09100290e+00 -1.66636489e+00 -2.43672436e+00 -3.40172279e+00 -4.53470824e+00 -5.78976837e+00 -7.11451551e+00 -8.46146317e+00 -9.79398489e+00 -1.10872861e+01 -1.23266479e+01 -1.35048341e+01 -1.46196615e+01 -1.56720982e+01 -1.66649169e+01 -1.76020179e+01 -1.83461637e+01 -2.03645312e+01 -1.69427680e+01 -2.64710888e+01 -9.52494924e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14833057e-16 -3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 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-5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323357e-16 -3.65199103e-07 --1.15162223e-05 -1.14771245e-05 -8.51821143e-04 -4.03440295e-03 -1.13980720e-02 -2.62323319e-02 -5.36693198e-02 -1.01175860e-01 -1.78763829e-01 -2.98195829e-01 -4.70733791e-01 -7.03666211e-01 -9.97080122e-01 -1.34289871e+00 -1.72702330e+00 -2.13328060e+00 -2.54695754e+00 -2.95666838e+00 -3.35467505e+00 -3.73635627e+00 -4.09941162e+00 -4.44311275e+00 -4.76771504e+00 -5.07404036e+00 -5.36329434e+00 -5.59201489e+00 -6.22219281e+00 -5.14478023e+00 -8.11970397e+00 -2.71927774e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 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-1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79102126e-17 -3.55816408e-07 --1.12147653e-05 -1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.29259824e-17 -6.36216732e-06 --2.57266074e-04 -1.45588378e-03 -1.31770886e-02 -2.91804608e-02 -4.94602465e-02 -8.24856943e-02 -1.36503574e-01 -2.22271226e-01 -3.52658511e-01 -5.40151653e-01 -7.93128920e-01 -1.11227029e+00 -1.48935253e+00 -1.90942587e+00 -2.35504184e+00 -2.81013013e+00 -3.26210989e+00 -3.70231652e+00 -4.12547741e+00 -4.52887372e+00 -4.91153545e+00 -5.27360109e+00 -5.61585888e+00 -5.93951709e+00 -6.19761247e+00 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-3.55814261e-07 --1.12154690e-05 -1.14320107e-05 -8.42193418e-04 -3.95996135e-03 -1.10892999e-02 -2.52061313e-02 -5.06950573e-02 -9.34081363e-02 -1.60266570e-01 -2.57967823e-01 -3.90961009e-01 -5.59525742e-01 -7.59150911e-01 -9.81734642e-01 -1.21787272e+00 -1.45893971e+00 -1.69821015e+00 -1.93107298e+00 -2.15473912e+00 -2.36778551e+00 -2.56972077e+00 -2.76064139e+00 -2.94098634e+00 -3.11143000e+00 -3.24653612e+00 -3.61617216e+00 -2.98902309e+00 -4.72582393e+00 -1.59123152e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79102126e-17 -3.55816408e-07 --1.12147653e-05 -1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 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-2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.94569800e-17 -1.49710241e-04 --1.40401075e-02 -3.22982680e-01 -3.91465825e-01 -2.22105921e-01 -1.73548291e-01 -1.60338589e-01 -1.42598720e-01 -1.32471413e-01 -1.24993082e-01 -1.19455114e-01 -1.15280009e-01 -1.12109617e-01 -1.09702661e-01 -1.07887877e-01 -1.06539207e-01 -1.05563598e-01 -1.04180339e-01 -1.09645628e-01 -8.82838426e-02 -1.32100829e-01 -4.71583764e-02 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 --1.37694227e-18 -3.07434405e-06 --1.34155792e-04 -8.69976575e-04 -8.04448605e-03 -1.61099803e-02 -2.20244425e-02 -2.80329408e-02 -3.43596184e-02 -4.08169727e-02 -4.73188478e-02 -5.37581206e-02 -6.00562495e-02 -6.61618455e-02 -7.20456794e-02 -7.76946669e-02 -8.31066550e-02 -8.82880506e-02 -9.24898695e-02 -1.03502859e-01 -8.58482180e-02 -1.36072110e-01 -5.38498041e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715068e-18 -1.34311817e-07 --4.68423286e-06 -1.23632430e-05 -4.15039750e-04 -1.59092187e-03 -3.47982778e-03 -5.99994411e-03 -9.03145453e-03 -1.24095798e-02 -1.59819551e-02 -1.96266393e-02 -2.32558210e-02 -2.68113136e-02 -3.02576638e-02 -3.35755792e-02 -3.67566493e-02 -3.98005186e-02 -4.23288103e-02 -4.82336983e-02 -3.98708054e-02 -6.50278835e-02 -2.31130513e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-1.60307648e-01 -1.46450662e-01 -1.27791603e-01 -1.16860576e-01 -1.08623295e-01 -1.02360984e-01 -9.74799579e-02 -9.36127112e-02 -9.05140515e-02 -8.80121681e-02 -8.59838444e-02 -8.37942016e-02 -8.69813864e-02 -6.96384937e-02 -1.02599565e-01 -3.68977584e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600441e-18 -1.00157478e-07 --3.60006348e-06 -1.05335264e-05 -3.26618419e-04 -1.21392122e-03 -2.56139058e-03 -4.27347675e-03 -6.26242498e-03 -8.42581916e-03 -1.06778042e-02 -1.29532822e-02 -1.52069640e-02 -1.74095559e-02 -1.95435750e-02 -2.15997613e-02 -2.35750002e-02 -2.52349385e-02 -2.89628523e-02 -2.39653923e-02 -3.94260585e-02 -1.41287284e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.00030184e-06 -3.29176115e-06 -9.78325716e-05 -3.44140059e-04 -6.75863201e-04 -1.05612350e-03 -1.47019078e-03 -1.90375610e-03 -2.34669584e-03 -2.79163022e-03 -3.23345803e-03 -3.62795495e-03 -4.38146659e-03 -3.65683933e-03 -6.37114400e-03 -2.36906181e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --9.61196446e-20 -2.53150827e-08 --1.00034771e-06 -3.29248783e-06 -9.78314186e-05 -3.44184948e-04 -6.76161300e-04 -1.05709149e-03 -1.47241286e-03 -1.90788830e-03 -2.35337563e-03 -2.80141907e-03 -3.24681473e-03 -3.64492879e-03 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-8.90710915e-03 -9.52257205e-03 -1.00831386e-02 -1.05170988e-02 -1.17245367e-02 -9.66265456e-03 -1.53060111e-02 -6.58527726e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.98362206e-20 -1.80254316e-08 --7.18269625e-07 -2.29039866e-06 -7.10924686e-05 -2.50443153e-04 -4.90702711e-04 -7.64152313e-04 -1.06072453e-03 -1.37094688e-03 -1.68827461e-03 -2.00800655e-03 -2.29896677e-03 -2.83626952e-03 -2.37556563e-03 -4.23462129e-03 -1.59274377e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-2.69238642e+00 -4.70826466e+00 -8.19670563e+00 -1.41992207e+01 -2.44596923e+01 -4.18559735e+01 -7.10398701e+01 -1.19307901e+02 -1.97612477e+02 -3.21366605e+02 -5.10292812e+02 -7.86250367e+02 -1.16833794e+03 -1.66617291e+03 -2.27447922e+03 -2.97267040e+03 -3.73029162e+03 -4.51512661e+03 -5.29965034e+03 -6.06387336e+03 -6.79525981e+03 -7.48724087e+03 -8.13744396e+03 -8.74616792e+03 -9.31525431e+03 -9.84732748e+03 -1.03454043e+04 -1.07333943e+04 -1.18377642e+04 -9.86215631e+03 -1.52498746e+04 -5.14472959e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76199288e-13 -1.12225206e-06 --3.90710828e-05 -1.22032262e-04 -6.92477130e-04 -4.30630839e-03 -1.20233205e-02 -2.84190609e-02 -6.04317057e-02 -1.20240866e-01 -2.29264207e-01 -4.24659715e-01 -7.70742032e-01 -1.37828105e+00 -2.43707070e+00 -4.27032699e+00 -7.42424272e+00 -1.28123016e+01 -2.19403675e+01 -3.72400836e+01 -6.25219062e+01 -1.03500196e+02 -1.68209119e+02 -2.66918889e+02 -4.10998127e+02 -6.10359136e+02 -8.69959928e+02 -1.18699712e+03 -1.55070557e+03 -1.94520453e+03 -2.35372037e+03 -2.76193924e+03 -3.15947918e+03 -3.53984030e+03 -3.89962680e+03 -4.23762340e+03 -4.55400126e+03 -4.84973088e+03 -5.12618715e+03 -5.38496456e+03 -5.58555088e+03 -6.16642570e+03 -5.11631035e+03 -7.95846741e+03 -2.53365411e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.52470701e-12 -2.33397863e-04 --1.93226257e-02 -3.80054407e-01 -4.47573812e-01 -2.86953057e-01 -2.62298667e-01 -2.81844936e-01 -3.19615822e-01 -3.94090319e-01 -5.22856785e-01 -7.42322713e-01 -1.11626243e+00 -1.75471131e+00 -2.84565413e+00 -4.70746309e+00 -7.87365754e+00 -1.32254477e+01 -2.21885829e+01 -3.70017070e+01 -6.10289450e+01 -9.90106184e+01 -1.57021790e+02 -2.41809516e+02 -3.59289192e+02 -5.12472973e+02 -6.99792638e+02 -9.14955639e+02 -1.14860832e+03 -1.39082903e+03 -1.63312099e+03 -1.86929772e+03 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-1.17597217e-01 -2.21792169e-01 -4.04206919e-01 -7.16217081e-01 -1.23650751e+00 -2.07814405e+00 -3.38922500e+00 -5.33884002e+00 -8.08201402e+00 -1.17087789e+01 -1.61999095e+01 -2.14181509e+01 -2.71444552e+01 -3.31376609e+01 -3.91849654e+01 -4.51265159e+01 -5.08575334e+01 -5.63188252e+01 -6.14842413e+01 -6.63493888e+01 -7.09230172e+01 -7.52210565e+01 -7.92639316e+01 -8.24313431e+01 -9.13708613e+01 -7.56680597e+01 -1.18598427e+02 -3.88073422e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 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-4.47313505e-01 -2.86282269e-01 -2.61207698e-01 -2.79898029e-01 -3.15694268e-01 -3.85861514e-01 -5.04685680e-01 -7.00559721e-01 -1.01790621e+00 -1.52119628e+00 -2.29533924e+00 -3.43774180e+00 -5.03826866e+00 -7.14989713e+00 -9.76293455e+00 -1.27994874e+01 -1.61339282e+01 -1.96271559e+01 -2.31558395e+01 -2.66268690e+01 -2.99788261e+01 -3.31766687e+01 -3.62045661e+01 -3.90594032e+01 -4.17457963e+01 -4.42726276e+01 -4.66515047e+01 -4.85156643e+01 -5.37885016e+01 -4.45247062e+01 -6.98386967e+01 -2.29503319e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54487233e-15 -6.60538435e-06 --2.66011822e-04 -1.48538862e-03 -1.34899069e-02 -3.01588468e-02 -5.21775286e-02 -8.98434766e-02 -1.55791233e-01 -2.70983777e-01 -4.70331785e-01 -8.09968251e-01 -1.37632505e+00 -2.29428594e+00 -3.72841932e+00 -5.86802095e+00 -8.88864733e+00 -1.28953888e+01 -1.78726323e+01 -2.36726792e+01 -3.00547026e+01 -3.67507677e+01 -4.35225351e+01 -5.01895186e+01 -5.66322235e+01 -6.27820701e+01 -6.86076566e+01 -7.41022532e+01 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--1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 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--1.19124641e-05 -1.16160923e-05 -8.62341316e-04 -4.12372292e-03 -1.17975304e-02 -2.76155031e-02 -5.77790918e-02 -1.12204496e-01 -2.06205099e-01 -3.62001634e-01 -6.09037879e-01 -9.81418392e-01 -1.51111655e+00 -2.21781543e+00 -3.09975772e+00 -4.13143994e+00 -5.27034408e+00 -6.46866735e+00 -7.68354607e+00 -8.88226161e+00 -1.00429367e+01 -1.11528205e+01 -1.22058743e+01 -1.32005485e+01 -1.41380593e+01 -1.50211794e+01 -1.58537044e+01 -1.65091593e+01 -1.83366901e+01 -1.51712513e+01 -2.38686983e+01 -7.91427368e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.91592850e-16 -3.77204206e-07 --1.19122724e-05 -1.16537639e-05 -8.62446382e-04 -4.11822941e-03 -1.17541793e-02 -2.74466091e-02 -5.73248298e-02 -1.11236428e-01 -2.04447049e-01 -3.59163178e-01 -6.04857206e-01 -9.75709818e-01 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-3.66653014e-01 -4.64387225e-01 -6.14592639e-01 -8.35471110e-01 -1.14443999e+00 -1.55239808e+00 -2.05853655e+00 -2.64890714e+00 -3.30001687e+00 -3.98527082e+00 -4.68066638e+00 -5.36775105e+00 -6.03407839e+00 -6.67230129e+00 -7.27885145e+00 -7.85270731e+00 -8.39443082e+00 -8.90548690e+00 -9.38795234e+00 -9.76678134e+00 -1.08401834e+01 -8.96107892e+00 -1.40970785e+01 -4.69835997e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14833057e-16 -3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.99589040e-16 -6.51683500e-06 --2.62804557e-04 -1.47466925e-03 -1.33778174e-02 -2.98032544e-02 -5.11775078e-02 -8.70798698e-02 -1.48333373e-01 -2.51377219e-01 -4.20392706e-01 -6.87670003e-01 -1.09100290e+00 -1.66636489e+00 -2.43672436e+00 -3.40172279e+00 -4.53470824e+00 -5.78976837e+00 -7.11451551e+00 -8.46146317e+00 -9.79398489e+00 -1.10872861e+01 -1.23266479e+01 -1.35048341e+01 -1.46196615e+01 -1.56720982e+01 -1.66649169e+01 -1.76020179e+01 -1.83461637e+01 -2.03645312e+01 -1.69427680e+01 -2.64710888e+01 -9.52494924e+00 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-2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14833057e-16 -3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 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-6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.67336398e-17 -6.45441490e-06 --2.60568022e-04 -1.46715589e-03 -1.32973430e-02 -2.95520362e-02 -5.04791244e-02 -8.51885949e-02 -1.43379168e-01 -2.38901337e-01 -3.90481262e-01 -6.20153387e-01 -9.49107975e-01 -1.39120083e+00 -1.94686785e+00 -2.60123595e+00 -3.32805218e+00 -4.09704543e+00 -4.88057024e+00 -5.65715223e+00 -6.41213324e+00 -7.13670604e+00 -7.82643682e+00 -8.47986515e+00 -9.09739938e+00 -9.68053037e+00 -1.02314370e+01 -1.06698043e+01 -1.18526958e+01 -9.85953928e+00 -1.54231670e+01 -5.59016557e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323357e-16 -3.65199103e-07 --1.15162223e-05 -1.14771245e-05 -8.51821143e-04 -4.03440295e-03 -1.13980720e-02 -2.62323319e-02 -5.36693198e-02 -1.01175860e-01 -1.78763829e-01 -2.98195829e-01 -4.70733791e-01 -7.03666211e-01 -9.97080122e-01 -1.34289871e+00 -1.72702330e+00 -2.13328060e+00 -2.54695754e+00 -2.95666838e+00 -3.35467505e+00 -3.73635627e+00 -4.09941162e+00 -4.44311275e+00 -4.76771504e+00 -5.07404036e+00 -5.36329434e+00 -5.59201489e+00 -6.22219281e+00 -5.14478023e+00 -8.11970397e+00 -2.71927774e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79102126e-17 -3.55816408e-07 --1.12147653e-05 -1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.70531904e-15 -2.26485153e-04 --1.89249549e-02 -3.76733800e-01 -4.44553230e-01 -2.82065276e-01 -2.53821034e-01 -2.66942845e-01 -2.91055191e-01 -3.37802226e-01 -4.08930880e-01 -5.09205088e-01 -6.41792396e-01 -8.06479505e-01 -9.98993094e-01 -1.21198014e+00 -1.43697784e+00 -1.66622760e+00 -1.89366330e+00 -2.11510797e+00 -2.32802094e+00 -2.53109494e+00 -2.72386857e+00 -2.90641734e+00 -3.07913190e+00 -3.24262780e+00 -3.37075189e+00 -3.74018850e+00 -3.08741443e+00 -4.86236550e+00 -1.63826261e+00 -0.00000000e+00 -0.00000000e+00 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-2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79101699e-17 -3.55814261e-07 --1.12154690e-05 -1.14320107e-05 -8.42193418e-04 -3.95996135e-03 -1.10892999e-02 -2.52061313e-02 -5.06950573e-02 -9.34081363e-02 -1.60266570e-01 -2.57967823e-01 -3.90961009e-01 -5.59525742e-01 -7.59150911e-01 -9.81734642e-01 -1.21787272e+00 -1.45893971e+00 -1.69821015e+00 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--4.59194731e-18 -1.72598923e-07 --5.85588198e-06 -1.35521275e-05 -5.06847343e-04 -2.01382653e-03 -4.59518512e-03 -8.25197194e-03 -1.28634512e-02 -1.81870724e-02 -2.39575699e-02 -2.99411233e-02 -3.59584872e-02 -4.18854778e-02 -4.76435104e-02 -5.31878606e-02 -5.84971949e-02 -6.35654592e-02 -6.83977814e-02 -7.23672901e-02 -8.19796179e-02 -6.77146252e-02 -1.09641250e-01 -3.86800204e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.59194731e-18 -1.72598923e-07 --5.85588198e-06 -1.35521275e-05 -5.06847343e-04 -2.01382653e-03 -4.59518512e-03 -8.25197194e-03 -1.28634512e-02 -1.81870724e-02 -2.39575699e-02 -2.99411233e-02 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-2.37768662e-02 -2.96977732e-02 -3.56538916e-02 -4.15237443e-02 -4.72301476e-02 -5.27288645e-02 -5.79984830e-02 -6.30325615e-02 -6.78356824e-02 -7.17850868e-02 -8.13379822e-02 -6.71918669e-02 -1.08823205e-01 -3.83760735e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.59194731e-18 -1.72598923e-07 --5.85588198e-06 -1.35521275e-05 -5.06847343e-04 -2.01382653e-03 -4.59518512e-03 -8.25197194e-03 -1.28634512e-02 -1.81870724e-02 -2.39575699e-02 -2.99411233e-02 -3.59584872e-02 -4.18854778e-02 -4.76435104e-02 -5.31878606e-02 -5.84971949e-02 -6.35654592e-02 -6.83977814e-02 -7.23672901e-02 -8.19796179e-02 -6.77146252e-02 -1.09641250e-01 -3.86800204e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.59194731e-18 -1.72598923e-07 --5.85588198e-06 -1.35521275e-05 -5.06847343e-04 -2.01382653e-03 -4.59518512e-03 -8.25197194e-03 -1.28634512e-02 -1.81870724e-02 -2.39575699e-02 -2.99411233e-02 -3.59584872e-02 -4.18854778e-02 -4.76435104e-02 -5.31878606e-02 -5.84971949e-02 -6.35654592e-02 -6.83977814e-02 -7.23672901e-02 -8.19796179e-02 -6.77146252e-02 -1.09641250e-01 -3.86800204e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.94569800e-17 -1.49710241e-04 --1.40401075e-02 -3.22982680e-01 -3.91465825e-01 -2.22105921e-01 -1.73548291e-01 -1.60338589e-01 -1.42598720e-01 -1.32471413e-01 -1.24993082e-01 -1.19455114e-01 -1.15280009e-01 -1.12109617e-01 -1.09702661e-01 -1.07887877e-01 -1.06539207e-01 -1.05563598e-01 -1.04180339e-01 -1.09645628e-01 -8.82838426e-02 -1.32100829e-01 -4.71583764e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.37694227e-18 -3.07434405e-06 --1.34155792e-04 -8.69976575e-04 -8.04448605e-03 -1.61099803e-02 -2.20244425e-02 -2.80329408e-02 -3.43596184e-02 -4.08169727e-02 -4.73188478e-02 -5.37581206e-02 -6.00562495e-02 -6.61618455e-02 -7.20456794e-02 -7.76946669e-02 -8.31066550e-02 -8.82880506e-02 -9.24898695e-02 -1.03502859e-01 -8.58482180e-02 -1.36072110e-01 -5.38498041e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715068e-18 -1.34311817e-07 --4.68423286e-06 -1.23632430e-05 -4.15039750e-04 -1.59092187e-03 -3.47982778e-03 -5.99994411e-03 -9.03145453e-03 -1.24095798e-02 -1.59819551e-02 -1.96266393e-02 -2.32558210e-02 -2.68113136e-02 -3.02576638e-02 -3.35755792e-02 -3.67566493e-02 -3.98005186e-02 -4.23288103e-02 -4.82336983e-02 -3.98708054e-02 -6.50278835e-02 -2.31130513e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -1.12223512e-18 -1.33862686e-04 --1.29521824e-02 -3.07005521e-01 -3.75107322e-01 -2.09056199e-01 -1.60307648e-01 -1.46450662e-01 -1.27791603e-01 -1.16860576e-01 -1.08623295e-01 -1.02360984e-01 -9.74799579e-02 -9.36127112e-02 -9.05140515e-02 -8.80121681e-02 -8.59838444e-02 -8.37942016e-02 -8.69813864e-02 -6.96384937e-02 -1.02599565e-01 -3.68977584e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.29901207e-19 -2.45459346e-06 --1.09130239e-04 -7.12372434e-04 -6.82866804e-03 -1.35543550e-02 -1.80120269e-02 -2.21860869e-02 -2.63739608e-02 -3.04882291e-02 -3.45341580e-02 -3.84811472e-02 -4.23065617e-02 -4.59964010e-02 -4.95442094e-02 -5.29490926e-02 -5.62149447e-02 -5.88624532e-02 -6.58655493e-02 -5.45849600e-02 -8.65825800e-02 -3.47076113e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 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-3.96600275e-07 --1.66635809e-05 -4.50388210e-05 -1.43547843e-03 -3.25097210e-03 -4.35507499e-03 -5.09278578e-03 -5.68054688e-03 -6.14659704e-03 -6.48508731e-03 -7.28177725e-03 -6.00415195e-03 -9.55082003e-03 -4.24740549e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575741e-19 -9.52470653e-09 --3.79718513e-07 -1.07914645e-06 -3.83522183e-05 -1.36833621e-04 -2.69388616e-04 -4.19614346e-04 -5.81888445e-04 -7.51394964e-04 -9.11755396e-04 -1.19176164e-03 -1.00738023e-03 -1.90201267e-03 -7.33149815e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-4.43258766e-04 -5.64012561e-04 -7.70724549e-04 -6.55575702e-04 -1.28970142e-03 -5.05083062e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.33489274e-18 -7.31715320e-05 --7.56876770e-03 -1.83228534e-01 -2.34585278e-01 -1.34352945e-01 -1.01383936e-01 -8.96419921e-02 -7.55440979e-02 -6.62204712e-02 -6.16864851e-02 -4.71486208e-02 -6.19397271e-02 -2.32574367e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 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-1.52498746e+04 -5.14472959e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76199288e-13 -1.12225206e-06 --3.90710828e-05 -1.22032262e-04 -6.92477130e-04 -4.30630839e-03 -1.20233205e-02 -2.84190609e-02 -6.04317057e-02 -1.20240866e-01 -2.29264207e-01 -4.24659715e-01 -7.70742032e-01 -1.37828105e+00 -2.43707070e+00 -4.27032699e+00 -7.42424272e+00 -1.28123016e+01 -2.19403675e+01 -3.72400836e+01 -6.25219062e+01 -1.03500196e+02 -1.68209119e+02 -2.66918889e+02 -4.10998127e+02 -6.10359136e+02 -8.69959928e+02 -1.18699712e+03 -1.55070557e+03 -1.94520453e+03 -2.35372037e+03 -2.76193924e+03 -3.15947918e+03 -3.53984030e+03 -3.89962680e+03 -4.23762340e+03 -4.55400126e+03 -4.84973088e+03 -5.12618715e+03 -5.38496456e+03 -5.58555088e+03 -6.16642570e+03 -5.11631035e+03 -7.95846741e+03 -2.53365411e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 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--1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.52470701e-12 -2.33397863e-04 --1.93226257e-02 -3.80054407e-01 -4.47573812e-01 -2.86953057e-01 -2.62298667e-01 -2.81844936e-01 -3.19615822e-01 -3.94090319e-01 -5.22856785e-01 -7.42322713e-01 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 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-1.36784858e+02 -1.66318411e+02 -1.95996863e+02 -2.25048328e+02 -2.52976124e+02 -2.79508053e+02 -3.04532530e+02 -3.28042234e+02 -3.50091661e+02 -3.70768105e+02 -3.90178366e+02 -4.05319047e+02 -4.48508602e+02 -3.71723664e+02 -5.80757851e+02 -1.87871260e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.30958923e-14 -4.50508917e-07 --1.42682008e-05 -1.99448924e-05 -8.57037321e-04 -4.19310238e-03 -1.20609182e-02 -2.85401875e-02 -6.06711719e-02 -1.20586288e-01 -2.29221856e-01 -4.22413240e-01 -7.60857578e-01 -1.34583480e+00 -2.34282135e+00 -4.01414231e+00 -6.75783277e+00 -1.11404849e+01 -1.78966092e+01 -2.78540492e+01 -4.17563408e+01 -6.00110643e+01 -8.24781568e+01 -1.08438713e+02 -1.36784858e+02 -1.66318411e+02 -1.95996863e+02 -2.25048328e+02 -2.52976124e+02 -2.79508053e+02 -3.04532530e+02 -3.28042234e+02 -3.50091661e+02 -3.70768105e+02 -3.90178366e+02 -4.05319047e+02 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-3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 -5.40368887e+00 -7.17824752e+00 -9.13288104e+00 -1.11854997e+01 -1.32629160e+01 -1.53095799e+01 -1.72886045e+01 -1.91787199e+01 -2.09700834e+01 -2.26604527e+01 -2.42522366e+01 -2.57504353e+01 -2.71617251e+01 -2.82708929e+01 -3.13773692e+01 -2.59690838e+01 -4.08016083e+01 -1.34663011e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.35016854e-15 -3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 -5.40368887e+00 -7.17824752e+00 -9.13288104e+00 -1.11854997e+01 -1.32629160e+01 -1.53095799e+01 -1.72886045e+01 -1.91787199e+01 -2.09700834e+01 -2.26604527e+01 -2.42522366e+01 -2.57504353e+01 -2.71617251e+01 -2.82708929e+01 -3.13773692e+01 -2.59690838e+01 -4.08016083e+01 -1.34663011e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.35016854e-15 -3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 -5.40368887e+00 -7.17824752e+00 -9.13288104e+00 -1.11854997e+01 -1.32629160e+01 -1.53095799e+01 -1.72886045e+01 -1.91787199e+01 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-3.10629720e-01 -3.75479686e-01 -4.82544031e-01 -6.52240931e-01 -9.12294207e-01 -1.29514506e+00 -1.83127869e+00 -2.53936461e+00 -3.41739348e+00 -4.44043510e+00 -5.56713576e+00 -6.75105221e+00 -7.95053875e+00 -9.13379080e+00 -1.02795285e+01 -1.13753414e+01 -1.24153498e+01 -1.33980462e+01 -1.43246198e+01 -1.51977797e+01 -1.60212432e+01 -1.66676298e+01 -1.84946672e+01 -1.52966804e+01 -2.40421963e+01 -7.97324975e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.83778031e-16 -6.55875155e-06 --2.64312386e-04 -1.47969705e-03 -1.34313003e-02 -2.99717135e-02 -5.16498588e-02 -8.83770573e-02 -1.51801375e-01 -2.60368733e-01 -4.42833120e-01 -7.41056027e-01 -1.21071214e+00 -1.91655198e+00 -2.91963646e+00 -4.25808814e+00 -5.92958604e+00 -7.88670903e+00 -1.00494432e+01 -1.23273318e+01 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-2.38565707e+01 -7.91012302e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.91592118e-16 -3.77226767e-07 --1.19124641e-05 -1.16160923e-05 -8.62341316e-04 -4.12372292e-03 -1.17975304e-02 -2.76155031e-02 -5.77790918e-02 -1.12204496e-01 -2.06205099e-01 -3.62001634e-01 -6.09037879e-01 -9.81418392e-01 -1.51111655e+00 -2.21781543e+00 -3.09975772e+00 -4.13143994e+00 -5.27034408e+00 -6.46866735e+00 -7.68354607e+00 -8.88226161e+00 -1.00429367e+01 -1.11528205e+01 -1.22058743e+01 -1.32005485e+01 -1.41380593e+01 -1.50211794e+01 -1.58537044e+01 -1.65091593e+01 -1.83366901e+01 -1.51712513e+01 -2.38686983e+01 -7.91427368e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-1.17975304e-02 -2.76155031e-02 -5.77790918e-02 -1.12204496e-01 -2.06205099e-01 -3.62001634e-01 -6.09037879e-01 -9.81418392e-01 -1.51111655e+00 -2.21781543e+00 -3.09975772e+00 -4.13143994e+00 -5.27034408e+00 -6.46866735e+00 -7.68354607e+00 -8.88226161e+00 -1.00429367e+01 -1.11528205e+01 -1.22058743e+01 -1.32005485e+01 -1.41380593e+01 -1.50211794e+01 -1.58537044e+01 -1.65091593e+01 -1.83366901e+01 -1.51712513e+01 -2.38686983e+01 -7.91427368e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14833057e-16 -3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14833057e-16 -3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-6.51683500e-06 --2.62804557e-04 -1.47466925e-03 -1.33778174e-02 -2.98032544e-02 -5.11775078e-02 -8.70798698e-02 -1.48333373e-01 -2.51377219e-01 -4.20392706e-01 -6.87670003e-01 -1.09100290e+00 -1.66636489e+00 -2.43672436e+00 -3.40172279e+00 -4.53470824e+00 -5.78976837e+00 -7.11451551e+00 -8.46146317e+00 -9.79398489e+00 -1.10872861e+01 -1.23266479e+01 -1.35048341e+01 -1.46196615e+01 -1.56720982e+01 -1.66649169e+01 -1.76020179e+01 -1.83461637e+01 -2.03645312e+01 -1.69427680e+01 -2.64710888e+01 -9.52494924e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14832844e-16 -3.72121853e-07 --1.17446876e-05 -1.15701550e-05 -8.58185713e-04 -4.08467984e-03 -1.16103055e-02 -2.69521667e-02 -5.58181491e-02 -1.07018501e-01 -1.93427897e-01 -3.32220093e-01 -5.43439836e-01 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-1.25616202e-01 -1.34407578e-01 -1.42807125e-01 -1.49612568e-01 -1.67371573e-01 -1.38914096e-01 -2.19930843e-01 -8.59814690e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.59194783e-18 -1.72597011e-07 --5.85607269e-06 -1.35628115e-05 -5.06838191e-04 -2.01221994e-03 -4.58518921e-03 -8.22027005e-03 -1.27939709e-02 -1.80661583e-02 -2.37768662e-02 -2.96977732e-02 -3.56538916e-02 -4.15237443e-02 -4.72301476e-02 -5.27288645e-02 -5.79984830e-02 -6.30325615e-02 -6.78356824e-02 -7.17850868e-02 -8.13379822e-02 -6.71918669e-02 -1.08823205e-01 -3.83760735e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.59194731e-18 -1.72598923e-07 --5.85588198e-06 -1.35521275e-05 -5.06847343e-04 -2.01382653e-03 -4.59518512e-03 -8.25197194e-03 -1.28634512e-02 -1.81870724e-02 -2.39575699e-02 -2.99411233e-02 -3.59584872e-02 -4.18854778e-02 -4.76435104e-02 -5.31878606e-02 -5.84971949e-02 -6.35654592e-02 -6.83977814e-02 -7.23672901e-02 -8.19796179e-02 -6.77146252e-02 -1.09641250e-01 -3.86800204e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--5.85588198e-06 -1.35521275e-05 -5.06847343e-04 -2.01382653e-03 -4.59518512e-03 -8.25197194e-03 -1.28634512e-02 -1.81870724e-02 -2.39575699e-02 -2.99411233e-02 -3.59584872e-02 -4.18854778e-02 -4.76435104e-02 -5.31878606e-02 -5.84971949e-02 -6.35654592e-02 -6.83977814e-02 -7.23672901e-02 -8.19796179e-02 -6.77146252e-02 -1.09641250e-01 -3.86800204e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.94569800e-17 -1.49710241e-04 --1.40401075e-02 -3.22982680e-01 -3.91465825e-01 -2.22105921e-01 -1.73548291e-01 -1.60338589e-01 -1.42598720e-01 -1.32471413e-01 -1.24993082e-01 -1.19455114e-01 -1.15280009e-01 -1.12109617e-01 -1.09702661e-01 -1.07887877e-01 -1.06539207e-01 -1.05563598e-01 -1.04180339e-01 -1.09645628e-01 -8.82838426e-02 -1.32100829e-01 -4.71583764e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.37694227e-18 -3.07434405e-06 --1.34155792e-04 -8.69976575e-04 -8.04448605e-03 -1.61099803e-02 -2.20244425e-02 -2.80329408e-02 -3.43596184e-02 -4.08169727e-02 -4.73188478e-02 -5.37581206e-02 -6.00562495e-02 -6.61618455e-02 -7.20456794e-02 -7.76946669e-02 -8.31066550e-02 -8.82880506e-02 -9.24898695e-02 -1.03502859e-01 -8.58482180e-02 -1.36072110e-01 -5.38498041e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715068e-18 -1.34311817e-07 --4.68423286e-06 -1.23632430e-05 -4.15039750e-04 -1.59092187e-03 -3.47982778e-03 -5.99994411e-03 -9.03145453e-03 -1.24095798e-02 -1.59819551e-02 -1.96266393e-02 -2.32558210e-02 -2.68113136e-02 -3.02576638e-02 -3.35755792e-02 -3.67566493e-02 -3.98005186e-02 -4.23288103e-02 -4.82336983e-02 -3.98708054e-02 -6.50278835e-02 -2.31130513e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -1.12223512e-18 -1.33862686e-04 --1.29521824e-02 -3.07005521e-01 -3.75107322e-01 -2.09056199e-01 -1.60307648e-01 -1.46450662e-01 -1.27791603e-01 -1.16860576e-01 -1.08623295e-01 -1.02360984e-01 -9.74799579e-02 -9.36127112e-02 -9.05140515e-02 -8.80121681e-02 -8.59838444e-02 -8.37942016e-02 -8.69813864e-02 -6.96384937e-02 -1.02599565e-01 -3.68977584e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--2.72281847e-21 -1.30076064e-08 --5.19595874e-07 -1.57620241e-06 -5.19727400e-05 -1.84003647e-04 -3.60865995e-04 -5.61314203e-04 -7.77948138e-04 -1.00410876e-03 -1.23540011e-03 -1.44965954e-03 -1.83361502e-03 -1.54210635e-03 -2.81958620e-03 -1.07243536e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.72284269e-21 -1.30083123e-08 --5.19650617e-07 -1.57705152e-06 -5.19724802e-05 -1.84013220e-04 -3.60948118e-04 -5.61597776e-04 -7.78626976e-04 -1.00542282e-03 -1.23760835e-03 -1.45292277e-03 -1.83898187e-03 -1.54665749e-03 -2.83057799e-03 -1.07725487e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.72284269e-21 -1.30083123e-08 --5.19650617e-07 -1.57705152e-06 -5.19724802e-05 -1.84013220e-04 -3.60948118e-04 -5.61597776e-04 -7.78626976e-04 -1.00542282e-03 -1.23760835e-03 -1.45292277e-03 -1.83898187e-03 -1.54665749e-03 -2.83057799e-03 -1.07725487e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.67880365e-18 -7.60571318e-05 --7.95213134e-03 -1.94921697e-01 -2.48766445e-01 -1.40779573e-01 -1.05735401e-01 -9.35770943e-02 -7.87180712e-02 -6.93083955e-02 -6.17739706e-02 -5.85311329e-02 -4.50717779e-02 -6.01731131e-02 -2.24788232e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 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--1.33489274e-18 -7.31715320e-05 --7.56876770e-03 -1.83228534e-01 -2.34585278e-01 -1.34352945e-01 -1.01383936e-01 -8.96419921e-02 -7.55440979e-02 -6.62204712e-02 -6.16864851e-02 -4.71486208e-02 -6.19397271e-02 -2.32574367e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.06073545e-20 -3.08773319e-07 --1.24108883e-05 -1.69935584e-05 -1.13822412e-03 -2.67491850e-03 -3.64584009e-03 -4.29488190e-03 -4.80759219e-03 -5.16339994e-03 -5.86721695e-03 -4.85123651e-03 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.45891246e-13 -3.10567056e-05 --1.42330713e-03 -9.22784080e-03 -8.00631745e-02 -2.24986236e-01 -4.92228717e-01 -9.91625294e-01 -1.91074905e+00 -3.58384114e+00 -6.60304634e+00 -1.20103031e+01 -2.16248079e+01 -3.85932245e+01 -6.82945667e+01 -1.19781470e+02 -2.07964469e+02 -3.56663900e+02 -6.02297008e+02 -9.97102131e+02 -1.60936717e+03 -2.51685212e+03 -3.79052983e+03 -5.47109075e+03 -7.54866470e+03 -9.95902508e+03 -1.26005399e+04 -1.53617972e+04 -1.81448274e+04 -2.08763071e+04 -2.35084028e+04 -2.60143026e+04 -2.83823824e+04 -3.06109821e+04 -3.27044321e+04 -3.46703116e+04 -3.65182318e+04 -3.79624514e+04 -4.20657486e+04 -3.48187209e+04 -5.45711474e+04 -1.79189438e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.45891246e-13 -3.10567056e-05 --1.42330713e-03 -9.22784080e-03 -8.00631745e-02 -2.24986236e-01 -4.92228717e-01 -9.91625294e-01 -1.91074905e+00 -3.58384114e+00 -6.60304634e+00 -1.20103031e+01 -2.16248079e+01 -3.85932245e+01 -6.82945667e+01 -1.19781470e+02 -2.07964469e+02 -3.56663900e+02 -6.02297008e+02 -9.97102131e+02 -1.60936717e+03 -2.51685212e+03 -3.79052983e+03 -5.47109075e+03 -7.54866470e+03 -9.95902508e+03 -1.26005399e+04 -1.53617972e+04 -1.81448274e+04 -2.08763071e+04 -2.35084028e+04 -2.60143026e+04 -2.83823824e+04 -3.06109821e+04 -3.27044321e+04 -3.46703116e+04 -3.65182318e+04 -3.79624514e+04 -4.20657486e+04 -3.48187209e+04 -5.45711474e+04 -1.79189438e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.03297922e-12 -2.19688149e-04 --9.54542292e-03 -8.66367092e-02 -3.23919356e-01 -5.77602338e-01 -9.96972832e-01 -1.84004370e+00 -3.42351932e+00 -6.35829315e+00 -1.17209492e+01 -2.14148267e+01 -3.87763265e+01 -6.95978283e+01 -1.23814786e+02 -2.18200644e+02 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-1.81448274e+04 -2.08763071e+04 -2.35084028e+04 -2.60143026e+04 -2.83823824e+04 -3.06109821e+04 -3.27044321e+04 -3.46703116e+04 -3.65182318e+04 -3.79624514e+04 -4.20657486e+04 -3.48187209e+04 -5.45711474e+04 -1.79189438e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.45891246e-13 -3.10567056e-05 --1.42330713e-03 -9.22784080e-03 -8.00631745e-02 -2.24986236e-01 -4.92228717e-01 -9.91625294e-01 -1.91074905e+00 -3.58384114e+00 -6.60304634e+00 -1.20103031e+01 -2.16248079e+01 -3.85932245e+01 -6.82945667e+01 -1.19781470e+02 -2.07964469e+02 -3.56663900e+02 -6.02297008e+02 -9.97102131e+02 -1.60936717e+03 -2.51685212e+03 -3.79052983e+03 -5.47109075e+03 -7.54866470e+03 -9.95902508e+03 -1.26005399e+04 -1.53617972e+04 -1.81448274e+04 -2.08763071e+04 -2.35084028e+04 -2.60143026e+04 -2.83823824e+04 -3.06109821e+04 -3.27044321e+04 -3.46703116e+04 -3.65182318e+04 -3.79624514e+04 -4.20657486e+04 -3.48187209e+04 -5.45711474e+04 -1.79189438e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.45891246e-13 -3.10567056e-05 --1.42330713e-03 -9.22784080e-03 -8.00631745e-02 -2.24986236e-01 -4.92228717e-01 -9.91625294e-01 -1.91074905e+00 -3.58384114e+00 -6.60304634e+00 -1.20103031e+01 -2.16248079e+01 -3.85932245e+01 -6.82945667e+01 -1.19781470e+02 -2.07964469e+02 -3.56663900e+02 -6.02297008e+02 -9.97102131e+02 -1.60936717e+03 -2.51685212e+03 -3.79052983e+03 -5.47109075e+03 -7.54866470e+03 -9.95902508e+03 -1.26005399e+04 -1.53617972e+04 -1.81448274e+04 -2.08763071e+04 -2.35084028e+04 -2.60143026e+04 -2.83823824e+04 -3.06109821e+04 -3.27044321e+04 -3.46703116e+04 -3.65182318e+04 -3.79624514e+04 -4.20657486e+04 -3.48187209e+04 -5.45711474e+04 -1.79189438e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.45891246e-13 -3.10567056e-05 --1.42330713e-03 -9.22784080e-03 -8.00631745e-02 -2.24986236e-01 -4.92228717e-01 -9.91625294e-01 -1.91074905e+00 -3.58384114e+00 -6.60304634e+00 -1.20103031e+01 -2.16248079e+01 -3.85932245e+01 -6.82945667e+01 -1.19781470e+02 -2.07964469e+02 -3.56663900e+02 -6.02297008e+02 -9.97102131e+02 -1.60936717e+03 -2.51685212e+03 -3.79052983e+03 -5.47109075e+03 -7.54866470e+03 -9.95902508e+03 -1.26005399e+04 -1.53617972e+04 -1.81448274e+04 -2.08763071e+04 -2.35084028e+04 -2.60143026e+04 -2.83823824e+04 -3.06109821e+04 -3.27044321e+04 -3.46703116e+04 -3.65182318e+04 -3.79624514e+04 -4.20657486e+04 -3.48187209e+04 -5.45711474e+04 -1.79189438e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-1.19706319e+01 -2.15169111e+01 -3.83033814e+01 -6.75258568e+01 -1.17772561e+02 -2.02810503e+02 -3.43758506e+02 -5.71016490e+02 -9.24478454e+02 -1.44979137e+03 -2.18893343e+03 -3.16646779e+03 -4.37753378e+03 -5.78537652e+03 -7.33104292e+03 -8.94946831e+03 -1.05831351e+04 -1.21887630e+04 -1.37379255e+04 -1.52145137e+04 -1.66113614e+04 -1.79272008e+04 -1.91643344e+04 -2.03270212e+04 -2.14207666e+04 -2.22768908e+04 -2.47005576e+04 -2.04382591e+04 -3.20724007e+04 -1.05794077e+04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --9.64794479e-14 -3.10255948e-05 --1.42299497e-03 -9.22842263e-03 -8.00474278e-02 -2.24935244e-01 -4.92036039e-01 -9.91022394e-01 -1.90895990e+00 -3.57870833e+00 -6.58865667e+00 -1.19706319e+01 -2.15169111e+01 -3.83033814e+01 -6.75258568e+01 -1.17772561e+02 -2.02810503e+02 -3.43758506e+02 -5.71016490e+02 -9.24478454e+02 -1.44979137e+03 -2.18893343e+03 -3.16646779e+03 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--1.42254477e-03 -9.22805448e-03 -8.00273058e-02 -2.24854061e-01 -4.91744997e-01 -9.90109261e-01 -1.90625103e+00 -3.57094649e+00 -6.56693455e+00 -1.19109029e+01 -2.13551069e+01 -3.78713403e+01 -6.63903959e+01 -1.14845341e+02 -1.95449691e+02 -3.25849916e+02 -5.29298401e+02 -8.32535350e+02 -1.26034478e+03 -1.82753026e+03 -2.53181602e+03 -3.35225149e+03 -4.25473507e+03 -5.20135788e+03 -6.15842105e+03 -7.10042478e+03 -8.01050310e+03 -8.87899205e+03 -9.70148320e+03 -1.04770535e+04 -1.12069043e+04 -1.18934137e+04 -1.25397228e+04 -1.30464244e+04 -1.44755838e+04 -1.19733971e+04 -1.88135563e+04 -6.23560934e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.23712226e-14 -3.10002631e-05 --1.42254477e-03 -9.22805448e-03 -8.00273058e-02 -2.24854061e-01 -4.91744997e-01 -9.90109261e-01 -1.90625103e+00 -3.57094649e+00 -6.56693455e+00 -1.19109029e+01 -2.13551069e+01 -3.78713403e+01 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-8.46602826e+03 -6.99996077e+03 -1.10140290e+04 -3.66891312e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.88760596e-14 -3.09758946e-05 --1.42188791e-03 -9.22684246e-03 -7.99988676e-02 -2.24728775e-01 -4.91304659e-01 -9.88726997e-01 -1.90215459e+00 -3.55922946e+00 -6.53422959e+00 -1.18213320e+01 -2.11139219e+01 -3.72331809e+01 -6.47359419e+01 -1.10664963e+02 -1.85236206e+02 -3.01969380e+02 -4.76494816e+02 -7.23417451e+02 -1.05164393e+03 -1.46019397e+03 -1.93717702e+03 -2.46292527e+03 -3.01540624e+03 -3.57491890e+03 -4.12646807e+03 -4.66006388e+03 -5.16991779e+03 -5.65332354e+03 -6.10963068e+03 -6.53945082e+03 -6.94410218e+03 -7.32536918e+03 -7.62477138e+03 -8.46602826e+03 -6.99996077e+03 -1.10140290e+04 -3.66891312e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-3.55922946e+00 -6.53422959e+00 -1.18213320e+01 -2.11139219e+01 -3.72331809e+01 -6.47359419e+01 -1.10664963e+02 -1.85236206e+02 -3.01969380e+02 -4.76494816e+02 -7.23417451e+02 -1.05164393e+03 -1.46019397e+03 -1.93717702e+03 -2.46292527e+03 -3.01540624e+03 -3.57491890e+03 -4.12646807e+03 -4.66006388e+03 -5.16991779e+03 -5.65332354e+03 -6.10963068e+03 -6.53945082e+03 -6.94410218e+03 -7.32536918e+03 -7.62477138e+03 -8.46602826e+03 -6.99996077e+03 -1.10140290e+04 -3.66891312e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.74739491e-13 -2.18917848e-04 --9.53009023e-03 -8.65752436e-02 -3.23781020e-01 -5.77055585e-01 -9.95289804e-01 -1.83492853e+00 -3.40840239e+00 -6.31480732e+00 -1.15985507e+01 -2.10764300e+01 -3.78556908e+01 -6.71331229e+01 -1.17333439e+02 -2.01523102e+02 -3.38721995e+02 -5.54193996e+02 -8.77276189e+02 -1.33556292e+03 -1.94616076e+03 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-1.80466750e+00 -3.31995794e+00 -6.06426178e+00 -1.09093231e+01 -1.92348731e+01 -3.30903183e+01 -5.52578498e+01 -8.90533658e+01 -1.37716853e+02 -2.03442367e+02 -2.86442377e+02 -3.84621033e+02 -4.94123445e+02 -6.10425211e+02 -7.29340810e+02 -8.47578967e+02 -9.62860842e+02 -1.07378913e+03 -1.17963321e+03 -1.28012110e+03 -1.37527315e+03 -1.46528230e+03 -1.55045522e+03 -1.61842685e+03 -1.80060364e+03 -1.49664429e+03 -2.34771277e+03 -8.70327337e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.02164216e-15 -3.07642715e-05 --1.41391778e-03 -9.20903811e-03 -7.96504697e-02 -2.23150102e-01 -4.85818185e-01 -9.71604411e-01 -1.85188075e+00 -3.41744641e+00 -6.14677086e+00 -1.07930633e+01 -1.84696373e+01 -3.06799896e+01 -4.92051140e+01 -7.57701269e+01 -1.11520983e+02 -1.56527037e+02 -2.09617385e+02 -2.68688144e+02 -3.31293634e+02 -3.95186526e+02 -4.58610630e+02 -5.20358619e+02 -5.79697571e+02 -6.36251251e+02 -6.89887403e+02 -7.40628221e+02 -7.88586261e+02 -8.33937887e+02 -8.69807981e+02 -9.68948476e+02 -7.99723699e+02 -1.26634654e+03 -4.31627978e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.02164216e-15 -3.07642715e-05 --1.41391778e-03 -9.20903811e-03 -7.96504697e-02 -2.23150102e-01 -4.85818185e-01 -9.71604411e-01 -1.85188075e+00 -3.41744641e+00 -6.14677086e+00 -1.07930633e+01 -1.84696373e+01 -3.06799896e+01 -4.92051140e+01 -7.57701269e+01 -1.11520983e+02 -1.56527037e+02 -2.09617385e+02 -2.68688144e+02 -3.31293634e+02 -3.95186526e+02 -4.58610630e+02 -5.20358619e+02 -5.79697571e+02 -6.36251251e+02 -6.89887403e+02 -7.40628221e+02 -7.88586261e+02 -8.33937887e+02 -8.69807981e+02 -9.68948476e+02 -7.99723699e+02 -1.26634654e+03 -4.31627978e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.02164216e-15 -3.07642715e-05 --1.41391778e-03 -9.20903811e-03 -7.96504697e-02 -2.23150102e-01 -4.85818185e-01 -9.71604411e-01 -1.85188075e+00 -3.41744641e+00 -6.14677086e+00 -1.07930633e+01 -1.84696373e+01 -3.06799896e+01 -4.92051140e+01 -7.57701269e+01 -1.11520983e+02 -1.56527037e+02 -2.09617385e+02 -2.68688144e+02 -3.31293634e+02 -3.95186526e+02 -4.58610630e+02 -5.20358619e+02 -5.79697571e+02 -6.36251251e+02 -6.89887403e+02 -7.40628221e+02 -7.88586261e+02 -8.33937887e+02 -8.69807981e+02 -9.68948476e+02 -7.99723699e+02 -1.26634654e+03 -4.31627978e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.40888298e-03 -9.19772909e-03 -7.94292578e-02 -2.22155437e-01 -4.82381211e-01 -9.60981299e-01 -1.82113408e+00 -3.33258160e+00 -5.92216535e+00 -1.02241892e+01 -1.71003361e+01 -2.75784837e+01 -4.26642690e+01 -6.30406097e+01 -8.87772900e+01 -1.19228739e+02 -1.53203152e+02 -1.89299472e+02 -2.26219980e+02 -2.62942977e+02 -2.98760014e+02 -3.33235769e+02 -3.66141722e+02 -3.97391815e+02 -4.26990917e+02 -4.54997705e+02 -4.81509485e+02 -5.02519749e+02 -5.60330522e+02 -4.62226324e+02 -7.33280710e+02 -2.51583277e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.79235850e-15 -3.06324927e-05 --1.40888298e-03 -9.19772909e-03 -7.94292578e-02 -2.22155437e-01 -4.82381211e-01 -9.60981299e-01 -1.82113408e+00 -3.33258160e+00 -5.92216535e+00 -1.02241892e+01 -1.71003361e+01 -2.75784837e+01 -4.26642690e+01 -6.30406097e+01 -8.87772900e+01 -1.19228739e+02 -1.53203152e+02 -1.89299472e+02 -2.26219980e+02 -2.62942977e+02 -2.98760014e+02 -3.33235769e+02 -3.66141722e+02 -3.97391815e+02 -4.26990917e+02 -4.54997705e+02 -4.81509485e+02 -5.02519749e+02 -5.60330522e+02 -4.62226324e+02 -7.33280710e+02 -2.51583277e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.79235850e-15 -3.06324927e-05 --1.40888298e-03 -9.19772909e-03 -7.94292578e-02 -2.22155437e-01 -4.82381211e-01 -9.60981299e-01 -1.82113408e+00 -3.33258160e+00 -5.92216535e+00 -1.02241892e+01 -1.71003361e+01 -2.75784837e+01 -4.26642690e+01 -6.30406097e+01 -8.87772900e+01 -1.19228739e+02 -1.53203152e+02 -1.89299472e+02 -2.26219980e+02 -2.62942977e+02 -2.98760014e+02 -3.33235769e+02 -3.66141722e+02 -3.97391815e+02 -4.26990917e+02 -4.54997705e+02 -4.81509485e+02 -5.02519749e+02 -5.60330522e+02 -4.62226324e+02 -7.33280710e+02 -2.51583277e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.79235850e-15 -3.06324927e-05 --1.40888298e-03 -9.19772909e-03 -7.94292578e-02 -2.22155437e-01 -4.82381211e-01 -9.60981299e-01 -1.82113408e+00 -3.33258160e+00 -5.92216535e+00 -1.02241892e+01 -1.71003361e+01 -2.75784837e+01 -4.26642690e+01 -6.30406097e+01 -8.87772900e+01 -1.19228739e+02 -1.53203152e+02 -1.89299472e+02 -2.26219980e+02 -2.62942977e+02 -2.98760014e+02 -3.33235769e+02 -3.66141722e+02 -3.97391815e+02 -4.26990917e+02 -4.54997705e+02 -4.81509485e+02 -5.02519749e+02 -5.60330522e+02 -4.62226324e+02 -7.33280710e+02 -2.51583277e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.79235850e-15 -3.06324927e-05 --1.40888298e-03 -9.19772909e-03 -7.94292578e-02 -2.22155437e-01 -4.82381211e-01 -9.60981299e-01 -1.82113408e+00 -3.33258160e+00 -5.92216535e+00 -1.02241892e+01 -1.71003361e+01 -2.75784837e+01 -4.26642690e+01 -6.30406097e+01 -8.87772900e+01 -1.19228739e+02 -1.53203152e+02 -1.89299472e+02 -2.26219980e+02 -2.62942977e+02 -2.98760014e+02 -3.33235769e+02 -3.66141722e+02 -3.97391815e+02 -4.26990917e+02 -4.54997705e+02 -4.81509485e+02 -5.02519749e+02 -5.60330522e+02 -4.62226324e+02 -7.33280710e+02 -2.51583277e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.79235850e-15 -3.06324927e-05 --1.40888298e-03 -9.19772909e-03 -7.94292578e-02 -2.22155437e-01 -4.82381211e-01 -9.60981299e-01 -1.82113408e+00 -3.33258160e+00 -5.92216535e+00 -1.02241892e+01 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-3.04332478e-02 -3.88316467e-02 -4.68262095e-02 -5.44557252e-02 -6.17582265e-02 -6.79808667e-02 -8.08487261e-02 -6.60101967e-02 -1.14871615e-01 -4.79248676e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.39322534e-18 -3.55979589e-05 --1.97261005e-03 -2.33704327e-02 -8.18361891e-02 -1.09243765e-01 -1.12971330e-01 -1.23375030e-01 -1.31032874e-01 -1.38850416e-01 -1.46723430e-01 -1.53280146e-01 -1.72610260e-01 -1.41164180e-01 -2.29296202e-01 -1.13218731e-01 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.15874617e-19 -2.91510359e-06 --1.82089229e-04 -1.87955633e-03 -1.14657659e-02 -2.18145213e-02 -3.04332478e-02 -3.88316467e-02 -4.68262095e-02 -5.44557252e-02 -6.17582265e-02 -6.79808667e-02 -8.08487261e-02 -6.60101967e-02 -1.14871615e-01 -4.79248676e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.15874617e-19 -2.91510359e-06 --1.82089229e-04 -1.87955633e-03 -1.14657659e-02 -2.18145213e-02 -3.04332478e-02 -3.88316467e-02 -4.68262095e-02 -5.44557252e-02 -6.17582265e-02 -6.79808667e-02 -8.08487261e-02 -6.60101967e-02 -1.14871615e-01 -4.79248676e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-8.47697357e-02 -3.58784537e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.27108730e-19 -2.42989158e-06 --1.52072042e-04 -1.56723709e-03 -9.44480714e-03 -1.78008351e-02 -2.46591384e-02 -3.12884124e-02 -3.75550986e-02 -4.35107752e-02 -4.86112274e-02 -5.86654622e-02 -4.79591538e-02 -8.47697357e-02 -3.58784537e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 --1.61521911e-18 -3.12862349e-05 --1.72267111e-03 -2.01920473e-02 -7.09840204e-02 -9.49669377e-02 -9.79775762e-02 -1.06211216e-01 -1.11908057e-01 -1.17608844e-01 -1.22189746e-01 -1.36825732e-01 -1.11548970e-01 -1.80365126e-01 -9.07504178e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.27108730e-19 -2.42989158e-06 --1.52072042e-04 -1.56723709e-03 -9.44480714e-03 -1.78008351e-02 -2.46591384e-02 -3.12884124e-02 -3.75550986e-02 -4.35107752e-02 -4.86112274e-02 -5.86654622e-02 -4.79591538e-02 -8.47697357e-02 -3.58784537e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.27108730e-19 -2.42989158e-06 --1.52072042e-04 -1.56723709e-03 -9.44480714e-03 -1.78008351e-02 -2.46591384e-02 -3.12884124e-02 -3.75550986e-02 -4.35107752e-02 -4.86112274e-02 -5.86654622e-02 -4.79591538e-02 -8.47697357e-02 -3.58784537e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-6.08252279e-02 -1.21040024e-01 -2.30511706e-01 -4.25974557e-01 -7.70480390e-01 -1.37137504e+00 -2.40946685e+00 -4.18485339e+00 -7.18535327e+00 -1.21804352e+01 -2.03317738e+01 -3.32842445e+01 -5.31575122e+01 -8.23224502e+01 -1.22882228e+02 -1.75947856e+02 -2.41040685e+02 -3.16023124e+02 -3.97663481e+02 -4.82502031e+02 -5.67553293e+02 -6.50625869e+02 -7.30325621e+02 -8.05903225e+02 -8.77067135e+02 -9.43820410e+02 -1.00633878e+03 -1.06488785e+03 -1.11978479e+03 -1.16249370e+03 -1.28509272e+03 -1.06558408e+03 -1.66168853e+03 -5.33896243e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.56426241e-14 -5.80279692e-07 --1.88846528e-05 -3.89602038e-05 -8.26283680e-04 -4.21834817e-03 -1.20710606e-02 -2.85851739e-02 -6.08252279e-02 -1.21040024e-01 -2.30511706e-01 -4.25974557e-01 -7.70480390e-01 -1.37137504e+00 -2.40946685e+00 -4.18485339e+00 -7.18535327e+00 -1.21804352e+01 -2.03317738e+01 -3.32842445e+01 -5.31575122e+01 -8.23224502e+01 -1.22882228e+02 -1.75947856e+02 -2.41040685e+02 -3.16023124e+02 -3.97663481e+02 -4.82502031e+02 -5.67553293e+02 -6.50625869e+02 -7.30325621e+02 -8.05903225e+02 -8.77067135e+02 -9.43820410e+02 -1.00633878e+03 -1.06488785e+03 -1.11978479e+03 -1.16249370e+03 -1.28509272e+03 -1.06558408e+03 -1.66168853e+03 -5.33896243e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.56426241e-14 -5.80279692e-07 --1.88846528e-05 -3.89602038e-05 -8.26283680e-04 -4.21834817e-03 -1.20710606e-02 -2.85851739e-02 -6.08252279e-02 -1.21040024e-01 -2.30511706e-01 -4.25974557e-01 -7.70480390e-01 -1.37137504e+00 -2.40946685e+00 -4.18485339e+00 -7.18535327e+00 -1.21804352e+01 -2.03317738e+01 -3.32842445e+01 -5.31575122e+01 -8.23224502e+01 -1.22882228e+02 -1.75947856e+02 -2.41040685e+02 -3.16023124e+02 -3.97663481e+02 -4.82502031e+02 -5.67553293e+02 -6.50625869e+02 -7.30325621e+02 -8.05903225e+02 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63270000e-14 -5.00626424e-07 --1.60187720e-05 -2.71761132e-05 -8.45590707e-04 -4.19779778e-03 -1.20229349e-02 -2.83916805e-02 -6.02825265e-02 -1.19813923e-01 -2.28047388e-01 -4.21285768e-01 -7.61571588e-01 -1.35374239e+00 -2.37229776e+00 -4.10163941e+00 -6.99150855e+00 -1.17225978e+01 -1.92612781e+01 -3.08565546e+01 -4.79107461e+01 -7.16755377e+01 -1.02824586e+02 -1.41097550e+02 -1.85253245e+02 -2.33397559e+02 -2.83492558e+02 -3.33772485e+02 -3.82935679e+02 -4.30149343e+02 -4.74961491e+02 -5.17191523e+02 -5.56834239e+02 -5.93987841e+02 -6.28804860e+02 -6.61469580e+02 -6.86915561e+02 -7.59729435e+02 -6.29815830e+02 -9.83047067e+02 -3.16903923e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.05708775e-14 -6.62584844e-06 --2.66795827e-04 -1.48777256e-03 -1.35319354e-02 -3.02846115e-02 -5.25393932e-02 -9.08588967e-02 -1.58596370e-01 -2.78621205e-01 -4.90808962e-01 -8.63933537e-01 -1.51567207e+00 -2.64513976e+00 -4.58422329e+00 -7.87458712e+00 -1.33739585e+01 -2.23822560e+01 -3.67474504e+01 -5.88614811e+01 -9.14147497e+01 -1.36815618e+02 -1.96371333e+02 -2.69602556e+02 -3.54147915e+02 -4.46387720e+02 -5.42418383e+02 -6.38851528e+02 -7.33184697e+02 -8.23813005e+02 -9.09861923e+02 -9.90978280e+02 -1.06714647e+03 -1.13855034e+03 -1.20547898e+03 -1.26827851e+03 -1.31747164e+03 -1.45554900e+03 -1.21220037e+03 -1.87966163e+03 -6.45467318e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.80985989e-13 -2.32659226e-04 --1.92957466e-02 -3.79927656e-01 -4.47677868e-01 -2.86808451e-01 -2.62203244e-01 -2.81677891e-01 -3.19245840e-01 -3.93312152e-01 -5.21115839e-01 -7.38237723e-01 -1.10633959e+00 -1.73006174e+00 -2.78369338e+00 -4.55125308e+00 -7.48175969e+00 -1.22546650e+01 -1.98344233e+01 -3.14674044e+01 -4.85527801e+01 -7.23391346e+01 -1.03497893e+02 -1.41768101e+02 -1.85909786e+02 -2.34031408e+02 -2.84098091e+02 -3.34346865e+02 -3.83478193e+02 -4.30660706e+02 -4.75443260e+02 -5.17645680e+02 -5.57262922e+02 -5.94393174e+02 -6.29188864e+02 -6.61834130e+02 -6.87260609e+02 -7.60073380e+02 -6.30089607e+02 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-5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 -1.36112034e+00 -2.38256249e+00 -4.11538021e+00 -7.00930430e+00 -1.17449666e+01 -1.92886043e+01 -3.08889983e+01 -4.79481531e+01 -7.17173871e+01 -1.02870013e+02 -1.41145461e+02 -1.85302490e+02 -2.33447100e+02 -2.83541567e+02 -3.33820378e+02 -3.82982086e+02 -4.30194064e+02 -4.75004444e+02 -5.17232705e+02 -5.56873698e+02 -5.94025654e+02 -6.28841116e+02 -6.61504375e+02 -6.86948814e+02 -7.59762929e+02 -6.29842605e+02 -9.83084453e+02 -3.16916298e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.63275988e-14 -5.01169880e-07 --1.60423120e-05 -2.72354827e-05 -8.45314233e-04 -4.20352702e-03 -1.20677013e-02 -2.85680468e-02 -6.07636872e-02 -1.20859402e-01 -2.29997714e-01 -4.24553179e-01 -7.66630617e-01 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-1.20309744e-02 -2.84306811e-02 -6.03213965e-02 -1.19553361e-01 -2.26302238e-01 -4.14421306e-01 -7.39542792e-01 -1.29035902e+00 -2.20220561e+00 -3.66886023e+00 -5.94317754e+00 -9.31250518e+00 -1.40383624e+01 -2.02695986e+01 -2.79677825e+01 -3.68937460e+01 -4.66707191e+01 -5.68865707e+01 -6.71794613e+01 -7.72789703e+01 -8.70089870e+01 -9.62710571e+01 -1.05022756e+02 -1.13258367e+02 -1.20994207e+02 -1.28258509e+02 -1.35086841e+02 -1.40428196e+02 -1.55561922e+02 -1.28862630e+02 -2.01743275e+02 -6.57507812e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.57502550e-15 -4.01299807e-07 --1.26329941e-05 -1.33935110e-05 -8.66790674e-04 -4.17839713e-03 -1.20309744e-02 -2.84306811e-02 -6.03213965e-02 -1.19553361e-01 -2.26302238e-01 -4.14421306e-01 -7.39542792e-01 -1.29035902e+00 -2.20220561e+00 -3.66886023e+00 -5.94317754e+00 -9.31250518e+00 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-3.91248754e-07 --1.23317538e-05 -1.23708363e-05 -8.67697969e-04 -4.16527813e-03 -1.19581830e-02 -2.81559749e-02 -5.95306031e-02 -1.17597217e-01 -2.21792169e-01 -4.04206919e-01 -7.16217081e-01 -1.23650751e+00 -2.07814405e+00 -3.38922500e+00 -5.33884002e+00 -8.08201402e+00 -1.17087789e+01 -1.61999095e+01 -2.14181509e+01 -2.71444552e+01 -3.31376609e+01 -3.91849654e+01 -4.51265159e+01 -5.08575334e+01 -5.63188252e+01 -6.14842413e+01 -6.63493888e+01 -7.09230172e+01 -7.52210565e+01 -7.92639316e+01 -8.24313431e+01 -9.13708613e+01 -7.56680597e+01 -1.18598427e+02 -3.88073422e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.87602840e-15 -6.61755929e-06 --2.66468111e-04 -1.48694468e-03 -1.35051892e-02 -3.02084335e-02 -5.23176323e-02 -9.02358888e-02 -1.56871463e-01 -2.73907848e-01 -4.78103127e-01 -8.30178203e-01 -1.42747874e+00 -2.41933542e+00 -4.02071202e+00 -6.51374269e+00 -1.02213508e+01 -1.54407344e+01 -2.23462470e+01 -3.09044365e+01 -4.08563727e+01 -5.17859587e+01 -6.32335255e+01 -7.47923974e+01 -8.61562901e+01 -9.71237943e+01 -1.07580550e+02 -1.17475446e+02 -1.26799119e+02 -1.35567505e+02 -1.43810432e+02 -1.51565826e+02 -1.57679362e+02 -1.74569809e+02 -1.45319242e+02 -2.26094799e+02 -7.92970046e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.70421782e-14 -2.32136403e-04 --1.92687789e-02 -3.79706085e-01 -4.47456958e-01 -2.86487564e-01 -2.61591541e-01 -2.80586304e-01 -3.17063104e-01 -3.88715481e-01 -5.10925843e-01 -7.14683186e-01 -1.05040502e+00 -1.59573167e+00 -2.46236662e+00 -3.79663416e+00 -5.76553531e+00 -8.52203238e+00 -1.21546480e+01 -1.66436884e+01 -2.18526231e+01 -2.75640240e+01 -3.35386845e+01 -3.95655953e+01 -4.54862808e+01 -5.11968880e+01 -5.66387755e+01 -6.17860739e+01 -6.66344928e+01 -7.11927763e+01 -7.54767881e+01 -7.95068601e+01 -8.26613987e+01 -9.16004191e+01 -7.58505995e+01 -1.18850912e+02 -3.88922037e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 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-5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54487233e-15 -6.60538435e-06 --2.66011822e-04 -1.48538862e-03 -1.34899069e-02 -3.01588468e-02 -5.21775286e-02 -8.98434766e-02 -1.55791233e-01 -2.70983777e-01 -4.70331785e-01 -8.09968251e-01 -1.37632505e+00 -2.29428594e+00 -3.72841932e+00 -5.86802095e+00 -8.88864733e+00 -1.28953888e+01 -1.78726323e+01 -2.36726792e+01 -3.00547026e+01 -3.67507677e+01 -4.35225351e+01 -5.01895186e+01 -5.66322235e+01 -6.27820701e+01 -6.86076566e+01 -7.41022532e+01 -7.92741817e+01 -8.41401134e+01 -8.87216742e+01 -9.23395157e+01 -1.02291771e+02 -8.51410262e+01 -1.32593519e+02 -4.67804001e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.60323799e-14 -2.31873669e-04 --1.92529019e-02 -3.79568872e-01 -4.47313505e-01 -2.86282269e-01 -2.61207698e-01 -2.79898029e-01 -3.15694268e-01 -3.85861514e-01 -5.04685680e-01 -7.00559721e-01 -1.01790621e+00 -1.52119628e+00 -2.29533924e+00 -3.43774180e+00 -5.03826866e+00 -7.14989713e+00 -9.76293455e+00 -1.27994874e+01 -1.61339282e+01 -1.96271559e+01 -2.31558395e+01 -2.66268690e+01 -2.99788261e+01 -3.31766687e+01 -3.62045661e+01 -3.90594032e+01 -4.17457963e+01 -4.42726276e+01 -4.66515047e+01 -4.85156643e+01 -5.37885016e+01 -4.45247062e+01 -6.98386967e+01 -2.29503319e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 -5.40368887e+00 -7.17824752e+00 -9.13288104e+00 -1.11854997e+01 -1.32629160e+01 -1.53095799e+01 -1.72886045e+01 -1.91787199e+01 -2.09700834e+01 -2.26604527e+01 -2.42522366e+01 -2.57504353e+01 -2.71617251e+01 -2.82708929e+01 -3.13773692e+01 -2.59690838e+01 -4.08016083e+01 -1.34663011e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.35016854e-15 -3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 -5.40368887e+00 -7.17824752e+00 -9.13288104e+00 -1.11854997e+01 -1.32629160e+01 -1.53095799e+01 -1.72886045e+01 -1.91787199e+01 -2.09700834e+01 -2.26604527e+01 -2.42522366e+01 -2.57504353e+01 -2.71617251e+01 -2.82708929e+01 -3.13773692e+01 -2.59690838e+01 -4.08016083e+01 -1.34663011e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.35017458e-15 -3.81240956e-07 --1.20391245e-05 -1.17351401e-05 -8.65299937e-04 -4.14044709e-03 -1.18508310e-02 -2.77814785e-02 -5.83595868e-02 -1.14192679e-01 -2.12397444e-01 -3.79394895e-01 -6.53451803e-01 -1.08510806e+00 -1.73264445e+00 -2.65031815e+00 -3.87093624e+00 -5.39033990e+00 -7.16376028e+00 -9.11764189e+00 -1.11698570e+01 -1.32471515e+01 -1.52939028e+01 -1.72731598e+01 -1.91636014e+01 -2.09553467e+01 -2.26461268e+01 -2.42383321e+01 -2.57369508e+01 -2.71486511e+01 -2.82582867e+01 -3.13645383e+01 -2.59588142e+01 -4.07870518e+01 -1.34613458e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.61013105e-16 -6.58676496e-06 --2.65327968e-04 -1.48308653e-03 -1.34666479e-02 -3.00841023e-02 -5.19665034e-02 -8.92548315e-02 -1.54180760e-01 -2.66664017e-01 -4.59007097e-01 -7.81104303e-01 -1.30534496e+00 -2.12753947e+00 -3.35847915e+00 -5.10174720e+00 -7.42064560e+00 -1.03085257e+01 -1.36814944e+01 -1.74005389e+01 -2.13098116e+01 -2.52698726e+01 -2.91745201e+01 -3.29529421e+01 -3.65640517e+01 -3.99885809e+01 -4.32218220e+01 -4.62680127e+01 -4.91364042e+01 -5.18392755e+01 -5.39774288e+01 -5.98328271e+01 -4.97941779e+01 -7.76251071e+01 -2.75581214e+01 -0.00000000e+00 -0.00000000e+00 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-1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 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-1.60338589e-01 -1.42598720e-01 -1.32471413e-01 -1.24993082e-01 -1.19455114e-01 -1.15280009e-01 -1.12109617e-01 -1.09702661e-01 -1.07887877e-01 -1.06539207e-01 -1.05563598e-01 -1.04180339e-01 -1.09645628e-01 -8.82838426e-02 -1.32100829e-01 -4.71583764e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600441e-18 -1.00157478e-07 --3.60006348e-06 -1.05335264e-05 -3.26618419e-04 -1.21392122e-03 -2.56139058e-03 -4.27347675e-03 -6.26242498e-03 -8.42581916e-03 -1.06778042e-02 -1.29532822e-02 -1.52069640e-02 -1.74095559e-02 -1.95435750e-02 -2.15997613e-02 -2.35750002e-02 -2.52349385e-02 -2.89628523e-02 -2.39653923e-02 -3.94260585e-02 -1.41287284e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -5.36629422e-19 -7.22695127e-08 --2.67743646e-06 -8.42126740e-06 -2.48493362e-04 -9.01581957e-04 -1.84932671e-03 -3.00966082e-03 -4.32610753e-03 -5.73720032e-03 -7.19402773e-03 -8.66017822e-03 -1.01104376e-02 -1.15284293e-02 -1.29042690e-02 -1.42330463e-02 -1.53646392e-02 -1.77990405e-02 -1.47488565e-02 -2.45285174e-02 -8.87141922e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -5.36629502e-19 -7.22691073e-08 --2.67745816e-06 -8.42275268e-06 -2.48492241e-04 -9.01240304e-04 -1.84728254e-03 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--9.61196446e-20 -2.53150827e-08 --1.00034771e-06 -3.29248783e-06 -9.78314186e-05 -3.44184948e-04 -6.76161300e-04 -1.05709149e-03 -1.47241286e-03 -1.90788830e-03 -2.35337563e-03 -2.80141907e-03 -3.24681473e-03 -3.64492879e-03 -4.40494124e-03 -3.67665946e-03 -6.41112143e-03 -2.38563506e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --9.61196595e-20 -2.53144988e-08 --1.00030184e-06 -3.29176115e-06 -9.78325716e-05 -3.44140059e-04 -6.75863201e-04 -1.05612350e-03 -1.47019078e-03 -1.90375610e-03 -2.34669584e-03 -2.79163022e-03 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-4.88333200e-03 -6.35601956e-03 -7.36986469e-03 -8.20992330e-03 -8.90710915e-03 -9.52257205e-03 -1.00831386e-02 -1.05170988e-02 -1.17245367e-02 -9.66265456e-03 -1.53060111e-02 -6.58527726e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.16687840e-18 -8.41029810e-05 --8.89215256e-03 -2.22154184e-01 -2.81193216e-01 -1.55648080e-01 -1.16083645e-01 -1.03149991e-01 -8.66910759e-02 -7.65332459e-02 -6.87518875e-02 -6.27078774e-02 -5.75849480e-02 -5.61357093e-02 -4.37659826e-02 -6.01206040e-02 -2.22458879e-02 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--2.72284269e-21 -1.30083123e-08 --5.19650617e-07 -1.57705152e-06 -5.19724802e-05 -1.84013220e-04 -3.60948118e-04 -5.61597776e-04 -7.78626976e-04 -1.00542282e-03 -1.23760835e-03 -1.45292277e-03 -1.83898187e-03 -1.54665749e-03 -2.83057799e-03 -1.07725487e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.72284269e-21 -1.30083123e-08 --5.19650617e-07 -1.57705152e-06 -5.19724802e-05 -1.84013220e-04 -3.60948118e-04 -5.61597776e-04 -7.78626976e-04 -1.00542282e-03 -1.23760835e-03 -1.45292277e-03 -1.83898187e-03 -1.54665749e-03 -2.83057799e-03 -1.07725487e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.72284269e-21 -1.30083123e-08 --5.19650617e-07 -1.57705152e-06 -5.19724802e-05 -1.84013220e-04 -3.60948118e-04 -5.61597776e-04 -7.78626976e-04 -1.00542282e-03 -1.23760835e-03 -1.45292277e-03 -1.83898187e-03 -1.54665749e-03 -2.83057799e-03 -1.07725487e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22376227e-13 -8.74121830e-07 --2.97317685e-05 -8.36906715e-05 -7.54057709e-04 -4.26427114e-03 -1.20259118e-02 -2.84210946e-02 -6.04122143e-02 -1.20189279e-01 -2.29117158e-01 -4.24251165e-01 -7.69627926e-01 -1.37528498e+00 -2.42910237e+00 -4.24933806e+00 -7.36947616e+00 -1.26708758e+01 -2.15797597e+01 -3.63357560e+01 -6.03047038e+01 -9.82295632e+01 -1.56189001e+02 -2.40934342e+02 -3.58385141e+02 -5.11556484e+02 -6.98880854e+02 -9.14063916e+02 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--4.99020009e-15 -6.62508821e-06 --2.66758719e-04 -1.48794227e-03 -1.35153092e-02 -3.02412076e-02 -5.24104335e-02 -9.04964692e-02 -1.57591720e-01 -2.75869300e-01 -4.83363870e-01 -8.44047074e-01 -1.46329444e+00 -2.50944775e+00 -4.23987815e+00 -7.02380602e+00 -1.13440014e+01 -1.77504503e+01 -2.67456275e+01 -3.86185343e+01 -5.33012056e+01 -7.03414381e+01 -8.90221255e+01 -1.08556276e+02 -1.28251194e+02 -1.47587894e+02 -1.66227325e+02 -1.83978992e+02 -2.00759820e+02 -2.16557286e+02 -2.31401338e+02 -2.45345011e+02 -2.58454559e+02 -2.68771620e+02 -2.97394377e+02 -2.47593589e+02 -3.84868961e+02 -1.34222333e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.57502550e-15 -4.01299807e-07 --1.26329941e-05 -1.33935110e-05 -8.66790674e-04 -4.17839713e-03 -1.20309744e-02 -2.84306811e-02 -6.03213965e-02 -1.19553361e-01 -2.26302238e-01 -4.14421306e-01 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-2.01743275e+02 -6.57507812e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.57502550e-15 -4.01299807e-07 --1.26329941e-05 -1.33935110e-05 -8.66790674e-04 -4.17839713e-03 -1.20309744e-02 -2.84306811e-02 -6.03213965e-02 -1.19553361e-01 -2.26302238e-01 -4.14421306e-01 -7.39542792e-01 -1.29035902e+00 -2.20220561e+00 -3.66886023e+00 -5.94317754e+00 -9.31250518e+00 -1.40383624e+01 -2.02695986e+01 -2.79677825e+01 -3.68937460e+01 -4.66707191e+01 -5.68865707e+01 -6.71794613e+01 -7.72789703e+01 -8.70089870e+01 -9.62710571e+01 -1.05022756e+02 -1.13258367e+02 -1.20994207e+02 -1.28258509e+02 -1.35086841e+02 -1.40428196e+02 -1.55561922e+02 -1.28862630e+02 -2.01743275e+02 -6.57507812e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00926872e-15 -3.91248754e-07 --1.23317538e-05 -1.23708363e-05 -8.67697969e-04 -4.16527813e-03 -1.19581830e-02 -2.81559749e-02 -5.95306031e-02 -1.17597217e-01 -2.21792169e-01 -4.04206919e-01 -7.16217081e-01 -1.23650751e+00 -2.07814405e+00 -3.38922500e+00 -5.33884002e+00 -8.08201402e+00 -1.17087789e+01 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-2.86487564e-01 -2.61591541e-01 -2.80586304e-01 -3.17063104e-01 -3.88715481e-01 -5.10925843e-01 -7.14683186e-01 -1.05040502e+00 -1.59573167e+00 -2.46236662e+00 -3.79663416e+00 -5.76553531e+00 -8.52203238e+00 -1.21546480e+01 -1.66436884e+01 -2.18526231e+01 -2.75640240e+01 -3.35386845e+01 -3.95655953e+01 -4.54862808e+01 -5.11968880e+01 -5.66387755e+01 -6.17860739e+01 -6.66344928e+01 -7.11927763e+01 -7.54767881e+01 -7.95068601e+01 -8.26613987e+01 -9.16004191e+01 -7.58505995e+01 -1.18850912e+02 -3.88922037e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 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--2.69006833e-15 -3.85368563e-07 --1.21603022e-05 -1.19076661e-05 -8.67060090e-04 -4.15519393e-03 -1.19153534e-02 -2.80061643e-02 -5.90603728e-02 -1.16222579e-01 -2.17967902e-01 -3.93986052e-01 -6.89922563e-01 -1.17161155e+00 -1.92562478e+00 -3.05127905e+00 -4.64030951e+00 -6.74706115e+00 -9.36227428e+00 -1.24074178e+01 -1.57554230e+01 -1.92654456e+01 -2.28125547e+01 -2.63024112e+01 -2.96727712e+01 -3.28881016e+01 -3.59323226e+01 -3.88022290e+01 -4.15024436e+01 -4.40419089e+01 -4.64323169e+01 -4.83080759e+01 -5.35813197e+01 -4.43600091e+01 -6.96107442e+01 -2.28734232e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54487233e-15 -6.60538435e-06 --2.66011822e-04 -1.48538862e-03 -1.34899069e-02 -3.01588468e-02 -5.21775286e-02 -8.98434766e-02 -1.55791233e-01 -2.70983777e-01 -4.70331785e-01 -8.09968251e-01 -1.37632505e+00 -2.29428594e+00 -3.72841932e+00 -5.86802095e+00 -8.88864733e+00 -1.28953888e+01 -1.78726323e+01 -2.36726792e+01 -3.00547026e+01 -3.67507677e+01 -4.35225351e+01 -5.01895186e+01 -5.66322235e+01 -6.27820701e+01 -6.86076566e+01 -7.41022532e+01 -7.92741817e+01 -8.41401134e+01 -8.87216742e+01 -9.23395157e+01 -1.02291771e+02 -8.51410262e+01 -1.32593519e+02 -4.67804001e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69005467e-15 -3.85272572e-07 --1.21571726e-05 -1.18550022e-05 -8.66975792e-04 -4.16073607e-03 -1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 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-3.00841023e-02 -5.19665034e-02 -8.92548315e-02 -1.54180760e-01 -2.66664017e-01 -4.59007097e-01 -7.81104303e-01 -1.30534496e+00 -2.12753947e+00 -3.35847915e+00 -5.10174720e+00 -7.42064560e+00 -1.03085257e+01 -1.36814944e+01 -1.74005389e+01 -2.13098116e+01 -2.52698726e+01 -2.91745201e+01 -3.29529421e+01 -3.65640517e+01 -3.99885809e+01 -4.32218220e+01 -4.62680127e+01 -4.91364042e+01 -5.18392755e+01 -5.39774288e+01 -5.98328271e+01 -4.97941779e+01 -7.76251071e+01 -2.75581214e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.35016854e-15 -3.81224333e-07 --1.20391275e-05 -1.16960006e-05 -8.65194787e-04 -4.14597969e-03 -1.18946955e-02 -2.79530153e-02 -5.88232512e-02 -1.15187430e-01 -2.14220426e-01 -3.82373965e-01 -6.57908485e-01 -1.09131152e+00 -1.74076095e+00 -2.66036827e+00 -3.88277768e+00 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-1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.14833057e-16 -3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 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-4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.30581063e-15 -2.28536521e-04 --1.90500025e-02 -3.77824384e-01 -4.45610787e-01 -2.83674214e-01 -2.56590433e-01 -2.71717237e-01 -2.99888633e-01 -3.54344146e-01 -4.40032147e-01 -5.66637866e-01 -7.43728961e-01 -9.77472215e-01 -1.26755280e+00 -1.60623432e+00 -1.98029636e+00 -2.37464530e+00 -2.77555858e+00 -3.17240576e+00 -3.55794955e+00 -3.92785916e+00 -4.27997403e+00 -4.61360761e+00 -4.92899839e+00 -5.22691939e+00 -5.50851445e+00 -5.72953219e+00 -6.35949629e+00 -5.25376461e+00 -8.27088238e+00 -2.77112270e+00 -0.00000000e+00 -0.00000000e+00 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-3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79102126e-17 -3.55816408e-07 --1.12147653e-05 -1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 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-1.34311817e-07 --4.68423286e-06 -1.23632430e-05 -4.15039750e-04 -1.59092187e-03 -3.47982778e-03 -5.99994411e-03 -9.03145453e-03 -1.24095798e-02 -1.59819551e-02 -1.96266393e-02 -2.32558210e-02 -2.68113136e-02 -3.02576638e-02 -3.35755792e-02 -3.67566493e-02 -3.98005186e-02 -4.23288103e-02 -4.82336983e-02 -3.98708054e-02 -6.50278835e-02 -2.31130513e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.37694227e-18 -3.07434405e-06 --1.34155792e-04 -8.69976575e-04 -8.04448605e-03 -1.61099803e-02 -2.20244425e-02 -2.80329408e-02 -3.43596184e-02 -4.08169727e-02 -4.73188478e-02 -5.37581206e-02 -6.00562495e-02 -6.61618455e-02 -7.20456794e-02 -7.76946669e-02 -8.31066550e-02 -8.82880506e-02 -9.24898695e-02 -1.03502859e-01 -8.58482180e-02 -1.36072110e-01 -5.38498041e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.57502550e-15 -4.01299807e-07 --1.26329941e-05 -1.33935110e-05 -8.66790674e-04 -4.17839713e-03 -1.20309744e-02 -2.84306811e-02 -6.03213965e-02 -1.19553361e-01 -2.26302238e-01 -4.14421306e-01 -7.39542792e-01 -1.29035902e+00 -2.20220561e+00 -3.66886023e+00 -5.94317754e+00 -9.31250518e+00 -1.40383624e+01 -2.02695986e+01 -2.79677825e+01 -3.68937460e+01 -4.66707191e+01 -5.68865707e+01 -6.71794613e+01 -7.72789703e+01 -8.70089870e+01 -9.62710571e+01 -1.05022756e+02 -1.13258367e+02 -1.20994207e+02 -1.28258509e+02 -1.35086841e+02 -1.40428196e+02 -1.55561922e+02 -1.28862630e+02 -2.01743275e+02 -6.57507812e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.17186425e-13 -2.32309911e-04 --1.92790191e-02 -3.79795295e-01 -4.47554648e-01 -2.86620244e-01 -2.61847023e-01 -2.81043519e-01 -3.17975056e-01 -3.90628808e-01 -5.15146618e-01 -7.24365598e-01 -1.07313303e+00 -1.64937328e+00 -2.58743008e+00 -4.07970578e+00 -6.37724469e+00 -9.76528169e+00 -1.45032937e+01 -2.07387058e+01 -2.84327649e+01 -3.73472064e+01 -4.71070494e+01 -5.73022450e+01 -6.75728222e+01 -7.76497679e+01 -8.73578983e+01 -9.65992940e+01 -1.05331787e+02 -1.13549740e+02 -1.21269440e+02 -1.28519031e+02 -1.35333971e+02 -1.40661937e+02 -1.55794806e+02 -1.29047775e+02 -2.01998802e+02 -6.58363316e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.57502550e-15 -4.01299807e-07 --1.26329941e-05 -1.33935110e-05 -8.66790674e-04 -4.17839713e-03 -1.20309744e-02 -2.84306811e-02 -6.03213965e-02 -1.19553361e-01 -2.26302238e-01 -4.14421306e-01 -7.39542792e-01 -1.29035902e+00 -2.20220561e+00 -3.66886023e+00 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-1.19595633e-02 -2.81794770e-02 -5.95304106e-02 -1.17235648e-01 -2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.69006833e-15 -3.85368563e-07 --1.21603022e-05 -1.19076661e-05 -8.67060090e-04 -4.15519393e-03 -1.19153534e-02 -2.80061643e-02 -5.90603728e-02 -1.16222579e-01 -2.17967902e-01 -3.93986052e-01 -6.89922563e-01 -1.17161155e+00 -1.92562478e+00 -3.05127905e+00 -4.64030951e+00 -6.74706115e+00 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-8.51821143e-04 -4.03440295e-03 -1.13980720e-02 -2.62323319e-02 -5.36693198e-02 -1.01175860e-01 -1.78763829e-01 -2.98195829e-01 -4.70733791e-01 -7.03666211e-01 -9.97080122e-01 -1.34289871e+00 -1.72702330e+00 -2.13328060e+00 -2.54695754e+00 -2.95666838e+00 -3.35467505e+00 -3.73635627e+00 -4.09941162e+00 -4.44311275e+00 -4.76771504e+00 -5.07404036e+00 -5.36329434e+00 -5.59201489e+00 -6.22219281e+00 -5.14478023e+00 -8.11970397e+00 -2.71927774e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 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--1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 -5.37040162e+00 -5.59892236e+00 -6.22928738e+00 -5.15046789e+00 -8.12786504e+00 -2.72210356e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.30581063e-15 -2.28536521e-04 --1.90500025e-02 -3.77824384e-01 -4.45610787e-01 -2.83674214e-01 -2.56590433e-01 -2.71717237e-01 -2.99888633e-01 -3.54344146e-01 -4.40032147e-01 -5.66637866e-01 -7.43728961e-01 -9.77472215e-01 -1.26755280e+00 -1.60623432e+00 -1.98029636e+00 -2.37464530e+00 -2.77555858e+00 -3.17240576e+00 -3.55794955e+00 -3.92785916e+00 -4.27997403e+00 -4.61360761e+00 -4.92899839e+00 -5.22691939e+00 -5.50851445e+00 -5.72953219e+00 -6.35949629e+00 -5.25376461e+00 -8.27088238e+00 -2.77112270e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54323444e-16 -3.65202257e-07 --1.15152369e-05 -1.14354732e-05 -8.51737210e-04 -4.03972491e-03 -1.14395494e-02 -2.63916832e-02 -5.40904541e-02 -1.02053007e-01 -1.80310481e-01 -3.00603003e-01 -4.74128375e-01 -7.08082259e-01 -1.00245406e+00 -1.34909028e+00 -1.73385193e+00 -2.14056122e+00 -2.55452480e+00 -2.96438752e+00 -3.36244308e+00 -3.74409820e+00 -4.10707502e+00 -4.45066242e+00 -4.77512849e+00 -5.08130416e+00 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-9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.29259824e-17 -6.36216732e-06 --2.57266074e-04 -1.45588378e-03 -1.31770886e-02 -2.91804608e-02 -4.94602465e-02 -8.24856943e-02 -1.36503574e-01 -2.22271226e-01 -3.52658511e-01 -5.40151653e-01 -7.93128920e-01 -1.11227029e+00 -1.48935253e+00 -1.90942587e+00 -2.35504184e+00 -2.81013013e+00 -3.26210989e+00 -3.70231652e+00 -4.12547741e+00 -4.52887372e+00 -4.91153545e+00 -5.27360109e+00 -5.61585888e+00 -5.93951709e+00 -6.19761247e+00 -6.89032184e+00 -5.73065177e+00 -8.97606976e+00 -3.27848368e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.79102126e-17 -3.55816408e-07 --1.12147653e-05 -1.13929618e-05 -8.42116310e-04 -3.96513928e-03 -1.11291558e-02 -2.53574696e-02 -5.10893330e-02 -9.42148928e-02 -1.61659017e-01 -2.60082622e-01 -3.93866135e-01 -5.63208093e-01 -7.63527258e-01 -9.86678608e-01 -1.22324445e+00 -1.46460792e+00 -1.70406357e+00 -1.93702347e+00 -2.16072017e+00 -2.37374868e+00 -2.57563190e+00 -2.76647711e+00 -2.94673124e+00 -3.11707457e+00 -3.25204175e+00 -3.62184995e+00 -2.99357871e+00 -4.73239565e+00 -1.59352157e+00 -0.00000000e+00 -0.00000000e+00 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--2.52437962e-04 -1.43897447e-03 -1.29990659e-02 -2.86378029e-02 -4.80028594e-02 -7.87324313e-02 -1.27335882e-01 -2.01241926e-01 -3.07851327e-01 -4.52248093e-01 -6.35115988e-01 -8.51966342e-01 -1.09433024e+00 -1.35217904e+00 -1.61618544e+00 -1.87898303e+00 -2.13544848e+00 -2.38242164e+00 -2.61823253e+00 -2.84223978e+00 -3.05446002e+00 -3.25530045e+00 -3.44542510e+00 -3.59737924e+00 -4.00294477e+00 -3.32861672e+00 -5.22094842e+00 -1.92247545e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.88226374e-17 -3.43371509e-07 --1.08309351e-05 -1.14853708e-05 -8.27543860e-04 -3.85644923e-03 -1.06869693e-02 -2.39273659e-02 -4.71048022e-02 -8.43428308e-02 -1.39641106e-01 -2.15692503e-01 -3.12754444e-01 -4.28266356e-01 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-4.82336983e-02 -3.98708054e-02 -6.50278835e-02 -2.31130513e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.37694227e-18 -3.07434405e-06 --1.34155792e-04 -8.69976575e-04 -8.04448605e-03 -1.61099803e-02 -2.20244425e-02 -2.80329408e-02 -3.43596184e-02 -4.08169727e-02 -4.73188478e-02 -5.37581206e-02 -6.00562495e-02 -6.61618455e-02 -7.20456794e-02 -7.76946669e-02 -8.31066550e-02 -8.82880506e-02 -9.24898695e-02 -1.03502859e-01 -8.58482180e-02 -1.36072110e-01 -5.38498041e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.94569800e-17 -1.49710241e-04 --1.40401075e-02 -3.22982680e-01 -3.91465825e-01 -2.22105921e-01 -1.73548291e-01 -1.60338589e-01 -1.42598720e-01 -1.32471413e-01 -1.24993082e-01 -1.19455114e-01 -1.15280009e-01 -1.12109617e-01 -1.09702661e-01 -1.07887877e-01 -1.06539207e-01 -1.05563598e-01 -1.04180339e-01 -1.09645628e-01 -8.82838426e-02 -1.32100829e-01 -4.71583764e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600441e-18 -1.00157478e-07 --3.60006348e-06 -1.05335264e-05 -3.26618419e-04 -1.21392122e-03 -2.56139058e-03 -4.27347675e-03 -6.26242498e-03 -8.42581916e-03 -1.06778042e-02 -1.29532822e-02 -1.52069640e-02 -1.74095559e-02 -1.95435750e-02 -2.15997613e-02 -2.35750002e-02 -2.52349385e-02 -2.89628523e-02 -2.39653923e-02 -3.94260585e-02 -1.41287284e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 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-1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 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--2.51848223e-13 -1.46612980e-06 --5.20888564e-05 -1.75249241e-04 -6.07385194e-04 -4.36875231e-03 -1.20644808e-02 -2.85888800e-02 -6.09285450e-02 -1.21324632e-01 -2.31322256e-01 -4.28221757e-01 -7.76591617e-01 -1.38775412e+00 -2.45284204e+00 -4.29845026e+00 -7.47938957e+00 -1.29310629e+01 -2.22144913e+01 -3.78976339e+01 -6.41187887e+01 -1.07349781e+02 -1.77276281e+02 -2.87486414e+02 -4.55307063e+02 -6.99856352e+02 -1.03771266e+03 -1.47701971e+03 -2.01279648e+03 -2.62666939e+03 -3.29173071e+03 -3.97967607e+03 -4.66643494e+03 -5.33461374e+03 -5.97337827e+03 -6.57712070e+03 -7.14389252e+03 -7.67406312e+03 -8.16933121e+03 -8.63206169e+03 -9.06497439e+03 -9.40014712e+03 -1.03734906e+04 -8.60854513e+03 -1.33803782e+04 -4.24777646e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.96515391e-12 -2.34577918e-04 --1.93666021e-02 -3.80236525e-01 -4.47309031e-01 -2.87142008e-01 -2.62310709e-01 -2.81853052e-01 -3.19707213e-01 -3.94268050e-01 -5.23254012e-01 -7.43256874e-01 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-1.03500196e+02 -1.68209119e+02 -2.66918889e+02 -4.10998127e+02 -6.10359136e+02 -8.69959928e+02 -1.18699712e+03 -1.55070557e+03 -1.94520453e+03 -2.35372037e+03 -2.76193924e+03 -3.15947918e+03 -3.53984030e+03 -3.89962680e+03 -4.23762340e+03 -4.55400126e+03 -4.84973088e+03 -5.12618715e+03 -5.38496456e+03 -5.58555088e+03 -6.16642570e+03 -5.11631035e+03 -7.95846741e+03 -2.53365411e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --9.04852241e-14 -6.54166058e-06 --2.63345721e-04 -1.47246579e-03 -1.35635991e-02 -3.02801313e-02 -5.25826866e-02 -9.09821653e-02 -1.58924695e-01 -2.79528378e-01 -4.93279712e-01 -8.70599747e-01 -1.53349820e+00 -2.69238642e+00 -4.70826466e+00 -8.19670563e+00 -1.41992207e+01 -2.44596923e+01 -4.18559735e+01 -7.10398701e+01 -1.19307901e+02 -1.97612477e+02 -3.21366605e+02 -5.10292812e+02 -7.86250367e+02 -1.16833794e+03 -1.66617291e+03 -2.27447922e+03 -2.97267040e+03 -3.73029162e+03 -4.51512661e+03 -5.29965034e+03 -6.06387336e+03 -6.79525981e+03 -7.48724087e+03 -8.13744396e+03 -8.74616792e+03 -9.31525431e+03 -9.84732748e+03 -1.03454043e+04 -1.07333943e+04 -1.18377642e+04 -9.86215631e+03 -1.52498746e+04 -5.14472959e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.76192483e-13 -1.12098291e-06 --3.90183289e-05 -1.21771897e-04 -6.92726777e-04 -4.31166571e-03 -1.20682225e-02 -2.85958234e-02 -6.09141666e-02 -1.21290196e-01 -2.31224417e-01 -4.27950232e-01 -7.75851616e-01 -1.38576426e+00 -2.44754618e+00 -4.28447589e+00 -7.44280510e+00 -1.28360675e+01 -2.19701589e+01 -3.72767202e+01 -6.25661483e+01 -1.03552656e+02 -1.68270140e+02 -2.66988397e+02 -4.11075505e+02 -6.10443165e+02 -8.70048874e+02 -1.18708896e+03 -1.55079828e+03 -1.94529640e+03 -2.35381009e+03 -2.76202597e+03 -3.15956243e+03 -3.53991988e+03 -3.89970271e+03 -4.23769573e+03 -4.55407018e+03 -4.84979661e+03 -5.12624989e+03 -5.38502454e+03 -5.58560801e+03 -6.16648300e+03 -5.11635616e+03 -7.95853095e+03 -2.53367481e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.14900463e-12 -2.33889929e-04 --1.93407995e-02 -3.80130467e-01 -4.47467065e-01 -2.87033031e-01 -2.62307663e-01 -2.81856525e-01 -3.19669296e-01 -3.94197297e-01 -5.23096076e-01 -7.42885432e-01 -1.11763441e+00 -1.75813884e+00 -2.85434405e+00 -4.72965703e+00 -7.93043053e+00 -1.33701978e+01 -2.25546553e+01 -3.79149114e+01 -6.32603189e+01 -1.04303327e+02 -1.69075168e+02 -2.67842066e+02 -4.11967931e+02 -6.11360489e+02 -8.70974559e+02 -1.18800603e+03 -1.55169178e+03 -1.94615511e+03 -2.35462704e+03 -2.76279798e+03 -3.16028914e+03 -3.54060276e+03 -3.90034427e+03 -4.23829899e+03 -4.55463829e+03 -4.85033263e+03 -5.12675673e+03 -5.38550483e+03 -5.58606189e+03 -6.16693447e+03 -5.11671567e+03 -7.95902499e+03 -2.53383639e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--2.97317685e-05 -8.36906715e-05 -7.54057709e-04 -4.26427114e-03 -1.20259118e-02 -2.84210946e-02 -6.04122143e-02 -1.20189279e-01 -2.29117158e-01 -4.24251165e-01 -7.69627926e-01 -1.37528498e+00 -2.42910237e+00 -4.24933806e+00 -7.36947616e+00 -1.26708758e+01 -2.15797597e+01 -3.63357560e+01 -6.03047038e+01 -9.82295632e+01 -1.56189001e+02 -2.40934342e+02 -3.58385141e+02 -5.11556484e+02 -6.98880854e+02 -9.14063916e+02 -1.14774841e+03 -1.39000846e+03 -1.63234347e+03 -1.86856409e+03 -2.09477502e+03 -2.30892204e+03 -2.51024860e+03 -2.69882651e+03 -2.87520772e+03 -3.04018938e+03 -3.19470435e+03 -3.31461681e+03 -3.66087718e+03 -3.03684755e+03 -4.72762936e+03 -1.50951108e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 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--1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 -7.74731373e-01 -1.38275535e+00 -2.43955196e+00 -4.26343633e+00 -7.38794193e+00 -1.26944617e+01 -2.16092231e+01 -3.63718095e+01 -6.03479379e+01 -9.82803382e+01 -1.56247317e+02 -2.40999723e+02 -3.58456574e+02 -5.11632490e+02 -6.98959676e+02 -9.14143791e+02 -1.14782780e+03 -1.39008621e+03 -1.63241881e+03 -1.86863655e+03 -2.09484441e+03 -2.30898832e+03 -2.51031184e+03 -2.69888685e+03 -2.87526532e+03 -3.04024442e+03 -3.19475701e+03 -3.31466699e+03 -3.66092757e+03 -3.03688782e+03 -4.72768532e+03 -1.50952937e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.22370638e-13 -8.73322369e-07 --2.97121618e-05 -8.35695699e-05 -7.54085920e-04 -4.26977087e-03 -1.20707992e-02 -2.85977830e-02 -6.08945330e-02 -1.21238148e-01 -2.31076175e-01 -4.27538886e-01 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-2.29221856e-01 -4.22413240e-01 -7.60857578e-01 -1.34583480e+00 -2.34282135e+00 -4.01414231e+00 -6.75783277e+00 -1.11404849e+01 -1.78966092e+01 -2.78540492e+01 -4.17563408e+01 -6.00110643e+01 -8.24781568e+01 -1.08438713e+02 -1.36784858e+02 -1.66318411e+02 -1.95996863e+02 -2.25048328e+02 -2.52976124e+02 -2.79508053e+02 -3.04532530e+02 -3.28042234e+02 -3.50091661e+02 -3.70768105e+02 -3.90178366e+02 -4.05319047e+02 -4.48508602e+02 -3.71723664e+02 -5.80757851e+02 -1.87871260e+02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.12886387e-13 -2.32540197e-04 --1.92909127e-02 -3.79894903e-01 -4.47660199e-01 -2.86764594e-01 -2.62129287e-01 -2.81546553e-01 -3.18980894e-01 -3.92751122e-01 -5.19863111e-01 -7.35309141e-01 -1.09926604e+00 -1.71264112e+00 -2.74047182e+00 -4.44440385e+00 -7.22138923e+00 -1.16364012e+01 -1.84217665e+01 -2.84027613e+01 -4.23204396e+01 -6.05806611e+01 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-4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 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-1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 -3.40120339e+00 -5.35360124e+00 -8.09945071e+00 -1.17285691e+01 -1.62215615e+01 -2.14410893e+01 -2.71681163e+01 -3.31615619e+01 -3.92087349e+01 -4.51498924e+01 -5.08803479e+01 -5.63409789e+01 -6.15056857e+01 -6.63701092e+01 -7.09430209e+01 -7.52403642e+01 -7.92825720e+01 -8.24492502e+01 -9.13890093e+01 -7.56825759e+01 -1.18618879e+02 -3.88142351e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.00925957e-15 -3.91112223e-07 --1.23245197e-05 -1.23003467e-05 -8.67642205e-04 -4.17081763e-03 -1.20026222e-02 -2.83304747e-02 -6.00049167e-02 -1.18622690e-01 -2.23691655e-01 -4.07357148e-01 -7.21025056e-01 -1.24337870e+00 -2.08743891e+00 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-2.19836271e-01 -3.97065926e-01 -6.94583998e-01 -1.17819866e+00 -1.93440564e+00 -3.06239102e+00 -4.65371497e+00 -6.76253462e+00 -9.37943462e+00 -1.24257986e+01 -1.57745536e+01 -1.92849132e+01 -2.28320340e+01 -2.63216672e+01 -2.96916462e+01 -3.29064986e+01 -3.59501882e+01 -3.88195404e+01 -4.15191979e+01 -4.40581162e+01 -4.64479951e+01 -4.83231633e+01 -5.35966411e+01 -4.43722677e+01 -6.96280650e+01 -2.28792894e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.54487233e-15 -6.60538435e-06 --2.66011822e-04 -1.48538862e-03 -1.34899069e-02 -3.01588468e-02 -5.21775286e-02 -8.98434766e-02 -1.55791233e-01 -2.70983777e-01 -4.70331785e-01 -8.09968251e-01 -1.37632505e+00 -2.29428594e+00 -3.72841932e+00 -5.86802095e+00 -8.88864733e+00 -1.28953888e+01 -1.78726323e+01 -2.36726792e+01 -3.00547026e+01 -3.67507677e+01 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-3.72139802e-07 --1.17439095e-05 -1.15288824e-05 -8.58093013e-04 -4.09010163e-03 -1.16528996e-02 -2.71171670e-02 -5.62587412e-02 -1.07948477e-01 -1.95095589e-01 -3.34869493e-01 -5.47265474e-01 -8.51187317e-01 -1.25851886e+00 -1.76871271e+00 -2.36732054e+00 -3.02980978e+00 -3.72836827e+00 -4.43790383e+00 -5.13914832e+00 -5.81912453e+00 -6.47018513e+00 -7.08862424e+00 -7.67338697e+00 -8.22506323e+00 -8.74517838e+00 -9.23588197e+00 -9.62295347e+00 -1.06967967e+01 -8.84727904e+00 -1.39395896e+01 -4.64460717e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.21189258e-15 -2.29924632e-04 --1.91344557e-02 -3.78553516e-01 -4.46316903e-01 -2.84760278e-01 -2.58486984e-01 -2.75046373e-01 -3.06216030e-01 -3.66653014e-01 -4.64387225e-01 -6.14592639e-01 -8.35471110e-01 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-1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.37694227e-18 -3.07434405e-06 --1.34155792e-04 -8.69976575e-04 -8.04448605e-03 -1.61099803e-02 -2.20244425e-02 -2.80329408e-02 -3.43596184e-02 -4.08169727e-02 -4.73188478e-02 -5.37581206e-02 -6.00562495e-02 -6.61618455e-02 -7.20456794e-02 -7.76946669e-02 -8.31066550e-02 -8.82880506e-02 -9.24898695e-02 -1.03502859e-01 -8.58482180e-02 -1.36072110e-01 -5.38498041e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.56715103e-18 -1.34312852e-07 --4.68410939e-06 -1.23567419e-05 -4.15047110e-04 -1.59195644e-03 -3.48610679e-03 -6.01953102e-03 -9.07397700e-03 -1.24833554e-02 -1.60924482e-02 -1.97763040e-02 -2.34446782e-02 -2.70377175e-02 -3.05189827e-02 -3.38687041e-02 -3.70783350e-02 -4.01476042e-02 -4.26951300e-02 -4.86458253e-02 -4.02081209e-02 -6.55686494e-02 -2.33167384e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.94569800e-17 -1.49710241e-04 --1.40401075e-02 -3.22982680e-01 -3.91465825e-01 -2.22105921e-01 -1.73548291e-01 -1.60338589e-01 -1.42598720e-01 -1.32471413e-01 -1.24993082e-01 -1.19455114e-01 -1.15280009e-01 -1.12109617e-01 -1.09702661e-01 -1.07887877e-01 -1.06539207e-01 -1.05563598e-01 -1.04180339e-01 -1.09645628e-01 -8.82838426e-02 -1.32100829e-01 -4.71583764e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600441e-18 -1.00157478e-07 --3.60006348e-06 -1.05335264e-05 -3.26618419e-04 -1.21392122e-03 -2.56139058e-03 -4.27347675e-03 -6.26242498e-03 -8.42581916e-03 -1.06778042e-02 -1.29532822e-02 -1.52069640e-02 -1.74095559e-02 -1.95435750e-02 -2.15997613e-02 -2.35750002e-02 -2.52349385e-02 -2.89628523e-02 -2.39653923e-02 -3.94260585e-02 -1.41287284e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.85600440e-18 -1.00158108e-07 --3.59999886e-06 -1.05300435e-05 -3.26622448e-04 -1.21453629e-03 -2.56507280e-03 -4.28487970e-03 -6.28716244e-03 -8.46893680e-03 -1.07429237e-02 -1.30424336e-02 -1.53208041e-02 -1.75477192e-02 -1.97050158e-02 -2.17830295e-02 -2.37784513e-02 -2.54547501e-02 -2.92165937e-02 -2.41741970e-02 -3.97709044e-02 -1.42606194e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.29901207e-19 -2.45459346e-06 --1.09130239e-04 -7.12372434e-04 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--5.19650617e-07 -1.57705152e-06 -5.19724802e-05 -1.84013220e-04 -3.60948118e-04 -5.61597776e-04 -7.78626976e-04 -1.00542282e-03 -1.23760835e-03 -1.45292277e-03 -1.83898187e-03 -1.54665749e-03 -2.83057799e-03 -1.07725487e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.19270967e-20 -5.10935979e-07 --2.22381771e-05 -8.40534883e-05 -1.81594816e-03 -3.97439902e-03 -5.24140477e-03 -6.09539546e-03 -6.78662743e-03 -7.34549741e-03 -7.82756262e-03 -8.19006663e-03 -9.14657112e-03 -7.53565349e-03 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-7.51394964e-04 -9.11755396e-04 -1.19176164e-03 -1.00738023e-03 -1.90201267e-03 -7.33149815e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.25767025e-20 -3.96600275e-07 --1.66635809e-05 -4.50388210e-05 -1.43547843e-03 -3.25097210e-03 -4.35507499e-03 -5.09278578e-03 -5.68054688e-03 -6.14659704e-03 -6.48508731e-03 -7.28177725e-03 -6.00415195e-03 -9.55082003e-03 -4.24740549e-03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.02575753e-19 -9.52543106e-09 --3.79772725e-07 -1.07994697e-06 -3.83524056e-05 -1.36837485e-04 -2.69432210e-04 -4.19772181e-04 -5.82274949e-04 -7.52157912e-04 -9.13011061e-04 -1.19410919e-03 -1.00935387e-03 -1.90742765e-03 -7.35606324e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--2.80730103e-07 -7.37311376e-07 -2.86236007e-05 -1.03098950e-04 -2.04143806e-04 -3.18982083e-04 -4.43258766e-04 -5.64012561e-04 -7.70724549e-04 -6.55575702e-04 -1.28970142e-03 -5.05083062e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.18632933e-19 -7.07678606e-09 --2.80730103e-07 -7.37311376e-07 -2.86236007e-05 -1.03098950e-04 -2.04143806e-04 -3.18982083e-04 -4.43258766e-04 -5.64012561e-04 -7.70724549e-04 -6.55575702e-04 -1.28970142e-03 -5.05083062e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.18632933e-19 -7.07678606e-09 --2.80730103e-07 -7.37311376e-07 -2.86236007e-05 -1.03098950e-04 -2.04143806e-04 -3.18982083e-04 -4.43258766e-04 -5.64012561e-04 -7.70724549e-04 -6.55575702e-04 -1.28970142e-03 -5.05083062e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-4.30365745e+03 -1.38984589e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.65785580e-15 -4.70427204e-07 --1.76671497e-05 -4.28794703e-05 -6.31543429e-04 -3.28187520e-03 -9.24108130e-03 -2.17644111e-02 -4.63448050e-02 -9.26981775e-02 -1.78021236e-01 -3.32498671e-01 -6.08887395e-01 -1.09883655e+00 -1.96044857e+00 -3.46413361e+00 -6.06727785e+00 -1.05319609e+01 -1.81013735e+01 -3.07429980e+01 -5.14366140e+01 -8.44148573e+01 -1.35150727e+02 -2.09791442e+02 -3.13826224e+02 -4.50211975e+02 -6.17811275e+02 -8.11185569e+02 -1.02203234e+03 -1.24141769e+03 -1.46160100e+03 -1.67687669e+03 -1.88359521e+03 -2.07977669e+03 -2.26463114e+03 -2.43813747e+03 -2.60072775e+03 -2.75307202e+03 -2.89597984e+03 -3.00724882e+03 -3.32605376e+03 -2.75674746e+03 -4.30365745e+03 -1.38984589e+03 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.65785580e-15 -4.70427204e-07 --1.76671497e-05 -4.28794703e-05 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--9.55011875e-06 -8.84201057e-06 -6.86054782e-04 -3.23426114e-03 -9.20729888e-03 -2.16349738e-02 -4.59090794e-02 -9.14046171e-02 -1.74318247e-01 -3.22209352e-01 -5.80963715e-01 -1.02466011e+00 -1.76773490e+00 -2.97610125e+00 -4.86920194e+00 -7.70055679e+00 -1.17067938e+01 -1.70318190e+01 -2.36589733e+01 -3.13946514e+01 -3.99193430e+01 -4.88755234e+01 -5.79437765e+01 -6.68811889e+01 -7.55260975e+01 -8.37849758e+01 -9.16142462e+01 -9.90036172e+01 -1.05963210e+02 -1.12514555e+02 -1.18686643e+02 -1.23535418e+02 -1.37138070e+02 -1.13443805e+02 -1.78370778e+02 -5.91514407e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --2.38375767e-16 -3.16370015e-07 --9.55011875e-06 -8.84201057e-06 -6.86054782e-04 -3.23426114e-03 -9.20729888e-03 -2.16349738e-02 -4.59090794e-02 -9.14046171e-02 -1.74318247e-01 -3.22209352e-01 -5.80963715e-01 -1.02466011e+00 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-1.89288223e-01 -3.40990448e-01 -6.07783715e-01 -1.06853981e+00 -1.84610384e+00 -3.12002315e+00 -5.12981129e+00 -8.15501647e+00 -1.24605756e+01 -1.82137797e+01 -2.54081145e+01 -3.38420946e+01 -4.31723225e+01 -5.30088070e+01 -6.29992715e+01 -7.28729298e+01 -8.24472280e+01 -9.16144721e+01 -1.00322389e+02 -1.08556017e+02 -1.16323564e+02 -1.23646435e+02 -1.30554251e+02 -1.36030057e+02 -1.50949925e+02 -1.25549569e+02 -1.96113828e+02 -7.08307917e+01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.36501013e-16 -3.14003452e-07 --9.44117836e-06 -8.49504881e-06 -6.85942350e-04 -3.22893913e-03 -9.18569907e-03 -2.15589578e-02 -4.56680189e-02 -9.06899666e-02 -1.72293203e-01 -3.16668235e-01 -5.66269969e-01 -9.86951058e-01 -1.67458752e+00 -2.75656875e+00 -4.38088815e+00 -6.68684906e+00 -9.76097415e+00 -1.35970156e+01 -1.80854921e+01 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-2.06384066e-02 -4.28140284e-02 -8.24924520e-02 -1.50113458e-01 -2.59834768e-01 -4.28524618e-01 -6.72666848e-01 -1.00343518e+00 -1.42194262e+00 -1.91758265e+00 -2.47081598e+00 -3.05869835e+00 -3.65999774e+00 -4.25801363e+00 -4.84117785e+00 -5.40239178e+00 -5.93793763e+00 -6.44642427e+00 -6.92794398e+00 -7.38346562e+00 -7.81458247e+00 -8.15643888e+00 -9.09435196e+00 -7.50534826e+00 -1.19009842e+01 -4.06869375e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --9.43530485e-18 -3.07982250e-07 --9.30006968e-06 -9.07690311e-06 -6.76870396e-04 -3.16762369e-03 -8.92043330e-03 -2.06384066e-02 -4.28140284e-02 -8.24924520e-02 -1.50113458e-01 -2.59834768e-01 -4.28524618e-01 -6.72666848e-01 -1.00343518e+00 -1.42194262e+00 -1.91758265e+00 -2.47081598e+00 -3.05869835e+00 -3.65999774e+00 -4.25801363e+00 -4.84117785e+00 -5.40239178e+00 -5.93793763e+00 -6.44642427e+00 -6.92794398e+00 -7.38346562e+00 -7.81458247e+00 -8.15643888e+00 -9.09435196e+00 -7.50534826e+00 -1.19009842e+01 -4.06869375e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --9.43530485e-18 -3.07982250e-07 --9.30006968e-06 -9.07690311e-06 -6.76870396e-04 -3.16762369e-03 -8.92043330e-03 -2.06384066e-02 -4.28140284e-02 -8.24924520e-02 -1.50113458e-01 -2.59834768e-01 -4.28524618e-01 -6.72666848e-01 -1.00343518e+00 -1.42194262e+00 -1.91758265e+00 -2.47081598e+00 -3.05869835e+00 -3.65999774e+00 -4.25801363e+00 -4.84117785e+00 -5.40239178e+00 -5.93793763e+00 -6.44642427e+00 -6.92794398e+00 -7.38346562e+00 -7.81458247e+00 -8.15643888e+00 -9.09435196e+00 -7.50534826e+00 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--9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 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-4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.61620841e-17 -3.50125544e-06 --1.26436944e-04 -6.45751402e-04 -6.39013077e-03 -1.60388491e-02 -2.98893513e-02 -5.37232707e-02 -9.49289929e-02 -1.64318139e-01 -2.76846871e-01 -4.50637286e-01 -7.03821636e-01 -1.04930073e+00 -1.48949516e+00 -2.01424418e+00 -2.60347156e+00 -3.23296246e+00 -3.87989995e+00 -4.52604233e+00 -5.15852372e+00 -5.76925345e+00 -6.35380919e+00 -6.91033102e+00 -7.43862081e+00 -7.93948473e+00 -8.41441366e+00 -8.79508607e+00 -9.80422472e+00 -8.14411150e+00 -1.28169709e+01 -4.85388290e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 -3.70663307e-01 -5.58336620e-01 -7.96973875e-01 -1.08075044e+00 -1.39859341e+00 -1.73733795e+00 -2.08469689e+00 -2.43092896e+00 -2.76922575e+00 -3.09535673e+00 -3.40705587e+00 -3.70341908e+00 -3.98441805e+00 -4.25054799e+00 -4.50268324e+00 -4.70306174e+00 -5.24975852e+00 -4.33000392e+00 -6.88053649e+00 -2.36966720e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --3.14504920e-18 -3.04064396e-07 --9.19692634e-06 -9.31032827e-06 -6.71463338e-04 -3.12912645e-03 -8.75842319e-03 -2.00878770e-02 -4.11618323e-02 -7.79652971e-02 -1.38651967e-01 -2.33000040e-01 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-1.06427860e+00 -8.82676405e-01 -1.40105042e+00 -5.59135605e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --6.38483873e-21 -2.61175478e-07 --8.02850799e-06 -1.10542251e-05 -6.08797524e-04 -2.70562732e-03 -7.10667312e-03 -1.49748520e-02 -2.75496102e-02 -4.57648550e-02 -6.99278435e-02 -9.95606927e-02 -1.33534486e-01 -1.70409801e-01 -2.08782937e-01 -2.47498074e-01 -2.85713495e-01 -3.22876897e-01 -3.58664489e-01 -3.92916339e-01 -4.25581966e-01 -4.56679602e-01 -4.86280184e-01 -5.10083430e-01 -5.72918511e-01 -4.71328679e-01 -7.57275288e-01 -2.69974250e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-2.02965326e-01 -2.23088815e-01 -2.42314576e-01 -2.60645539e-01 -2.78117495e-01 -2.92227287e-01 -3.28980646e-01 -2.70473296e-01 -4.36197030e-01 -1.57062648e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.41682796e-20 -2.39738000e-07 --7.44812567e-06 -1.17201068e-05 -5.73354369e-04 -2.48831841e-03 -6.33807065e-03 -1.28668000e-02 -2.27001952e-02 -3.60769369e-02 -5.27610899e-02 -7.21146075e-02 -9.32984540e-02 -1.15480928e-01 -1.37968514e-01 -1.60249724e-01 -1.81983589e-01 -2.02965326e-01 -2.23088815e-01 -2.42314576e-01 -2.60645539e-01 -2.78117495e-01 -2.92227287e-01 -3.28980646e-01 -2.70473296e-01 -4.36197030e-01 -1.57062648e-01 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.41682796e-20 -2.39738000e-07 --7.44812567e-06 -1.17201068e-05 -5.73354369e-04 -2.48831841e-03 -6.33807065e-03 -1.28668000e-02 -2.27001952e-02 -3.60769369e-02 -5.27610899e-02 -7.21146075e-02 -9.32984540e-02 -1.15480928e-01 -1.37968514e-01 -1.60249724e-01 -1.81983589e-01 -2.02965326e-01 -2.23088815e-01 -2.42314576e-01 -2.60645539e-01 -2.78117495e-01 -2.92227287e-01 -3.28980646e-01 -2.70473296e-01 -4.36197030e-01 -1.57062648e-01 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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--1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 -1.89347601e-01 -1.55584037e-01 -2.52013651e-01 -9.16936031e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 -1.89347601e-01 -1.55584037e-01 -2.52013651e-01 -9.16936031e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 -1.89347601e-01 -1.55584037e-01 -2.52013651e-01 -9.16936031e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 -1.89347601e-01 -1.55584037e-01 -2.52013651e-01 -9.16936031e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-0.00000000e+00 -0.00000000e+00 --1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 -1.89347601e-01 -1.55584037e-01 -2.52013651e-01 -9.16936031e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 -1.89347601e-01 -1.55584037e-01 -2.52013651e-01 -9.16936031e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --1.49209123e-19 -2.12986343e-07 --6.71769949e-06 -1.22605297e-05 -5.26063529e-04 -2.21743418e-03 -5.44348467e-03 -1.05937724e-02 -1.78789763e-02 -2.71996694e-02 -3.81991746e-02 -5.03839380e-02 -6.32533436e-02 -7.63832236e-02 -8.94560388e-02 -1.02256332e-01 -1.14651314e-01 -1.26568803e-01 -1.37978065e-01 -1.48875142e-01 -1.59276973e-01 -1.67720341e-01 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-1.08575787e-05 -3.26480194e-04 -1.24237546e-03 -2.69316004e-03 -4.61528576e-03 -6.92447689e-03 -9.50303160e-03 -1.22400751e-02 -1.50451126e-02 -1.78515609e-02 -2.06141897e-02 -2.33045185e-02 -2.59062138e-02 -2.84112855e-02 -3.08182960e-02 -3.28174675e-02 -3.75555629e-02 -3.08361958e-02 -5.08997579e-02 -1.91436645e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.17275547e-20 -1.14939614e-07 --3.91141685e-06 -1.08575787e-05 -3.26480194e-04 -1.24237546e-03 -2.69316004e-03 -4.61528576e-03 -6.92447689e-03 -9.50303160e-03 -1.22400751e-02 -1.50451126e-02 -1.78515609e-02 -2.06141897e-02 -2.33045185e-02 -2.59062138e-02 -2.84112855e-02 -3.08182960e-02 -3.28174675e-02 -3.75555629e-02 -3.08361958e-02 -5.08997579e-02 -1.91436645e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --5.17275547e-20 -1.14939614e-07 --3.91141685e-06 -1.08575787e-05 -3.26480194e-04 -1.24237546e-03 -2.69316004e-03 -4.61528576e-03 -6.92447689e-03 -9.50303160e-03 -1.22400751e-02 -1.50451126e-02 -1.78515609e-02 -2.06141897e-02 -2.33045185e-02 -2.59062138e-02 -2.84112855e-02 -3.08182960e-02 -3.28174675e-02 -3.75555629e-02 -3.08361958e-02 -5.08997579e-02 -1.91436645e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 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-8.17644183e-03 -9.92025854e-03 -1.16541246e-02 -1.33555836e-02 -1.50107785e-02 -1.66119487e-02 -1.81561474e-02 -1.94524953e-02 -2.24190248e-02 -1.84137912e-02 -3.06703345e-02 -1.16660558e-02 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --8.03468781e-21 -8.54574830e-08 --3.00567418e-06 -9.21314422e-06 -2.56997421e-04 -9.49555576e-04 -1.98672214e-03 -3.29399349e-03 -4.80839580e-03 -6.45656406e-03 -8.17644183e-03 -9.92025854e-03 -1.16541246e-02 -1.33555836e-02 -1.50107785e-02 -1.66119487e-02 -1.81561474e-02 -1.94524953e-02 -2.24190248e-02 -1.84137912e-02 -3.06703345e-02 -1.16660558e-02 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-8.00484742e-09 --3.16100711e-07 -9.57856966e-07 -3.03000476e-05 -1.08017882e-04 -2.11863372e-04 -3.28755383e-04 -4.54241367e-04 -5.84619283e-04 -7.06852374e-04 -9.24623874e-04 -7.71742850e-04 -1.47322398e-03 -6.07717125e-04 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 --4.35881532e-22 -8.00484742e-09 --3.16100711e-07 -9.57856966e-07 -3.03000476e-05 -1.08017882e-04 -2.11863372e-04 -3.28755383e-04 -4.54241367e-04 -5.84619283e-04 -7.06852374e-04 -9.24623874e-04 -7.71742850e-04 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-0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 From 540d9313bc0795a4c1df5586a20edcf76a0a885c Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Tue, 20 May 2025 19:32:31 +0200 Subject: [PATCH 26/49] Try to fix dimensionality problem --- pineappl_capi/src/lib.rs | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 796d67bf4..5c72a6018 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2169,7 +2169,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let op_info = unsafe { slice::from_raw_parts(op_info, conv_types.len() * evolve_info.fac1.len()) - .chunks_exact(conv_types.len()) + .chunks_exact(evolve_info.fac1.len()) }; let total_shape: usize = eko_shape.iter().product(); @@ -2178,7 +2178,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( operators, conv_types.len() * evolve_info.fac1.len() * total_shape, ) - .chunks_exact(total_shape) + .chunks_exact(evolve_info.fac1.len() * total_shape) }; let slices = op_info @@ -2186,7 +2186,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .map(|(op_infos, op_vals)| { op_infos .iter() - .zip(std::iter::once(op_vals)) + .zip(op_vals.chunks_exact(total_shape)) .map(|(op_info, values)| { let operator_slice_info = OperatorSliceInfo { pid_basis: op_info.pid_basis, From 4cbb8f65bc8e1593e362b5c6d6842731525acc08 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 20 May 2025 22:31:27 +0200 Subject: [PATCH 27/49] Address parts of the Code Review --- pineappl_capi/src/lib.rs | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 5c72a6018..1fc2152c0 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2135,14 +2135,14 @@ pub unsafe extern "C" fn pineappl_grid_evolve( op_info: *mut OperatorInfo, max_orders: *const u8, operators: *mut f64, - x_in: *mut f64, - x_out: *mut f64, - pids_in: *mut i32, - pids_out: *mut i32, - eko_shape: *mut usize, - xi: *mut f64, - ren1: *mut f64, - alphas: *mut f64, + x_in: *const f64, + x_out: *const f64, + pids_in: *const i32, + pids_out: *const i32, + eko_shape: *const usize, + xi: *const f64, + ren1: *const f64, + alphas: *const f64, ) -> Box { let grid = unsafe { &mut *grid }; @@ -2220,7 +2220,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( }, ); - Box::new(fk_table.expect("Evolving grid failed")) + Box::new(fk_table.unwrap()) } /// Delete an FK table. From eec6705009c2d348dce4412cd8e69753028c9bd0 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Fri, 23 May 2025 13:22:42 +0200 Subject: [PATCH 28/49] Replace last instance of `expect` in favor of `unwrap` --- pineappl_capi/src/lib.rs | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 1fc2152c0..c6a96ee5b 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2203,7 +2203,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), values.to_vec(), ) - .expect("Shape mismatch or invalid input."); + .unwrap(); Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) }) From be81384f03cdf73ede9c8a539fa9146e9e1489c8 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sat, 24 May 2025 21:32:52 +0200 Subject: [PATCH 29/49] Pass the computation of a Operator slice as a callback --- examples/cpp/evolve-grid-identity.cpp | 47 +++++++------- examples/cpp/evolve-grid.cpp | 47 ++++++++------ pineappl_capi/src/lib.rs | 91 ++++++++++++++++----------- 3 files changed, 102 insertions(+), 83 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index aff78ecb7..67271e154 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -24,27 +24,36 @@ std::vector unravel_index(std::size_t flat_index, const std::vector return coords; } -std::vector generate_fake_ekos( - std::vector pids_in, - std::vector x_in, - std::vector pids_out, - std::vector x_out +extern "C" void generate_fake_ekos( + const int* pids_in, + const double* x_in, + const int* pids_out, + const double* x_out, + double* eko_buffer, + pineappl_conv_type conv_type, + std::size_t pids_in_len, + std::size_t x_in_len, + std::size_t pids_out_len, + std::size_t x_out_len ) { - std::size_t flat_len = x_out.size() * x_in.size() * pids_out.size() * pids_in.size(); - std::vector ops(flat_len); - + // Ignore unused variables + (void)pids_in; + (void)x_in; + (void)pids_out; + (void)x_out; + (void) conv_type; + + std::size_t flat_len = pids_in_len * x_in_len * pids_out_len * x_out_len; // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) - std::vector shape = {pids_in.size(), x_in.size(), pids_out.size(), x_out.size()}; + std::vector shape = {pids_in_len, x_in_len, pids_out_len, x_out_len}; for (std::size_t i = 0; i != flat_len; i++) { std::vector coords = unravel_index(i, shape); double delta_ik = (coords[0] == coords[2]) ? 1.0 : 0.0; double delta_jl = (coords[1] == coords[3]) ? 1.0 : 0.0; - ops[i] = delta_ik * delta_jl; + eko_buffer[i] = delta_ik * delta_jl; } - - return ops; } void print_results(std::vector dxsec_grid, std::vector dxsec_fktable) { @@ -152,18 +161,6 @@ int main() { // std::vector pids_out = {-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 21, 22}; std::vector pids_out = pids_in; - // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` - std::vector op_slices; - std::size_t flat_len = x_in.size() * x_in.size() * pids_in.size() * pids_out.size(); - for (std::size_t _i = 0; _i != conv_types.size(); _i++) { - for (std::size_t j = 0; j != fac1.size(); j++) { - std::vector eko = generate_fake_ekos(pids_in, x_in, pids_out, x_in); - for (std::size_t k = 0; k != flat_len; k++) { - op_slices.push_back(eko[k]); - } - } - } - // Construct the values of alphas table std::vector alphas_table; for (double q2 : ren1) { @@ -189,7 +186,7 @@ int main() { // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - max_orders.data(), op_slices.data(), x_in.data(), + max_orders.data(), generate_fake_ekos, x_in.data(), x_in.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 6e504bb15..2fe414fcb 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -82,16 +82,36 @@ std::vector unravel_index(std::size_t flat_index, const std::vector return coords; } -std::vector generate_fake_ekos(std::string filename) { - std::ifstream input_file(filename); - std::vector ops; +extern "C" void generate_fake_ekos( + const int* pids_in, + const double* x_in, + const int* pids_out, + const double* x_out, + double* eko_buffer, + pineappl_conv_type conv_type, + std::size_t pids_in_len, + std::size_t x_in_len, + std::size_t pids_out_len, + std::size_t x_out_len +) { + // Ignore unused variables + (void)pids_in; + (void)x_in; + (void)pids_out; + (void)x_out; + (void) conv_type; + (void)pids_in_len; + (void)x_in_len; + (void)pids_out_len; + (void)x_out_len; + + std::ifstream input_file("../../test-data/EKO_LHCB_WP_7TEV.txt"); double weight_value; + std::size_t count = 0; while (input_file >> weight_value) { - ops.push_back(weight_value); + eko_buffer[count++] = weight_value; } - - return ops; } void print_results(std::vector dxsec_grid, std::vector dxsec_fktable) { @@ -126,7 +146,6 @@ void print_results(std::vector dxsec_grid, std::vector dxsec_fkt int main() { // TODO: How to get a Grid that can be evolved?? std::string filename = "../../test-data/LHCB_WP_7TEV_opt.pineappl.lz4"; - std::string ekoname = "../../test-data/EKO_LHCB_WP_7TEV.txt"; // disable LHAPDF banners to guarantee deterministic output LHAPDF::setVerbosity(0); @@ -200,18 +219,6 @@ int main() { std::vector pids_in = PIDS; std::vector pids_out = PIDS; - // The Evolution Operator is a vector with length `N_conv * N_Q2_slices * Σ product(OP shape)` - std::vector op_slices; - std::size_t flat_len = XGRID.size() * XGRID.size() * pids_in.size() * pids_out.size(); - for (std::size_t _i = 0; _i != conv_types.size(); _i++) { - for (std::size_t j = 0; j != fac1.size(); j++) { - std::vector eko = generate_fake_ekos(ekoname); - for (std::size_t k = 0; k != flat_len; k++) { - op_slices.push_back(eko[k]); - } - } - } - // Construct the values of alphas table std::vector alphas_table; for (double q2 : ren1) { @@ -237,7 +244,7 @@ int main() { // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - max_orders.data(), op_slices.data(), XGRID.data(), + max_orders.data(), generate_fake_ekos, XGRID.data(), XGRID.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index c6a96ee5b..8e8caae48 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2132,9 +2132,20 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve( grid: *mut Grid, - op_info: *mut OperatorInfo, + operator_infos: *mut OperatorInfo, max_orders: *const u8, - operators: *mut f64, + operators: extern "C" fn( + *const i32, + *const f64, + *const i32, + *const f64, + *mut f64, + ConvType, + usize, + usize, + usize, + usize, + ), x_in: *const f64, x_out: *const f64, pids_in: *const i32, @@ -2167,46 +2178,50 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .map(pineappl::convolutions::Conv::conv_type) .collect(); - let op_info = unsafe { - slice::from_raw_parts(op_info, conv_types.len() * evolve_info.fac1.len()) + let operator_infos = unsafe { + slice::from_raw_parts(operator_infos, conv_types.len() * evolve_info.fac1.len()) .chunks_exact(evolve_info.fac1.len()) }; - let total_shape: usize = eko_shape.iter().product(); - let operators = unsafe { - slice::from_raw_parts( - operators, - conv_types.len() * evolve_info.fac1.len() * total_shape, - ) - .chunks_exact(evolve_info.fac1.len() * total_shape) - }; - let slices = op_info - .zip(operators) - .map(|(op_infos, op_vals)| { - op_infos - .iter() - .zip(op_vals.chunks_exact(total_shape)) - .map(|(op_info, values)| { - let operator_slice_info = OperatorSliceInfo { - pid_basis: op_info.pid_basis, - fac0: op_info.fac0, - pids0: pids_out.to_vec(), - x0: x_out.to_vec(), - fac1: op_info.fac1, - pids1: pids_in.to_vec(), - x1: x_in.to_vec(), - conv_type: op_info.conv_type, - }; - - let array = Array4::from_shape_vec( - Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), - values.to_vec(), - ) - .unwrap(); - - Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) - }) + let slices = operator_infos + .map(|op_infos| { + op_infos.iter().map(|op_info| { + let operator_slice_info = OperatorSliceInfo { + pid_basis: op_info.pid_basis, + fac0: op_info.fac0, + pids0: pids_out.to_vec(), + x0: x_out.to_vec(), + fac1: op_info.fac1, + pids1: pids_in.to_vec(), + x1: x_in.to_vec(), + conv_type: op_info.conv_type, + }; + + // Let Rust manages the memory by allocating a flat vector of zeros as a placeholder + // to hold the evolution operator data. + let mut eko_slice = vec![0.0; total_shape]; + operators( + pids_in.as_ptr(), + x_in.as_ptr(), + pids_out.as_ptr(), + x_out.as_ptr(), + eko_slice.as_mut_ptr(), + op_info.conv_type, + pids_in.len(), + x_in.len(), + pids_out.len(), + x_out.len(), + ); + + let array = Array4::from_shape_vec( + Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), + eko_slice, + ) + .unwrap(); + + Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) + }) }) .collect(); From 9efc9bc62fecb1782eea5cfd0572aca17743c37d Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sun, 25 May 2025 22:30:01 +0200 Subject: [PATCH 30/49] Extend the object that can be passed as argument of `operator` in `evolve` of F-API --- examples/cpp/evolve-grid-identity.cpp | 17 +++++++---- examples/cpp/evolve-grid.cpp | 25 ++++++++++------ pineappl_capi/src/lib.rs | 42 ++++++++++++++++----------- 3 files changed, 53 insertions(+), 31 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 67271e154..f68a094d4 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -30,18 +30,25 @@ extern "C" void generate_fake_ekos( const int* pids_out, const double* x_out, double* eko_buffer, + void* pdf_state, pineappl_conv_type conv_type, + double fac1, std::size_t pids_in_len, std::size_t x_in_len, std::size_t pids_out_len, std::size_t x_out_len ) { // Ignore unused variables - (void)pids_in; - (void)x_in; - (void)pids_out; - (void)x_out; + (void) pids_in; + (void) x_in; + (void) pids_out; + (void) x_out; (void) conv_type; + (void) fac1; + + // Check to get the μ0 from the PDF + const double mu0_scale = static_cast (pdf_state)->q2Min(); + (void) mu0_scale; // Mark as unused variable std::size_t flat_len = pids_in_len * x_in_len * pids_out_len * x_out_len; // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) @@ -186,7 +193,7 @@ int main() { // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - max_orders.data(), generate_fake_ekos, x_in.data(), + generate_fake_ekos, max_orders.data(), pdf.get(), x_in.data(), x_in.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 2fe414fcb..d683b2464 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -88,22 +88,29 @@ extern "C" void generate_fake_ekos( const int* pids_out, const double* x_out, double* eko_buffer, + void* pdf_state, pineappl_conv_type conv_type, + double fac1, std::size_t pids_in_len, std::size_t x_in_len, std::size_t pids_out_len, std::size_t x_out_len ) { // Ignore unused variables - (void)pids_in; - (void)x_in; - (void)pids_out; - (void)x_out; + (void) pids_in; + (void) x_in; + (void) pids_out; + (void) x_out; (void) conv_type; - (void)pids_in_len; - (void)x_in_len; - (void)pids_out_len; - (void)x_out_len; + (void) pids_in_len; + (void) x_in_len; + (void) pids_out_len; + (void) x_out_len; + (void) fac1; + + // Check to get the μ0 from the PDF + const double mu0_scale = static_cast (pdf_state)->q2Min(); + (void) mu0_scale; // Mark as unused variable std::ifstream input_file("../../test-data/EKO_LHCB_WP_7TEV.txt"); double weight_value; @@ -244,7 +251,7 @@ int main() { // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales pineappl_fk_table* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - max_orders.data(), generate_fake_ekos, XGRID.data(), + generate_fake_ekos, max_orders.data(), pdf.get(), XGRID.data(), XGRID.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 8e8caae48..336212e19 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2098,6 +2098,22 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( ren1.copy_from_slice(&grid.evolve_info(&order_mask).ren1); } +/// Type alias for the operator callback +type OperatorCallback = extern "C" fn( + *const i32, // pids_in + *const f64, // x_in + *const i32, // pids_out + *const f64, // x_out + *mut f64, // Evolution Operator data buffer + *mut c_void, // Callable of PDF object + ConvType, // Convolution type + f64, // fac1 + usize, // Length of pids_in + usize, // Length of x_in + usize, // Length of pids_out + usize, // Length of x_out +); + /// Evolve a grid with an evolution operator and dump the resulting FK table. /// /// # Arguments @@ -2132,20 +2148,10 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve( grid: *mut Grid, - operator_infos: *mut OperatorInfo, + operator_info: *mut OperatorInfo, + operator: OperatorCallback, max_orders: *const u8, - operators: extern "C" fn( - *const i32, - *const f64, - *const i32, - *const f64, - *mut f64, - ConvType, - usize, - usize, - usize, - usize, - ), + pdf_state: *mut c_void, x_in: *const f64, x_out: *const f64, pids_in: *const i32, @@ -2178,13 +2184,13 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .map(pineappl::convolutions::Conv::conv_type) .collect(); - let operator_infos = unsafe { - slice::from_raw_parts(operator_infos, conv_types.len() * evolve_info.fac1.len()) + let operator_info = unsafe { + slice::from_raw_parts(operator_info, conv_types.len() * evolve_info.fac1.len()) .chunks_exact(evolve_info.fac1.len()) }; let total_shape: usize = eko_shape.iter().product(); - let slices = operator_infos + let slices = operator_info .map(|op_infos| { op_infos.iter().map(|op_info| { let operator_slice_info = OperatorSliceInfo { @@ -2201,13 +2207,15 @@ pub unsafe extern "C" fn pineappl_grid_evolve( // Let Rust manages the memory by allocating a flat vector of zeros as a placeholder // to hold the evolution operator data. let mut eko_slice = vec![0.0; total_shape]; - operators( + operator( pids_in.as_ptr(), x_in.as_ptr(), pids_out.as_ptr(), x_out.as_ptr(), eko_slice.as_mut_ptr(), + pdf_state, op_info.conv_type, + op_info.fac1, pids_in.len(), x_in.len(), pids_out.len(), From d420682641dc7d4ae19cd56b168b99101822aee3 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Sat, 31 May 2025 22:22:39 +0200 Subject: [PATCH 31/49] Minor cosmetic changes --- examples/cpp/evolve-grid-identity.cpp | 9 +++++---- examples/cpp/evolve-grid.cpp | 7 ++++--- pineappl_capi/src/lib.rs | 26 ++++++++++++-------------- 3 files changed, 21 insertions(+), 21 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index f68a094d4..759f47001 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -30,7 +30,7 @@ extern "C" void generate_fake_ekos( const int* pids_out, const double* x_out, double* eko_buffer, - void* pdf_state, + void* params_state, pineappl_conv_type conv_type, double fac1, std::size_t pids_in_len, @@ -46,8 +46,8 @@ extern "C" void generate_fake_ekos( (void) conv_type; (void) fac1; - // Check to get the μ0 from the PDF - const double mu0_scale = static_cast (pdf_state)->q2Min(); + // Check to get the μ0 of the PDF from the `params_state` + const double mu0_scale = static_cast (params_state)->q2Min(); (void) mu0_scale; // Mark as unused variable std::size_t flat_len = pids_in_len * x_in_len * pids_out_len * x_out_len; @@ -182,8 +182,9 @@ int main() { // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: // - `grid`: PineAPPL Grid // - `op_info`: operator info + // - `operator`: callback that returns an evolution operator // - `max_orders`: max orders to apply the evolution - // - `operators`: evolution operator + // - `params_state`: parameters that get passed to `operator` // - `x_in`: x-grid of the Grid // - `x_out`: x-grid of the FK table // - `pids_in`: PIDs basis representation of the Grid diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index d683b2464..41d0004d8 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -88,7 +88,7 @@ extern "C" void generate_fake_ekos( const int* pids_out, const double* x_out, double* eko_buffer, - void* pdf_state, + void* params_state, pineappl_conv_type conv_type, double fac1, std::size_t pids_in_len, @@ -109,7 +109,7 @@ extern "C" void generate_fake_ekos( (void) fac1; // Check to get the μ0 from the PDF - const double mu0_scale = static_cast (pdf_state)->q2Min(); + const double mu0_scale = static_cast (params_state)->q2Min(); (void) mu0_scale; // Mark as unused variable std::ifstream input_file("../../test-data/EKO_LHCB_WP_7TEV.txt"); @@ -240,8 +240,9 @@ int main() { // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: // - `grid`: PineAPPL Grid // - `op_info`: operator info + // - `operator`: callback that returns an evolution operator // - `max_orders`: max orders to apply the evolution - // - `operators`: evolution operator + // - `params_state`: parameters that get passed to `operator` // - `x_in`: x-grid of the Grid // - `x_out`: x-grid of the FK table // - `pids_in`: PIDs basis representation of the Grid diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 336212e19..822443f21 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2120,18 +2120,16 @@ type OperatorCallback = extern "C" fn( /// /// * `grid` - A `Grid` object /// * `op_info` - An array of `OperatorInfo` objects containing the information about the evolution. -/// Its length must be `(N_{conv} * N_{Q2_slices})`. -/// * `orders` - The maximum QCD and EW orders `(αs, α)` -/// * `operators` - An array of evolution operators. Each operator is a flattend version of a rank-4 -/// tensor whose shape is defined by: `pids_out`, `x_out`, `pids_in`, `x_in`, in that -/// order. The size of `operators` must be `(N_{conv} * N_{Q2_slices} * len_flat_op)`. -/// * `x_in` - The x-grid that defines the Grid -/// * `x_out` - The x-grid that will define the evolved Grid -/// * `pids_in` - The list of PID values that defines the Grid -/// * `pids_out` - The list of PID values that will define the evolved Grid -/// * `eko_shape` - The shape of the evolution operator -/// * `xi` - The values that defines that scale variations -/// * `ren` - An array containing the values of the renormalization scale variation +/// * `operator` - A callack that returns the evolution operator. +/// * `max_orders` - The maximum QCD and EW orders `(αs, α)`. +/// * `params_state` - Parameters that get passed to `operator`. +/// * `x_in` - The x-grid that defines the Grid. +/// * `x_out` - The x-grid that will define the evolved Grid. +/// * `pids_in` - The list of PID values that defines the Grid. +/// * `pids_out` - The list of PID values that will define the evolved Grid. +/// * `eko_shape` - The shape of the evolution operator. +/// * `xi` - The values that defines that scale variations. +/// * `ren` - An array containing the values of the renormalization scale variation. /// * `alphas` - An array containing the values of `αs`. It must have the same size as `ren1`. /// /// # Safety @@ -2151,7 +2149,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( operator_info: *mut OperatorInfo, operator: OperatorCallback, max_orders: *const u8, - pdf_state: *mut c_void, + params_state: *mut c_void, x_in: *const f64, x_out: *const f64, pids_in: *const i32, @@ -2213,7 +2211,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( pids_out.as_ptr(), x_out.as_ptr(), eko_slice.as_mut_ptr(), - pdf_state, + params_state, op_info.conv_type, op_info.fac1, pids_in.len(), From 52c8fb9f4d72a3442d4d930e4c619c240b0c7232 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 3 Jun 2025 14:44:45 +0200 Subject: [PATCH 32/49] Attempt to solve the issue of duplicating Grid & FKTable functions --- examples/cpp/evolve-grid-identity.cpp | 6 +- examples/cpp/evolve-grid.cpp | 6 +- pineappl_capi/src/lib.rs | 86 ++++++++++----------------- 3 files changed, 39 insertions(+), 59 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 7fc964602..be6ec33e9 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -211,8 +211,8 @@ int main() { // [ convolve the FK Table ] std::vector dxsec_fktable(bins); - pineappl_fk_table_convolve(fktable, xfx, pdf_states, nullptr, - nullptr, dxsec_fktable.data()); + pineappl_fktable_convolve(fktable, xfx, pdf_states, nullptr, + nullptr, 1, nullptr, dxsec_fktable.data()); // Print the results print_results(dxsec_grid, dxsec_fktable); @@ -220,5 +220,5 @@ int main() { pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); pineappl_grid_delete(grid); - pineappl_fk_table_delete(fktable); + pineappl_fktable_delete(fktable); } diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index f11a78000..bf17e81e0 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -269,8 +269,8 @@ int main() { // [ convolve the FK Table ] std::vector dxsec_fktable(bins); - pineappl_fk_table_convolve(fktable, xfx, pdf_states, nullptr, - nullptr, dxsec_fktable.data()); + pineappl_fktable_convolve(fktable, xfx, pdf_states, nullptr, + nullptr, 1, nullptr, dxsec_fktable.data()); // Print the results print_results(dxsec_grid, dxsec_fktable); @@ -278,5 +278,5 @@ int main() { pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); pineappl_grid_delete(grid); - pineappl_fk_table_delete(fktable); + pineappl_fktable_delete(fktable); } diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 048cd3bf9..bdf6f9599 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2185,7 +2185,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( xi: *const f64, ren1: *const f64, alphas: *const f64, -) -> Box { +) -> Box { let grid = unsafe { &mut *grid }; let max_orders = unsafe { slice::from_raw_parts(max_orders, 2) }; @@ -2268,20 +2268,20 @@ pub unsafe extern "C" fn pineappl_grid_evolve( }, ); - Box::new(fk_table.unwrap()) + Box::new(fk_table.unwrap().grid().clone()) } /// Delete an FK table. #[no_mangle] #[allow(unused_variables)] -pub extern "C" fn pineappl_fk_table_delete(fktable: Option>) {} +pub extern "C" fn pineappl_fktable_delete(fktable: Option>) {} /// Write `fktable` to a file with name `filename`. If `filename` ends in `.lz4` the Fk table is /// automatically LZ4 compressed. /// /// # Safety /// -/// If `fktable` does not point to a valid `FkTable` object, for example when `fktable` is a null +/// If `fktable` does not point to a valid `Grid` object, for example when `fktable` is a null /// pointer, this function is not safe to call. The parameter `filename` must be a non-`NULL`, /// non-empty, and valid C string pointing to a non-existing, but writable file. /// @@ -2289,17 +2289,9 @@ pub extern "C" fn pineappl_fk_table_delete(fktable: Option>) {} /// /// TODO #[no_mangle] -pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const FkTable, filename: *const c_char) { - let fktable = unsafe { &*fktable }; - let filename = unsafe { CStr::from_ptr(filename) }; - let filename = filename.to_string_lossy(); - let path = Path::new(filename.as_ref()); - let writer = File::create(path).unwrap(); - - if path.extension().is_some_and(|ext| ext == "lz4") { - fktable.grid().write_lz4(writer).unwrap(); - } else { - fktable.grid().write(writer).unwrap(); +pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const Grid, filename: *const c_char) { + unsafe { + pineappl_grid_write(fktable, filename); } } @@ -2307,55 +2299,43 @@ pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const FkTable, filenam /// /// # Safety /// -/// If `fktable` does not point to a valid `FkTable` object, for example when `fktable` is +/// If `fktable` does not point to a valid `Grid` object, for example when `fktable` is /// a null pointer, this function is not safe to call. The function pointer `xfx` must not /// be null pointers and point to valid functions. The parameter `channel_mask` must either /// be null pointers or point to arrays that are as long as `fktable` has channels, respectively. /// Finally, `results` must be as long as `FkTable` has bins. #[no_mangle] -pub unsafe extern "C" fn pineappl_fk_table_convolve( - fktable: *const FkTable, +pub unsafe extern "C" fn pineappl_fktable_convolve( + fktable: *const Grid, xfx: extern "C" fn(pdg_id: i32, x: f64, q2: f64, state: *mut c_void) -> f64, pdfs_state: *mut *mut c_void, channel_mask: *const bool, bin_indices: *const usize, + nb_scales: usize, + mu_scales: *const f64, results: *mut f64, ) { - let fktable = unsafe { &*fktable }; - - let channel_mask = if channel_mask.is_null() { - &[] - } else { - unsafe { slice::from_raw_parts(channel_mask, fktable.channels().len()) } - }; - - let bin_indices = if bin_indices.is_null() { - &[] - } else { - unsafe { slice::from_raw_parts(bin_indices, fktable.grid().bwfl().len()) } - }; - - // TODO: Better way to do this? - let mut als = |_| 1.0; - - let pdfs_slices = - unsafe { slice::from_raw_parts(pdfs_state, fktable.grid().convolutions().len()) }; - let mut xfx_funcs: Vec<_> = pdfs_slices - .iter() - .map(|&state| move |id, x, q2| xfx(id, x, q2, state)) - .collect(); - - // Construct the Convolution cache - let mut convolution_cache = ConvolutionCache::new( - fktable.grid().convolutions().to_vec(), - xfx_funcs - .iter_mut() - .map(|fx| fx as &mut dyn FnMut(i32, f64, f64) -> f64) - .collect(), - &mut als, - ); + // define a dummy `alphas` function with the expected C ABI and signatures + const extern "C" fn alphas(_q2: f64, _state: *mut c_void) -> f64 { + 1.0 + } - let results = unsafe { slice::from_raw_parts_mut(results, fktable.grid().bwfl().len()) }; + let order_mask = std::ptr::null(); + let alphas_state = std::ptr::null_mut(); - results.copy_from_slice(&fktable.convolve(&mut convolution_cache, bin_indices, channel_mask)); + unsafe { + pineappl_grid_convolve( + fktable, + xfx, + alphas, + pdfs_state, + alphas_state, + order_mask, + channel_mask, + bin_indices, + nb_scales, + mu_scales, + results, + ); + } } From c5f4f27b3ebc71cd79074035dffd92c99e09560f Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 3 Jun 2025 22:20:41 +0200 Subject: [PATCH 33/49] Address comments from Code Review --- examples/cpp/evolve-grid-identity.cpp | 59 +++++++------- examples/cpp/evolve-grid.cpp | 69 ++++++++-------- pineappl/src/convolutions.rs | 2 +- pineappl_capi/cbindgen.toml | 1 - pineappl_capi/src/lib.rs | 108 ++++++++------------------ 5 files changed, 101 insertions(+), 138 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index be6ec33e9..323b89fa3 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -25,30 +25,21 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } extern "C" void generate_fake_ekos( - const int* pids_in, - const double* x_in, - const int* pids_out, - const double* x_out, + const int* /*pids_in*/, + const double* /*x_in*/, + const int* /*pids_out*/, + const double* /*x_out*/, double* eko_buffer, void* params_state, - pineappl_conv_type conv_type, - double fac1, + pineappl_conv_type /*conv_type*/, + double /*fac1*/, std::size_t pids_in_len, std::size_t x_in_len, std::size_t pids_out_len, std::size_t x_out_len ) { - // Ignore unused variables - (void) pids_in; - (void) x_in; - (void) pids_out; - (void) x_out; - (void) conv_type; - (void) fac1; - // Check to get the μ0 of the PDF from the `params_state` - const double mu0_scale = static_cast (params_state)->q2Min(); - (void) mu0_scale; // Mark as unused variable + const double _ = static_cast (params_state)->q2Min(); std::size_t flat_len = pids_in_len * x_in_len * pids_out_len * x_out_len; // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) @@ -133,8 +124,12 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::vector max_orders = {2, 3}; - pineappl_grid_evolve_info_shape(grid, max_orders.data(), evinfo_shape.data()); + // NOTE: The argument of `pineappl_grid_evolve_info_shape` must follow the following orders: + // - `grid`: PineAPPL Grid + // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, + // `nullptr` selects all the orders + // - `evinfo_shape`: placeholder to store the shape of the Evolution Operator + pineappl_grid_evolve_info_shape(grid, nullptr, evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the // information on the `x`-grid and `PID` used to interpolate the Grid. @@ -144,7 +139,12 @@ int main() { std::vector pids_in(evinfo_shape[2]); std::vector x_in(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); - pineappl_grid_evolve_info(grid, max_orders.data(), fac1.data(), + // NOTE: The argument of `pineappl_grid_evolve_info` must follow the following orders: + // - `grid`: PineAPPL Grid + // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, + // `nullptr` selects all the orders + // The rest of the arguments are placeholders to store data + pineappl_grid_evolve_info(grid, nullptr, fac1.data(), frg1.data(), pids_in.data(), x_in.data(), ren1.data()); // ------------------ Construct the Operator Info ------------------ @@ -183,8 +183,10 @@ int main() { // - `grid`: PineAPPL Grid // - `op_info`: operator info // - `operator`: callback that returns an evolution operator - // - `max_orders`: max orders to apply the evolution + // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, + // `nullptr` selects all the orders // - `params_state`: parameters that get passed to `operator` + // - `nb_convolutions`: the number of convolutions/Evolution Operators required // - `x_in`: x-grid of the Grid // - `x_out`: x-grid of the FK table // - `pids_in`: PIDs basis representation of the Grid @@ -193,10 +195,11 @@ int main() { // - `xi`: scale variation // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales - pineappl_fktable* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - generate_fake_ekos, max_orders.data(), pdf.get(), x_in.data(), - x_in.data(), pids_in.data(), pids_out.data(), - tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); + pineappl_grid* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), + generate_fake_ekos, nullptr, pdf.get(), + conv_types.size(), x_in.data(), x_in.data(), + pids_in.data(), pids_out.data(), tensor_shape.data(), + xi.data(), ren1.data(), alphas_table.data()); // ------------------ Compare Grid & FK after convolution ------------------ // how many bins does this grid have? @@ -211,13 +214,15 @@ int main() { // [ convolve the FK Table ] std::vector dxsec_fktable(bins); - pineappl_fktable_convolve(fktable, xfx, pdf_states, nullptr, - nullptr, 1, nullptr, dxsec_fktable.data()); + auto as_one = [](double /*q2*/, void* /*pdf*/) { return 1.0; }; + pineappl_grid_convolve(fktable, xfx, as_one, pdf_states, nullptr, + nullptr, nullptr, nullptr, 1, + mu_scales.data(), dxsec_fktable.data()); // Print the results print_results(dxsec_grid, dxsec_fktable); - pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); + pineappl_fktable_write(fktable, "evolved-grid-identity.pineappl.lz4"); pineappl_grid_delete(grid); pineappl_fktable_delete(fktable); diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index bf17e81e0..3efdf0cfa 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -83,34 +83,21 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } extern "C" void generate_fake_ekos( - const int* pids_in, - const double* x_in, - const int* pids_out, - const double* x_out, + const int* /*pids_in*/, + const double* /*x_in*/, + const int* /*pids_out*/, + const double* /*x_out*/, double* eko_buffer, void* params_state, - pineappl_conv_type conv_type, - double fac1, - std::size_t pids_in_len, - std::size_t x_in_len, - std::size_t pids_out_len, - std::size_t x_out_len + pineappl_conv_type /*conv_type*/, + double /*fac1*/, + std::size_t /*pids_in_len*/, + std::size_t /*x_in_len*/, + std::size_t /*pids_out_len*/, + std::size_t /*x_out_len*/ ) { - // Ignore unused variables - (void) pids_in; - (void) x_in; - (void) pids_out; - (void) x_out; - (void) conv_type; - (void) pids_in_len; - (void) x_in_len; - (void) pids_out_len; - (void) x_out_len; - (void) fac1; - // Check to get the μ0 from the PDF - const double mu0_scale = static_cast (params_state)->q2Min(); - (void) mu0_scale; // Mark as unused variable + const double _ = static_cast (params_state)->q2Min(); std::ifstream input_file("../../test-data/EKO_LHCB_WP_7TEV.txt"); double weight_value; @@ -191,8 +178,12 @@ int main() { // Get the shape of the evolve info objects std::vector evinfo_shape(5); - std::vector max_orders = {2, 3}; - pineappl_grid_evolve_info_shape(grid, max_orders.data(), evinfo_shape.data()); + // NOTE: The argument of `pineappl_grid_evolve_info_shape` must follow the following orders: + // - `grid`: PineAPPL Grid + // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, + // `nullptr` selects all the orders + // - `evinfo_shape`: placeholder to store the shape of the Evolution Operator + pineappl_grid_evolve_info_shape(grid, nullptr, evinfo_shape.data()); // Get the values of the evolve info parameters. These contain, for example, the // information on the `x`-grid and `PID` used to interpolate the Grid. @@ -202,7 +193,12 @@ int main() { std::vector _pids_in(evinfo_shape[2]); std::vector _x_in(evinfo_shape[3]); std::vector ren1(evinfo_shape[4]); - pineappl_grid_evolve_info(grid, max_orders.data(), fac1.data(), + // NOTE: The argument of `pineappl_grid_evolve_info` must follow the following orders: + // - `grid`: PineAPPL Grid + // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, + // `nullptr` selects all the orders + // The rest of the arguments are placeholders to store data + pineappl_grid_evolve_info(grid, nullptr, fac1.data(), frg1.data(), _pids_in.data(), _x_in.data(), ren1.data()); // ------------------ Construct the Operator Info ------------------ @@ -241,8 +237,10 @@ int main() { // - `grid`: PineAPPL Grid // - `op_info`: operator info // - `operator`: callback that returns an evolution operator - // - `max_orders`: max orders to apply the evolution + // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, + // `nullptr` selects all the orders // - `params_state`: parameters that get passed to `operator` + // - `nb_convolutions`: the number of convolutions/Evolution Operators required // - `x_in`: x-grid of the Grid // - `x_out`: x-grid of the FK table // - `pids_in`: PIDs basis representation of the Grid @@ -251,10 +249,11 @@ int main() { // - `xi`: scale variation // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales - pineappl_fktable* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - generate_fake_ekos, max_orders.data(), pdf.get(), XGRID.data(), - XGRID.data(), pids_in.data(), pids_out.data(), - tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); + pineappl_grid* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), + generate_fake_ekos, nullptr, pdf.get(), + conv_types.size(), XGRID.data(), XGRID.data(), + pids_in.data(), pids_out.data(), tensor_shape.data(), + xi.data(), ren1.data(), alphas_table.data()); // ------------------ Compare Grid & FK after convolution ------------------ // how many bins does this grid have? @@ -269,8 +268,10 @@ int main() { // [ convolve the FK Table ] std::vector dxsec_fktable(bins); - pineappl_fktable_convolve(fktable, xfx, pdf_states, nullptr, - nullptr, 1, nullptr, dxsec_fktable.data()); + auto as_one = [](double /*q2*/, void* /*pdf*/) { return 1.0; }; + pineappl_grid_convolve(fktable, xfx, as_one, pdf_states, nullptr, + nullptr, nullptr, nullptr, 1, + mu_scales.data(), dxsec_fktable.data()); // Print the results print_results(dxsec_grid, dxsec_fktable); diff --git a/pineappl/src/convolutions.rs b/pineappl/src/convolutions.rs index b3503ab64..331f76020 100644 --- a/pineappl/src/convolutions.rs +++ b/pineappl/src/convolutions.rs @@ -282,7 +282,7 @@ impl GridConvCache<'_, '_> { /// TODO #[repr(C)] -#[derive(Clone, Copy, Debug, Deserialize, Eq, PartialEq, Serialize, Hash)] +#[derive(Clone, Copy, Debug, Deserialize, Eq, PartialEq, Serialize)] pub enum ConvType { /// Unpolarized parton distribution function. UnpolPDF, diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index 731d4869a..84210f0f1 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -38,7 +38,6 @@ rename_variants = "ScreamingSnakeCase" "Channels" = "pineappl_channels" "Conv" = "pineappl_conv" "ConvType" = "pineappl_conv_type" -"FkTable" = "pineappl_fktable" "Grid" = "pineappl_grid" "GridOptFlags" = "pineappl_gof" "Interp" = "pineappl_interp" diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index bdf6f9599..d4f313cb8 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -60,14 +60,12 @@ use ndarray::{Array4, CowArray, Ix4}; use pineappl::boc::{Bin, BinsWithFillLimits, Channel, Kinematics, Order, ScaleFuncForm, Scales}; use pineappl::convolutions::{Conv, ConvType, ConvolutionCache}; use pineappl::evolution::{AlphasTable, OperatorSliceInfo}; -use pineappl::fk_table::FkTable; use pineappl::grid::{Grid, GridOptFlags}; use pineappl::interpolation::{Interp as InterpMain, InterpMeth, Map, ReweightMeth}; use pineappl::packed_array::ravel_multi_index; use pineappl::pids::PidBasis; use pineappl::subgrid::Subgrid; use std::collections::HashMap; -use std::collections::HashSet; use std::ffi::{CStr, CString}; use std::fs::File; use std::mem; @@ -2069,16 +2067,20 @@ pub unsafe extern "C" fn pineappl_grid_subgrid_array( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( grid: *const Grid, - orders: *const u8, + order_mask: *const bool, shape_info: *mut usize, ) { let grid = unsafe { &*grid }; - let orders = unsafe { slice::from_raw_parts(orders, 2) }; - let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); + let order_mask = if order_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } + }; + let shape_info = unsafe { slice::from_raw_parts_mut(shape_info, 5) }; - let evolve_info = grid.evolve_info(&order_mask); + let evolve_info = grid.evolve_info(order_mask); let evinfo_shapes = [ evolve_info.fac1.len(), evolve_info.frg1.len(), @@ -2099,7 +2101,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info_shape( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve_info( grid: *const Grid, - orders: *const u8, + order_mask: *const bool, fac1: *mut f64, frg1: *mut f64, pids1: *mut i32, @@ -2108,21 +2110,24 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( ) { let grid = unsafe { &*grid }; - let orders = unsafe { slice::from_raw_parts(orders, 2) }; - let order_mask = Order::create_mask(grid.orders(), orders[0], orders[1], true); + let order_mask = if order_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } + }; - let evolve_info = grid.evolve_info(&order_mask); + let evolve_info = grid.evolve_info(order_mask); let fac1 = unsafe { slice::from_raw_parts_mut(fac1, evolve_info.fac1.len()) }; let frg1 = unsafe { slice::from_raw_parts_mut(frg1, evolve_info.frg1.len()) }; let pids1 = unsafe { slice::from_raw_parts_mut(pids1, evolve_info.pids1.len()) }; let x1 = unsafe { slice::from_raw_parts_mut(x1, evolve_info.x1.len()) }; let ren1 = unsafe { slice::from_raw_parts_mut(ren1, evolve_info.ren1.len()) }; - fac1.copy_from_slice(&grid.evolve_info(&order_mask).fac1); - frg1.copy_from_slice(&grid.evolve_info(&order_mask).frg1); - pids1.copy_from_slice(&grid.evolve_info(&order_mask).pids1); - x1.copy_from_slice(&grid.evolve_info(&order_mask).x1); - ren1.copy_from_slice(&grid.evolve_info(&order_mask).ren1); + fac1.copy_from_slice(&grid.evolve_info(order_mask).fac1); + frg1.copy_from_slice(&grid.evolve_info(order_mask).frg1); + pids1.copy_from_slice(&grid.evolve_info(order_mask).pids1); + x1.copy_from_slice(&grid.evolve_info(order_mask).x1); + ren1.copy_from_slice(&grid.evolve_info(order_mask).ren1); } /// Type alias for the operator callback @@ -2175,8 +2180,9 @@ pub unsafe extern "C" fn pineappl_grid_evolve( grid: *mut Grid, operator_info: *mut OperatorInfo, operator: OperatorCallback, - max_orders: *const u8, + order_mask: *const bool, params_state: *mut c_void, + nb_convolutions: usize, x_in: *const f64, x_out: *const f64, pids_in: *const i32, @@ -2188,29 +2194,26 @@ pub unsafe extern "C" fn pineappl_grid_evolve( ) -> Box { let grid = unsafe { &mut *grid }; - let max_orders = unsafe { slice::from_raw_parts(max_orders, 2) }; + let order_mask = if order_mask.is_null() { + &[] + } else { + unsafe { slice::from_raw_parts(order_mask, grid.orders().len()) } + }; + let eko_shape = unsafe { slice::from_raw_parts(eko_shape, 4) }; let pids_in = unsafe { slice::from_raw_parts(pids_in, eko_shape[0]) }; let x_in = unsafe { slice::from_raw_parts(x_in, eko_shape[1]) }; let pids_out = unsafe { slice::from_raw_parts(pids_out, eko_shape[2]) }; let x_out = unsafe { slice::from_raw_parts(x_out, eko_shape[3]) }; - let order_mask = Order::create_mask(grid.orders(), max_orders[0], max_orders[1], true); - let evolve_info = grid.evolve_info(&order_mask); - + let evolve_info = grid.evolve_info(order_mask); let ren1_len = evolve_info.ren1.len(); let ren1 = unsafe { slice::from_raw_parts(ren1, ren1_len) }; let alphas = unsafe { slice::from_raw_parts(alphas, ren1_len) }; let xi = unsafe { slice::from_raw_parts(xi, 3) }; - let conv_types: HashSet<_> = grid - .convolutions() - .iter() - .map(pineappl::convolutions::Conv::conv_type) - .collect(); - let operator_info = unsafe { - slice::from_raw_parts(operator_info, conv_types.len() * evolve_info.fac1.len()) + slice::from_raw_parts(operator_info, nb_convolutions * evolve_info.fac1.len()) .chunks_exact(evolve_info.fac1.len()) }; let total_shape: usize = eko_shape.iter().product(); @@ -2260,7 +2263,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let fk_table = grid.evolve( slices, - &order_mask, + order_mask, (xi[0], xi[1], xi[2]), &AlphasTable { ren1: ren1.to_vec(), @@ -2268,13 +2271,13 @@ pub unsafe extern "C" fn pineappl_grid_evolve( }, ); - Box::new(fk_table.unwrap().grid().clone()) + Box::new(fk_table.unwrap().into_grid()) } /// Delete an FK table. #[no_mangle] #[allow(unused_variables)] -pub extern "C" fn pineappl_fktable_delete(fktable: Option>) {} +pub extern "C" fn pineappl_fktable_delete(fktable: Option>) {} /// Write `fktable` to a file with name `filename`. If `filename` ends in `.lz4` the Fk table is /// automatically LZ4 compressed. @@ -2294,48 +2297,3 @@ pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const Grid, filename: pineappl_grid_write(fktable, filename); } } - -/// A generalization of the convolution function for FK tables. -/// -/// # Safety -/// -/// If `fktable` does not point to a valid `Grid` object, for example when `fktable` is -/// a null pointer, this function is not safe to call. The function pointer `xfx` must not -/// be null pointers and point to valid functions. The parameter `channel_mask` must either -/// be null pointers or point to arrays that are as long as `fktable` has channels, respectively. -/// Finally, `results` must be as long as `FkTable` has bins. -#[no_mangle] -pub unsafe extern "C" fn pineappl_fktable_convolve( - fktable: *const Grid, - xfx: extern "C" fn(pdg_id: i32, x: f64, q2: f64, state: *mut c_void) -> f64, - pdfs_state: *mut *mut c_void, - channel_mask: *const bool, - bin_indices: *const usize, - nb_scales: usize, - mu_scales: *const f64, - results: *mut f64, -) { - // define a dummy `alphas` function with the expected C ABI and signatures - const extern "C" fn alphas(_q2: f64, _state: *mut c_void) -> f64 { - 1.0 - } - - let order_mask = std::ptr::null(); - let alphas_state = std::ptr::null_mut(); - - unsafe { - pineappl_grid_convolve( - fktable, - xfx, - alphas, - pdfs_state, - alphas_state, - order_mask, - channel_mask, - bin_indices, - nb_scales, - mu_scales, - results, - ); - } -} From 8593c86cc611309c90052604aa824f6ce45e504c Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 3 Jun 2025 22:26:57 +0200 Subject: [PATCH 34/49] Add remaining changes from Code Review --- examples/cpp/evolve-grid-identity.cpp | 4 ++-- examples/cpp/evolve-grid.cpp | 4 ++-- pineappl_capi/src/lib.rs | 24 ------------------------ 3 files changed, 4 insertions(+), 28 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 323b89fa3..834f01391 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -222,8 +222,8 @@ int main() { // Print the results print_results(dxsec_grid, dxsec_fktable); - pineappl_fktable_write(fktable, "evolved-grid-identity.pineappl.lz4"); + pineappl_grid_write(fktable, "evolved-grid-identity.pineappl.lz4"); pineappl_grid_delete(grid); - pineappl_fktable_delete(fktable); + pineappl_grid_delete(fktable); } diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 3efdf0cfa..ece9c0d05 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -276,8 +276,8 @@ int main() { // Print the results print_results(dxsec_grid, dxsec_fktable); - pineappl_fktable_write(fktable, "evolved-grid.pineappl.lz4"); + pineappl_grid_write(fktable, "evolved-grid.pineappl.lz4"); pineappl_grid_delete(grid); - pineappl_fktable_delete(fktable); + pineappl_grid_delete(fktable); } diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index d4f313cb8..6d42ea9b0 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2273,27 +2273,3 @@ pub unsafe extern "C" fn pineappl_grid_evolve( Box::new(fk_table.unwrap().into_grid()) } - -/// Delete an FK table. -#[no_mangle] -#[allow(unused_variables)] -pub extern "C" fn pineappl_fktable_delete(fktable: Option>) {} - -/// Write `fktable` to a file with name `filename`. If `filename` ends in `.lz4` the Fk table is -/// automatically LZ4 compressed. -/// -/// # Safety -/// -/// If `fktable` does not point to a valid `Grid` object, for example when `fktable` is a null -/// pointer, this function is not safe to call. The parameter `filename` must be a non-`NULL`, -/// non-empty, and valid C string pointing to a non-existing, but writable file. -/// -/// # Panics -/// -/// TODO -#[no_mangle] -pub unsafe extern "C" fn pineappl_fktable_write(fktable: *const Grid, filename: *const c_char) { - unsafe { - pineappl_grid_write(fktable, filename); - } -} From 7aa2928e098cad65ab088861b5e4d0f020e4f3ec Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 4 Jun 2025 22:06:25 +0200 Subject: [PATCH 35/49] Add a function to optimize FK tables in the C-API --- examples/cpp/evolve-grid.cpp | 5 +++++ pineappl/src/fk_table.rs | 1 + pineappl_capi/cbindgen.toml | 2 ++ pineappl_capi/src/lib.rs | 22 ++++++++++++++++++++++ 4 files changed, 30 insertions(+) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index ece9c0d05..a8a27d0ca 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -276,8 +276,13 @@ int main() { // Print the results print_results(dxsec_grid, dxsec_fktable); + // write the unoptimised FK table into disk pineappl_grid_write(fktable, "evolved-grid.pineappl.lz4"); + // optimise the FK table and then write into disk + pineappl_fktable* fktable_opt = pineappl_fktable_optimize(fktable, PINEAPPL_FK_ASSUMPTIONS_NF3_SYM); + pineappl_grid_write(fktable_opt, "evolved-grid-optimised.pineappl.lz4"); + pineappl_grid_delete(grid); pineappl_grid_delete(fktable); } diff --git a/pineappl/src/fk_table.rs b/pineappl/src/fk_table.rs index 437fcc4fa..4a9c63505 100644 --- a/pineappl/src/fk_table.rs +++ b/pineappl/src/fk_table.rs @@ -31,6 +31,7 @@ pub struct FkTable { /// tables are typically stored at very small `Q2 = Q0`, the PDFs `f(x,Q0)` of heavy quarks are /// typically set to zero at this scale or set to the same value as their anti-quark PDF. This is /// used to optimize the size of FK tables. +#[repr(C)] #[derive(Debug, Clone, Copy, Eq, PartialEq)] pub enum FkAssumptions { /// All quark PDFs are non-zero at the FK table scale and completely independent. diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index 84210f0f1..ea22a2599 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -38,6 +38,8 @@ rename_variants = "ScreamingSnakeCase" "Channels" = "pineappl_channels" "Conv" = "pineappl_conv" "ConvType" = "pineappl_conv_type" +"FkAssumptions" = "pineappl_fk_assumptions" +"FkTable" = "pineappl_fktable" "Grid" = "pineappl_grid" "GridOptFlags" = "pineappl_gof" "Interp" = "pineappl_interp" diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 6d42ea9b0..dd7ef0166 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -60,6 +60,7 @@ use ndarray::{Array4, CowArray, Ix4}; use pineappl::boc::{Bin, BinsWithFillLimits, Channel, Kinematics, Order, ScaleFuncForm, Scales}; use pineappl::convolutions::{Conv, ConvType, ConvolutionCache}; use pineappl::evolution::{AlphasTable, OperatorSliceInfo}; +use pineappl::fk_table::{FkAssumptions, FkTable}; use pineappl::grid::{Grid, GridOptFlags}; use pineappl::interpolation::{Interp as InterpMain, InterpMeth, Map, ReweightMeth}; use pineappl::packed_array::ravel_multi_index; @@ -2273,3 +2274,24 @@ pub unsafe extern "C" fn pineappl_grid_evolve( Box::new(fk_table.unwrap().into_grid()) } + +/// Optimize the size of this FK-table by removing heavy quark flavors assumed to be zero. +/// +/// # Safety +/// +/// If `grid` does not point to a valid `Grid` object, for example when `grid` is the null pointer, +/// this function is not safe to call. +/// +/// # Panics +/// +/// This function panics if `grid` is not an FK table-like object. +#[no_mangle] +pub unsafe extern "C" fn pineappl_fktable_optimize( + grid: *mut Grid, + assumptions: FkAssumptions, +) -> Box { + let grid = unsafe { &mut *grid }; + let mut fktable = FkTable::try_from(grid.clone()).unwrap(); + fktable.optimize(assumptions); + Box::new(fktable) +} From 22f5e4030533f6fb6d9f82fc726ada4b37f99036 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Thu, 5 Jun 2025 00:17:34 +0200 Subject: [PATCH 36/49] Steal pointer in `pineappl_fktable_optimize` instead of returning `FkTable` --- examples/cpp/evolve-grid.cpp | 4 ++-- pineappl_capi/src/lib.rs | 7 ++----- 2 files changed, 4 insertions(+), 7 deletions(-) diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index a8a27d0ca..4e2ad7ca4 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -280,8 +280,8 @@ int main() { pineappl_grid_write(fktable, "evolved-grid.pineappl.lz4"); // optimise the FK table and then write into disk - pineappl_fktable* fktable_opt = pineappl_fktable_optimize(fktable, PINEAPPL_FK_ASSUMPTIONS_NF3_SYM); - pineappl_grid_write(fktable_opt, "evolved-grid-optimised.pineappl.lz4"); + pineappl_fktable_optimize(fktable, PINEAPPL_FK_ASSUMPTIONS_NF3_SYM); + pineappl_grid_write(fktable, "evolved-grid-optimised.pineappl.lz4"); pineappl_grid_delete(grid); pineappl_grid_delete(fktable); diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index dd7ef0166..4e5f32dce 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2286,12 +2286,9 @@ pub unsafe extern "C" fn pineappl_grid_evolve( /// /// This function panics if `grid` is not an FK table-like object. #[no_mangle] -pub unsafe extern "C" fn pineappl_fktable_optimize( - grid: *mut Grid, - assumptions: FkAssumptions, -) -> Box { +pub unsafe extern "C" fn pineappl_fktable_optimize(grid: *mut Grid, assumptions: FkAssumptions) { let grid = unsafe { &mut *grid }; let mut fktable = FkTable::try_from(grid.clone()).unwrap(); fktable.optimize(assumptions); - Box::new(fktable) + unsafe { std::ptr::replace(grid, fktable.into_grid()) }; } From e90e0975a872d464afc03364207e0d348804d9a8 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Thu, 5 Jun 2025 17:48:02 +0200 Subject: [PATCH 37/49] Use `std::ptr::{read, write}` to avoid copies i `pineappl_fktable_optimize` of F-API --- pineappl_capi/src/lib.rs | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 4e5f32dce..59e03916d 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2288,7 +2288,8 @@ pub unsafe extern "C" fn pineappl_grid_evolve( #[no_mangle] pub unsafe extern "C" fn pineappl_fktable_optimize(grid: *mut Grid, assumptions: FkAssumptions) { let grid = unsafe { &mut *grid }; - let mut fktable = FkTable::try_from(grid.clone()).unwrap(); + let read_grid = unsafe { std::ptr::read(grid) }; + let mut fktable = FkTable::try_from(read_grid).unwrap(); fktable.optimize(assumptions); - unsafe { std::ptr::replace(grid, fktable.into_grid()) }; + unsafe { std::ptr::write(grid, fktable.into_grid()) }; } From 2af90959084e9c3d8d7ffdc0c8a965cae3a2b7cd Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 10:27:52 +0200 Subject: [PATCH 38/49] Make more arguments of `pineappl_grid_evolve` constant --- pineappl_capi/src/lib.rs | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 59e03916d..9b7fb48d0 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2178,8 +2178,8 @@ type OperatorCallback = extern "C" fn( /// with the `Grid`. #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve( - grid: *mut Grid, - operator_info: *mut OperatorInfo, + grid: *const Grid, + operator_info: *const OperatorInfo, operator: OperatorCallback, order_mask: *const bool, params_state: *mut c_void, @@ -2193,7 +2193,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( ren1: *const f64, alphas: *const f64, ) -> Box { - let grid = unsafe { &mut *grid }; + let grid = unsafe { &*grid }; let order_mask = if order_mask.is_null() { &[] From aeaf47cd927eb3a48626342d9baf930a01842f6c Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 10:33:35 +0200 Subject: [PATCH 39/49] Rename callback function type --- pineappl_capi/cbindgen.toml | 1 + 1 file changed, 1 insertion(+) diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index ea22a2599..90f71bcdb 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -48,6 +48,7 @@ rename_variants = "ScreamingSnakeCase" "Kinematics" = "pineappl_kinematics" "Lumi" = "pineappl_lumi" "Map" = "pineappl_map" +"OperatorCallback" = "pineappl_operator_callback" "OperatorInfo" = "pineappl_operator_info" "PidBasis" = "pineappl_pid_basis" "ReweightMeth" = "pineappl_reweight_meth" From 7aa969f4f2e067417aa51952e3db7bf00774aa63 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 10:59:42 +0200 Subject: [PATCH 40/49] Avoid copying large buffer in `pineappl_grid_evolve` --- pineappl_capi/src/lib.rs | 28 +++++++++++++++------------- 1 file changed, 15 insertions(+), 13 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 9b7fb48d0..a871fbe78 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -56,7 +56,7 @@ //! [translation tables]: https://github.com/eqrion/cbindgen/blob/master/docs.md#std-types use itertools::izip; -use ndarray::{Array4, CowArray, Ix4}; +use ndarray::{Array4, CowArray}; use pineappl::boc::{Bin, BinsWithFillLimits, Channel, Kinematics, Order, ScaleFuncForm, Scales}; use pineappl::convolutions::{Conv, ConvType, ConvolutionCache}; use pineappl::evolution::{AlphasTable, OperatorSliceInfo}; @@ -2217,7 +2217,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve( slice::from_raw_parts(operator_info, nb_convolutions * evolve_info.fac1.len()) .chunks_exact(evolve_info.fac1.len()) }; - let total_shape: usize = eko_shape.iter().product(); + + let shape: (usize, usize, usize, usize) = <[usize; 4]>::try_from(eko_shape) + // UNWRAP: guaranteed to work since `eko_shape` is exactly 4 elements long + .unwrap() + .into(); let slices = operator_info .map(|op_infos| { @@ -2233,15 +2237,18 @@ pub unsafe extern "C" fn pineappl_grid_evolve( conv_type: op_info.conv_type, }; - // Let Rust manages the memory by allocating a flat vector of zeros as a placeholder - // to hold the evolution operator data. - let mut eko_slice = vec![0.0; total_shape]; + let mut array = CowArray::from(Array4::zeros(shape)); + operator( pids_in.as_ptr(), x_in.as_ptr(), pids_out.as_ptr(), x_out.as_ptr(), - eko_slice.as_mut_ptr(), + array + .as_slice_mut() + // UNWRAP: `array` is by construction contiguous and in standard order + .unwrap() + .as_mut_ptr(), params_state, op_info.conv_type, op_info.fac1, @@ -2251,13 +2258,8 @@ pub unsafe extern "C" fn pineappl_grid_evolve( x_out.len(), ); - let array = Array4::from_shape_vec( - Ix4(eko_shape[0], eko_shape[1], eko_shape[2], eko_shape[3]), - eko_slice, - ) - .unwrap(); - - Ok::<_, std::io::Error>((operator_slice_info, CowArray::from(array))) + // we specify an arbitrary error type since we don't return an error anywhere + Ok::<_, std::io::Error>((operator_slice_info, array)) }) }) .collect(); From efcdf83c6228f6b0c137f3e31871c7a3642f6cd0 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 11:06:19 +0200 Subject: [PATCH 41/49] Make `OperatorCallback` public and unsafe --- pineappl_capi/src/lib.rs | 40 +++++++++++++++++++++------------------- 1 file changed, 21 insertions(+), 19 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index a871fbe78..1a32d069f 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2132,7 +2132,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( } /// Type alias for the operator callback -type OperatorCallback = extern "C" fn( +pub type OperatorCallback = unsafe extern "C" fn( *const i32, // pids_in *const f64, // x_in *const i32, // pids_out @@ -2239,24 +2239,26 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let mut array = CowArray::from(Array4::zeros(shape)); - operator( - pids_in.as_ptr(), - x_in.as_ptr(), - pids_out.as_ptr(), - x_out.as_ptr(), - array - .as_slice_mut() - // UNWRAP: `array` is by construction contiguous and in standard order - .unwrap() - .as_mut_ptr(), - params_state, - op_info.conv_type, - op_info.fac1, - pids_in.len(), - x_in.len(), - pids_out.len(), - x_out.len(), - ); + unsafe { + operator( + pids_in.as_ptr(), + x_in.as_ptr(), + pids_out.as_ptr(), + x_out.as_ptr(), + array + .as_slice_mut() + // UNWRAP: `array` is by construction contiguous and in standard order + .unwrap() + .as_mut_ptr(), + params_state, + op_info.conv_type, + op_info.fac1, + pids_in.len(), + x_in.len(), + pids_out.len(), + x_out.len(), + ); + } // we specify an arbitrary error type since we don't return an error anywhere Ok::<_, std::io::Error>((operator_slice_info, array)) From 7ffc08613ba444a89362b81db97184d88e35a7c1 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 11:12:44 +0200 Subject: [PATCH 42/49] Move and document `unwrap` at the right place --- pineappl_capi/src/lib.rs | 25 ++++++++++++++----------- 1 file changed, 14 insertions(+), 11 deletions(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 1a32d069f..66600e8fb 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2266,17 +2266,20 @@ pub unsafe extern "C" fn pineappl_grid_evolve( }) .collect(); - let fk_table = grid.evolve( - slices, - order_mask, - (xi[0], xi[1], xi[2]), - &AlphasTable { - ren1: ren1.to_vec(), - alphas: alphas.to_vec(), - }, - ); - - Box::new(fk_table.unwrap().into_grid()) + let fk_table = grid + .evolve( + slices, + order_mask, + (xi[0], xi[1], xi[2]), + &AlphasTable { + ren1: ren1.to_vec(), + alphas: alphas.to_vec(), + }, + ) + // UNWRAP: error handling in the CAPI is to abort + .unwrap(); + + Box::new(fk_table.into_grid()) } /// Optimize the size of this FK-table by removing heavy quark flavors assumed to be zero. From 093993b6c88aee70e9c261f4d212631ac93d7cf7 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 11:13:22 +0200 Subject: [PATCH 43/49] Add some comments to `pineappl_fktable_optimize` --- pineappl_capi/src/lib.rs | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 66600e8fb..793fad268 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2295,8 +2295,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve( #[no_mangle] pub unsafe extern "C" fn pineappl_fktable_optimize(grid: *mut Grid, assumptions: FkAssumptions) { let grid = unsafe { &mut *grid }; + // SAFETY: this code has been copied from the `take_mut` crate let read_grid = unsafe { std::ptr::read(grid) }; - let mut fktable = FkTable::try_from(read_grid).unwrap(); + let mut fktable = FkTable::try_from(read_grid) + // UNWRAP: error handling in the CAPI is to abort + .unwrap(); fktable.optimize(assumptions); unsafe { std::ptr::write(grid, fktable.into_grid()) }; } From 178866ed59522038d36c5d22c61dd80436ee31a8 Mon Sep 17 00:00:00 2001 From: Christopher Schwan Date: Sat, 7 Jun 2025 13:43:44 +0200 Subject: [PATCH 44/49] Remove `FkTable` from `[export.rename]` --- pineappl_capi/cbindgen.toml | 1 - 1 file changed, 1 deletion(-) diff --git a/pineappl_capi/cbindgen.toml b/pineappl_capi/cbindgen.toml index 90f71bcdb..61ba6a882 100644 --- a/pineappl_capi/cbindgen.toml +++ b/pineappl_capi/cbindgen.toml @@ -39,7 +39,6 @@ rename_variants = "ScreamingSnakeCase" "Conv" = "pineappl_conv" "ConvType" = "pineappl_conv_type" "FkAssumptions" = "pineappl_fk_assumptions" -"FkTable" = "pineappl_fktable" "Grid" = "pineappl_grid" "GridOptFlags" = "pineappl_gof" "Interp" = "pineappl_interp" From 81b17b8e069bb5127f31a352d823114da51de4c8 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Mon, 9 Jun 2025 12:17:37 +0200 Subject: [PATCH 45/49] Change `pineappl_grid_conv_type` to return an array --- examples/cpp/evolve-grid-identity.cpp | 24 +++++++++++++----------- examples/cpp/evolve-grid.cpp | 24 +++++++++++++----------- pineappl_capi/src/lib.rs | 14 ++++++++++---- 3 files changed, 36 insertions(+), 26 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 834f01391..31043ce53 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -109,16 +109,18 @@ int main() { pineappl_pid_basis pid_basis = pineappl_grid_pid_basis(grid); assert(pid_basis == PINEAPPL_PID_BASIS_PDG); - // Get the number of convolutions + // Get the number of convolutions and their types std::size_t n_convs = pineappl_grid_convolutions_len(grid); + std::vector conv_types(n_convs); + pineappl_grid_conv_types(grid, conv_types.data()); - // Fill the vector of unique convolution types. If the EKOs required for the Grid - // are the same, then it suffices to only pass ONE single EKO. - std::vector conv_types; + // Fill the vector of unique convolution types. If the Operators required for the Grid + // are the same, then it suffices to only pass ONE single Operator. + std::vector unique_convs; for (std::size_t i = 0; i != n_convs; i++) { - pineappl_conv_type conv = pineappl_grid_conv_type(grid, i); - if (std::find(conv_types.begin(), conv_types.end(), conv) == conv_types.end()) { - conv_types.push_back(conv); + pineappl_conv_type conv = conv_types[i]; + if (std::find(unique_convs.begin(), unique_convs.end(), conv) == unique_convs.end()) { + unique_convs.push_back(conv); } } @@ -150,14 +152,14 @@ int main() { // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose // elements are `OperatorInfo` objects. - std::vector opinfo_slices(conv_types.size() * fac1.size()); - for (std::size_t i = 0; i != conv_types.size(); i++) { + std::vector opinfo_slices(unique_convs.size() * fac1.size()); + for (std::size_t i = 0; i != unique_convs.size(); i++) { for (std::size_t j = 0; j != fac1.size(); j++) { pineappl_operator_info opinfo = { FAC0, // fac0 fac1[j], // fac1 pid_basis, - conv_types[i], + unique_convs[i], }; opinfo_slices[i * fac1.size() + j] = opinfo; } @@ -197,7 +199,7 @@ int main() { // - `alphas_table`: values of alphas for each renormalization scales pineappl_grid* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), generate_fake_ekos, nullptr, pdf.get(), - conv_types.size(), x_in.data(), x_in.data(), + unique_convs.size(), x_in.data(), x_in.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 4e2ad7ca4..8662ef8f7 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -163,16 +163,18 @@ int main() { pineappl_pid_basis pid_basis = pineappl_grid_pid_basis(grid); assert(pid_basis == PINEAPPL_PID_BASIS_PDG); - // Get the number of convolutions + // Get the number of convolutions and their types std::size_t n_convs = pineappl_grid_convolutions_len(grid); + std::vector conv_types(n_convs); + pineappl_grid_conv_types(grid, conv_types.data()); - // Fill the vector of unique convolution types. If the EKOs required for the Grid - // are the same, then it suffices to only pass ONE single EKO. - std::vector conv_types; + // Fill the vector of unique convolution types. If the Operators required for the Grid + // are the same, then it suffices to only pass ONE single Operator. + std::vector unique_convs; for (std::size_t i = 0; i != n_convs; i++) { - pineappl_conv_type conv = pineappl_grid_conv_type(grid, i); - if (std::find(conv_types.begin(), conv_types.end(), conv) == conv_types.end()) { - conv_types.push_back(conv); + pineappl_conv_type conv = conv_types[i]; + if (std::find(unique_convs.begin(), unique_convs.end(), conv) == unique_convs.end()) { + unique_convs.push_back(conv); } } @@ -204,14 +206,14 @@ int main() { // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose // elements are `OperatorInfo` objects. - std::vector opinfo_slices(conv_types.size() * fac1.size()); - for (std::size_t i = 0; i != conv_types.size(); i++) { + std::vector opinfo_slices(unique_convs.size() * fac1.size()); + for (std::size_t i = 0; i != unique_convs.size(); i++) { for (std::size_t j = 0; j != fac1.size(); j++) { pineappl_operator_info opinfo = { FAC0, // fac0 fac1[j], // fac1 pid_basis, - conv_types[i], + unique_convs[i], }; opinfo_slices[i * fac1.size() + j] = opinfo; } @@ -251,7 +253,7 @@ int main() { // - `alphas_table`: values of alphas for each renormalization scales pineappl_grid* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), generate_fake_ekos, nullptr, pdf.get(), - conv_types.size(), XGRID.data(), XGRID.data(), + unique_convs.size(), XGRID.data(), XGRID.data(), pids_in.data(), pids_out.data(), tensor_shape.data(), xi.data(), ren1.data(), alphas_table.data()); diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 793fad268..66dba6124 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -55,7 +55,7 @@ //! //! [translation tables]: https://github.com/eqrion/cbindgen/blob/master/docs.md#std-types -use itertools::izip; +use itertools::{izip, Itertools}; use ndarray::{Array4, CowArray}; use pineappl::boc::{Bin, BinsWithFillLimits, Channel, Kinematics, Order, ScaleFuncForm, Scales}; use pineappl::convolutions::{Conv, ConvType, ConvolutionCache}; @@ -1939,16 +1939,22 @@ pub unsafe extern "C" fn pineappl_grid_convolve( )); } -/// Get the type of convolutions for this Grid given an index. +/// Get the type of convolutions for this Grid. /// /// # Safety /// /// TODO #[no_mangle] -pub unsafe extern "C" fn pineappl_grid_conv_type(grid: *const Grid, index: usize) -> ConvType { +pub unsafe extern "C" fn pineappl_grid_conv_types(grid: *const Grid, conv_types: *mut ConvType) { let grid = unsafe { &*grid }; + let conv_types = unsafe { slice::from_raw_parts_mut(conv_types, grid.convolutions().len()) }; + let convs_array = grid + .convolutions() + .iter() + .map(Conv::conv_type) + .collect_vec(); - grid.convolutions()[index].conv_type() + conv_types.copy_from_slice(&convs_array); } /// Get the number of convolutions for a given Grid. From d8a0e15a87a5e6a17a86f36074a83098064beb06 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 10 Jun 2025 00:16:30 +0200 Subject: [PATCH 46/49] Rename and Re-order the arguments of `pineappl_grid_evolve` --- examples/cpp/evolve-grid-identity.cpp | 22 ++++++++++------------ examples/cpp/evolve-grid.cpp | 22 ++++++++++------------ pineappl_capi/src/lib.rs | 22 +++++++++++----------- 3 files changed, 31 insertions(+), 35 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 31043ce53..4a596a90e 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -183,25 +183,23 @@ int main() { // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: // - `grid`: PineAPPL Grid - // - `op_info`: operator info - // - `operator`: callback that returns an evolution operator + // - `nb_slices`: the number of convolution(s)/Evolution Operator(s) required + // - `slices`: callback that returns the evolution operator(s) in slices + // - `state`: parameters that get passed to `operator` // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, // `nullptr` selects all the orders - // - `params_state`: parameters that get passed to `operator` - // - `nb_convolutions`: the number of convolutions/Evolution Operators required + // - `xi`: scale variation + // - `ren1`: values of the renormalization scales + // - `alphas_table`: values of alphas for each renormalization scales + // - `operator_info`: operator info // - `x_in`: x-grid of the Grid // - `x_out`: x-grid of the FK table // - `pids_in`: PIDs basis representation of the Grid // - `pids_out`: PIDs basis representation of the FK table // - `eko_shape`: shape of the evolution operators - // - `xi`: scale variation - // - `ren1`: values of the renormalization scales - // - `alphas_table`: values of alphas for each renormalization scales - pineappl_grid* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - generate_fake_ekos, nullptr, pdf.get(), - unique_convs.size(), x_in.data(), x_in.data(), - pids_in.data(), pids_out.data(), tensor_shape.data(), - xi.data(), ren1.data(), alphas_table.data()); + pineappl_grid* fktable = pineappl_grid_evolve(grid, unique_convs.size(), generate_fake_ekos, + opinfo_slices.data(), pdf.get(), nullptr, xi.data(), ren1.data(), alphas_table.data(), + x_in.data(), x_in.data(), pids_in.data(), pids_out.data(), tensor_shape.data()); // ------------------ Compare Grid & FK after convolution ------------------ // how many bins does this grid have? diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 8662ef8f7..28dd4fc1a 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -237,25 +237,23 @@ int main() { // NOTE: The arguments of `pineappl_grid_evolve` must follow the following orders: // - `grid`: PineAPPL Grid - // - `op_info`: operator info - // - `operator`: callback that returns an evolution operator + // - `nb_slices`: the number of convolution(s)/Evolution Operator(s) required + // - `slices`: callback that returns the evolution operator(s) in slices + // - `state`: parameters that get passed to `operator` // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, // `nullptr` selects all the orders - // - `params_state`: parameters that get passed to `operator` - // - `nb_convolutions`: the number of convolutions/Evolution Operators required + // - `xi`: scale variation + // - `ren1`: values of the renormalization scales + // - `alphas_table`: values of alphas for each renormalization scales + // - `operator_info`: operator info // - `x_in`: x-grid of the Grid // - `x_out`: x-grid of the FK table // - `pids_in`: PIDs basis representation of the Grid // - `pids_out`: PIDs basis representation of the FK table // - `eko_shape`: shape of the evolution operators - // - `xi`: scale variation - // - `ren1`: values of the renormalization scales - // - `alphas_table`: values of alphas for each renormalization scales - pineappl_grid* fktable = pineappl_grid_evolve(grid, opinfo_slices.data(), - generate_fake_ekos, nullptr, pdf.get(), - unique_convs.size(), XGRID.data(), XGRID.data(), - pids_in.data(), pids_out.data(), tensor_shape.data(), - xi.data(), ren1.data(), alphas_table.data()); + pineappl_grid* fktable = pineappl_grid_evolve(grid, unique_convs.size(), generate_fake_ekos, + opinfo_slices.data(), pdf.get(), nullptr, xi.data(), ren1.data(), alphas_table.data(), + XGRID.data(), XGRID.data(), pids_in.data(), pids_out.data(), tensor_shape.data()); // ------------------ Compare Grid & FK after convolution ------------------ // how many bins does this grid have? diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 66dba6124..0f916c5fb 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2185,19 +2185,19 @@ pub type OperatorCallback = unsafe extern "C" fn( #[no_mangle] pub unsafe extern "C" fn pineappl_grid_evolve( grid: *const Grid, + nb_slices: usize, + slices: OperatorCallback, operator_info: *const OperatorInfo, - operator: OperatorCallback, + state: *mut c_void, order_mask: *const bool, - params_state: *mut c_void, - nb_convolutions: usize, + xi: *const f64, + ren1: *const f64, + alphas: *const f64, x_in: *const f64, x_out: *const f64, pids_in: *const i32, pids_out: *const i32, eko_shape: *const usize, - xi: *const f64, - ren1: *const f64, - alphas: *const f64, ) -> Box { let grid = unsafe { &*grid }; @@ -2220,7 +2220,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let xi = unsafe { slice::from_raw_parts(xi, 3) }; let operator_info = unsafe { - slice::from_raw_parts(operator_info, nb_convolutions * evolve_info.fac1.len()) + slice::from_raw_parts(operator_info, nb_slices * evolve_info.fac1.len()) .chunks_exact(evolve_info.fac1.len()) }; @@ -2229,7 +2229,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .unwrap() .into(); - let slices = operator_info + let op_slices = operator_info .map(|op_infos| { op_infos.iter().map(|op_info| { let operator_slice_info = OperatorSliceInfo { @@ -2246,7 +2246,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let mut array = CowArray::from(Array4::zeros(shape)); unsafe { - operator( + slices( pids_in.as_ptr(), x_in.as_ptr(), pids_out.as_ptr(), @@ -2256,7 +2256,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( // UNWRAP: `array` is by construction contiguous and in standard order .unwrap() .as_mut_ptr(), - params_state, + state, op_info.conv_type, op_info.fac1, pids_in.len(), @@ -2274,7 +2274,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let fk_table = grid .evolve( - slices, + op_slices, order_mask, (xi[0], xi[1], xi[2]), &AlphasTable { From a57c48fdfe56d962121144fe2980ce86dc3bf242 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Tue, 10 Jun 2025 00:35:29 +0200 Subject: [PATCH 47/49] Re-order the parameters of the `OperatorCallback` struct --- examples/cpp/evolve-grid-identity.cpp | 14 ++++++------ examples/cpp/evolve-grid.cpp | 14 ++++++------ pineappl_capi/src/lib.rs | 32 +++++++++++++-------------- 3 files changed, 30 insertions(+), 30 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 4a596a90e..69e98c78a 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -25,18 +25,18 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } extern "C" void generate_fake_ekos( - const int* /*pids_in*/, - const double* /*x_in*/, - const int* /*pids_out*/, - const double* /*x_out*/, - double* eko_buffer, - void* params_state, pineappl_conv_type /*conv_type*/, double /*fac1*/, std::size_t pids_in_len, + const int* /*pids_in*/, std::size_t x_in_len, + const double* /*x_in*/, std::size_t pids_out_len, - std::size_t x_out_len + const int* /*pids_out*/, + std::size_t x_out_len, + const double* /*x_out*/, + double* eko_buffer, + void* params_state ) { // Check to get the μ0 of the PDF from the `params_state` const double _ = static_cast (params_state)->q2Min(); diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 28dd4fc1a..fc7657fe4 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -83,18 +83,18 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } extern "C" void generate_fake_ekos( - const int* /*pids_in*/, - const double* /*x_in*/, - const int* /*pids_out*/, - const double* /*x_out*/, - double* eko_buffer, - void* params_state, pineappl_conv_type /*conv_type*/, double /*fac1*/, std::size_t /*pids_in_len*/, + const int* /*pids_in*/, std::size_t /*x_in_len*/, + const double* /*x_in*/, std::size_t /*pids_out_len*/, - std::size_t /*x_out_len*/ + const int* /*pids_out*/, + std::size_t /*x_out_len*/, + const double* /*x_out*/, + double* eko_buffer, + void* params_state ) { // Check to get the μ0 from the PDF const double _ = static_cast (params_state)->q2Min(); diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 0f916c5fb..211c7819e 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2139,18 +2139,18 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( /// Type alias for the operator callback pub type OperatorCallback = unsafe extern "C" fn( - *const i32, // pids_in - *const f64, // x_in - *const i32, // pids_out - *const f64, // x_out - *mut f64, // Evolution Operator data buffer - *mut c_void, // Callable of PDF object ConvType, // Convolution type f64, // fac1 - usize, // Length of pids_in - usize, // Length of x_in - usize, // Length of pids_out - usize, // Length of x_out + usize, // size of `pids_in` + *const i32, // `pids_in` + usize, // size of `x_in` + *const f64, // `x_in` + usize, // size of `pids_out` + *const i32, // `pids_out` + usize, // size of `x_out` + *const f64, // `x_out` + *mut f64, // Evolution Operator data buffer + *mut c_void, // Callable state of parameters ); /// Evolve a grid with an evolution operator and dump the resulting FK table. @@ -2247,9 +2247,15 @@ pub unsafe extern "C" fn pineappl_grid_evolve( unsafe { slices( + op_info.conv_type, + op_info.fac1, + pids_in.len(), pids_in.as_ptr(), + x_in.len(), x_in.as_ptr(), + pids_out.len(), pids_out.as_ptr(), + x_out.len(), x_out.as_ptr(), array .as_slice_mut() @@ -2257,12 +2263,6 @@ pub unsafe extern "C" fn pineappl_grid_evolve( .unwrap() .as_mut_ptr(), state, - op_info.conv_type, - op_info.fac1, - pids_in.len(), - x_in.len(), - pids_out.len(), - x_out.len(), ); } From be40eb0b89ffc52dd80eadeaf90202a09cb10ab0 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Wed, 11 Jun 2025 15:41:19 +0200 Subject: [PATCH 48/49] Re-order and simplify the parameters of `pineappl_grid_evolve` and `OperatorCallback` --- examples/cpp/evolve-grid-identity.cpp | 43 +++++++++++++++++---------- examples/cpp/evolve-grid.cpp | 34 +++++++++++++-------- pineappl_capi/src/lib.rs | 36 ++++++++++------------ 3 files changed, 65 insertions(+), 48 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index 69e98c78a..d346e7a24 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -8,6 +8,7 @@ #include #include #include +#include // NOTE: Uses the scale of the Grid as the starting scale such that we can use an IDENTITY EKO. double FAC0 = 6456.44; @@ -27,23 +28,22 @@ std::vector unravel_index(std::size_t flat_index, const std::vector extern "C" void generate_fake_ekos( pineappl_conv_type /*conv_type*/, double /*fac1*/, - std::size_t pids_in_len, const int* /*pids_in*/, - std::size_t x_in_len, const double* /*x_in*/, - std::size_t pids_out_len, const int* /*pids_out*/, - std::size_t x_out_len, const double* /*x_out*/, + const std::size_t* eko_shape, double* eko_buffer, void* params_state ) { // Check to get the μ0 of the PDF from the `params_state` const double _ = static_cast (params_state)->q2Min(); - std::size_t flat_len = pids_in_len * x_in_len * pids_out_len * x_out_len; - // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) - std::vector shape = {pids_in_len, x_in_len, pids_out_len, x_out_len}; + // NOTE: This has to work because the Evolution Operator is always 4D + std::vector shape(eko_shape, eko_shape + 4); + // Compute the length of the flattened shape by multiplying the entries + std::size_t flat_len = std::accumulate(shape.begin(), + shape.end(), 1, std::multiplies()); for (std::size_t i = 0; i != flat_len; i++) { std::vector coords = unravel_index(i, shape); @@ -185,21 +185,34 @@ int main() { // - `grid`: PineAPPL Grid // - `nb_slices`: the number of convolution(s)/Evolution Operator(s) required // - `slices`: callback that returns the evolution operator(s) in slices + // - `operator_info`: operator info + // - `pids_in`: PIDs basis representation of the Grid + // - `x_in`: x-grid of the Grid + // - `pids_out`: PIDs basis representation of the FK table + // - `x_out`: x-grid of the FK table // - `state`: parameters that get passed to `operator` // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, // `nullptr` selects all the orders // - `xi`: scale variation // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales - // - `operator_info`: operator info - // - `x_in`: x-grid of the Grid - // - `x_out`: x-grid of the FK table - // - `pids_in`: PIDs basis representation of the Grid - // - `pids_out`: PIDs basis representation of the FK table // - `eko_shape`: shape of the evolution operators - pineappl_grid* fktable = pineappl_grid_evolve(grid, unique_convs.size(), generate_fake_ekos, - opinfo_slices.data(), pdf.get(), nullptr, xi.data(), ren1.data(), alphas_table.data(), - x_in.data(), x_in.data(), pids_in.data(), pids_out.data(), tensor_shape.data()); + pineappl_grid* fktable = pineappl_grid_evolve( + grid, // `grid` + unique_convs.size(), // `nb_slices` + generate_fake_ekos, // `slices` + opinfo_slices.data(), // `operator_info` + pids_in.data(), // `pids_in` + x_in.data(), // `x_in` + pids_out.data(), // `pids_out` + x_in.data(), // `x_out` + tensor_shape.data(), // `eko_shape` + pdf.get(), // `state` + nullptr, // `order_mask` + xi.data(), // `xi` + ren1.data(), // `ren1` + alphas_table.data() // `alphas_table` + ); // ------------------ Compare Grid & FK after convolution ------------------ // how many bins does this grid have? diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index fc7657fe4..0cca89fb3 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -85,14 +85,11 @@ std::vector unravel_index(std::size_t flat_index, const std::vector extern "C" void generate_fake_ekos( pineappl_conv_type /*conv_type*/, double /*fac1*/, - std::size_t /*pids_in_len*/, const int* /*pids_in*/, - std::size_t /*x_in_len*/, const double* /*x_in*/, - std::size_t /*pids_out_len*/, const int* /*pids_out*/, - std::size_t /*x_out_len*/, const double* /*x_out*/, + const std::size_t* /*eko_shape*/, double* eko_buffer, void* params_state ) { @@ -239,21 +236,34 @@ int main() { // - `grid`: PineAPPL Grid // - `nb_slices`: the number of convolution(s)/Evolution Operator(s) required // - `slices`: callback that returns the evolution operator(s) in slices + // - `operator_info`: operator info + // - `pids_in`: PIDs basis representation of the Grid + // - `x_in`: x-grid of the Grid + // - `pids_out`: PIDs basis representation of the FK table + // - `x_out`: x-grid of the FK table // - `state`: parameters that get passed to `operator` // - `order_mask`: array of booleans to mask the order(s) to apply the Evolution to, // `nullptr` selects all the orders // - `xi`: scale variation // - `ren1`: values of the renormalization scales // - `alphas_table`: values of alphas for each renormalization scales - // - `operator_info`: operator info - // - `x_in`: x-grid of the Grid - // - `x_out`: x-grid of the FK table - // - `pids_in`: PIDs basis representation of the Grid - // - `pids_out`: PIDs basis representation of the FK table // - `eko_shape`: shape of the evolution operators - pineappl_grid* fktable = pineappl_grid_evolve(grid, unique_convs.size(), generate_fake_ekos, - opinfo_slices.data(), pdf.get(), nullptr, xi.data(), ren1.data(), alphas_table.data(), - XGRID.data(), XGRID.data(), pids_in.data(), pids_out.data(), tensor_shape.data()); + pineappl_grid* fktable = pineappl_grid_evolve( + grid, // `grid` + unique_convs.size(), // `nb_slices` + generate_fake_ekos, // `slices` + opinfo_slices.data(), // `operator_info` + pids_in.data(), // `pids_in` + XGRID.data(), // `x_in` + pids_out.data(), // `pids_out` + XGRID.data(), // `x_out` + tensor_shape.data(), // `eko_shape` + pdf.get(), // `state` + nullptr, // `order_mask` + xi.data(), // `xi` + ren1.data(), // `ren1` + alphas_table.data() // `alphas_table` + ); // ------------------ Compare Grid & FK after convolution ------------------ // how many bins does this grid have? diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 211c7819e..6f750e38f 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2139,18 +2139,15 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( /// Type alias for the operator callback pub type OperatorCallback = unsafe extern "C" fn( - ConvType, // Convolution type - f64, // fac1 - usize, // size of `pids_in` - *const i32, // `pids_in` - usize, // size of `x_in` - *const f64, // `x_in` - usize, // size of `pids_out` - *const i32, // `pids_out` - usize, // size of `x_out` - *const f64, // `x_out` - *mut f64, // Evolution Operator data buffer - *mut c_void, // Callable state of parameters + ConvType, // Convolution type + f64, // fac1 + *const i32, // `pids_in` + *const f64, // `x_in` + *const i32, // `pids_out` + *const f64, // `x_out` + *const usize, // shape of the EKO + *mut f64, // Evolution Operator data buffer + *mut c_void, // Callable state of parameters ); /// Evolve a grid with an evolution operator and dump the resulting FK table. @@ -2188,16 +2185,16 @@ pub unsafe extern "C" fn pineappl_grid_evolve( nb_slices: usize, slices: OperatorCallback, operator_info: *const OperatorInfo, + pids_in: *const i32, + x_in: *const f64, + pids_out: *const i32, + x_out: *const f64, + eko_shape: *const usize, state: *mut c_void, order_mask: *const bool, xi: *const f64, ren1: *const f64, alphas: *const f64, - x_in: *const f64, - x_out: *const f64, - pids_in: *const i32, - pids_out: *const i32, - eko_shape: *const usize, ) -> Box { let grid = unsafe { &*grid }; @@ -2249,14 +2246,11 @@ pub unsafe extern "C" fn pineappl_grid_evolve( slices( op_info.conv_type, op_info.fac1, - pids_in.len(), pids_in.as_ptr(), - x_in.len(), x_in.as_ptr(), - pids_out.len(), pids_out.as_ptr(), - x_out.len(), x_out.as_ptr(), + eko_shape.as_ptr(), array .as_slice_mut() // UNWRAP: `array` is by construction contiguous and in standard order From 1a43bc5714abdcfba9613b64faad6c4dd20ef578 Mon Sep 17 00:00:00 2001 From: Radonirinaunimi Date: Fri, 13 Jun 2025 21:58:58 +0200 Subject: [PATCH 49/49] Replace `OperatorCallback.ConvType` in favor of `OperatorCallback.usize` --- examples/cpp/evolve-grid-identity.cpp | 23 +++++++++++++++++++---- examples/cpp/evolve-grid.cpp | 23 +++++++++++++++++++---- pineappl_capi/src/lib.rs | 6 +++--- 3 files changed, 41 insertions(+), 11 deletions(-) diff --git a/examples/cpp/evolve-grid-identity.cpp b/examples/cpp/evolve-grid-identity.cpp index d346e7a24..df22d424e 100644 --- a/examples/cpp/evolve-grid-identity.cpp +++ b/examples/cpp/evolve-grid-identity.cpp @@ -13,6 +13,13 @@ // NOTE: Uses the scale of the Grid as the starting scale such that we can use an IDENTITY EKO. double FAC0 = 6456.44; +/** @brief This struct can contain arbitrary parameters that need to be passed to Evolution + * Operator Callback (`generated_fake_ekos`). + */ +struct OperatorParams { + std::vector conv_types; +}; + std::vector unravel_index(std::size_t flat_index, const std::vector& shape) { std::size_t ndim = shape.size(); std::vector coords(ndim); @@ -26,7 +33,7 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } extern "C" void generate_fake_ekos( - pineappl_conv_type /*conv_type*/, + std::size_t op_index, double /*fac1*/, const int* /*pids_in*/, const double* /*x_in*/, @@ -36,8 +43,9 @@ extern "C" void generate_fake_ekos( double* eko_buffer, void* params_state ) { - // Check to get the μ0 of the PDF from the `params_state` - const double _ = static_cast (params_state)->q2Min(); + // select the type of convolution based on the Operator index + OperatorParams* op_params = static_cast(params_state); + pineappl_conv_type _ = op_params->conv_types[op_index]; // NOTE: This has to work because the Evolution Operator is always 4D std::vector shape(eko_shape, eko_shape + 4); @@ -152,6 +160,7 @@ int main() { // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose // elements are `OperatorInfo` objects. + std::vector convtypes(unique_convs.size()); std::vector opinfo_slices(unique_convs.size() * fac1.size()); for (std::size_t i = 0; i != unique_convs.size(); i++) { for (std::size_t j = 0; j != fac1.size(); j++) { @@ -163,6 +172,7 @@ int main() { }; opinfo_slices[i * fac1.size() + j] = opinfo; } + conv_types[i] = unique_convs[i]; } // ------------------ Construct the Evolution Operator ------------------ @@ -177,6 +187,11 @@ int main() { alphas_table.push_back(alpha); } + // Construct the Parameters that will get passed to the Callback + OperatorParams* op_params = new OperatorParams; + op_params->conv_types = convtypes; + void* params = static_cast(op_params); + std::vector xi = {1.0, 1.0, 1.0}; // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) std::vector tensor_shape = {pids_in.size(), x_in.size(), pids_out.size(), x_in.size()}; @@ -207,7 +222,7 @@ int main() { pids_out.data(), // `pids_out` x_in.data(), // `x_out` tensor_shape.data(), // `eko_shape` - pdf.get(), // `state` + params, // `state` nullptr, // `order_mask` xi.data(), // `xi` ren1.data(), // `ren1` diff --git a/examples/cpp/evolve-grid.cpp b/examples/cpp/evolve-grid.cpp index 0cca89fb3..1ab863e50 100644 --- a/examples/cpp/evolve-grid.cpp +++ b/examples/cpp/evolve-grid.cpp @@ -70,6 +70,13 @@ std::vector XGRID = { // Particle PIDs for both `in` and `out` std::vector PIDS = {- 22 , -6 , -5 , -4 , -3 , -2 , -1 , 21 , 1 , 2 , 3 , 4 , 5 , 6}; +/** @brief This struct can contain arbitrary parameters that need to be passed to Evolution + * Operator Callback (`generated_fake_ekos`). + */ +struct OperatorParams { + std::vector conv_types; +}; + std::vector unravel_index(std::size_t flat_index, const std::vector& shape) { std::size_t ndim = shape.size(); std::vector coords(ndim); @@ -83,7 +90,7 @@ std::vector unravel_index(std::size_t flat_index, const std::vector } extern "C" void generate_fake_ekos( - pineappl_conv_type /*conv_type*/, + std::size_t op_index, double /*fac1*/, const int* /*pids_in*/, const double* /*x_in*/, @@ -93,8 +100,9 @@ extern "C" void generate_fake_ekos( double* eko_buffer, void* params_state ) { - // Check to get the μ0 from the PDF - const double _ = static_cast (params_state)->q2Min(); + // select the type of convolution based on the Operator index + OperatorParams* op_params = static_cast(params_state); + pineappl_conv_type _ = op_params->conv_types[op_index]; std::ifstream input_file("../../test-data/EKO_LHCB_WP_7TEV.txt"); double weight_value; @@ -203,6 +211,7 @@ int main() { // ------------------ Construct the Operator Info ------------------ // The Operator Info is a vector with length `N_conv * N_Q2_slices` whose // elements are `OperatorInfo` objects. + std::vector convtypes(unique_convs.size()); std::vector opinfo_slices(unique_convs.size() * fac1.size()); for (std::size_t i = 0; i != unique_convs.size(); i++) { for (std::size_t j = 0; j != fac1.size(); j++) { @@ -214,6 +223,7 @@ int main() { }; opinfo_slices[i * fac1.size() + j] = opinfo; } + conv_types[i] = unique_convs[i]; } // ------------------ Construct the Evolution Operator ------------------ @@ -228,6 +238,11 @@ int main() { alphas_table.push_back(alpha); } + // Construct the Parameters that will get passed to the Callback + OperatorParams* op_params = new OperatorParams; + op_params->conv_types = convtypes; + void* params = static_cast(op_params); + std::vector xi = {1.0, 1.0, 1.0}; // NOTE: The EKO has to have as shape: (pids_in, x_in, pids_out, x_out) std::vector tensor_shape = {pids_in.size(), XGRID.size(), pids_out.size(), XGRID.size()}; @@ -258,7 +273,7 @@ int main() { pids_out.data(), // `pids_out` XGRID.data(), // `x_out` tensor_shape.data(), // `eko_shape` - pdf.get(), // `state` + params, // `state` nullptr, // `order_mask` xi.data(), // `xi` ren1.data(), // `ren1` diff --git a/pineappl_capi/src/lib.rs b/pineappl_capi/src/lib.rs index 6f750e38f..ca82e8b5d 100644 --- a/pineappl_capi/src/lib.rs +++ b/pineappl_capi/src/lib.rs @@ -2139,7 +2139,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve_info( /// Type alias for the operator callback pub type OperatorCallback = unsafe extern "C" fn( - ConvType, // Convolution type + usize, // index which selects Evolution parameters f64, // fac1 *const i32, // `pids_in` *const f64, // `x_in` @@ -2228,7 +2228,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( let op_slices = operator_info .map(|op_infos| { - op_infos.iter().map(|op_info| { + op_infos.iter().enumerate().map(|(op_index, op_info)| { let operator_slice_info = OperatorSliceInfo { pid_basis: op_info.pid_basis, fac0: op_info.fac0, @@ -2244,7 +2244,7 @@ pub unsafe extern "C" fn pineappl_grid_evolve( unsafe { slices( - op_info.conv_type, + op_index, op_info.fac1, pids_in.as_ptr(), x_in.as_ptr(),