diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/README.md b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/README.md new file mode 100644 index 000000000000..4a58b6ab84ca --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/README.md @@ -0,0 +1,338 @@ + + +# dlagbrpvgrw + +> LAPACK routine to computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. + +
+ +The `dlagbrpvgrw` routine computes the reciprocal pivot growth factor for a general banded matrix `A`. The factorization has the form: + + + +```math +\text{RPGFactor} = \frac{\text||A||}{\text||U||} +``` + + + + +
+ + + + +
+ +## Usage + + + +```javascript +var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); +``` + +#### dlagbrpvgrw( order, N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB ) + +Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); + +/* + A = [ + [ 1.0, 2.0, 0.0, 0.0 ], + [ 3.0, 4.0, 5.0, 0.0 ], + [ 0.0, 6.0, 7.0, 8.0 ], + [ 0.0, 0.0, 9.0,10.0 ] +] +*/ + +var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + +var out = dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); +// returns 1.0 +``` + +The function has the following parameters: + +- **order**: storage layout. +- **N**: number of columns in matrix `A`. +- **KL**: number of subdiagonals within the band of matrix `A`. +- **KU**: number of superdiagonals within the band of matrix `A`. +- **NCOLS**: number of columns in matrix `A`. +- **AB**: the matrix `A` in band storage, stored in linear memory as a [`Float64Array`][mdn-float64array]. +- **LDAB**: stride of the first dimension of `AB` (a.k.a., leading dimension of the matrix `AB`). +- **AFB**: the details of the LU factorization of the band matrix `A` stored in linear memory as a [`Float64Array`][mdn-float64array]. +- **LDAFB**: stride of the first dimension of `AFB` (a.k.a., leading dimension of the matrix `AFB`). + +The function returns the reciprocal pivot growth factor. + +Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); + +// Initial arrays... +var AB0 = new Float64Array( [ 0.0, 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +var AFB0 = new Float64Array( [ 0.0, 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + +/* + A = [ + [ 1.0, 2.0, 0.0, 0.0 ], + [ 3.0, 4.0, 5.0, 0.0 ], + [ 0.0, 6.0, 7.0, 8.0 ], + [ 0.0, 0.0, 9.0,10.0 ] +] +*/ + +// Create offset views... +var AB = new Float64Array( AB0.buffer, AB0.BYTES_PER_ELEMENT*1 ); // start at 2nd element +var AFB = new Float64Array( AFB0.buffer, AFB0.BYTES_PER_ELEMENT*1 ); // start at 2nd element + +var out = dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); +// returns 1.0 +``` + + + +#### dlagbrpvgrw.ndarray( N, KL, KU, NCOLS, AB, strideAB1, strideAB2, offsetAB, AFB, strideAFB1, strideAFB2, offsetAFB ) + +Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A` using alternative indexing semantics. + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); + +/* + A = [ + [ 1.0, 2.0, 0.0, 0.0 ], + [ 3.0, 4.0, 5.0, 0.0 ], + [ 0.0, 6.0, 7.0, 8.0 ], + [ 0.0, 0.0, 9.0,10.0 ] +] +*/ + +var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + +var out = dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); +// returns 1.0 +``` + +The function has the following parameters: + +- **N**: number of columns in matrix `A`. +- **KL**: number of subdiagonals within the band of matrix `A`. +- **KU**: number of superdiagonals within the band of matrix `A`. +- **NCOLS**: number of columns in matrix `A`. +- **AB**: the matrix `A` in band storage, stored in linear memory as a [`Float64Array`][mdn-float64array]. +- **strideAB1**: stride of the first dimension of `AB`. +- **strideAB2**: stride of the second dimension of `AB`. +- **offsetAB**: index offset for `AB`. +- **AFB**: the details of the LU factorization of the band matrix `A` stored in linear memory as a [`Float64Array`][mdn-float64array]. +- **strideAB1**: stride of the first dimension of `AFB`. +- **strideAB2**: stride of the second dimension of `AFB`. +- **offsetAB**: index offset for `AFB`. + +While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); + +/* + A = [ + [ 1.0, 2.0, 0.0, 0.0 ], + [ 3.0, 4.0, 5.0, 0.0 ], + [ 0.0, 6.0, 7.0, 8.0 ], + [ 0.0, 0.0, 9.0,10.0 ] +] +*/ + +var AB = new Float64Array( [ 0.0, 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +var AFB = new Float64Array( [ 0.0, 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + +var out = dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 1, AFB, 4, 1, 1 ); +// returns 1.0 +``` + +
+ + + +
+ +## Notes + +- The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. + +- Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. + +- Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. + +- The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. + +- The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. + +- `dlagbrpvgrw()` corresponds to the [LAPACK][LAPACK] function [`dlagbrpvgrw`][lapack-dlagbrpvgrw]. + +
+ + + +
+ +## Examples + + + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var ndarray2array = require( '@stdlib/ndarray/base/to-array' ); +var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); + +var N = 4; +var KL = 1; +var KU = 1; +var NCOLS = 4; +var LDAB = 3; +var LDAFB = 4; + +var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + +console.log( 'The matrix `AB` i.e, the matrix `A` in band storage, in rows 1 to KL+KU+1:' ); +console.log( ndarray2array( AB, [ LDAB, N ], [ N, 1 ], 0, 'row-major' ) ); + +console.log( 'The matrix `AFB` containing the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`:' ); +console.log( ndarray2array( AFB, [ LDAFB, N ], [ N, 1 ], 0, 'row-major' ) ); + +console.log( 'The reciprocal pivot growth factor norm(A)/norm(U) for `AB`:' ); +console.log( dlagbrpvgrw( 'row-major', N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB ) ); +``` + +
+ + + + + +* * * + +
+ +## C APIs + + + +
+ +
+ + + + + +
+ +### Usage + +```c +TODO +``` + +#### TODO + +TODO. + +```c +TODO +``` + +TODO + +```c +TODO +``` + +
+ + + + + +
+ +
+ + + + + +
+ +### Examples + +```c +TODO +``` + +
+ + + +
+ + + + + + + + + + + + + + diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/benchmark/benchmark.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/benchmark/benchmark.js new file mode 100644 index 000000000000..61733c053dfd --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/benchmark/benchmark.js @@ -0,0 +1,123 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/* eslint-disable camelcase */ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var dla_gbrpvgrw = require( './../lib/dlagbrpvgrw.js' ); + + +// VARIABLES // + +var LAYOUTS = [ + 'row-major', + 'column-major' +]; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {string} order - storage layout +* @param {PositiveInteger} N - matrix order (N-by-N) +* @returns {Function} benchmark function +*/ +function createBenchmark( order, N ) { + var opts; + var AFB; + var AB; + + opts = { + 'dtype': 'float64' + }; + + AFB = uniform( 4*N*N, -1.0, 1.0, opts ); + AB = uniform( 4*N*N, -1.0, 1.0, opts ); + + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var i; + var z; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = dla_gbrpvgrw( order, N, N, N, N, AB, 4*N, AFB, 4*N ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var min; + var max; + var ord; + var N; + var f; + var i; + var k; + + min = 1; // 10^min + max = 6; // 10^max + + for ( k = 0; k < LAYOUTS.length; k++ ) { + ord = LAYOUTS[ k ]; + for ( i = min; i <= max; i++ ) { + N = floor( pow( pow( 10, i ), 1.0/2.0 ) ); + f = createBenchmark( ord, N ); + bench( format( '%s:order=%s,size=%d', pkg, ord, N*N ), f ); + } + } +} + +main(); diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/benchmark/benchmark.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/benchmark/benchmark.ndarray.js new file mode 100644 index 000000000000..c32e2aee2e8f --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/benchmark/benchmark.ndarray.js @@ -0,0 +1,133 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/* eslint-disable camelcase */ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var format = require( '@stdlib/string/format' ); +var pkg = require( './../package.json' ).name; +var dla_gbrpvgrw = require( './../lib/ndarray.js' ); + + +// VARIABLES // + +var LAYOUTS = [ + 'row-major', + 'column-major' +]; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {string} order - storage layout +* @param {PositiveInteger} N - matrix order (N-by-N) +* @returns {Function} benchmark function +*/ +function createBenchmark( order, N ) { + var sa1; + var sa2; + var AFB; + var AB; + + if ( isColumnMajor( order ) ) { + sa1 = 1; + sa2 = 4*N; + } else { + sa1 = N; + sa2 = 1; + } + + AFB = uniform( 4*N*N, -1.0, 1.0, { + 'dtype': 'float64' + }); + AB = uniform( 4*N*N, -1.0, 1.0, { + 'dtype': 'float64' + }); + + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var i; + var z; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + z = dla_gbrpvgrw( N, N, N, N, AB, sa1, sa2, 0, AFB, sa1, sa2, 0 ); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( z ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var min; + var max; + var ord; + var N; + var f; + var i; + var k; + + min = 1; // 10^min + max = 6; // 10^max + + for ( k = 0; k < LAYOUTS.length; k++ ) { + ord = LAYOUTS[ k ]; + for ( i = min; i <= max; i++ ) { + N = floor( pow( pow( 10, i ), 1.0/2.0 ) ); + f = createBenchmark( ord, N ); + bench( format( '%s:ndarray:order=%s,size=%d', pkg, ord, N*N ), f ); + } + } +} + +main(); diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/repl.txt b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/repl.txt new file mode 100644 index 000000000000..89ffd1bb6a49 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/repl.txt @@ -0,0 +1,121 @@ + +{{alias}}( order, N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB ) + Computes the reciprocal pivot growth factor norm(A)/norm(U) for a + general banded matrix `A`. + + Indexing is relative to the first index. To introduce an offset, use typed + array views. + + Parameters + ---------- + order: string + Row-major (C-style) or column-major (Fortran-style) order. Must be + either 'row-major' or 'column-major'. + + N: integer + Number of rows in matrix `A`. + + KL: integer + Number of subdiagonals within the band of matrix `A`. + + KU: integer + Number of superdiagonals within the band of matrix `A`. + + NCOLS: integer + Number of columns in matrix `A`. + + AB: Float64Array + The matrix `A` in band storage. + + LDAB: integer + Stride of the first dimension of `AB` (a.k.a., leading dimension + of the matrix `AB`) `LDAB` >= KL+KU+1. + + AFB: Float64Array + The details of the LU factorization of the band matrix `A`. + + LDAFB: integer + Stride of the first dimension of `AFB` (a.k.a., leading dimension + of the matrix `AFB`) `LDAFB` >= 2*KL+KU+1. + + Returns + ------- + rpgFactor: number + The reciprocal pivot growth factor for `A`. + + Examples + -------- + > var AB = new {{alias:@stdlib/array/float64}}([ 0,10,1,3,2,0 ]); + > var AFB = new {{alias:@stdlib/array/float64}}([ 0,0,0,10,1,-17,2,0 ]); + > {{alias}}( 'row-major', 2, 1, 1, 2, AB, 3, AFB, 4 ) + 1.0 + + // Using typed array views: + > var AB0 = new {{alias:@stdlib/array/float64}}([ 0,0,10,1,3,2,0 ]); + > var AFB0 = new {{alias:@stdlib/array/float64}}([ 0,0,0,0,10,1,-17,2,0 ]); + > AB = new Float64Array( AB0.buffer, AB0.BYTES_PER_ELEMENT*1 ); + > AFB = new Float64Array( AFB0.buffer, AFB0.BYTES_PER_ELEMENT*1 ); + > {{alias}}( 'row-major', 2, 1, 1, 2, AB, 3, AFB, 4 ) + 1.0 + + +{{alias}}.ndarray( N,KL,KU,NCOLS,AB,sab1,sab2,oab,AFB,safb1,safb2,oafb ) + Computes the reciprocal pivot growth factor norm(A)/norm(U) for a + general banded matrix `A`. + + While typed array views mandate a view offset based on the underlying + buffer, the offset parameters support indexing semantics based on starting + indices. + + Parameters + ---------- + N: integer + Number of rows in matrix `A`. + + KL: integer + Number of subdiagonals within the band of matrix `A`. + + KU: integer + Number of superdiagonals within the band of matrix `A`. + + NCOLS: integer + Number of columns in matrix `A`. + + AB: Float64Array + The matrix `A` in band storage. + + sab1: integer + Stride of the first dimension of `AB`. + + sab2: integer + Stride of the second dimension of `AB`. + + oab: integer + Index offset for `AB`. + + AFB: Float64Array + The details of the LU factorization of the band matrix `A`. + + safb1: integer + Stride of the first dimension of `AFB`. + + safb2: integer + Stride of the second dimension of `AFB`. + + oafb: integer + Index offset for `AFB`. + + Returns + ------- + rpgFactor: number + The reciprocal pivot growth factor for `A`. + + Examples + -------- + > var AB = new {{alias:@stdlib/array/float64}}([ 0,10,1,3,2,0 ]); + > var AFB = new {{alias:@stdlib/array/float64}}([ 0,0,0,10,1,-17,2,0 ]); + > {{alias}}.ndarray( 2, 1, 1, 2, AB, 2, 1, 0, AFB, 2, 1, 0 ) + 1.0 + + See Also + -------- diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/types/index.d.ts b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/types/index.d.ts new file mode 100644 index 000000000000..467b63d84036 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/types/index.d.ts @@ -0,0 +1,144 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +// TypeScript Version: 4.1 + +/// + +import { Layout } from '@stdlib/types/blas'; + +/** +* Interface describing `dla-gbrpvgrw`. +*/ +interface Routine { + /** + * Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. + * + * ## Notes + * + * - The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. + * - Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. + * - Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. + * - The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. + * - The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. + * + * @param order - order of matrix `A` + * @param N - number of rows in matrix `A` + * @param KL - number of subdiagonals within the band of matrix `A` + * @param KU - number of superdiagonals within the band of matrix `A` + * @param NCOLS - number of columns in matrix `A` + * @param AB - the matrix A in band storage + * @param LDAB - the leading dimension of the matrix `AB` + * @param AFB - details of the LU factorization of the band matrix `A` + * @param LDAFB - the leading dimension of the matrix `AFB` + * @returns the reciprocal pivot growth factor + * + * @example + * var Float64Array = require( '@stdlib/array/float64' ); + * + * var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); + * var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + * + * var out = dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); + * // returns 1.0 + */ + ( order: Layout, N: number, KL: number, KU: number, NCOLS: number, AB: Float64Array, LDAB: number, AFB: Float64Array, LDAFB: number ): number; + + /** + * Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A` using alternating indexing semantics. + * + * ## Notes + * + * - The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. + * - Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. + * - Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. + * - The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. + * - The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. + * + * @param N - number of rows in matrix `A` + * @param KL - number of subdiagonals within the band of matrix `A` + * @param KU - number of superdiagonals within the band of matrix `A` + * @param NCOLS - number of columns in matrix `A` + * @param AB - the matrix A in band storage + * @param strideAB1 - stride of the first dimension of `AB` + * @param strideAB2 - stride of the second dimension of `AB` + * @param offsetAB - index offset for `AB` + * @param AFB - details of the LU factorization of the band matrix `A` + * @param strideAFB1 - stride of the first dimension of `AFB` + * @param strideAFB2 - stride of the second dimension of `AFB` + * @param offsetAFB - index offset for `AFB` + * @returns the reciprocal pivot growth factor + * + * @example + * var Float64Array = require( '@stdlib/array/float64' ); + * + * var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); + * var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); + * + * var out = dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); + * // returns 1.0 + */ + ndarray( N: number, KL: number, KU: number, NCOLS: number, AB: Float64Array, strideAB1: number, strideAB2: number, offsetAB: number, AFB: Float64Array, strideAFB1: number, strideAFB2: number, offsetAFB: number ): number; // eslint-disable-line max-len +} + +/** +* Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. +* +* ## Notes +* +* - The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. +* - Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. +* - Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. +* - The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. +* - The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. +* +* @param order - order of matrix `A` +* @param N - number of rows in matrix `A` +* @param KL - number of subdiagonals within the band of matrix `A` +* @param KU - number of superdiagonals within the band of matrix `A` +* @param NCOLS - number of columns in matrix `A` +* @param AB - the matrix A in band storage +* @param LDAB - the leading dimension of the matrix `AB` +* @param AFB - details of the LU factorization of the band matrix `A` +* @param LDAFB - the leading dimension of the matrix `AFB` +* @returns the reciprocal pivot growth factor +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); +* // returns 1.0 +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); +* // returns 1.0 +*/ +declare var dlagbrpvgrw: Routine; + + +// EXPORTS // + +export = dlagbrpvgrw; diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/types/test.ts b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/types/test.ts new file mode 100644 index 000000000000..04a595774c25 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/docs/types/test.ts @@ -0,0 +1,373 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +import dlagbrpvgrw = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is not a string... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 5, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( true, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( false, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( null, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( void 0, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( [], 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( {}, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( ( x: number ): number => x, 4, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', '4', 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', true, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', false, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', null, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', void 0, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', [], 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', {}, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', ( x: number ): number => x, 1, 1, 4, AB, 3, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a third argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, '4', 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, true, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, false, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, null, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, void 0, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, [], 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, {}, 1, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, ( x: number ): number => x, 1, 4, AB, 3, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fourth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, 1, '4', 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, true, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, false, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, null, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, void 0, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, [], 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, {}, 4, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, ( x: number ): number => x, 4, AB, 3, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fifth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, 1, 1, '4', AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, true, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, false, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, null, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, void 0, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, [], AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, {}, AB, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, ( x: number ): number => x, AB, 3, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a sixth argument which is not a Float64Array... +{ + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, '4', 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, 4, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, true, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, false, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, null, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, void 0, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, [], 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, {}, 3, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, ( x: number ): number => x, 3, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a seventh argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, '4', AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, true, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, false, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, null, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, void 0, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, [], AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, {}, AFB, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, ( x: number ): number => x, AFB, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a eighth argument which is not a Float64Array... +{ + const AB = new Float64Array( 12 ); + + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, '4', 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, 4, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, true, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, false, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, null, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, void 0, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, [], 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, {}, 4 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, ( x: number ): number => x, 4 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a ninth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, '4' ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, true ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, false ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, null ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, void 0 ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, [] ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, {} ); // $ExpectError + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, ( x: number ): number => x ); // $ExpectError +} + +// Attached to main export is an `ndarray` method which returns a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a first argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( '3', 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( true, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( false, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( null, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( void 0, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( [], 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( {}, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( ( x: number ): number => x, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, '3', 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, true, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, false, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, null, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, void 0, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, [], 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, {}, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, ( x: number ): number => x, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a third argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, '3', 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, true, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, false, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, null, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, void 0, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, [], 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, {}, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, ( x: number ): number => x, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fourth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, '3', AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, true, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, false, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, null, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, void 0, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, [], AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, {}, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, ( x: number ): number => x, AB, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fifth argument which is not a Float64Array... +{ + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, 3, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, '3', 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, true, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, false, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, null, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, void 0, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, [], 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, {}, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, ( x: number ): number => x, 4, 1, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a sixth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, '3', 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, true, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, false, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, null, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, void 0, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, [], 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, {}, 1, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, ( x: number ): number => x, 1, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a seventh argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, '3', 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, true, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, false, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, null, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, void 0, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, [], 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, {}, 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, ( x: number ): number => x, 0, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a eight argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, '3', AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, true, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, false, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, null, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, void 0, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, [], AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, {}, AFB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, ( x: number ): number => x, AFB, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a ninth argument which is not a Float64Array... +{ + const AB = new Float64Array( 12 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, 3, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, '3', 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, true, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, false, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, null, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, void 0, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, [], 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, {}, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, ( x: number ): number => x, 4, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a tenth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, '3', 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, true, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, false, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, null, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, void 0, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, [], 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, {}, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, ( x: number ): number => x, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a eleventh argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, '3', 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, true, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, false, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, null, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, void 0, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, [], 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, {}, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, ( x: number ): number => x, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a twelveth argument which is not a number... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, '3' ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, true ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, false ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, null ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, void 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, [] ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, {} ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the `ndarray` method is provided an unsupported number of arguments... +{ + const AB = new Float64Array( 12 ); + const AFB = new Float64Array( 16 ); + + dlagbrpvgrw.ndarray(); // $ExpectError + dlagbrpvgrw.ndarray( 4 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1 ); // $ExpectError + dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0, 10 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/examples/index.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/examples/index.js new file mode 100644 index 000000000000..63c5f62fa4d0 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/examples/index.js @@ -0,0 +1,72 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +var Float64Array = require( '@stdlib/array/float64' ); +var ndarray2array = require( '@stdlib/ndarray/base/to-array' ); +var dlagbrpvgrw = require( './../lib' ); + +var N = 4; +var KL = 1; +var KU = 1; +var NCOLS = 4; +var LDAB = 3; +var LDAFB = 4; + +var AB = new Float64Array([ + 0.0, + 2.0, + 5.0, + 8.0, + 1.0, + 4.0, + 7.0, + 10.0, + 3.0, + 6.0, + 9.0, + 0.0 +]); +var AFB = new Float64Array([ + 0.0, + 0.0, + 5.0, + 8.0, + 0.0, + 4.0, + 7.0, + 10.0, + 3.0, + 6.0, + 9.0, + 1.8272, + 0.3333, + 0.1111, + -0.2716, + 0.0 +]); + +console.log( 'The matrix `AB` i.e, the matrix `A` in band storage, in rows 1 to KL+KU+1:' ); +console.log( ndarray2array( AB, [ LDAB, N ], [ N, 1 ], 0, 'row-major' ) ); + +console.log( 'The matrix `AFB` containing the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`:' ); +console.log( ndarray2array( AFB, [ LDAFB, N ], [ N, 1 ], 0, 'row-major' ) ); + +console.log( 'The reciprocal pivot growth factor norm(A)/norm(U) for `AB`:' ); +console.log( dlagbrpvgrw( 'row-major', N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB ) ); diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/base.js new file mode 100644 index 000000000000..80db60085039 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/base.js @@ -0,0 +1,116 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var abs = require( '@stdlib/math/base/special/abs' ); +var max = require( '@stdlib/math/base/special/max' ); +var min = require( '@stdlib/math/base/special/min' ); + + +// MAIN // + +/** +* Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. +* +* ## Notes +* +* - The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. +* - Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. +* - Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. +* - The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. +* - The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. +* +* @private +* @param {NonNegativeInteger} N - number of rows in matrix `A` +* @param {NonNegativeInteger} KL - number of subdiagonals within the band of matrix `A` +* @param {NonNegativeInteger} KU - number of superdiagonals within the band of matrix `A` +* @param {NonNegativeInteger} NCOLS - number of columns in matrix `A` +* @param {Float64Array} AB - the matrix A in band storage +* @param {integer} strideAB1 - stride of the first dimension of `AB` +* @param {integer} strideAB2 - stride of the second dimension of `AB` +* @param {NonNegativeInteger} offsetAB - index offset for `AB` +* @param {Float64Array} AFB - details of the LU factorization of the band matrix `A` +* @param {integer} strideAFB1 - stride of the first dimension of `AFB` +* @param {integer} strideAFB2 - stride of the second dimension of `AFB` +* @param {NonNegativeInteger} offsetAFB - index offset for `AFB` +* @returns {number} the reciprocal pivot growth factor +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); +* // returns 1.0 +*/ +function dlagbrpvgrw( N, KL, KU, NCOLS, AB, strideAB1, strideAB2, offsetAB, AFB, strideAFB1, strideAFB2, offsetAFB ) { // eslint-disable-line max-params, max-len + var rowEndAB; + var rowStart; + var rpvgrw; + var amax; + var iafb; + var umax; + var iab; + var kd; + var i; + var j; + + rpvgrw = 1.0; + + kd = KU + 1; + iab = offsetAB; + iafb = offsetAFB; + for ( j = 0; j < NCOLS; j++ ) { + amax = 0.0; + umax = 0.0; + + rowStart = max( j - KU, 0 ); // Starting index for row + rowEndAB = min( j + KL + 1, N ); // Ending index for row in AB + iab += ( kd + rowStart - j - 1 )*strideAB1; + iafb += ( kd + rowStart - j - 1 )*strideAFB1; + + for ( i = rowStart; i < rowEndAB; i++ ) { + amax = max( abs( AB[ iab ] ), amax ); + iab += strideAB1; + } + + for ( i = rowStart; i <= j; i++ ) { + umax = max( abs( AFB[ iafb ] ), umax ); + iafb += strideAFB1; + } + + if ( umax !== 0.0 ) { + rpvgrw = min( amax / umax, rpvgrw ); + } + + // Shift the index for both matrices to the beginning of the next column + iab += strideAB2 - ( ( kd + rowEndAB - j - 1 )*strideAB1 ); + iafb += strideAFB2 - ( kd*strideAFB1 ); + } + + return rpvgrw; +} + + +// EXPORTS // + +module.exports = dlagbrpvgrw; diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/dlagbrpvgrw.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/dlagbrpvgrw.js new file mode 100644 index 000000000000..9e94e0ef0bcc --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/dlagbrpvgrw.js @@ -0,0 +1,97 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var isLayout = require( '@stdlib/blas/base/assert/is-layout' ); +var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' ); +var format = require( '@stdlib/string/format' ); +var base = require( './base.js' ); + + +// MAIN // + +/** +* Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. +* +* ## Notes +* +* - The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. +* - Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. +* - Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. +* - The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. +* - The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. +* +* @param {string} order - order of matrix `A` +* @param {NonNegativeInteger} N - number of rows in matrix `A` +* @param {NonNegativeInteger} KL - number of subdiagonals within the band of matrix `A` +* @param {NonNegativeInteger} KU - number of superdiagonals within the band of matrix `A` +* @param {NonNegativeInteger} NCOLS - number of columns in matrix `A` +* @param {Float64Array} AB - the matrix `A` in band storage +* @param {PositiveInteger} LDAB - the leading dimension of the matrix `AB` +* @param {Float64Array} AFB - details of the LU factorization of the band matrix `A` +* @param {PositiveInteger} LDAFB - the leading dimension of the matrix `AFB` +* @throws {TypeError} first argument must be a valid order +* @throws {RangeError} seventh argument must be >= KL+KU+1 +* @throws {RangeError} ninth argument must be >= 2*KL+KU+1 +* @returns {number} the reciprocal pivot growth factor +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); +* // returns 1.0 +*/ +function dlagbrpvgrw( order, N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB ) { + var safb1; + var safb2; + var sab1; + var sab2; + + if ( !isLayout( order ) ) { + throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) ); + } + if ( LDAB < KL + KU + 1 ) { + throw new RangeError( format( 'invalid argument. Seventh argument must be greater than or equal to KL + KU + 1 = %d. Value: `%d`.', KL + KU + 1, LDAB ) ); + } + if ( LDAFB < ( 2*KL ) + KU + 1 ) { + throw new RangeError( format( 'invalid argument. Ninth argument must be greater than or equal to ( 2*KL ) + KU + 1 = %d. Value: `%d`.', ( 2*KL ) + KU + 1, LDAFB ) ); + } + if ( isColumnMajor( order ) ) { + sab1 = 1; + sab2 = LDAB; + safb1 = 1; + safb2 = LDAFB; + } else { // order === 'row-major' + sab1 = N; + sab2 = 1; + safb1 = N; + safb2 = 1; + } + return base( N, KL, KU, NCOLS, AB, sab1, sab2, 0, AFB, safb1, safb2, 0 ); +} + + +// EXPORTS // + +module.exports = dlagbrpvgrw; diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/index.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/index.js new file mode 100644 index 000000000000..91ad8dbcd201 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/index.js @@ -0,0 +1,68 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +/** +* LAPACK routine to compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A`. +* +* @module @stdlib/lapack/base/dla-gbrpvgrw +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, 4 ); +* // returns 1.0 +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var dlagbrpvgrw = require( '@stdlib/lapack/base/dla-gbrpvgrw' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw.ndarray( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); +* // returns 1.0 +*/ + +// MODULES // + +var join = require( 'path' ).join; +var tryRequire = require( '@stdlib/utils/try-require' ); +var isError = require( '@stdlib/assert/is-error' ); +var main = require( './main.js' ); + + +// MAIN // + +var dlagbrpvgrw; +var tmp = tryRequire( join( __dirname, './native.js' ) ); +if ( isError( tmp ) ) { + dlagbrpvgrw = main; +} else { + dlagbrpvgrw = tmp; +} + + +// EXPORTS // + +module.exports = dlagbrpvgrw; diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/main.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/main.js new file mode 100644 index 000000000000..e1b273b4fe3e --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/main.js @@ -0,0 +1,35 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' ); +var dlagbrpvgrw = require( './dlagbrpvgrw.js' ); +var ndarray = require( './ndarray.js' ); + + +// MAIN // + +setReadOnly( dlagbrpvgrw, 'ndarray', ndarray ); + + +// EXPORTS // + +module.exports = dlagbrpvgrw; diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/ndarray.js new file mode 100644 index 000000000000..5e187c6c45c5 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/lib/ndarray.js @@ -0,0 +1,69 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var base = require( './base.js' ); + + +// MAIN // + +/** +* Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix `A` using alternating indexing semantics. +* +* ## Notes +* +* - The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix `A` could be poor. This also means that the solution `X`, estimated condition numbers, and error bounds could be unreliable. +* - Matrix `AB` is the matrix A in band storage, in rows 0 to `KL+KU`. The j-th column of A is stored in the j-th column of the matrix `AB` as `AB( KU+i-j, j ) = A( i, j )` for `max( 0, j - KU ) <= i <= min( N - 1, j + KL )`. +* - Matrix `AFB` stores the details of the LU factorization of the band matrix `A`, as computed by `DGBTRF`. `U` is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 0 to `KL+KU+1`, and the multipliers used during the factorization are stored in rows `KL+KU+1` to `2*KL+KU`. +* - The leading dimension of `AB`, `LDAB` >= `KL+KU+1`. +* - The leading dimension of `AFB`, `LDAFB` >= `2*KL+KU+1`. +* +* @param {NonNegativeInteger} N - number of rows in matrix `A` +* @param {NonNegativeInteger} KL - number of subdiagonals within the band of matrix `A` +* @param {NonNegativeInteger} KU - number of superdiagonals within the band of matrix `A` +* @param {NonNegativeInteger} NCOLS - number of columns in matrix `A` +* @param {Float64Array} AB - the matrix A in band storage +* @param {integer} strideAB1 - stride of the first dimension of `AB` +* @param {integer} strideAB2 - stride of the second dimension of `AB` +* @param {NonNegativeInteger} offsetAB - index offset for `AB` +* @param {Float64Array} AFB - details of the LU factorization of the band matrix `A` +* @param {integer} strideAFB1 - stride of the first dimension of `AFB` +* @param {integer} strideAFB2 - stride of the second dimension of `AFB` +* @param {NonNegativeInteger} offsetAFB - index offset for `AFB` +* @returns {number} the reciprocal pivot growth factor +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* +* var AB = new Float64Array( [ 0.0, 2.0, 5.0, 8.0, 1.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 0.0 ] ); +* var AFB = new Float64Array( [ 0.0, 0.0, 5.0, 8.0, 0.0, 4.0, 7.0, 10.0, 3.0, 6.0, 9.0, 1.8272, 0.3333, 0.1111, -0.2716, 0.0 ] ); +* +* var out = dlagbrpvgrw( 4, 1, 1, 4, AB, 4, 1, 0, AFB, 4, 1, 0 ); +* // returns 1.0 +*/ +function dlagbrpvgrw( N, KL, KU, NCOLS, AB, strideAB1, strideAB2, offsetAB, AFB, strideAFB1, strideAFB2, offsetAFB ) { // eslint-disable-line max-len, max-params + return base( N, KL, KU, NCOLS, AB, strideAB1, strideAB2, offsetAB, AFB, strideAFB1, strideAFB2, offsetAFB ); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = dlagbrpvgrw; diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/package.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/package.json new file mode 100644 index 000000000000..0d6c50a43f64 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/package.json @@ -0,0 +1,73 @@ +{ + "name": "@stdlib/lapack/base/dla-gbrpvgrw", + "version": "0.0.0", + "description": "LAPACK routine to computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "lapack", + "dla_gbrpvgrw", + "orthogonal", + "qr", + "decomposition", + "householder", + "reflectors", + "matrix", + "linear", + "algebra", + "subroutines", + "array", + "ndarray", + "float64", + "double", + "float64array" + ] +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/column_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/column_major.json new file mode 100644 index 000000000000..de46a814cdb6 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/column_major.json @@ -0,0 +1,59 @@ +{ + "order": "column-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 0.0, + 1.0, + 3.0, + 2.0, + 4.0, + 6.0, + 5.0, + 7.0, + 9.0, + 8.0, + 10.0, + 0.0 + ], + "strideAB1": 1, + "strideAB2": 3, + "offsetAB": 0, + "AFB_mat": [ + [ 0.0, 0.0, 5.0, 8.0 ], + [ 0.0, 4.0, 7.0, 10.0 ], + [ 3.0, 6.0, 9.0, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0.0 ] + ], + "AFB": [ + 0.0, + 0.0, + 3.0, + 0.3333, + 0.0, + 4.0, + 6.0, + 0.1111, + 5.0, + 7.0, + 9.0, + -0.2716, + 8.0, + 10.0, + 1.8272, + 0.0 + ], + "strideAFB1": 1, + "strideAFB2": 4, + "offsetAFB": 0 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/large_strides/column_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/large_strides/column_major.json new file mode 100644 index 000000000000..434d8d8e676c --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/large_strides/column_major.json @@ -0,0 +1,87 @@ +{ + "order": "column-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 0, + 9999, + 1, + 9999, + 3, + 9999, + 2, + 9999, + 4, + 9999, + 6, + 9999, + 5, + 9999, + 7, + 9999, + 9, + 9999, + 8, + 9999, + 10, + 9999, + 0, + 9999 + ], + "strideAB1": 2, + "strideAB2": 6, + "offsetAB": 0, + "AFB_mat": [ + [ 0.0, 0.0, 5.0, 8.0 ], + [ 0.0, 4.0, 7.0, 10.0 ], + [ 3.0, 6.0, 9.0, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0.0 ] + ], + "AFB": [ + 0, + 9999, + 0, + 9999, + 3, + 9999, + 0.3333, + 9999, + 0, + 9999, + 4, + 9999, + 6, + 9999, + 0.1111, + 9999, + 5, + 9999, + 7, + 9999, + 9, + 9999, + -0.2716, + 9999, + 8, + 9999, + 10, + 9999, + 1.8272, + 9999, + 0, + 9999 + ], + "strideAFB1": 2, + "strideAFB2": 8, + "offsetAFB": 0 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/large_strides/row_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/large_strides/row_major.json new file mode 100644 index 000000000000..e2361efc22c0 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/large_strides/row_major.json @@ -0,0 +1,87 @@ +{ + "order": "row-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 0, + 9999, + 2, + 9999, + 5, + 9999, + 8, + 9999, + 1, + 9999, + 4, + 9999, + 7, + 9999, + 10, + 9999, + 3, + 9999, + 6, + 9999, + 9, + 9999, + 0, + 9999 + ], + "strideAB1": 8, + "strideAB2": 2, + "offsetAB": 0, + "AFB_mat": [ + [ 0, 0, 5, 8 ], + [ 0, 4, 7, 10 ], + [ 3, 6, 9, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0 ] + ], + "AFB": [ + 0, + 9999, + 0, + 9999, + 5, + 9999, + 8, + 9999, + 0, + 9999, + 4, + 9999, + 7, + 9999, + 10, + 9999, + 3, + 9999, + 6, + 9999, + 9, + 9999, + 1.8272, + 9999, + 0.3333, + 9999, + 0.1111, + 9999, + -0.2716, + 9999, + 0, + 9999 + ], + "strideAFB1": 8, + "strideAFB2": 2, + "offsetAFB": 0 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/mixed_strides/column_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/mixed_strides/column_major.json new file mode 100644 index 000000000000..75aa027fb168 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/mixed_strides/column_major.json @@ -0,0 +1,59 @@ +{ + "order": "column-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 8, + 10, + 0, + 5, + 7, + 9, + 2, + 4, + 6, + 0, + 1, + 3 + ], + "strideAB1": 1, + "strideAB2": -3, + "offsetAB": 9, + "AFB_mat": [ + [ 0.0, 0.0, 5.0, 8.0 ], + [ 0.0, 4.0, 7.0, 10.0 ], + [ 3.0, 6.0, 9.0, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0.0 ] + ], + "AFB": [ + 8, + 10, + 1.8272, + 0, + 5, + 7, + 9, + -0.2716, + 0, + 4, + 6, + 0.1111, + 0, + 0, + 3, + 0.3333 + ], + "strideAFB1": 1, + "strideAFB2": -4, + "offsetAFB": 12 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/mixed_strides/row_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/mixed_strides/row_major.json new file mode 100644 index 000000000000..a614102c86bc --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/mixed_strides/row_major.json @@ -0,0 +1,59 @@ +{ + "order": "row-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 3, + 6, + 9, + 0, + 1, + 4, + 7, + 10, + 0, + 2, + 5, + 8 + ], + "strideAB1": -4, + "strideAB2": 1, + "offsetAB": 8, + "AFB_mat": [ + [ 0, 0, 5, 8 ], + [ 0, 4, 7, 10 ], + [ 3, 6, 9, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0 ] + ], + "AFB": [ + 0.3333, + 0.1111, + -0.2716, + 0, + 3, + 6, + 9, + 1.8272, + 0, + 4, + 7, + 10, + 0, + 0, + 5, + 8 + ], + "strideAFB1": -4, + "strideAFB2": 1, + "offsetAFB": 12 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/negative_strides/column_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/negative_strides/column_major.json new file mode 100644 index 000000000000..8c0f66396e7d --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/negative_strides/column_major.json @@ -0,0 +1,59 @@ +{ + "order": "column-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 0, + 10, + 8, + 9, + 7, + 5, + 6, + 4, + 2, + 3, + 1, + 0 + ], + "strideAB1": -1, + "strideAB2": -3, + "offsetAB": 11, + "AFB_mat": [ + [ 0.0, 0.0, 5.0, 8.0 ], + [ 0.0, 4.0, 7.0, 10.0 ], + [ 3.0, 6.0, 9.0, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0.0 ] + ], + "AFB": [ + 0, + 1.8272, + 10, + 8, + -0.2716, + 9, + 7, + 5, + 0.1111, + 6, + 4, + 0, + 0.3333, + 3, + 0, + 0 + ], + "strideAFB1": -1, + "strideAFB2": -4, + "offsetAFB": 15 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/negative_strides/row_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/negative_strides/row_major.json new file mode 100644 index 000000000000..cd37105e1a6f --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/negative_strides/row_major.json @@ -0,0 +1,59 @@ +{ + "order": "row-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 0, + 9, + 6, + 3, + 10, + 7, + 4, + 1, + 8, + 5, + 2, + 0 + ], + "strideAB1": -4, + "strideAB2": -1, + "offsetAB": 11, + "AFB_mat": [ + [ 0, 0, 5, 8 ], + [ 0, 4, 7, 10 ], + [ 3, 6, 9, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0 ] + ], + "AFB": [ + 0, + -0.2716, + 0.1111, + 0.3333, + 1.8272, + 9, + 6, + 3, + 10, + 7, + 4, + 0, + 8, + 5, + 0, + 0 + ], + "strideAFB1": -4, + "strideAFB2": -1, + "offsetAFB": 15 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/offsets/column_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/offsets/column_major.json new file mode 100644 index 000000000000..82e5b3fa9620 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/offsets/column_major.json @@ -0,0 +1,61 @@ +{ + "order": "column-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 9999, + 0, + 1, + 3, + 2, + 4, + 6, + 5, + 7, + 9, + 8, + 10, + 0 + ], + "strideAB1": 1, + "strideAB2": 3, + "offsetAB": 1, + "AFB_mat": [ + [ 0.0, 0.0, 5.0, 8.0 ], + [ 0.0, 4.0, 7.0, 10.0 ], + [ 3.0, 6.0, 9.0, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0.0 ] + ], + "AFB": [ + 9999, + 0, + 0, + 3, + 0.3333, + 0, + 4, + 6, + 0.1111, + 5, + 7, + 9, + -0.2716, + 8, + 10, + 1.8272, + 0 + ], + "strideAFB1": 1, + "strideAFB2": 4, + "offsetAFB": 1 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/offsets/row_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/offsets/row_major.json new file mode 100644 index 000000000000..0219a9c1a58e --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/offsets/row_major.json @@ -0,0 +1,61 @@ +{ + "order": "row-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 9999, + 0, + 2, + 5, + 8, + 1, + 4, + 7, + 10, + 3, + 6, + 9, + 0 + ], + "strideAB1": 4, + "strideAB2": 1, + "offsetAB": 1, + "AFB_mat": [ + [ 0, 0, 5, 8 ], + [ 0, 4, 7, 10 ], + [ 3, 6, 9, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0 ] + ], + "AFB": [ + 9999, + 0, + 0, + 5, + 8, + 0, + 4, + 7, + 10, + 3, + 6, + 9, + 1.8272, + 0.3333, + 0.1111, + -0.2716, + 0 + ], + "strideAFB1": 4, + "strideAFB2": 1, + "offsetAFB": 1 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/row_major.json b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/row_major.json new file mode 100644 index 000000000000..584c2405bfe1 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/fixtures/row_major.json @@ -0,0 +1,59 @@ +{ + "order": "row-major", + "N": 4, + "KL": 1, + "KU": 1, + "NCOLS": 4, + "LDAB": 3, + "LDAFB": 4, + "rpgFactor": 1, + "AB_mat": [ + [ 0, 2, 5, 8 ], + [ 1, 4, 7, 10 ], + [ 3, 6, 9, 0 ] + ], + "AB": [ + 0.0, + 2.0, + 5.0, + 8.0, + 1.0, + 4.0, + 7.0, + 10.0, + 3.0, + 6.0, + 9.0, + 0.0 + ], + "strideAB1": 4, + "strideAB2": 1, + "offsetAB": 0, + "AFB_mat": [ + [ 0, 0, 5, 8 ], + [ 0, 4, 7, 10 ], + [ 3, 6, 9, 1.8272 ], + [ 0.3333, 0.1111, -0.2716, 0 ] + ], + "AFB": [ + 0.0, + 0.0, + 5.0, + 8.0, + 0.0, + 4.0, + 7.0, + 10.0, + 3.0, + 6.0, + 9.0, + 1.8272, + 0.3333, + 0.1111, + -0.2716, + 0.0 + ], + "strideAFB1": 4, + "strideAFB2": 1, + "offsetAFB": 0 +} diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.dlagbrpvgrw.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.dlagbrpvgrw.js new file mode 100644 index 000000000000..c915a2285e76 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.dlagbrpvgrw.js @@ -0,0 +1,204 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var Float64Array = require( '@stdlib/array/float64' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var dlagbrpvgrw = require( './../lib/dlagbrpvgrw.js' ); + + +// FIXTURES // + +// Note: the outputs are tested against the outputs of the Fortran implementation. + +var COL_MAJOR = require( './fixtures/column_major.json' ); +var ROW_MAJOR = require( './fixtures/row_major.json' ); + + +// FUNCTIONS // + +/** +* Tests for element-wise approximate equality. +* +* @private +* @param {Object} t - test object +* @param {Collection} actual - actual values +* @param {Collection} expected - expected values +* @param {number} rtol - relative tolerance +*/ +function isApprox( t, actual, expected, rtol ) { + var delta; + var tol; + var i; + + t.strictEqual( actual.length, expected.length, 'returns expected value' ); + for ( i = 0; i < expected.length; i++ ) { + if ( actual[ i ] === expected[ i ] ) { + t.strictEqual( actual[ i ], expected[ i ], 'returns expected value' ); + } else { + delta = abs( actual[ i ] - expected[ i ] ); + tol = rtol * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. actual: '+actual[ i ]+'. expected: '+expected[ i ]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } +} + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dlagbrpvgrw, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 9', function test( t ) { + t.strictEqual( dlagbrpvgrw.length, 9, 'returns expected value' ); + t.end(); +}); + +tape( 'the function throws an error if provided a first argument which is not a valid order', function test( t ) { + var values; + var AFB; + var AB; + var i; + + values = [ + 'foo', + 'bar', + 'beep', + 'boop', + -5, + NaN, + true, + false, + null, + void 0, + [], + {}, + function noop() {} + ]; + + AFB = new Float64Array( 16 ); + AB = new Float64Array( 16 ); + + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + dlagbrpvgrw( value, 4, 1, 1, 4, AB, 3, AFB, 4 ); + }; + } +}); + +tape( 'the function throws an error if provided a seventh argument which is not a valid `LDAB` value', function test( t ) { + var values; + var AFB; + var AB; + var i; + + values = [ + 0, + 1, + 2 + ]; + + AFB = new Float64Array( 16 ); + AB = new Float64Array( 16 ); + + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, value, AFB, 4 ); + }; + } +}); + +tape( 'the function throws an error if provided a ninth argument which is not a valid `LDAFB` value', function test( t ) { + var values; + var AFB; + var AB; + var i; + + values = [ + 0, + 1, + 2, + 3 + ]; + + AFB = new Float64Array( 16 ); + AB = new Float64Array( 16 ); + + for ( i = 0; i < values.length; i++ ) { + t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] ); + } + t.end(); + + function badValue( value ) { + return function badValue() { + dlagbrpvgrw( 'row-major', 4, 1, 1, 4, AB, 3, AFB, value ); + }; + } +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (column-major)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = COL_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.order, data.N, data.KL, data.KU, data.NCOLS, AB, data.LDAB, AFB, data.LDAFB ); // eslint-disable-line max-len + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (row-major)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = ROW_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.order, data.N, data.KL, data.KU, data.NCOLS, AB, data.LDAB, AFB, data.LDAFB ); // eslint-disable-line max-len + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.js new file mode 100644 index 000000000000..c1ed83d47be0 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.js @@ -0,0 +1,82 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var proxyquire = require( 'proxyquire' ); +var IS_BROWSER = require( '@stdlib/assert/is-browser' ); +var dlagbrpvgrw = require( './../lib' ); + + +// VARIABLES // + +var opts = { + 'skip': IS_BROWSER +}; + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dlagbrpvgrw, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'attached to the main export is a method providing an ndarray interface', function test( t ) { + t.strictEqual( typeof dlagbrpvgrw.ndarray, 'function', 'method is a function' ); + t.end(); +}); + +tape( 'if a native implementation is available, the main export is the native implementation', opts, function test( t ) { + var dlagbrpvgrw = proxyquire( './../lib', { + '@stdlib/utils/try-require': tryRequire + }); + + t.strictEqual( dlagbrpvgrw, mock, 'returns expected value' ); + t.end(); + + function tryRequire() { + return mock; + } + + function mock() { + // Mock... + } +}); + +tape( 'if a native implementation is not available, the main export is a JavaScript implementation', opts, function test( t ) { + var dlagbrpvgrw; + var main; + + main = require( './../lib/dlagbrpvgrw.js' ); + + dlagbrpvgrw = proxyquire( './../lib', { + '@stdlib/utils/try-require': tryRequire + }); + + t.strictEqual( dlagbrpvgrw, main, 'returns expected value' ); + t.end(); + + function tryRequire() { + return new Error( 'Cannot find module' ); + } +}); diff --git a/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.ndarray.js b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.ndarray.js new file mode 100644 index 000000000000..afdd07e98b37 --- /dev/null +++ b/lib/node_modules/@stdlib/lapack/base/dla-gbrpvgrw/test/test.ndarray.js @@ -0,0 +1,258 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/* eslint-disable max-len */ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var Float64Array = require( '@stdlib/array/float64' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var dlagbrpvgrw = require( './../lib/ndarray.js' ); + + +// FIXTURES // + +// Note: the outputs are tested against the outputs of the Fortran implementation. + +var COL_MAJOR = require( './fixtures/column_major.json' ); +var ROW_MAJOR = require( './fixtures/row_major.json' ); +var LARGE_STRIDES_COL_MAJOR = require( './fixtures/large_strides/column_major.json' ); +var LARGE_STRIDES_ROW_MAJOR = require( './fixtures/large_strides/row_major.json' ); +var NEGATIVE_STRIDES_COL_MAJOR = require( './fixtures/negative_strides/column_major.json' ); +var NEGATIVE_STRIDES_ROW_MAJOR = require( './fixtures/negative_strides/row_major.json' ); +var MIXED_STRIDES_COL_MAJOR = require( './fixtures/mixed_strides/column_major.json' ); +var MIXED_STRIDES_ROW_MAJOR = require( './fixtures/mixed_strides/row_major.json' ); +var OFFSETS_COL_MAJOR = require( './fixtures/offsets/column_major.json' ); +var OFFSETS_ROW_MAJOR = require( './fixtures/offsets/row_major.json' ); + + +// FUNCTIONS // + +/** +* Tests for element-wise approximate equality. +* +* @private +* @param {Object} t - test object +* @param {Collection} actual - actual values +* @param {Collection} expected - expected values +* @param {number} rtol - relative tolerance +*/ +function isApprox( t, actual, expected, rtol ) { + var delta; + var tol; + var i; + + t.strictEqual( actual.length, expected.length, 'returns expected value' ); + for ( i = 0; i < expected.length; i++ ) { + if ( actual[ i ] === expected[ i ] ) { + t.strictEqual( actual[ i ], expected[ i ], 'returns expected value' ); + } else { + delta = abs( actual[ i ] - expected[ i ] ); + tol = rtol * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. actual: '+actual[ i ]+'. expected: '+expected[ i ]+'. delta: '+delta+'. tol: '+tol+'.' ); + } + } +} + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof dlagbrpvgrw, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 12', function test( t ) { + t.strictEqual( dlagbrpvgrw.length, 12, 'returns expected value' ); + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (column-major)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = COL_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (rpw-major)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = ROW_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (column-major, large strides)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = LARGE_STRIDES_COL_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (row-major, large strides)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = LARGE_STRIDES_ROW_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (column-major, negative strides)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = NEGATIVE_STRIDES_COL_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (row-major, negative strides)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = NEGATIVE_STRIDES_ROW_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (column-major, offsets)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = OFFSETS_COL_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (row-major, offsets)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = OFFSETS_ROW_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (column-major, mixed strides)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = MIXED_STRIDES_COL_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +}); + +tape( 'the function computes the reciprocal pivot growth factor for a general banded matrix `AB` (row-major, mixed strides)', function test( t ) { + var rpgFactor; + var data; + var AFB; + var AB; + + data = MIXED_STRIDES_ROW_MAJOR; + + AFB = new Float64Array( data.AFB ); + AB = new Float64Array( data.AB ); + + rpgFactor = dlagbrpvgrw( data.N, data.KL, data.KU, data.NCOLS, AB, data.strideAB1, data.strideAB2, data.offsetAB, AFB, data.strideAFB1, data.strideAFB2, data.offsetAFB ); + isApprox( t, rpgFactor, data.rpgFactor, 1.0 ); + + t.end(); +});