Various sign/indexing fixes and performance improvements (#2)

* - made changes that agree with the Julia version (analytic Exchange matrix elements) up to flipping b field sign (complex conjugate and a sign).

* Did checks and compared Julia implementation results to revised package results

* added additional comments

* fix: Update README to include sigma notation for matrix elements and exchange kernels

* added sigma feature to planewave part
- next to do the same for exchange matrix element

* fix: Update execution counts and correct sigma parameter in Checks_exchange_pwme notebook

* fix: Remove unused code cell from Checks_exchange_pwme notebook

* Edited Exchange matrix elements to include boths sign of sigma (B_z * charge carrier).
- Added h5 file that has planewave and exchange elements for randomly sampled G points

* Refactoring and performance improvements

* fix: Correct LaTeX formatting for magnetic field sign in README

* fix: Add missing line breaks in wavefunction section of README

* fix: Add Sparsh Mishra as an author in CITATION.cff and pyproject.toml

* Initial plan

* Initial plan

* Initial plan

* Enhance docstring for get_exchange_kernels_GaussLegendre function

Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

* Remove commented-out code and placeholder comments from exchange_hankel.py

Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

* Initial plan

* Address code review feedback on docstring clarity

Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

* Add sign_magneticfield validation to exchange_legendre.py

Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

* Add missing blank line before Notes section header

Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

* Initial plan

* Address PR review comments: trailing whitespace, validation, docstring, grammar, unused variable

Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

---------

Co-authored-by: sparsh mishra <sparshmishra1@gmail.com>
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: skilledwolf <18141588+skilledwolf@users.noreply.github.com>

Author: 3 people

CITATION.cff

@@ -6,6 +6,8 @@ version: "0.1.0"
 doi: 10.5281/zenodo.17646158
 date-released: "2025-11-18"
 authors:
+  - family-names: Mishra
+    given-names: Sparsh
   - family-names: Wolf
     given-names: Tobias
 repository-code: "https://github.com/wolft/quantumhall_matrixelements"

README.md

@@ -4,17 +4,18 @@
 
 Landau-level plane-wave form factors and exchange kernels for quantum Hall systems in a small, reusable package (useful for Hartree-Fock and related calculations). It provides:
 
-- Analytic Landau-level plane-wave form factors $F_{n',n}(\mathbf{q})$.
-- Exchange kernels $X_{n_1 m_1 n_2 m_2}(\mathbf{G})$. 
+- Analytic Landau-level plane-wave form factors $F_{n',n}^\sigma(\mathbf{q})$.
+- Exchange kernels $X_{n_1 m_1 n_2 m_2}^\sigma(\mathbf{G})$. 
 - Symmetry diagnostics for verifying kernel implementations. 
 
 ### Plane-Wave Landau-level Form Factors 
-The plane-wave matrix element $F_{n',n}(\mathbf{q}) = \langle n' | e^{i \mathbf{q} \cdot \mathbf{R}} | n \rangle$ can be written as
+For $\sigma = \mathrm{sgn}(qB_z)$, where $q$ is the charge of the carrier and $B_z$ is the magnetic field direction,
+The plane-wave matrix element $F^\sigma_{n',n}(\mathbf{q}) = \langle n' | e^{i \mathbf{q} \cdot \mathbf{R}_\sigma} | n \rangle$ can be written as
 
 $$
-F_{n',n}(\mathbf{q}) =
+F_{n',n}^\sigma(\mathbf{q}) =
 i^{|n-n'|}
-e^{i(n-n')\theta_{\mathbf{q}}}
+e^{i\sigma(n'-n)\theta_{\mathbf{q}}}
 \sqrt{\frac{n_{<}!}{n_{>}!}}
 \left( \frac{|\mathbf{q}|\ell_{B}}{\sqrt{2}} \right)^{|n-n'|}
 L_{n_<}^{|n-n'|}\left( \frac{|\mathbf{q}|^2 \ell_{B}^2}{2} \right)
@@ -26,7 +27,7 @@ where $n_< = \min(n, n')$, $n_> = \max(n, n')$, and $L_n^\alpha$ are the general
 ### Exchange Kernels
 
 
-$$ X_{n_1 m_1 n_2 m_2}(\mathbf{G}) = \int \frac{d^2 q}{(2\pi)^2} V(q) F_{m_1, n_1}(\mathbf{q}) F_{n_2, m_2}(-\mathbf{q}) e^{i (\mathbf{q} \times \mathbf{G})_z \ell_B^2} $$
+$$ X_{n_1 m_1 n_2 m_2}^\sigma(\mathbf{G}) = \int \frac{d^2 q}{(2\pi)^2} V(q) F_{m_1, n_1}^\sigma(\mathbf{q}) F_{n_2, m_2}^\sigma(-\mathbf{q}) e^{i\sigma (\mathbf{q} \times \mathbf{G})_z \ell_B^2} $$
 
 where $V(q)$ is the interaction potential. For the Coulomb interaction, $V(q) = \frac{2\pi e^2}{\epsilon q}$.
 
@@ -92,11 +93,25 @@ X_coulomb = get_exchange_kernels(
 
 For more detailed examples, see the example scripts under `examples/` and the tests under `tests/`.
 
+## Magnetic-field sign
+
+The public APIs expose a `sign_magneticfield` keyword that represents
+$\sigma = \mathrm{sgn}(q B_z)$, the sign of the charge–field product.
+The default `sign_magneticfield=-1` matches the package's internal convention
+(electrons in a positive $B_z$). Passing `sign_magneticfield=+1` returns the
+appropriate complex-conjugated form factors or exchange kernels for the
+opposite field direction without requiring any manual phase adjustments:
+
+```python
+F_plusB = get_form_factors(Gs_dimless, thetas, nmax, sign_magneticfield=+1)
+X_plusB = get_exchange_kernels(Gs_dimless, thetas, nmax, method="hankel", sign_magneticfield=+1)
+```
+
 ## Citation
 
 If you use the package `quantumhall-matrixelements` in academic work, you must cite:
 
-> Tobias Wolf, *quantumhall-matrixelements: Quantum Hall Landau-Level Matrix Elements*, version 0.1.0, 2025.  
+> Sparsh Mishra and Tobias Wolf, *quantumhall-matrixelements: Quantum Hall Landau-Level Matrix Elements*, version 0.1.0, 2025.  
 > DOI: https://doi.org/10.5281/zenodo.17646158
 
 [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.17646158.svg)](https://doi.org/10.5281/zenodo.17646158)
@@ -105,25 +120,30 @@ A machine-readable `CITATION.cff` file is included in the repository and can be
 
 ## Backends and Reliability
 
-The package provides three backends for computing exchange kernels, each with different performance and stability characteristics:
+The package provides two backends for computing exchange kernels:
+
+1. **`gausslegendre` (Default)**
+   - **Method**: Gauss-Legendre quadrature mapped from $[-1, 1]$ to $[0, \infty)$ via a rational mapping.
+   - **Pros**: Fast and numerically stable for all Landau-level indices ($n$).
+   - **Cons**: May require tuning `nquad` for extremely large momenta or indices ($n > 100$).
+   - **Recommended for**: General usage, especially for $n \ge 10$.
 
-1.  **`gausslegendre` (Default)**:
-    -   **Method**: Gauss-Legendre quadrature mapped from $[-1, 1]$ to $[0, \infty)$ via a rational mapping.
-    -   **Pros**: Fast and numerically stable for all Landau level indices ($n$).
-    -   **Cons**: May require tuning `nquad` for extremely large momenta or indices ($n > 100$).
-    -   **Recommended for**: General usage, especially for large $n$ ($n \ge 10$).
+2. **`hankel`**
+   - **Method**: Discrete Hankel transform.
+   - **Pros**: High precision and stability.
+   - **Cons**: Significantly slower than quadrature methods.
+   - **Recommended for**: Reference calculations and verifying the Gauss–Legendre backend.
 
-2.  **`gausslag`**:
-    -   **Method**: Generalized Gauss-Laguerre quadrature.
-    -   **Pros**: Very fast for small $n$.
-    -   **Cons**: Numerically unstable for large $n$ ($n \ge 12$) due to high-order Laguerre polynomial roots.
-    -   **Recommended for**: Small systems ($n < 10$) where speed is critical.
+## Notes
+The following wavefunction is used to find all matrix elements:
 
-3.  **`hankel`**:
-    -   **Method**: Discrete Hankel transform.
-    -   **Pros**: High precision and stability.
-    -   **Cons**: Significantly slower than quadrature methods.
-    -   **Recommended for**: Reference calculations and verifying other backends.
+$$
+\Psi_{nX}^\sigma(x,y)
+= \frac{e^{i\sigma X y \ell_B^{-2}}}{\sqrt{L_y}}i^n\,
+\phi_{n}(x -X),
+\qquad
+X = \sigma k_y \ell_B^{2}.
+$$
 
 ## Development
 
@@ -142,6 +162,6 @@ The package provides three backends for computing exchange kernels, each with di
 
 ## Authors and license
 
-- Author: Dr. Tobias Wolf
+- Authors: Dr. Tobias Wolf, Sparsh Mishra
 - Copyright © 2025 Tobias Wolf
 - License: MIT (see `LICENSE`).

examples/compare_exchange_backends.py

@@ -1,8 +1,8 @@
-"""Compare Gauss–Laguerre and Hankel exchange-kernel backends.
+"""Compare Gauss–Legendre and Hankel exchange-kernel backends.
 
 For a small |G|ℓ_B grid and nmax=2, this script computes the exchange
-kernels using both the Gauss–Laguerre and Hankel backends and plots the
-relative difference of a representative diagonal element X_{0000}(G).
+kernels using both the Gauss–Legendre (default) and Hankel backends and plots
+the relative difference of a representative diagonal element X_{0000}(G).
 """
 from __future__ import annotations
 
@@ -13,11 +13,11 @@
 
 
 def main() -> None:
-    nmax = 2
-    q = np.linspace(0.2, 3.0, 60)
+    nmax = 10
+    q = np.linspace(0.2, 20.0, 60)
     theta = np.zeros_like(q)
 
-    X_gl = get_exchange_kernels(q, theta, nmax, method="gausslag")
+    X_gl = get_exchange_kernels(q, theta, nmax, method="gausslegendre")
     X_hk = get_exchange_kernels(q, theta, nmax, method="hankel")
 
     # Focus on X_{0000}(G) as a simple representative component
@@ -32,12 +32,11 @@ def main() -> None:
     ax.plot(q, rel_diff, marker="o", linestyle="-")
     ax.set_xlabel(r"$|G| \ell_B$")
     ax.set_ylabel(r"relative difference")
-    ax.set_title(r"Relative difference of $X_{0000}(G)$: Gauss–Laguerre vs Hankel")
+    ax.set_title(r"Relative difference of $X_{0000}(G)$: Gauss–Legendre vs Hankel")
     ax.grid(True, alpha=0.3)
     fig.tight_layout()
     plt.show()
 
 
 if __name__ == "__main__":
     main()
-

examples/plot_exchange_kernels_radial.py

@@ -1,7 +1,7 @@
 """Exchange kernel diagonal elements X_{nnnn}(G) vs |G|ℓ_B.
 
 This example computes selected diagonal components of the exchange kernel
-using the Gauss–Laguerre backend and plots their real parts as a function
+using the Gauss–Legendre backend and plots their real parts as a function
 of |G|ℓ_B.
 """
 from __future__ import annotations
@@ -18,7 +18,7 @@ def main() -> None:
     q = np.linspace(0.2, 4.0, 80)
     theta = np.zeros_like(q)
 
-    X = get_exchange_kernels(q, theta, nmax, method="gausslag")
+    X = get_exchange_kernels(q, theta, nmax, method="gausslegendre")
 
     fig, ax = plt.subplots()
     for n in range(nmax):
@@ -31,7 +31,7 @@ def main() -> None:
 
     ax.set_xlabel(r"$|G| \ell_B$")
     ax.set_ylabel(r"$\mathrm{Re}\,X_{nnnn}(G)$  (κ=1)")
-    ax.set_title("Diagonal exchange kernels (Gauss–Laguerre backend)")
+    ax.set_title("Diagonal exchange kernels (Gauss–Legendre backend)")
     ax.legend()
     ax.grid(True, alpha=0.3)
     fig.tight_layout()
@@ -40,4 +40,3 @@ def main() -> None:
 
 if __name__ == "__main__":
     main()
-

pyproject.toml

@@ -7,7 +7,8 @@ name = "quantumhall_matrixelements"
 description = "Landau-level plane-wave form factors and exchange kernels for quantum Hall systems."
 readme = "README.md"
 authors = [
-  { name = "Tobias Wolf", email = "public@wolft.xyz" }
+  { name = "Tobias Wolf", email = "public@wolft.xyz" },
+  { name = "Sparsh Mishra" }
 ]
 license = { text = "MIT" }
 requires-python = ">=3.10"

src/quantumhall_matrixelements/__init__.py

@@ -10,15 +10,16 @@
 """
 from __future__ import annotations
 
+from importlib.metadata import PackageNotFoundError
+from importlib.metadata import version as _metadata_version
 from typing import TYPE_CHECKING
 
 import numpy as np
-from importlib.metadata import PackageNotFoundError, version as _metadata_version
 
-from .planewave import get_form_factors
-from .exchange_gausslag import get_exchange_kernels_GaussLag
+from .diagnostic import get_exchange_kernels_opposite_field, get_form_factors_opposite_field
 from .exchange_hankel import get_exchange_kernels_hankel
 from .exchange_legendre import get_exchange_kernels_GaussLegendre
+from .planewave import get_form_factors
 
 if TYPE_CHECKING:
     from numpy.typing import NDArray
@@ -28,13 +29,13 @@
 
 
 def get_exchange_kernels(
-    G_magnitudes: "RealArray",
-    G_angles: "RealArray",
+    G_magnitudes: RealArray,
+    G_angles: RealArray,
     nmax: int,
     *,
     method: str | None = None,
     **kwargs,
-) -> "ComplexArray":
+) -> ComplexArray:
     """Dispatcher for exchange kernels.
 
     Parameters
@@ -49,26 +50,24 @@ def get_exchange_kernels(
 
         - ``'gausslegendre'`` (default): Gauss-Legendre quadrature with rational mapping.
           Recommended for all nmax.
-        - ``'gausslag'``: generalized Gauss–Laguerre quadrature.
-          Fast for small nmax (< 10), but unstable for large nmax.
         - ``'hankel'``: Hankel-transform based implementation.
 
     **kwargs :
         Additional arguments passed to the backend (e.g. ``nquad``, ``scale``).
+        Common keywords include ``sign_magneticfield`` (±1) to select the
+        magnetic-field orientation convention.
 
     Notes
     -----
     Both backends return kernels normalized for :math:`\\kappa = 1`. Any
     physical interaction strength should be applied by the caller.
     """
     chosen = (method or "gausslegendre").strip().lower()
-    if chosen in {"gausslag", "gauss-lag", "gausslaguerre", "gauss-laguerre", "gl"}:
-        return get_exchange_kernels_GaussLag(G_magnitudes, G_angles, nmax, **kwargs)
     if chosen in {"hankel", "hk"}:
         return get_exchange_kernels_hankel(G_magnitudes, G_angles, nmax, **kwargs)
     if chosen in {"gausslegendre", "gauss-legendre", "legendre", "leg"}:
         return get_exchange_kernels_GaussLegendre(G_magnitudes, G_angles, nmax, **kwargs)
-    raise ValueError(f"Unknown exchange-kernel method: {method!r}. Use 'gausslegendre', 'gausslag', or 'hankel'.")
+    raise ValueError(f"Unknown exchange-kernel method: {method!r}. Use 'gausslegendre' or 'hankel'.")
 
 
 try:
@@ -81,7 +80,6 @@ def get_exchange_kernels(
 __all__ = [
     "get_form_factors",
     "get_exchange_kernels",
-    "get_exchange_kernels_GaussLag",
     "get_exchange_kernels_hankel",
     "get_exchange_kernels_GaussLegendre",
     "__version__",