add stable forward/inverse memory efficient Wigner transforms

Author: CosmoMatt

docs/api/precompute_transforms/fourier_wigner.rst

@@ -0,0 +1,7 @@
+:html_theme.sidebar_secondary.remove:
+
+**************************
+Fourier-Wigner Transform
+**************************
+.. automodule:: s2fft.precompute_transforms.fourier_wigner
+   :members: 

docs/api/precompute_transforms/index.rst

@@ -50,6 +50,21 @@ Precompute Functions
    * - :func:`~s2fft.precompute_transforms.wigner.forward_transform_torch`
      - Forward Wigner transform (Torch)
 
+.. list-table:: Fourier-Wigner transforms.
+   :widths: 25 25
+   :header-rows: 1
+
+   * - Function Name
+     - Description
+   * - :func:`~s2fft.precompute_transforms.fourier_wigner.inverse_transform`
+     - Inverse Wigner transform with Fourier method (NumPy)
+   * - :func:`~s2fft.precompute_transforms.fourier_wigner.inverse_transform_jax`
+     - Inverse Wigner transform with Fourier method (JAX)
+   * - :func:`~s2fft.precompute_transforms.fourier_wigner.forward_transform`
+     - Forward Wigner transform with Fourier method (NumPy)
+   * - :func:`~s2fft.precompute_transforms.fourier_wigner.forward_transform_jax`
+     - Forward Wigner transform with Fourier method (JAX)
+
 .. list-table:: Constructing Kernels for precompute transforms.
    :widths: 25 25
    :header-rows: 1
@@ -64,6 +79,10 @@ Precompute Functions
      - Builds a kernel including quadrature weights and Wigner-D coefficients for spherical harmonic transform (JAX).
    * - :func:`~s2fft.precompute_transforms.construct.wigner_kernel_jax`
      - Builds a kernel including quadrature weights and Wigner-D coefficients for Wigner transform (JAX).
+   * - :func:`~s2fft.precompute_transforms.construct.fourier_wigner_kernel`
+     - Builds a kernel including quadrature weights and Fourier coefficienfs of Wigner d-functions
+   * - :func:`~s2fft.precompute_transforms.construct.fourier_wigner_kernel_jax`
+     - Builds a kernel including quadrature weights and Fourier coefficienfs of Wigner d-functions (JAX).
    * - :func:`~s2fft.precompute_transforms.construct.healpix_phase_shifts`
      - Builds a vector of corresponding phase shifts for each HEALPix latitudinal ring.
 
@@ -76,4 +95,5 @@ Precompute Functions
    alt_construct
    spin_spherical 
    wigner
+   fourier_wigner
 

s2fft/precompute_transforms/__init__.py

@@ -1 +1 @@
-from . import construct, spherical, wigner
+from . import construct, fourier_wigner, spherical, wigner

s2fft/precompute_transforms/construct.py

@@ -1,3 +1,4 @@
+from typing import Tuple
 from warnings import warn
 
 import jax
@@ -610,6 +611,62 @@ def wigner_kernel_jax(
     return dl
 
 
+def fourier_wigner_kernel(L: int) -> Tuple[np.ndarray, np.ndarray]:
+    """
+    Computes Fourier coefficients of the reduced Wigner d-functions and quadrature
+    weights upsampled for the forward Fourier-Wigner transform.
+
+    Args:
+        L (int): Harmonic band-limit.
+
+    Returns:
+        Tuple[np.ndarray, np.ndarray]: Tuple of delta Fourier coefficients and weights.
+
+    """
+    # Calculate deltas (np.pi/2 Fourier coefficients of Wigner matrices)
+    deltas = np.zeros((L, 2 * L - 1, 2 * L - 1), dtype=np.float64)
+    d = np.zeros((2 * L - 1, 2 * L - 1), dtype=np.float64)
+    for el in range(L):
+        d = recursions.risbo.compute_full(d, np.pi / 2, L, el)
+        deltas[el] = d
+
+    # Calculate upsampled quadrature weights
+    w = np.zeros(4 * L - 3, dtype=np.complex128)
+    for mm in range(-2 * (L - 1), 2 * (L - 1) + 1):
+        w[mm + 2 * (L - 1)] = quadrature.mw_weights(-mm)
+    w = np.fft.ifft(np.fft.ifftshift(w), norm="forward")
+
+    return deltas, w
+
+
+def fourier_wigner_kernel_jax(L: int) -> Tuple[jnp.ndarray, jnp.ndarray]:
+    """
+    Computes Fourier coefficients of the reduced Wigner d-functions and quadrature
+    weights upsampled for the forward Fourier-Wigner transform (JAX implementation).
+
+    Args:
+        L (int): Harmonic band-limit.
+
+    Returns:
+        Tuple[jnp.ndarray, jnp.ndarray]: Tuple of delta Fourier coefficients and weights.
+
+    """
+    # Calculate deltas (np.pi/2 Fourier coefficients of Wigner matrices)
+    deltas = jnp.zeros((L, 2 * L - 1, 2 * L - 1), dtype=jnp.float64)
+    d = jnp.zeros((2 * L - 1, 2 * L - 1), dtype=jnp.float64)
+    for el in range(L):
+        d = recursions.risbo_jax.compute_full(d, jnp.pi / 2, L, el)
+        deltas = deltas.at[el].set(d)
+
+    # Calculate upsampled quadrature weights
+    w = jnp.zeros(4 * L - 3, dtype=jnp.complex128)
+    for mm in range(-2 * (L - 1), 2 * (L - 1) + 1):
+        w = w.at[mm + 2 * (L - 1)].set(quadrature_jax.mw_weights(-mm))
+    w = jnp.fft.ifft(jnp.fft.ifftshift(w), norm="forward")
+
+    return deltas, w
+
+
 def healpix_phase_shifts(L: int, nside: int, forward: bool = False) -> np.ndarray:
     r"""
     Generates a phase shift vector for HEALPix for all :math:`\theta` rings.