Merge pull request #245 from astro-informatics/mmg/reindexing-loops

Avoid loops in `s2fft.sampling.reindex` functions to reduce compile and run times

s2fft/sampling/reindex.py

@@ -1,13 +1,14 @@
 from functools import partial
 
 import jax.numpy as jnp
+import numpy as np
 from jax import jit
 
 
 @partial(jit, static_argnums=(1))
 def flm_1d_to_2d_fast(flm_1d: jnp.ndarray, L: int) -> jnp.ndarray:
     r"""
-    Convert from 1D indexed harmnonic coefficients to 2D indexed coefficients (JAX).
+    Convert from 1D indexed harmonic coefficients to 2D indexed coefficients (JAX).
     
     Note:
         Storage conventions for harmonic coefficients :math:`flm_{(\ell,m)}`, for 
@@ -35,13 +36,12 @@ def flm_1d_to_2d_fast(flm_1d: jnp.ndarray, L: int) -> jnp.ndarray:
         jnp.ndarray: 2D indexed harmonic coefficients.
 
     """
-    flm_2d = jnp.zeros((L, 2 * L - 1), dtype=jnp.complex128)
-    els = jnp.arange(L)
-    offset = els**2 + els
-    for el in range(L):
-        m_array = jnp.arange(-el, el + 1)
-        flm_2d = flm_2d.at[el, L - 1 + m_array].set(flm_1d[offset[el] + m_array])
-    return flm_2d
+    flm_2d = jnp.zeros((L, 2 * L - 1), dtype=flm_1d.dtype)
+    row_indices, col_indices = np.arange(L)[:, None], np.arange(2 * L - 1)[None, :]
+    el_indices, m_indices = np.where(
+        (row_indices <= col_indices)[::-1, :] & (row_indices <= col_indices)[::-1, ::-1]
+    )
+    return flm_2d.at[el_indices, m_indices].set(flm_1d)
 
 
 @partial(jit, static_argnums=(1))
@@ -75,13 +75,11 @@ def flm_2d_to_1d_fast(flm_2d: jnp.ndarray, L: int) -> jnp.ndarray:
         jnp.ndarray: 1D indexed harmonic coefficients.
 
     """
-    flm_1d = jnp.zeros(L**2, dtype=jnp.complex128)
-    els = jnp.arange(L)
-    offset = els**2 + els
-    for el in range(L):
-        m_array = jnp.arange(-el, el + 1)
-        flm_1d = flm_1d.at[offset[el] + m_array].set(flm_2d[el, L - 1 + m_array])
-    return flm_1d
+    row_indices, col_indices = np.arange(L)[:, None], np.arange(2 * L - 1)[None, :]
+    el_indices, m_indices = np.where(
+        (row_indices <= col_indices)[::-1, :] & (row_indices <= col_indices)[::-1, ::-1]
+    )
+    return flm_2d[el_indices, m_indices]
 
 
 @partial(jit, static_argnums=(1))
@@ -127,17 +125,13 @@ def flm_hp_to_2d_fast(flm_hp: jnp.ndarray, L: int) -> jnp.ndarray:
         jnp.ndarray: 2D indexed harmonic coefficients.
 
     """
-    flm_2d = jnp.zeros((L, 2 * L - 1), dtype=jnp.complex128)
-
-    for el in range(L):
-        flm_2d = flm_2d.at[el, L - 1].set(flm_hp[el])
-        m_array = jnp.arange(1, el + 1)
-        hp_idx = m_array * (2 * L - 1 - m_array) // 2 + el
-        flm_2d = flm_2d.at[el, L - 1 + m_array].set(flm_hp[hp_idx])
-        flm_2d = flm_2d.at[el, L - 1 - m_array].set(
-            (-1) ** m_array * jnp.conj(flm_hp[hp_idx])
-        )
-
+    flm_2d = jnp.zeros((L, 2 * L - 1), dtype=flm_hp.dtype)
+    m_indices, el_indices = np.triu_indices(n=L, k=1, m=L) + np.array([[1], [0]])
+    flm_2d = flm_2d.at[:L, L - 1].set(flm_hp[:L])
+    flm_2d = flm_2d.at[el_indices, L - 1 + m_indices].set(flm_hp[L:])
+    flm_2d = flm_2d.at[el_indices, L - 1 - m_indices].set(
+        (-1) ** m_indices * flm_hp[L:].conj()
+    )
     return flm_2d
 
 
@@ -185,11 +179,5 @@ def flm_2d_to_hp_fast(flm_2d: jnp.ndarray, L: int) -> jnp.ndarray:
         jnp.ndarray: HEALPix indexed harmonic coefficients.
 
     """
-    flm_hp = jnp.zeros(int(L * (L + 1) / 2), dtype=jnp.complex128)
-
-    for el in range(L):
-        m_array = jnp.arange(el + 1)
-        hp_idx = m_array * (2 * L - 1 - m_array) // 2 + el
-        flm_hp = flm_hp.at[hp_idx].set(flm_2d[el, L - 1 + m_array])
-
-    return flm_hp
+    m_indices, el_indices = np.triu_indices(n=L + 1, m=L)
+    return flm_2d[el_indices, L - 1 + m_indices]