Add support for N-D FFTs with D>3.

CHANGELOG.md

@@ -30,6 +30,12 @@ When releasing, please add the new-release-boilerplate to docs/pallas/CHANGELOG.
     are now deprecated, having been replaced by symbols of the same name
     in {mod}`jax.core`.
 
+* New Features
+  * {func}`jax.numpy.fft.fftn`, {func}`jax.numpy.fft.rfftn`,
+    {func}`jax.numpy.fft.ifftn`, and {func}`jax.numpy.fft.irfftn` now support
+    transforms in more than 3 dimensions, which was previously the limit. See
+    {jax-issue}`#25606` for more details.
+
 ## jax 0.4.38 (Dec 17, 2024)
 
 * Changes:

jax/_src/numpy/fft.py

@@ -72,12 +72,6 @@ def _fft_core(func_name: str, fft_type: lax.FftType, a: ArrayLike,
     raise ValueError(
         f"{full_name} does not support repeated axes. Got axes {axes}.")
 
-  if len(axes) > 3:
-    # XLA does not support FFTs over more than 3 dimensions
-    raise ValueError(
-        "%s only supports 1D, 2D, and 3D FFTs. "
-        "Got axes %s with input rank %s." % (full_name, orig_axes, arr.ndim))
-
   # XLA only supports FFTs over the innermost axes, so rearrange if necessary.
   if orig_axes is not None:
     axes = tuple(range(arr.ndim - len(axes), arr.ndim))
@@ -100,7 +94,7 @@ def _fft_core(func_name: str, fft_type: lax.FftType, a: ArrayLike,
         s += [max(0, 2 * (arr.shape[axes[-1]] - 1))]
     else:
       s = [arr.shape[axis] for axis in axes]
-  transformed = lax.fft(arr, fft_type, tuple(s))
+  transformed = _fft_core_nd(arr, fft_type, s)
   if norm is not None:
     transformed *= _fft_norm(
         jnp.array(s, dtype=transformed.dtype), func_name, norm)
@@ -110,6 +104,31 @@ def _fft_core(func_name: str, fft_type: lax.FftType, a: ArrayLike,
   return transformed
 
 
+def _fft_core_nd(arr: Array, fft_type: lax.FftType, s: Shape) -> Array:
+  # XLA supports N-D transforms up to N=3 so we use XLA's FFT N-D directly.
+  if len(s) <= 3:
+    return lax.fft(arr, fft_type, tuple(s))
+
+  # For larger N, we repeatedly apply N<=3 transforms until we reach the
+  # requested dimension. We special case N=4 to use two 2-D transforms instead
+  # of one 3-D and one 1-D, since we typically expect better accelerator
+  # performance when N>1.
+  n = 2 if len(s) == 4 else 3
+  src = tuple(range(arr.ndim - len(s), arr.ndim - n))
+  dst = tuple(range(arr.ndim - len(s) + n, arr.ndim))
+  if fft_type in {lax.FftType.RFFT, lax.FftType.FFT}:
+    arr = lax.fft(arr, fft_type, tuple(s)[-n:])
+    arr = jnp.moveaxis(arr, src, dst)
+    arr = _fft_core_nd(arr, lax.FftType.FFT, s[:-n])
+    arr = jnp.moveaxis(arr, dst, src)
+  else:
+    arr = jnp.moveaxis(arr, src, dst)
+    arr = _fft_core_nd(arr, lax.FftType.IFFT, s[:-n])
+    arr = jnp.moveaxis(arr, dst, src)
+    arr = lax.fft(arr, fft_type, tuple(s)[-n:])
+  return arr
+
+
 def fftn(a: ArrayLike, s: Shape | None = None,
          axes: Sequence[int] | None = None,
          norm: str | None = None) -> Array:

tests/fft_test.py

@@ -41,12 +41,9 @@ all_dtypes = real_dtypes + jtu.dtypes.complex
 
 
 def _get_fftn_test_axes(shape):
-  axes = [[]]
+  axes = [[], None]
   ndims = len(shape)
-  # XLA's FFT op only supports up to 3 innermost dimensions.
-  if ndims <= 3:
-    axes.append(None)
-  for naxes in range(1, min(ndims, 3) + 1):
+  for naxes in range(1, ndims + 1):
     axes.extend(itertools.combinations(range(ndims), naxes))
   for index in range(1, ndims + 1):
     axes.append((-index,))
@@ -145,7 +142,7 @@ class FftTest(jtu.JaxTestCase):
      for dtype in (real_dtypes if real and not inverse else all_dtypes)
     ],
     [dict(shape=shape, axes=axes, s=s)
-     for shape in [(10,), (10, 10), (9,), (2, 3, 4), (2, 3, 4, 5)]
+     for shape in [(10,), (10, 10), (9,), (2, 3, 4), (2, 3, 4, 5), (2, 3, 4, 5, 6)]
      for axes in _get_fftn_test_axes(shape)
      for s in _get_fftn_test_s(shape, axes)
     ],
@@ -203,11 +200,6 @@ class FftTest(jtu.JaxTestCase):
     if inverse:
       name = 'i' + name
     func = _get_fftn_func(jnp.fft, inverse, real)
-    self.assertRaisesRegex(
-        ValueError,
-        "jax.numpy.fft.{} only supports 1D, 2D, and 3D FFTs. "
-        "Got axes None with input rank 4.".format(name),
-        lambda: func(rng([2, 3, 4, 5], dtype=np.float64), axes=None))
     self.assertRaisesRegex(
         ValueError,
         f"jax.numpy.fft.{name} does not support repeated axes. Got axes \\[1, 1\\].",