Source code for jax._src.numpy.fft

# Copyright 2018 Google LLC
#
# 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
#
#     https://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 numpy as np

from jax import lax
from jax.lib import xla_client
from .util import _wraps
from . import lax_numpy as jnp
from jax import ops as jaxops


def _fft_core(func_name, fft_type, a, s, axes, norm):
  # TODO(skye): implement padding/cropping based on 's'.
  full_name = "jax.numpy.fft." + func_name
  if s is not None:
    raise NotImplementedError("%s only supports s=None, got %s" % (full_name, s))
  if norm is not None:
    raise NotImplementedError("%s only supports norm=None, got %s" % (full_name, norm))
  if s is not None and axes is not None and len(s) != len(axes):
    # Same error as numpy.
    raise ValueError("Shape and axes have different lengths.")

  orig_axes = axes
  if axes is None:
    if s is None:
      axes = range(a.ndim)
    else:
      axes = range(a.ndim - len(s), a.ndim)

  if len(axes) != len(set(axes)):
    raise ValueError(
        "%s does not support repeated axes. Got axes %s." % (full_name, 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, a.ndim))

  # XLA only supports FFTs over the innermost axes, so rearrange if necessary.
  if orig_axes is not None:
    axes = tuple(range(a.ndim - len(axes), a.ndim))
    a = jnp.moveaxis(a, orig_axes, axes)

  if s is None:
    if fft_type == xla_client.FftType.IRFFT:
      s = [a.shape[axis] for axis in axes[:-1]]
      if axes:
        s += [max(0, 2 * (a.shape[axes[-1]] - 1))]
    else:
      s = [a.shape[axis] for axis in axes]

  transformed = lax.fft(a, fft_type, s)

  if orig_axes is not None:
    transformed = jnp.moveaxis(transformed, axes, orig_axes)
  return transformed


[docs]@_wraps(np.fft.fftn) def fftn(a, s=None, axes=None, norm=None): return _fft_core('fftn', xla_client.FftType.FFT, a, s, axes, norm)
[docs]@_wraps(np.fft.ifftn) def ifftn(a, s=None, axes=None, norm=None): return _fft_core('ifftn', xla_client.FftType.IFFT, a, s, axes, norm)
[docs]@_wraps(np.fft.rfftn) def rfftn(a, s=None, axes=None, norm=None): return _fft_core('rfftn', xla_client.FftType.RFFT, a, s, axes, norm)
[docs]@_wraps(np.fft.irfftn) def irfftn(a, s=None, axes=None, norm=None): return _fft_core('irfftn', xla_client.FftType.IRFFT, a, s, axes, norm)
def _axis_check_1d(func_name, axis): full_name = "jax.numpy.fft." + func_name if isinstance(axis, (list, tuple)): raise ValueError( "%s does not support multiple axes. Please use %sn. " "Got axis = %r." % (full_name, full_name, axis) ) def _fft_core_1d(func_name, fft_type, a, s, axis, norm): _axis_check_1d(func_name, axis) axes = None if axis is None else [axis] return _fft_core(func_name, fft_type, a, s, axes, norm)
[docs]@_wraps(np.fft.fft) def fft(a, n=None, axis=-1, norm=None): return _fft_core_1d('fft', xla_client.FftType.FFT, a, s=n, axis=axis, norm=norm)
[docs]@_wraps(np.fft.ifft) def ifft(a, n=None, axis=-1, norm=None): return _fft_core_1d('ifft', xla_client.FftType.IFFT, a, s=n, axis=axis, norm=norm)
[docs]@_wraps(np.fft.rfft) def rfft(a, n=None, axis=-1, norm=None): return _fft_core_1d('rfft', xla_client.FftType.RFFT, a, s=n, axis=axis, norm=norm)
[docs]@_wraps(np.fft.irfft) def irfft(a, n=None, axis=-1, norm=None): return _fft_core_1d('irfft', xla_client.FftType.IRFFT, a, s=n, axis=axis, norm=norm)
[docs]@_wraps(np.fft.hfft) def hfft(a, n=None, axis=-1, norm=None): conj_a = jnp.conj(a) _axis_check_1d('hfft', axis) nn = (a.shape[axis] - 1) * 2 if n is None else n return _fft_core_1d('hfft', xla_client.FftType.IRFFT, conj_a, s=n, axis=axis, norm=norm) * nn
[docs]@_wraps(np.fft.ihfft) def ihfft(a, n=None, axis=-1, norm=None): _axis_check_1d('ihfft', axis) nn = a.shape[axis] if n is None else n output = _fft_core_1d('ihfft', xla_client.FftType.RFFT, a, s=n, axis=axis, norm=norm) return jnp.conj(output) * (1 / nn)
def _fft_core_2d(func_name, fft_type, a, s, axes, norm): full_name = "jax.numpy.fft." + func_name if len(axes) != 2: raise ValueError( "%s only supports 2 axes. Got axes = %r." % (full_name, axes) ) return _fft_core(func_name, fft_type, a, s, axes, norm)
[docs]@_wraps(np.fft.fft2) def fft2(a, s=None, axes=(-2,-1), norm=None): return _fft_core_2d('fft2', xla_client.FftType.FFT, a, s=s, axes=axes, norm=norm)
[docs]@_wraps(np.fft.ifft2) def ifft2(a, s=None, axes=(-2,-1), norm=None): return _fft_core_2d('ifft2', xla_client.FftType.IFFT, a, s=s, axes=axes, norm=norm)
[docs]@_wraps(np.fft.rfft2) def rfft2(a, s=None, axes=(-2,-1), norm=None): return _fft_core_2d('rfft2', xla_client.FftType.RFFT, a, s=s, axes=axes, norm=norm)
[docs]@_wraps(np.fft.irfft2) def irfft2(a, s=None, axes=(-2,-1), norm=None): return _fft_core_2d('irfft2', xla_client.FftType.IRFFT, a, s=s, axes=axes, norm=norm)
[docs]@_wraps(np.fft.fftfreq) def fftfreq(n, d=1.0): if isinstance(n, (list, tuple)): raise ValueError( "The n argument of jax.numpy.fft.fftfreq only takes an int. " "Got n = %s." % list(n)) elif isinstance(d, (list, tuple)): raise ValueError( "The d argument of jax.numpy.fft.fftfreq only takes a single value. " "Got d = %s." % list(d)) k = jnp.zeros(n) if n % 2 == 0: # k[0: n // 2 - 1] = jnp.arange(0, n // 2 - 1) k = jaxops.index_update(k, jaxops.index[0: n // 2], jnp.arange(0, n // 2)) # k[n // 2:] = jnp.arange(-n // 2, -1) k = jaxops.index_update(k, jaxops.index[n // 2:], jnp.arange(-n // 2, 0)) else: # k[0: (n - 1) // 2] = jnp.arange(0, (n - 1) // 2) k = jaxops.index_update(k, jaxops.index[0: (n - 1) // 2 + 1], jnp.arange(0, (n - 1) // 2 + 1)) # k[(n - 1) // 2 + 1:] = jnp.arange(-(n - 1) // 2, -1) k = jaxops.index_update(k, jaxops.index[(n - 1) // 2 + 1:], jnp.arange(-(n - 1) // 2, 0)) return k / (d * n)
[docs]@_wraps(np.fft.rfftfreq) def rfftfreq(n, d=1.0): if isinstance(n, (list, tuple)): raise ValueError( "The n argument of jax.numpy.fft.rfftfreq only takes an int. " "Got n = %s." % list(n)) elif isinstance(d, (list, tuple)): raise ValueError( "The d argument of jax.numpy.fft.rfftfreq only takes a single value. " "Got d = %s." % list(d)) if n % 2 == 0: k = jnp.arange(0, n // 2 + 1) else: k = jnp.arange(0, (n - 1) // 2 + 1) return k / (d * n)
[docs]@_wraps(np.fft.fftshift) def fftshift(x, axes=None): x = jnp.asarray(x) if axes is None: axes = tuple(range(x.ndim)) shift = [dim // 2 for dim in x.shape] elif isinstance(axes, int): shift = x.shape[axes] // 2 else: shift = [x.shape[ax] // 2 for ax in axes] return jnp.roll(x, shift, axes)
[docs]@_wraps(np.fft.ifftshift) def ifftshift(x, axes=None): x = jnp.asarray(x) if axes is None: axes = tuple(range(x.ndim)) shift = [-(dim // 2) for dim in x.shape] elif isinstance(axes, int): shift = -(x.shape[axes] // 2) else: shift = [-(x.shape[ax] // 2) for ax in axes] return jnp.roll(x, shift, axes)