# 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)
@_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
@_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)
@_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)
@_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)