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未验证 提交 81e0c1ba 编写于 作者: F Feiyu Chan 提交者： GitHub
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move fft and signal files, move signal APIs (#36540) 

* move signal apis

* move fft.py and signal.py to paddle/, fix typos

* fix relative imports from fft.py and signal.py

* fix typos
上级 21bece3f
隐藏空白更改
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Showing with 1621 addition and 1662 deletion
python/paddle/__init__.py
浏览文件 @ 81e0c1ba
......@@ -296,6 +296,7 @@ from .hapi import flops # noqa: F401
from . import hub # noqa: F401
from . import linalg # noqa: F401
from . import fft # noqa: F401
from . import signal # noqa: F401
import paddle.text # noqa: F401
import paddle.vision # noqa: F401
......
python/paddle/fft.py
浏览文件 @ 81e0c1ba
......@@ -12,50 +12,1613 @@
# See the License for the specific language governing permissions and
# limitations under the License.
from .tensor.fft import fft # noqa: F401
from .tensor.fft import fft2 # noqa: F401
from .tensor.fft import fftn # noqa: F401
from .tensor.fft import ifft # noqa: F401
from .tensor.fft import ifft2 # noqa: F401
from .tensor.fft import ifftn # noqa: F401
from .tensor.fft import rfft # noqa: F401
from .tensor.fft import rfft2 # noqa: F401
from .tensor.fft import rfftn # noqa: F401
from .tensor.fft import irfft # noqa: F401
from .tensor.fft import irfft2 # noqa: F401
from .tensor.fft import irfftn # noqa: F401
from .tensor.fft import hfft # noqa: F401
from .tensor.fft import hfft2 # noqa: F401
from .tensor.fft import hfftn # noqa: F401
from .tensor.fft import ihfft # noqa: F401
from .tensor.fft import ihfft2 # noqa: F401
from .tensor.fft import ihfftn # noqa: F401
from .tensor.fft import fftfreq # noqa: F401
from .tensor.fft import rfftfreq # noqa: F401
from .tensor.fft import fftshift # noqa: F401
from .tensor.fft import ifftshift # noqa: F401
__all__ = [ # noqa
from typing import Sequence
import numpy as np
import paddle
from .tensor.attribute import is_complex, is_floating_point, is_interger, _real_to_complex_dtype, _complex_to_real_dtype
from .fluid.framework import in_dygraph_mode
from . import _C_ops
from .fluid.data_feeder import check_variable_and_dtype
from .fluid.layer_helper import LayerHelper
__all__ = [
'fft',
'fft2',
'fftn',
'ifft',
'ifft2',
'ifftn',
'rfft',
'rfft2',
'rfftn',
'irfft',
'irfft2',
'irfftn',
'hfft',
'hfft2',
'hfftn',
'ihfft',
'fft2',
'ifft2',
'rfft2',
'irfft2',
'hfft2',
'ihfft2',
'fftn',
'ifftn',
'rfftn',
'irfftn',
'hfftn',
'ihfftn',
'fftfreq',
'rfftfreq',
'fftshift',
'ifftshift'
'ifftshift',
]
def _check_normalization(norm):
if norm not in ['forward', 'backward', 'ortho']:
raise ValueError(
"Unexpected norm: {}. Norm should be forward, backward or ortho".
format(norm))
def _check_fft_n(n):
if not isinstance(n, int):
raise ValueError(
"Invalid FFT argument n({}), it shoule be an integer.".format(n))
if n <= 0:
raise ValueError(
"Invalid FFT argument n({}), it should be positive.".format(n))
def _check_fft_shape(x, s):
ndim = x.ndim
if not isinstance(s, Sequence):
raise ValueError(
"Invaid FFT argument s({}), it should be a sequence of integers.")
if len(s) > ndim:
raise ValueError(
"Length of FFT argument s should not be larger than the rank of input. "
"Received s: {}, rank of x: {}".format(s, ndim))
for size in s:
if not isinstance(size, int) or size <= 0:
raise ValueError("FFT sizes {} contains invalid value ({})".format(
s, size))
def _check_fft_axis(x, axis):
ndim = x.ndim
if not isinstance(axis, int):
raise ValueError(
"Invalid FFT axis ({}), it shoule be an integer.".format(axis))
if axis < -ndim or axis >= ndim:
raise ValueError(
"Invalid FFT axis ({}), it should be in range [-{}, {})".format(
axis, ndim, ndim))
def _check_fft_axes(x, axes):
ndim = x.ndim
if not isinstance(axes, Sequence):
raise ValueError(
"Invalid FFT axes ({}), it should be a sequence of integers.".
format(axes))
if len(axes) > ndim:
raise ValueError(
"Length of fft axes should not be larger than the rank of input. "
"Received, len of axes: {}, rank of x: {}".format(len(axes), ndim))
for axis in axes:
if not isinstance(axis, int) or axis < -ndim or axis >= ndim:
raise ValueError(
"FFT axes {} contains invalid value ({}), it should be in range [-{}, {})".
format(axes, axis, ndim, ndim))
def _resize_fft_input(x, s, axes):
if len(s) != len(axes):
raise ValueError("length of `s` should equals length of `axes`.")
shape = x.shape
ndim = x.ndim
axes_to_pad = []
paddings = []
axes_to_slice = []
slices = []
for i, axis in enumerate(axes):
if shape[axis] < s[i]:
axes_to_pad.append(axis)
paddings.append(s[i] - shape[axis])
elif shape[axis] > s[i]:
axes_to_slice.append(axis)
slices.append((0, s[i]))
if axes_to_slice:
x = paddle.slice(
x,
axes_to_slice,
starts=[item[0] for item in slices],
ends=[item[1] for item in slices])
if axes_to_pad:
padding_widths = [0] * (2 * ndim)
for axis, pad in zip(axes_to_pad, paddings):
padding_widths[2 * axis + 1] = pad
x = paddle.nn.functional.pad(x, padding_widths)
return x
def _normalize_axes(x, axes):
ndim = x.ndim
return [item if item >= 0 else (item + ndim) for item in axes]
def _check_at_least_ndim(x, rank):
if x.ndim < rank:
raise ValueError("The rank of the input ({}) should >= {}".format(
x.ndim, rank))
# public APIs 1d
def fft(x, n=None, axis=-1, norm="backward", name=None):
"""
Calculate one-dimensional discrete Fourier transform.
This function uses the efficient fast Fourier transform (FFT) algorithm [1] to
calculate the 1-D * n * point discrete Fourier transform (DFT).
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. If `n` is less than
the length input, the input will be cropped. If larger, the input is filled
with zeros. If `n` is not given, the input length along the axis specified
by `axis` is used.
axis (int, optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axis indicated
by `axis`, or the last one if `axis` is not specified.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.exp(3j * np.pi * np.arange(7) / 7)
xp = paddle.to_tensor(x)
fft_xp = paddle.fft.fft(xp).numpy()
print(fft_xp)
# [1.+1.25396034e+00j 1.+4.38128627e+00j 1.-4.38128627e+00j
# 1.-1.25396034e+00j 1.-4.81574619e-01j 1.+8.88178420e-16j
# 1.+4.81574619e-01j]
"""
if is_interger(x) or is_floating_point(x):
return fft_r2c(
x, n, axis, norm, forward=True, onesided=False, name=name)
else:
return fft_c2c(x, n, axis, norm, forward=True, name=name)
def ifft(x, n=None, axis=-1, norm="backward", name=None):
"""
Compute the 1-D inverse discrete Fourier Transform.
This function computes the inverse of the 1-D *n*-point discrete Fourier transform
computed by `fft`. In other words, ``ifft(fft(x)) == x`` to within numerical accuracy.
The input should be ordered in the same way as is returned by `fft`,
i.e.,
* ``x[0]`` should contain the zero frequency term,
* ``x[1:n//2]`` should contain the positive-frequency terms,
* ``x[n//2 + 1:]`` should contain the negative-frequency terms, in
increasing order starting from the most negative frequency.
For an even number of input points, ``x[n//2]`` represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. If `n` is less than
the length input, the input will be cropped. If larger, the input is filled
with zeros. If `n` is not given, the input length along the axis specified
by `axis` is used.
axis (int, optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axis indicated
by `axis`, or the last one if `axis` is not specified.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.exp(3j * np.pi * np.arange(7) / 7)
xp = paddle.to_tensor(x)
ifft_xp = paddle.fft.ifft(xp).numpy()
print(ifft_xp)
# [0.14285714+1.79137191e-01j 0.14285714+6.87963741e-02j
# 0.14285714+1.26882631e-16j 0.14285714-6.87963741e-02j
# 0.14285714-1.79137191e-01j 0.14285714-6.25898038e-01j
# 0.14285714+6.25898038e-01j]
"""
if is_interger(x) or is_floating_point(x):
return fft_r2c(
x, n, axis, norm, forward=False, onesided=False, name=name)
else:
return fft_c2c(x, n, axis, norm, forward=False, name=name)
def rfft(x, n=None, axis=-1, norm="backward", name=None):
"""
The one dimensional FFT for real input.
This function computes the one dimensional *n*-point discrete Fourier
Transform (DFT) of a real-valued tensor by means of an efficient algorithm
called the Fast Fourier Transform (FFT).
When the DFT is computed for purely real input, the output is
Hermitian-symmetric. This function does not compute the negative frequency
terms, and the length of the transformed axis of the output is therefore
``n//2 + 1``.
Args:
x(Tensor) : Real-valued input tensor
n(int, optional): Number of points along transformation axis in the
input to use. If `n` is smaller than the length of the input, the
input is cropped. If it is larger, the input is padded with zeros.
If `n` is not given, the length of the input along the axis
specified by `axis` is used.
axis(int, optional): Axis over which to compute the FFT. Default value
is last axis.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : complex tensor
Raises:
Examples:
.. code-block:: python
import paddle
x = paddle.to_tensor([0.0, 1.0, 0.0, 0.0])
print(paddle.fft.rfft(x))
# Tensor(shape=[3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [ (1+0j), -1j , (-1+0j)])
"""
return fft_r2c(x, n, axis, norm, forward=True, onesided=True, name=name)
def irfft(x, n=None, axis=-1, norm="backward", name=None):
"""
Computes the inverse of `rfft`.
This function calculates the inverse of the one-dimensional *n* point discrete
Fourier transform of the actual input calculated by "rfft". In other words,
``irfft(rfft(a),len(a)) == a`` is within the numerical accuracy range.
The input shall be in the form of "rfft", i.e. the actual zero frequency term,
followed by the complex positive frequency term, in the order of increasing frequency.
Because the discrete Fourier transform of the actual input is Hermite symmetric,
the negative frequency term is regarded as the complex conjugate term of the corresponding
positive frequency term.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. For `n` output
points, ``n//2 + 1``input points are necessary. If the length of the input tensor is greater
than `n`, it will be cropped, if it is shorter than this, fill in zero. If `n` is not given,
it is considered to be ``2 * (k-1)``, where ``k`` is the length of the input axis specified
along the ` axis'.
axis (int, optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name` .
Returns:
Real tensor. Truncated or zero fill input for the transformation along the axis indicated by
`axis`, or the last input if `axis` is not specified. The length of the conversion axis
is `n`, or ``2 * k-2``, if `k` is None, where `k` is the length of the input conversion axis.
If the output is an odd number, you need to specify the value of 'n', such as ``2 * k-1``
in some cases.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([1, -1j, -1])
xp = paddle.to_tensor(x)
irfft_xp = paddle.fft.irfft(xp).numpy()
print(irfft_xp)
# [0. 1. 0. 0.]
"""
return fft_c2r(x, n, axis, norm, forward=False, name=name)
def hfft(x, n=None, axis=-1, norm="backward", name=None):
"""
Compute the FFT of a signal that has Hermitian symmetry, a real
spectrum.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. For `n` output
points, ``n//2 + 1`` input points are necessary. If the length of the input tensor is greater
than `n`, it will be cropped, if it is shorter than this, fill in zero. If `n` is not given,
it is considered to be ``2 * (k-1)``, where ``k`` is the length of the input axis specified
along the ` axis'.
axis (int,optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name` .
Returns:
Real tensor. Truncated or zero fill input for the transformation along the axis indicated by
`axis`, or the last input if `axis` is not specified. The length of the conversion axis
is `n`, or ``2 * k-2``, if `k` is None, where `k` is the length of the input conversion axis.
If the output is an odd number, you need to specify the value of 'n', such as ``2 * k-1`` in
some cases.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([1, -1j, -1])
xp = paddle.to_tensor(x)
hfft_xp = paddle.fft.hfft(xp).numpy()
print(hfft_xp)
# [0. 0. 0. 4.]
"""
return fft_c2r(x, n, axis, norm, forward=True, name=name)
def ihfft(x, n=None, axis=-1, norm="backward", name=None):
"""
The inverse FFT of a signal that has Hermitian symmetry.
This function computes the one dimensional *n*-point inverse FFT of a signal
that has Hermitian symmetry by means of an efficient algorithm called
the Fast Fourier Transform (FFT).
When the DFT is computed for purely real input, the output is
Hermitian-symmetric. This function does not compute the negative frequency
terms, and the length of the transformed axis of the output is therefore
``n//2 + 1``.
Args:
x(Tensor): Input tensor.
n(int, optional): The number of points along transformation axis in the
input to use. If `n` is smaller than the length of the input, the
input is cropped. If it is larger, the input is padded with zeros.
If `n` is not given, the length of the input along the axis
specified by `axis` is used.
axis(int, optional) : Axis over which to compute the inverse FFT. If not
given, the last axis is used.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : complex tensor.
Examples:
.. code-block:: python
import paddle
spectrum = paddle.to_tensor([10.0, -5.0, 0.0, -1.0, 0.0, -5.0])
print(paddle.fft.ifft(spectrum))
# Tensor(shape=[6], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j), (2.3333334922790527+1.9868215517249155e-08j), (1+1.9868215517249155e-08j)])
print(paddle.fft.ihfft(spectrum))
# Tensor(shape = [4], dtype = complex64, place = CUDAPlace(0), stop_gradient = True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j)])
"""
return fft_r2c(x, n, axis, norm, forward=False, onesided=True, name=name)
# public APIs nd
def fftn(x, s=None, axes=None, norm="backward", name=None):
"""
Compute the N-D discrete Fourier Transform.
This function calculates the n-D discrete Fourier transform on any number of axes
in the M-D array by fast Fourier transform (FFT).
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
This corresponds to ``n`` for ``fft(x, n)``.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes (sequence of ints, optional): Axes used to calculate FFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axes indicated by
`axes`, or by a combination of `s` and `x`, as explained in the parameters section above.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:4, :4, :4][1]
xp = paddle.to_tensor(x)
fftn_xp = paddle.fft.fftn(xp, axes=(1, 2)).numpy()
print(fftn_xp)
# [[[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]
# [[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]
# [[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]
# [[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]]
"""
if is_interger(x) or is_floating_point(x):
return fftn_r2c(
x, s, axes, norm, forward=True, onesided=False, name=name)
else:
return fftn_c2c(x, s, axes, norm, forward=True, name=name)
def ifftn(x, s=None, axes=None, norm="backward", name=None):
"""
Compute the N-D inverse discrete Fourier Transform.
This function computes the inverse of the N-D discrete
Fourier Transform over any number of axes in an M-D array by
means of the Fast Fourier Transform (FFT). In other words,
``ifftn(fftn(x)) == x`` to within numerical accuracy.
The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fftn`, i.e., it should have the term for zero frequency
in all axes in the low-order corner, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
This corresponds to ``n`` for ``fft(x, n)``.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes (sequence of ints, optional): Axes used to calculate FFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axes indicated by
`axes`, or by a combination of `s` and `x`, as explained in the parameters section above.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.eye(3)
xp = paddle.to_tensor(x)
ifftn_xp = paddle.fft.ifftn(xp, axes=(1,)).numpy()
print(ifftn_xp)
# [[ 0.33333333+0.j 0.33333333+0.j 0.33333333-0.j ]
# [ 0.33333333+0.j -0.16666667+0.28867513j -0.16666667-0.28867513j]
# [ 0.33333333+0.j -0.16666667-0.28867513j -0.16666667+0.28867513j]]
"""
if is_interger(x) or is_floating_point(x):
return fftn_r2c(
x, s, axes, norm, forward=False, onesided=False, name=name)
else:
return fftn_c2c(x, s, axes, norm, forward=False, name=name)
def rfftn(x, s=None, axes=None, norm="backward", name=None):
"""
The N dimensional FFT for real input.
This function computes the N-dimensional discrete Fourier Transform over
any number of axes in an M-dimensional real array by means of the Fast
Fourier Transform (FFT). By default, all axes are transformed, with the
real transform performed over the last axis, while the remaining
transforms are complex.
The transform for real input is performed over the last transformation
axis, as by `rfft`, then the transform over the remaining axes is
performed as by `fftn`. The order of the output is as for `rfft` for the
final transformation axis, and as for `fftn` for the remaining
transformation axes.
Args:
x(Tensor) : Input tensor, taken to be real.
s(Sequence[int]) : Shape to use from the exec fft. The final element of
`s` corresponds to `n` for ``rfft(x, n)``, while for the remaining
axes, it corresponds to `n` for ``fft(x, n)``. Along any axis, if
the given shape is smaller than that of the input, the input is
cropped. If it is larger, the input is padded with zeros. if `s` is
not given, the shape of the input along the axes specified by `axes`
is used.
axes(Sequence[int]) : Axes over which to compute the FFT. If not given,
the last ``len(s)`` axes are used, or all axes if `s` is also not
specified.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor): complex tensor
Raises:
ValueError: If `s` and `axes` have different length.
Examples:
.. code-block:: python
import paddle
# default, all axis will be used to exec fft
x = paddle.ones((2, 3, 4))
print(paddle.fft.rfftn(x))
# Tensor(shape=[2, 3, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [[[(24+0j), 0j , 0j ],
# [0j , 0j , 0j ],
# [0j , 0j , 0j ]],
#
# [[0j , 0j , 0j ],
# [0j , 0j , 0j ],
# [0j , 0j , 0j ]]])
# use axes(2, 0)
print(paddle.fft.rfftn(x, axes=(2, 0)))
# Tensor(shape=[2, 3, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [[[(8+0j), 0j , 0j ],
# [(8+0j), 0j , 0j ],
# [(8+0j), 0j , 0j ]],
#
# [[0j , 0j , 0j ],
# [0j , 0j , 0j ],
# [0j , 0j , 0j ]]])
"""
return fftn_r2c(x, s, axes, norm, forward=True, onesided=True, name=name)
def irfftn(x, s=None, axes=None, norm="backward", name=None):
"""
Computes the inverse of `rfftn`.
This function computes the inverse of the N-D discrete
Fourier Transform for real input over any number of axes in an
M-D array by means of the Fast Fourier Transform (FFT). In
other words, ``irfftn(rfftn(x), x.shape) == x`` to within numerical
accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`,
and for the same reason.)
The input should be ordered in the same way as is returned by `rfftn`,
i.e., as for `irfft` for the final transformation axis, and as for `ifftn`
along all the other axes.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): The length of the output transform axis.
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
number of input points used along this axis, except for the last axis,
where ``s[-1]//2+1`` points of the input are used. Along any axis, if
the shape indicated by `s` is smaller than that of the input, the input
is cropped. If it is larger, the input is padded with zeros.
If `s` is not given, the shape of the input along the axes specified by axes
is used. Except for the last axis which is taken to be ``2*(k-1)`` where
``k`` is the length of the input along that axis.
axes (sequence of ints, optional): Axes over which to compute the inverse FFT. If not given, the last
`len(s)` axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Real tensor. The truncated or zero-padded input, transformed along the axes indicated by `axes`,
or by a combination of `s` or `x`, as explained in the parameters section above. The length of
each transformed axis is as given by the corresponding element of `s`, or the length of the input
in every axis except for the last one if `s` is not given. In the final transformed axis the length
of the output when `s` is not given is ``2*(m-1)``, where ``m`` is the length of the final
transformed axis of the input. To get an odd number of output points in the final axis,
`s` must be specified.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([2, 2, 3]) + 1j * np.array([2, 2, 3])).astype(np.complex128)
xp = paddle.to_tensor(x)
irfftn_xp = paddle.fft.irfftn(xp).numpy()
print(irfftn_xp)
# [ 2.25 -1.25 0.25 0.75]
"""
return fftn_c2r(x, s, axes, norm, forward=False, name=name)
def hfftn(x, s=None, axes=None, norm="backward", name=None):
"""
Compute the N-D FFT of Hermitian symmetric complex input, i.e., a
signal with a real spectrum.
This function calculates the n-D discrete Fourier transform of Hermite symmetric
complex input on any axis in M-D array by fast Fourier transform (FFT).
In other words, ``ihfftn(hfftn(x, s)) == x is within the numerical accuracy range.
(``s`` here are ``x.shape`` and ``s[-1] = x.shape[- 1] * 2 - 1``. This is necessary
for the same reason that ``irfft` requires ``x.shape``.)
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): The length of the output transform axis.
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
number of input points used along this axis, except for the last axis,
where ``s[-1]//2+1`` points of the input are used. Along any axis, if
the shape indicated by `s` is smaller than that of the input, the input
is cropped. If it is larger, the input is padded with zeros.
If `s` is not given, the shape of the input along the axes specified by axes
is used. Except for the last axis which is taken to be ``2*(k-1)`` where
``k`` is the length of the input along that axis.
axes (sequence of ints, optional): Axes over which to compute the inverse FFT. If not given, the last
`len(s)` axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Real tensor. Truncate or zero fill input, transforming along the axis indicated by axis or
a combination of `s` or `X`.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([2, 2, 3]) + 1j * np.array([2, 2, 3])).astype(np.complex128)
xp = paddle.to_tensor(x)
hfftn_xp = paddle.fft.hfftn(xp).numpy()
print(hfftn_xp)
# [ 9. 3. 1. -5.]
"""
return fftn_c2r(x, s, axes, norm, forward=True, name=name)
def ihfftn(x, s=None, axes=None, norm="backward", name=None):
"""
The n dimensional inverse FFT of a signal that has Hermitian symmetry.
This function computes the n dimensional inverse FFT over any number of axes
in an M-dimensional of a signal that has Hermitian symmetry by means of an
efficient algorithm called the Fast Fourier Transform (FFT).
Args:
x(Tensor): Input tensor.
s(Sequence[int], optional) : Shape (length along each transformed axis)
to use from the input. (``s[0]`` refers to axis 0, ``s[1]`` to axis
1, etc.). Along any axis, if the given shape is smaller than that
of the input, the input is cropped. If it is larger, the input is
padded with zeros. if `s` is not given, the shape of the input
along the axes specified by `axes` is used.
axis(Sequence[int], optional) : Axis over which to compute the inverse FFT. If not
given, the last axis is used.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : complex tensor.
Examples:
.. code-block:: python
import paddle
spectrum = paddle.to_tensor([10.0, -5.0, 0.0, -1.0, 0.0, -5.0])
print(paddle.fft.ifft(spectrum))
# Tensor(shape=[6], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j), (2.3333334922790527+1.9868215517249155e-08j), (1+1.9868215517249155e-08j)])
print(paddle.fft.ihfft(spectrum))
# Tensor(shape = [4], dtype = complex64, place = CUDAPlace(0), stop_gradient = True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j)])
"""
return fftn_r2c(x, s, axes, norm, forward=False, onesided=True, name=name)
# public APIs 2d
def fft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the 2-D discrete Fourier Transform
This function computes the N-D discrete Fourier Transform
over any axes in an M-D array by means of the
Fast Fourier Transform (FFT). By default, the transform is computed over
the last two axes of the input array, i.e., a 2-dimensional FFT.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output.
It should be a sequence of 2 integers. This corresponds to ``n`` for ``fft(x, n)``.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used. Default is None.
axes (sequence of ints, optional): Axes over which to compute the FFT. It should be a
sequence of 2 integers. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Complex tensor. The truncated or zero-padded input, transformed along the axes indicated by `axes`,
or the last two axes if `axes` is not given.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:2, :2][1]
xp = paddle.to_tensor(x)
fft2_xp = paddle.fft.fft2(xp).numpy()
print(fft2_xp)
# [[ 2.+0.j -2.+0.j]
# [ 0.+0.j 0.+0.j]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return fftn(x, s, axes, norm, name)
def ifft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the 2-D inverse discrete Fourier Transform.
This function computes the inverse of the 2-D discrete Fourier
Transform over any number of axes in an M-D array by means of
the Fast Fourier Transform (FFT). In other words, ``ifft2(fft2(x)) == x``
to within numerical accuracy. By default, the inverse transform is
computed over the last two axes of the input array.
The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fft2`, i.e., it should have the term for zero frequency
in the low-order corner of the two axes, the positive frequency terms in
the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
both axes, in order of decreasingly negative frequency.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output.
It should be a sequence of 2 integers. This corresponds to ``n`` for ``fft(x, n)``.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used. Default is None.
axes (sequence of ints, optional): Axes over which to compute the FFT. It should be a
sequence of 2 integers. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Complex tensor. The truncated or zero-padded input, transformed along the axes indicated by `axes`,
or the last two axes if `axes` is not given.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:2, :2][1]
xp = paddle.to_tensor(x)
ifft2_xp = paddle.fft.ifft2(xp).numpy()
print(ifft2_xp)
# [[ 0.5+0.j -0.5+0.j]
# [ 0. +0.j 0. +0.j]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return ifftn(x, s, axes, norm, name)
def rfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
The two dimensional FFT with real tensor input.
This is really just `rfftn` with different default behavior.
For more details see `rfftn`.
Args:
x(Tensor): Input tensor, taken to be real.
s(Sequence[int]) : Shape of the FFT.
axes(Sequence[int], optional): Axes over which to compute the FFT.
norm(str, optional) : {"backward", "ortho", "forward"},
default is "backward". Indicates which direction of the
forward/backward pair of transforms is scaled and with what
normalization factor.
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor): The result of the real 2-D FFT.
Raises:
Examples:
.. code-block:: python
import paddle
import numpy as np
x = paddle.to_tensor(np.mgrid[:5, :5][0].astype(np.float32))
print(paddle.fft.rfft2(x))
# Tensor(shape=[5, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [[ (50+0j) , (1.1920928955078125e-07+0j) , 0j ],
# [(-12.5+17.204774856567383j) , (-9.644234211236835e-08+7.006946134424652e-08j) , 0j ],
# [(-12.500000953674316+4.061495304107666j) , (3.6837697336977726e-08-1.1337477445749755e-07j), 0j ],
# [(-12.500000953674316-4.061495304107666j) , (3.6837697336977726e-08+1.1337477445749755e-07j), 0j ],
# [(-12.5-17.204774856567383j) , (-9.644234211236835e-08-7.006946134424652e-08j) , 0j ]])
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return rfftn(x, s, axes, norm, name)
def irfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Computes the inverse of `rfft2`.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape of the real output to the inverse FFT. Default is None.
axes (sequence of ints, optional): The axes over which to compute the inverse FFT. Axes
must be two-dimensional. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name` .
Returns:
Real tensor. The result of the inverse real 2-D FFT.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([[3,2,3],[2, 2, 3]]) + 1j * np.array([[3,2,3],[2, 2, 3]])).astype(np.complex128)
xp = paddle.to_tensor(x)
irfft2_xp = paddle.fft.irfft2(xp).numpy()
print(irfft2_xp)
# [[ 2.375 -1.125 0.375 0.875]
# [ 0.125 0.125 0.125 0.125]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return irfftn(x, s, axes, norm, name)
def hfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the 2-D FFT of a Hermitian complex array.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape of the real output. Default is None.
axes (sequence of ints, optional): Axes over which to compute the FFT. Axes must be
two-dimensional. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Real tensor. The real result of the 2-D Hermitian complex real FFT.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([[3,2,3],[2, 2, 3]]) + 1j * np.array([[3,2,3],[2, 2, 3]])).astype(np.complex128)
xp = paddle.to_tensor(x)
hfft2_xp = paddle.fft.hfft2(xp).numpy()
print(hfft2_xp)
# [[19. 7. 3. -9.]
# [ 1. 1. 1. 1.]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return hfftn(x, s, axes, norm, name)
def ihfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the two dimensional inverse FFT of a real spectrum.
This is really `ihfftn` with different defaults.
For more details see `ihfftn`.
Args:
x(Tensor): Input tensor
s(Sequence[int], optional): Shape of the real input to the inverse FFT.
axes(Sequance[int], optional): The axes over which to compute the
inverse fft. Default is the last two axes.
norm(str, optional): {"backward", "ortho", "forward"}. Default is
"backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : The result of the inverse hermitian 2-D FFT.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:5, :5][0].astype(np.float64)
xp = paddle.to_tensor(x)
ihfft2_xp = paddle.fft.ihfft2(xp).numpy()
print(ihfft2_xp)
# [[ 2. +0.j 0. +0.j 0. +0.j ]
# [-0.5-0.68819096j 0. +0.j 0. +0.j ]
# [-0.5-0.16245985j 0. +0.j 0. +0.j ]
# [-0.5+0.16245985j 0. +0.j 0. +0.j ]
# [-0.5+0.68819096j 0. +0.j 0. +0.j ]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return ihfftn(x, s, axes, norm, name)
# public APIs utilities
def fftfreq(n, d=1.0, dtype=None, name=None):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given input length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd
Args:
n (int): Dimension inputed.
d (scalar, optional): Sample spacing (inverse of the sampling rate). Defaults is 1.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. A tensor of length 'n' containing the sampling frequency.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
scalar_temp = 0.5
n = x.size
fftfreq_xp = paddle.fft.fftfreq(n, d=scalar_temp)
print(fftfreq_xp)
# Tensor(shape=[5], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
# [ 0. , 0.40000001, 0.80000001, -0.80000001, -0.40000001])
"""
dtype = paddle.framework.get_default_dtype()
val = 1.0 / (n * d)
pos_max = (n + 1) // 2
neg_max = n // 2
indices = paddle.arange(-neg_max, pos_max, dtype=dtype, name=name)
indices = paddle.roll(indices, -neg_max, name=name)
return indices * val
def rfftfreq(n, d=1.0, dtype=None, name=None):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned floating-point array "F" contains the center of the frequency unit,
and the unit is the number of cycles of the sampling interval (the starting point is zero).
Given input length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd
the Nyquist frequency component is considered to be positive.
Args:
n (int): Dimension inputed.
d (scalar, optional): Sample spacing (inverse of the sampling rate). Defaults is 1.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. A tensor of length ``n//2 + 1`` containing the sample frequencies.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
scalar_temp = 0.3
n = x.size
rfftfreq_xp = paddle.fft.rfftfreq(n, d=scalar_temp)
print(rfftfreq_xp)
# Tensor(shape=[3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
# [0. , 0.66666669, 1.33333337])
"""
dtype = paddle.framework.get_default_dtype()
val = 1.0 / (n * d)
pos_max = 1 + n // 2
indices = paddle.arange(0, pos_max, dtype=dtype, name=name)
return indices * val
def fftshift(x, axes=None, name=None):
"""
Shift the zero-frequency component to the center of the spectrum.
This function swaps half spaces for all the axes listed (all by default).
Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
Args:
n (int): Dimension inputed.
axes (int|tuple, optional): The axis on which to move. The default is none, which moves all axes.
Default is None.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. The shifted tensor.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
n = x.size
fftfreq_xp = paddle.fft.fftfreq(n, d=0.3)
res = paddle.fft.fftshift(fftfreq_xp).numpy()
print(res)
# [-1.3333334 -0.6666667 0. 0.6666667 1.3333334]
"""
shape = paddle.shape(x)
if axes is None:
# shift all axes
rank = paddle.rank(x).reshape([1])
axes = axes or paddle.arange(0, rank)
shifts = [size // 2 for size in shape]
elif isinstance(axes, int):
shifts = shape[axes] // 2
else:
shifts = [shape[ax] // 2 for ax in axes]
return paddle.roll(x, shifts, axes, name=name)
def ifftshift(x, axes=None, name=None):
"""
The inverse of `fftshift`. Although the even length 'x' is the same, the function of the
odd length 'x' is different. An example.
Args:
n (int): Dimension inputed.
axes (int|tuple, optional): The axis on which to move. The default is none, which moves all axes.
Default is None.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. The shifted tensor.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
n = x.size
fftfreq_xp = paddle.fft.fftfreq(n, d=0.3)
res = paddle.fft.ifftshift(fftfreq_xp).numpy()
print(res)
# [ 1.3333334 -1.3333334 -0.6666667 0. 0.6666667]
"""
shape = paddle.shape(x)
if axes is None:
# shift all axes
rank = paddle.rank(x).reshape([1])
axes = axes or paddle.arange(0, rank)
shifts = [-size // 2 for size in shape]
elif isinstance(axes, int):
shifts = -shape[axes] // 2
else:
shifts = [-shape[ax] // 2 for ax in axes]
return paddle.roll(x, shifts, axes, name=name)
# internal functions
def fft_c2c(x, n, axis, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
axis = axis if axis is not None else -1
_check_fft_axis(x, axis)
axes = [axis]
axes = _normalize_axes(x, axes)
if n is not None:
_check_fft_n(n)
s = [n]
x = _resize_fft_input(x, s, axes)
op_type = 'fft_c2c'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(dtype)
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fft_r2c(x, n, axis, norm, forward, onesided, name):
if is_interger(x):
x = paddle.cast(x, paddle.get_default_dtype())
_check_normalization(norm)
axis = axis if axis is not None else -1
_check_fft_axis(x, axis)
axes = [axis]
axes = _normalize_axes(x, axes)
if n is not None:
_check_fft_n(n)
s = [n]
x = _resize_fft_input(x, s, axes)
op_type = 'fft_r2c'
check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'onesided', onesided)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {
'axes': axes,
'normalization': norm,
'forward': forward,
'onesided': onesided,
}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_real_to_complex_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fft_c2r(x, n, axis, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
axis = axis if axis is not None else -1
_check_fft_axis(x, axis)
axes = [axis]
axes = _normalize_axes(x, axes)
if n is not None:
_check_fft_n(n)
s = [n // 2 + 1]
x = _resize_fft_input(x, s, axes)
op_type = 'fft_c2r'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
if n is not None:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'last_dim_size', n)
else:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
if n is not None:
attrs['last_dim_size'] = n
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_complex_to_real_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fftn_c2c(x, s, axes, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
if s is not None:
_check_fft_shape(x, s)
rank = x.ndim
if axes is None:
if s is None:
axes = list(range(rank))
else:
fft_ndims = len(s)
axes = list(range(rank - fft_ndims, rank))
else:
_check_fft_axes(x, axes)
axes = _normalize_axes(x, axes)
axes_argsoft = np.argsort(axes).tolist()
axes = [axes[i] for i in axes_argsoft]
if s is not None:
if len(s) != len(axes):
raise ValueError(
"Length of s ({}) and length of axes ({}) does not match.".
format(len(s), len(axes)))
s = [s[i] for i in axes_argsoft]
if s is not None:
x = _resize_fft_input(x, s, axes)
op_type = 'fft_c2c'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(dtype)
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fftn_r2c(x, s, axes, norm, forward, onesided, name):
if is_interger(x):
x = paddle.cast(x, paddle.get_default_dtype())
_check_normalization(norm)
if s is not None:
_check_fft_shape(x, s)
rank = x.ndim
if axes is None:
if s is None:
axes = list(range(rank))
else:
fft_ndims = len(s)
axes = list(range(rank - fft_ndims, rank))
else:
_check_fft_axes(x, axes)
axes = _normalize_axes(x, axes)
axes_argsoft = np.argsort(axes[:-1]).tolist()
axes = [axes[i] for i in axes_argsoft] + [axes[-1]]
if s is not None:
if len(s) != len(axes):
raise ValueError(
"Length of s ({}) and length of axes ({}) does not match.".
format(len(s), len(axes)))
s = [s[i] for i in axes_argsoft] + [s[-1]]
if s is not None:
x = _resize_fft_input(x, s, axes)
op_type = 'fft_r2c'
check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'onesided', onesided)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {
'axes': axes,
'normalization': norm,
'forward': forward,
'onesided': onesided,
}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_real_to_complex_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fftn_c2r(x, s, axes, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
if s is not None:
_check_fft_shape(x, s)
rank = x.ndim
if axes is None:
if s is None:
axes = list(range(rank))
else:
fft_ndims = len(s)
axes = list(range(rank - fft_ndims, rank))
else:
_check_fft_axes(x, axes)
axes = _normalize_axes(x, axes)
axes_argsoft = np.argsort(axes[:-1]).tolist()
axes = [axes[i] for i in axes_argsoft] + [axes[-1]]
if s is not None:
if len(s) != len(axes):
raise ValueError(
"Length of s ({}) and length of axes ({}) does not match.".
format(len(s), len(axes)))
s = [s[i] for i in axes_argsoft] + [s[-1]]
if s is not None:
fft_input_shape = list(s)
fft_input_shape[-1] = fft_input_shape[-1] // 2 + 1
x = _resize_fft_input(x, fft_input_shape, axes)
op_type = 'fft_c2r'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
if s:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'last_dim_size', s[-1])
else:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
if s:
attrs["last_dim_size"] = s[-1]
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_complex_to_real_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
python/paddle/fluid/tests/unittests/test_signal.py
浏览文件 @ 81e0c1ba
......@@ -652,7 +652,7 @@ class TestFrame(unittest.TestCase):
self.assertTrue(
np.allclose(
frame_for_api_test(self.x, self.frame_length, self.hop_length, self.axis),
paddle.tensor.signal.frame(
paddle.signal.frame(
paddle.to_tensor(self.x),
self.frame_length,
self.hop_length,
......@@ -678,7 +678,7 @@ class TestFrameStatic(unittest.TestCase):
mp, sp = paddle.static.Program(), paddle.static.Program()
with paddle.static.program_guard(mp, sp):
input = paddle.static.data('input', self.x.shape, dtype=self.x.dtype)
output = paddle.tensor.signal.frame(
output = paddle.signal.frame(
input,
self.frame_length,
self.hop_length,
......@@ -708,7 +708,7 @@ class TestFrameStatic(unittest.TestCase):
class TestFrameException(unittest.TestCase):
def test_frame(self):
with self.assertRaises(self.expect_exception):
paddle.tensor.signal.frame(
paddle.signal.frame(
paddle.to_tensor(self.x),
self.frame_length,
self.hop_length,
......@@ -731,7 +731,7 @@ class TestOverlapAdd(unittest.TestCase):
self.assertTrue(
np.allclose(
overlap_add_for_api_test(self.x, self.hop_length, self.axis),
paddle.tensor.signal.overlap_add(
paddle.signal.overlap_add(
paddle.to_tensor(self.x),
self.hop_length,
self.axis),
......@@ -756,7 +756,7 @@ class TestOverlapAddStatic(unittest.TestCase):
mp, sp = paddle.static.Program(), paddle.static.Program()
with paddle.static.program_guard(mp, sp):
input = paddle.static.data('input', self.x.shape, dtype=self.x.dtype)
output = paddle.tensor.signal.overlap_add(
output = paddle.signal.overlap_add(
input,
self.hop_length,
self.axis),
......@@ -783,7 +783,7 @@ class TestOverlapAddStatic(unittest.TestCase):
class TestOverlapAddException(unittest.TestCase):
def test_overlap_add(self):
with self.assertRaises(self.expect_exception):
paddle.tensor.signal.overlap_add(
paddle.signal.overlap_add(
paddle.to_tensor(self.x),
self.hop_length,
self.axis)
......@@ -848,7 +848,7 @@ class TestStft(unittest.TestCase):
self.assertTrue(
np.allclose(
stft(self.x, self.n_fft, self.hop_length, self.win_length, win_l, self.center, self.pad_mode),
paddle.tensor.signal.stft(
paddle.signal.stft(
paddle.to_tensor(self.x),
self.n_fft,
self.hop_length,
......@@ -891,7 +891,7 @@ class TestStftException(unittest.TestCase):
win_p = paddle.to_tensor(self.window)
with self.assertRaises(self.expect_exception):
paddle.tensor.signal.stft(
paddle.signal.stft(
paddle.to_tensor(self.x),
self.n_fft,
self.hop_length,
......@@ -934,7 +934,7 @@ class TestIstft(unittest.TestCase):
self.assertTrue(
np.allclose(
istft(self.x, self.hop_length, self.win_length, win_l, self.center, self.length),
paddle.tensor.signal.istft(
paddle.signal.istft(
paddle.to_tensor(self.x),
self.n_fft,
self.hop_length,
......@@ -986,7 +986,7 @@ class TestIstftException(unittest.TestCase):
win_p = paddle.to_tensor(self.window)
with self.assertRaises(self.expect_exception):
paddle.tensor.signal.istft(
paddle.signal.istft(
paddle.to_tensor(self.x),
self.n_fft,
self.hop_length,
......
python/paddle/tensor/signal.py → python/paddle/signal.py
浏览文件 @ 81e0c1ba
......@@ -16,16 +16,14 @@ from typing import Optional
import paddle
from .attribute import is_complex, is_floating_point
from .tensor.attribute import is_complex, is_floating_point
from .fft import fft_r2c, fft_c2r, fft_c2c
from ..fluid.data_feeder import check_variable_and_dtype
from ..fluid.framework import in_dygraph_mode
from ..fluid.layer_helper import LayerHelper
from .. import _C_ops
from .fluid.data_feeder import check_variable_and_dtype
from .fluid.framework import in_dygraph_mode
from .fluid.layer_helper import LayerHelper
from . import _C_ops
__all__ = [
'frame',
'overlap_add',
'stft',
'istft',
]
......@@ -56,7 +54,7 @@ def frame(x, frame_length, hop_length, axis=-1, name=None):
.. code-block:: python
import paddle
from paddle.tensor.signal import frame
from paddle.signal import frame
# 1D
x = paddle.arange(8)
......@@ -177,7 +175,7 @@ def overlap_add(x, hop_length, axis=-1, name=None):
.. code-block:: python
import paddle
from paddle.tensor.signal import overlap_add
from paddle.signal import overlap_add
# 2D
x0 = paddle.arange(16).reshape([8, 2])
......@@ -291,11 +289,11 @@ def stft(x,
real-valued input and `onesided` is `True`) or `[..., n_fft, num_frames]`(
`onesided` is `False`)
Exampels:
Examples:
.. code-block:: python
import paddle
from paddle.tensor.signal import stft
from paddle.signal import stft
# real-valued input
x = paddle.randn([8, 48000], dtype=paddle.float64)
......@@ -415,7 +413,7 @@ def istft(x,
- :math:`N`: Value of `n_fft`.
- :math:`H`: Value of `hop_length`.
Result of `istft` expected to be the inverse of `paddle.tensor.signal.stft`, but it is
Result of `istft` expected to be the inverse of `paddle.signal.stft`, but it is
not guaranteed to reconstruct a exactly realizible time-domain signal from a STFT
complex tensor which has been modified (via masking or otherwise). Therefore, `istft`
gives the [Griffin-Lim optimal estimate](https://ieeexplore.ieee.org/document/1164317)
......@@ -454,12 +452,12 @@ def istft(x,
A tensor of least squares estimation of the reconstructed signal(s) with shape
`[..., seq_length]`
Exampels:
Examples:
.. code-block:: python
import numpy as np
import paddle
from paddle.tensor.signal import stft, istft
from paddle.signal import stft, istft
paddle.seed(0)
......
python/paddle/tensor/__init__.py
浏览文件 @ 81e0c1ba
......@@ -221,8 +221,6 @@ from .array import array_write # noqa: F401
from .array import create_array # noqa: F401
from .einsum import einsum # noqa: F401
from . import fft
from . import signal
#this list used in math_op_patch.py for _binary_creator_
tensor_method_func = [ #noqa
......
python/paddle/tensor/fft.py 已删除 100644 → 0
浏览文件 @ 21bece3f
# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
#
# 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
#
# http://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.
from typing import Sequence
import numpy as np
import paddle
from .attribute import is_complex, is_floating_point, is_interger, _real_to_complex_dtype, _complex_to_real_dtype
from ..fluid.framework import in_dygraph_mode
from .. import _C_ops
from ..fluid.data_feeder import check_variable_and_dtype
from ..fluid.layer_helper import LayerHelper
__all__ = []
def _check_normalization(norm):
if norm not in ['forward', 'backward', 'ortho']:
raise ValueError(
"Unexpected norm: {}. Norm should be forward, backward or ortho".
format(norm))
def _check_fft_n(n):
if not isinstance(n, int):
raise ValueError(
"Invalid FFT argument n({}), it shoule be an integer.".format(n))
if n <= 0:
raise ValueError(
"Invalid FFT argument n({}), it should be positive.".format(n))
def _check_fft_shape(x, s):
ndim = x.ndim
if not isinstance(s, Sequence):
raise ValueError(
"Invaid FFT argument s({}), it should be a sequence of integers.")
if len(s) > ndim:
raise ValueError(
"Length of FFT argument s should not be larger than the rank of input. "
"Received s: {}, rank of x: {}".format(s, ndim))
for size in s:
if not isinstance(size, int) or size <= 0:
raise ValueError("FFT sizes {} contains invalid value ({})".format(
s, size))
def _check_fft_axis(x, axis):
ndim = x.ndim
if not isinstance(axis, int):
raise ValueError(
"Invalid FFT axis ({}), it shoule be an integer.".format(axis))
if axis < -ndim or axis >= ndim:
raise ValueError(
"Invalid FFT axis ({}), it should be in range [-{}, {})".format(
axis, ndim, ndim))
def _check_fft_axes(x, axes):
ndim = x.ndim
if not isinstance(axes, Sequence):
raise ValueError(
"Invalid FFT axes ({}), it should be a sequence of integers.".
format(axes))
if len(axes) > ndim:
raise ValueError(
"Length of fft axes should not be larger than the rank of input. "
"Received, len of axes: {}, rank of x: {}".format(len(axes), ndim))
for axis in axes:
if not isinstance(axis, int) or axis < -ndim or axis >= ndim:
raise ValueError(
"FFT axes {} contains invalid value ({}), it should be in range [-{}, {})".
format(axes, axis, ndim, ndim))
def _resize_fft_input(x, s, axes):
if len(s) != len(axes):
raise ValueError("length of `s` should equals length of `axes`.")
shape = x.shape
ndim = x.ndim
axes_to_pad = []
paddings = []
axes_to_slice = []
slices = []
for i, axis in enumerate(axes):
if shape[axis] < s[i]:
axes_to_pad.append(axis)
paddings.append(s[i] - shape[axis])
elif shape[axis] > s[i]:
axes_to_slice.append(axis)
slices.append((0, s[i]))
if axes_to_slice:
x = paddle.slice(
x,
axes_to_slice,
starts=[item[0] for item in slices],
ends=[item[1] for item in slices])
if axes_to_pad:
padding_widths = [0] * (2 * ndim)
for axis, pad in zip(axes_to_pad, paddings):
padding_widths[2 * axis + 1] = pad
x = paddle.nn.functional.pad(x, padding_widths)
return x
def _normalize_axes(x, axes):
ndim = x.ndim
return [item if item >= 0 else (item + ndim) for item in axes]
def _check_at_least_ndim(x, rank):
if x.ndim < rank:
raise ValueError("The rank of the input ({}) should >= {}".format(
x.ndim, rank))
# public APIs 1d
def fft(x, n=None, axis=-1, norm="backward", name=None):
"""
Calculate one-dimensional discrete Fourier transform.
This function uses the efficient fast Fourier transform (FFT) algorithm [1] to
calculate the 1-D * n * point discrete Fourier transform (DFT).
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. If `n` is less than
the length input, the input will be cropped. If larger, the input is filled
with zeros. If `n` is not given, the input length along the axis specified
by `axis` is used.
axis (int, optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axis indicated
by `axis`, or the last one if `axis` is not specified.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.exp(3j * np.pi * np.arange(7) / 7)
xp = paddle.to_tensor(x)
fft_xp = paddle.fft.fft(xp).numpy()
print(fft_xp)
# [1.+1.25396034e+00j 1.+4.38128627e+00j 1.-4.38128627e+00j
# 1.-1.25396034e+00j 1.-4.81574619e-01j 1.+8.88178420e-16j
# 1.+4.81574619e-01j]
"""
if is_interger(x) or is_floating_point(x):
return fft_r2c(
x, n, axis, norm, forward=True, onesided=False, name=name)
else:
return fft_c2c(x, n, axis, norm, forward=True, name=name)
def ifft(x, n=None, axis=-1, norm="backward", name=None):
"""
Compute the 1-D inverse discrete Fourier Transform.
This function computes the inverse of the 1-D *n*-point discrete Fourier transform
computed by `fft`. In other words, ``ifft(fft(x)) == x`` to within numerical accuracy.
The input should be ordered in the same way as is returned by `fft`,
i.e.,
* ``x[0]`` should contain the zero frequency term,
* ``x[1:n//2]`` should contain the positive-frequency terms,
* ``x[n//2 + 1:]`` should contain the negative-frequency terms, in
increasing order starting from the most negative frequency.
For an even number of input points, ``x[n//2]`` represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. If `n` is less than
the length input, the input will be cropped. If larger, the input is filled
with zeros. If `n` is not given, the input length along the axis specified
by `axis` is used.
axis (int, optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axis indicated
by `axis`, or the last one if `axis` is not specified.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.exp(3j * np.pi * np.arange(7) / 7)
xp = paddle.to_tensor(x)
ifft_xp = paddle.fft.ifft(xp).numpy()
print(ifft_xp)
# [0.14285714+1.79137191e-01j 0.14285714+6.87963741e-02j
# 0.14285714+1.26882631e-16j 0.14285714-6.87963741e-02j
# 0.14285714-1.79137191e-01j 0.14285714-6.25898038e-01j
# 0.14285714+6.25898038e-01j]
"""
if is_interger(x) or is_floating_point(x):
return fft_r2c(
x, n, axis, norm, forward=False, onesided=False, name=name)
else:
return fft_c2c(x, n, axis, norm, forward=False, name=name)
def rfft(x, n=None, axis=-1, norm="backward", name=None):
"""
The one dimensional FFT for real input.
This function computes the one dimensional *n*-point discrete Fourier
Transform (DFT) of a real-valued tensor by means of an efficient algorithm
called the Fast Fourier Transform (FFT).
When the DFT is computed for purely real input, the output is
Hermitian-symmetric. This function does not compute the negative frequency
terms, and the length of the transformed axis of the output is therefore
``n//2 + 1``.
Args:
x(Tensor) : Real-valued input tensor
n(int, optional): Number of points along transformation axis in the
input to use. If `n` is smaller than the length of the input, the
input is cropped. If it is larger, the input is padded with zeros.
If `n` is not given, the length of the input along the axis
specified by `axis` is used.
axis(int, optional): Axis over which to compute the FFT. Default value
is last axis.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : complex tensor
Raises:
Examples:
.. code-block:: python
import paddle
x = paddle.to_tensor([0.0, 1.0, 0.0, 0.0])
print(paddle.fft.rfft(x))
# Tensor(shape=[3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [ (1+0j), -1j , (-1+0j)])
"""
return fft_r2c(x, n, axis, norm, forward=True, onesided=True, name=name)
def irfft(x, n=None, axis=-1, norm="backward", name=None):
"""
Computes the inverse of `rfft`.
This function calculates the inverse of the one-dimensional *n* point discrete
Fourier transform of the actual input calculated by "rfft". In other words,
``irfft(rfft(a),len(a)) == a`` is within the numerical accuracy range.
The input shall be in the form of "rfft", i.e. the actual zero frequency term,
followed by the complex positive frequency term, in the order of increasing frequency.
Because the discrete Fourier transform of the actual input is Hermite symmetric,
the negative frequency term is regarded as the complex conjugate term of the corresponding
positive frequency term.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. For `n` output
points, ``n//2 + 1``input points are necessary. If the length of the input tensor is greater
than `n`, it will be cropped, if it is shorter than this, fill in zero. If `n` is not given,
it is considered to be ``2 * (k-1)``, where ``k`` is the length of the input axis specified
along the ` axis'.
axis (int, optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name` .
Returns:
Real tensor. Truncated or zero fill input for the transformation along the axis indicated by
`axis`, or the last input if `axis` is not specified. The length of the conversion axis
is `n`, or ``2 * k-2``, if `k` is None, where `k` is the length of the input conversion axis.
If the output is an odd number, you need to specify the value of 'n', such as ``2 * k-1``
in some cases.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([1, -1j, -1])
xp = paddle.to_tensor(x)
irfft_xp = paddle.fft.irfft(xp).numpy()
print(irfft_xp)
# [0. 1. 0. 0.]
"""
return fft_c2r(x, n, axis, norm, forward=False, name=name)
def hfft(x, n=None, axis=-1, norm="backward", name=None):
"""
Compute the FFT of a signal that has Hermitian symmetry, a real
spectrum.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
n (int, optional): The length of the output transform axis. For `n` output
points, ``n//2 + 1`` input points are necessary. If the length of the input tensor is greater
than `n`, it will be cropped, if it is shorter than this, fill in zero. If `n` is not given,
it is considered to be ``2 * (k-1)``, where ``k`` is the length of the input axis specified
along the ` axis'.
axis (int,optional): Axis used to calculate FFT. If not specified, the last axis
is used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name` .
Returns:
Real tensor. Truncated or zero fill input for the transformation along the axis indicated by
`axis`, or the last input if `axis` is not specified. The length of the conversion axis
is `n`, or ``2 * k-2``, if `k` is None, where `k` is the length of the input conversion axis.
If the output is an odd number, you need to specify the value of 'n', such as ``2 * k-1`` in
some cases.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([1, -1j, -1])
xp = paddle.to_tensor(x)
hfft_xp = paddle.fft.hfft(xp).numpy()
print(hfft_xp)
# [0. 0. 0. 4.]
"""
return fft_c2r(x, n, axis, norm, forward=True, name=name)
def ihfft(x, n=None, axis=-1, norm="backward", name=None):
"""
The inverse FFT of a signal that has Hermitian symmetry.
This function computes the one dimensional *n*-point inverse FFT of a signal
that has Hermitian symmetry by means of an efficient algorithm called
the Fast Fourier Transform (FFT).
When the DFT is computed for purely real input, the output is
Hermitian-symmetric. This function does not compute the negative frequency
terms, and the length of the transformed axis of the output is therefore
``n//2 + 1``.
Args:
x(Tensor): Input tensor.
n(int, optional): The number of points along transformation axis in the
input to use. If `n` is smaller than the length of the input, the
input is cropped. If it is larger, the input is padded with zeros.
If `n` is not given, the length of the input along the axis
specified by `axis` is used.
axis(int, optional) : Axis over which to compute the inverse FFT. If not
given, the last axis is used.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : complex tensor.
Examples:
.. code-block:: python
import paddle
spectrum = paddle.to_tensor([10.0, -5.0, 0.0, -1.0, 0.0, -5.0])
print(paddle.fft.ifft(spectrum))
# Tensor(shape=[6], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j), (2.3333334922790527+1.9868215517249155e-08j), (1+1.9868215517249155e-08j)])
print(paddle.fft.ihfft(spectrum))
# Tensor(shape = [4], dtype = complex64, place = CUDAPlace(0), stop_gradient = True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j)])
"""
return fft_r2c(x, n, axis, norm, forward=False, onesided=True, name=name)
# public APIs nd
def fftn(x, s=None, axes=None, norm="backward", name=None):
"""
Compute the N-D discrete Fourier Transform.
This function calculates the n-D discrete Fourier transform on any number of axes
in the M-D array by fast Fourier transform (FFT).
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
This corresponds to ``n`` for ``fft(x, n)``.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes (sequence of ints, optional): Axes used to calculate FFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axes indicated by
`axes`, or by a combination of `s` and `x`, as explained in the parameters section above.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:4, :4, :4][1]
xp = paddle.to_tensor(x)
fftn_xp = paddle.fft.fftn(xp, axes=(1, 2)).numpy()
print(fftn_xp)
# [[[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]
# [[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]
# [[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]
# [[24.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+8.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.+0.j 0.+0.j 0.+0.j 0.-0.j]
# [-8.-8.j 0.+0.j 0.+0.j 0.-0.j]]]
"""
if is_interger(x) or is_floating_point(x):
return fftn_r2c(
x, s, axes, norm, forward=True, onesided=False, name=name)
else:
return fftn_c2c(x, s, axes, norm, forward=True, name=name)
def ifftn(x, s=None, axes=None, norm="backward", name=None):
"""
Compute the N-D inverse discrete Fourier Transform.
This function computes the inverse of the N-D discrete
Fourier Transform over any number of axes in an M-D array by
means of the Fast Fourier Transform (FFT). In other words,
``ifftn(fftn(x)) == x`` to within numerical accuracy.
The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fftn`, i.e., it should have the term for zero frequency
in all axes in the low-order corner, the positive frequency terms in the
first half of all axes, the term for the Nyquist frequency in the middle
of all axes and the negative frequency terms in the second half of all
axes, in order of decreasingly negative frequency.
Args:
x (Tensor): The input data. It's a Tensor type. It's a complex.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.).
This corresponds to ``n`` for ``fft(x, n)``.
Along any axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used.
axes (sequence of ints, optional): Axes used to calculate FFT. If not given, the last ``len(s)``
axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward", meaning no normalization on
the forward transforms and scaling by ``1/n`` on the `ifft`. "forward" instead applies
the ``1/n`` factor on the forward tranform. For ``norm="ortho"``, both directions are
scaled by ``1/sqrt(n)``.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
complex tensor. The truncated or zero-padded input, transformed along the axes indicated by
`axes`, or by a combination of `s` and `x`, as explained in the parameters section above.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.eye(3)
xp = paddle.to_tensor(x)
ifftn_xp = paddle.fft.ifftn(xp, axes=(1,)).numpy()
print(ifftn_xp)
# [[ 0.33333333+0.j 0.33333333+0.j 0.33333333-0.j ]
# [ 0.33333333+0.j -0.16666667+0.28867513j -0.16666667-0.28867513j]
# [ 0.33333333+0.j -0.16666667-0.28867513j -0.16666667+0.28867513j]]
"""
if is_interger(x) or is_floating_point(x):
return fftn_r2c(
x, s, axes, norm, forward=False, onesided=False, name=name)
else:
return fftn_c2c(x, s, axes, norm, forward=False, name=name)
def rfftn(x, s=None, axes=None, norm="backward", name=None):
"""
The N dimensional FFT for real input.
This function computes the N-dimensional discrete Fourier Transform over
any number of axes in an M-dimensional real array by means of the Fast
Fourier Transform (FFT). By default, all axes are transformed, with the
real transform performed over the last axis, while the remaining
transforms are complex.
The transform for real input is performed over the last transformation
axis, as by `rfft`, then the transform over the remaining axes is
performed as by `fftn`. The order of the output is as for `rfft` for the
final transformation axis, and as for `fftn` for the remaining
transformation axes.
Args:
x(Tensor) : Input tensor, taken to be real.
s(Sequence[int]) : Shape to use from the exec fft. The final element of
`s` corresponds to `n` for ``rfft(x, n)``, while for the remaining
axes, it corresponds to `n` for ``fft(x, n)``. Along any axis, if
the given shape is smaller than that of the input, the input is
cropped. If it is larger, the input is padded with zeros. if `s` is
not given, the shape of the input along the axes specified by `axes`
is used.
axes(Sequence[int]) : Axes over which to compute the FFT. If not given,
the last ``len(s)`` axes are used, or all axes if `s` is also not
specified.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor): complex tensor
Raises:
ValueError: If `s` and `axes` have different length.
Examples:
.. code-block:: python
import paddle
# default, all axis will be used to exec fft
x = paddle.ones((2, 3, 4))
print(paddle.fft.rfftn(x))
# Tensor(shape=[2, 3, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [[[(24+0j), 0j , 0j ],
# [0j , 0j , 0j ],
# [0j , 0j , 0j ]],
#
# [[0j , 0j , 0j ],
# [0j , 0j , 0j ],
# [0j , 0j , 0j ]]])
# use axes(2, 0)
print(paddle.fft.rfftn(x, axes=(2, 0)))
# Tensor(shape=[2, 3, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [[[(8+0j), 0j , 0j ],
# [(8+0j), 0j , 0j ],
# [(8+0j), 0j , 0j ]],
#
# [[0j , 0j , 0j ],
# [0j , 0j , 0j ],
# [0j , 0j , 0j ]]])
"""
return fftn_r2c(x, s, axes, norm, forward=True, onesided=True, name=name)
def irfftn(x, s=None, axes=None, norm="backward", name=None):
"""
Computes the inverse of `rfftn`.
This function computes the inverse of the N-D discrete
Fourier Transform for real input over any number of axes in an
M-D array by means of the Fast Fourier Transform (FFT). In
other words, ``irfftn(rfftn(x), x.shape) == x`` to within numerical
accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`,
and for the same reason.)
The input should be ordered in the same way as is returned by `rfftn`,
i.e., as for `irfft` for the final transformation axis, and as for `ifftn`
along all the other axes.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): The length of the output transform axis.
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
number of input points used along this axis, except for the last axis,
where ``s[-1]//2+1`` points of the input are used. Along any axis, if
the shape indicated by `s` is smaller than that of the input, the input
is cropped. If it is larger, the input is padded with zeros.
If `s` is not given, the shape of the input along the axes specified by axes
is used. Except for the last axis which is taken to be ``2*(k-1)`` where
``k`` is the length of the input along that axis.
axes (sequence of ints, optional): Axes over which to compute the inverse FFT. If not given, the last
`len(s)` axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Real tensor. The truncated or zero-padded input, transformed along the axes indicated by `axes`,
or by a combination of `s` or `x`, as explained in the parameters section above. The length of
each transformed axis is as given by the corresponding element of `s`, or the length of the input
in every axis except for the last one if `s` is not given. In the final transformed axis the length
of the output when `s` is not given is ``2*(m-1)``, where ``m`` is the length of the final
transformed axis of the input. To get an odd number of output points in the final axis,
`s` must be specified.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([2, 2, 3]) + 1j * np.array([2, 2, 3])).astype(np.complex128)
xp = paddle.to_tensor(x)
irfftn_xp = paddle.fft.irfftn(xp).numpy()
print(irfftn_xp)
# [ 2.25 -1.25 0.25 0.75]
"""
return fftn_c2r(x, s, axes, norm, forward=False, name=name)
def hfftn(x, s=None, axes=None, norm="backward", name=None):
"""
Compute the N-D FFT of Hermitian symmetric complex input, i.e., a
signal with a real spectrum.
This function calculates the n-D discrete Fourier transform of Hermite symmetric
complex input on any axis in M-D array by fast Fourier transform (FFT).
In other words, ``ihfftn(hfftn(x, s)) == x is within the numerical accuracy range.
(``s`` here are ``x.shape`` and ``s[-1] = x.shape[- 1] * 2 - 1``. This is necessary
for the same reason that ``irfft` requires ``x.shape``.)
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): The length of the output transform axis.
(``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the
number of input points used along this axis, except for the last axis,
where ``s[-1]//2+1`` points of the input are used. Along any axis, if
the shape indicated by `s` is smaller than that of the input, the input
is cropped. If it is larger, the input is padded with zeros.
If `s` is not given, the shape of the input along the axes specified by axes
is used. Except for the last axis which is taken to be ``2*(k-1)`` where
``k`` is the length of the input along that axis.
axes (sequence of ints, optional): Axes over which to compute the inverse FFT. If not given, the last
`len(s)` axes are used, or all axes if `s` is also not specified.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Real tensor. Truncate or zero fill input, transforming along the axis indicated by axis or
a combination of `s` or `X`.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([2, 2, 3]) + 1j * np.array([2, 2, 3])).astype(np.complex128)
xp = paddle.to_tensor(x)
hfftn_xp = paddle.fft.hfftn(xp).numpy()
print(hfftn_xp)
# [ 9. 3. 1. -5.]
"""
return fftn_c2r(x, s, axes, norm, forward=True, name=name)
def ihfftn(x, s=None, axes=None, norm="backward", name=None):
"""
The n dimensional inverse FFT of a signal that has Hermitian symmetry.
This function computes the n dimensional inverse FFT over any number of axes
in an M-dimensional of a signal that has Hermitian symmetry by means of an
efficient algorithm called the Fast Fourier Transform (FFT).
Args:
x(Tensor): Input tensor.
s(Sequence[int], optional) : Shape (length along each transformed axis)
to use from the input. (``s[0]`` refers to axis 0, ``s[1]`` to axis
1, etc.). Along any axis, if the given shape is smaller than that
of the input, the input is cropped. If it is larger, the input is
padded with zeros. if `s` is not given, the shape of the input
along the axes specified by `axes` is used.
axis(Sequence[int], optional) : Axis over which to compute the inverse FFT. If not
given, the last axis is used.
norm(str, optional) : Normalization mode, indicates which direction of
the forward/backward pair of transforms is scaled and with what
normalization factor. Include {"backward", "ortho", "forward"},
default value is "backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : complex tensor.
Examples:
.. code-block:: python
import paddle
spectrum = paddle.to_tensor([10.0, -5.0, 0.0, -1.0, 0.0, -5.0])
print(paddle.fft.ifft(spectrum))
# Tensor(shape=[6], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j), (2.3333334922790527+1.9868215517249155e-08j), (1+1.9868215517249155e-08j)])
print(paddle.fft.ihfft(spectrum))
# Tensor(shape = [4], dtype = complex64, place = CUDAPlace(0), stop_gradient = True,
# [(-0.1666666716337204+0j), (1-1.9868215517249155e-08j), (2.3333334922790527-1.9868215517249155e-08j), (3.5+0j)])
"""
return fftn_r2c(x, s, axes, norm, forward=False, onesided=True, name=name)
# public APIs 2d
def fft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the 2-D discrete Fourier Transform
This function computes the N-D discrete Fourier Transform
over any axes in an M-D array by means of the
Fast Fourier Transform (FFT). By default, the transform is computed over
the last two axes of the input array, i.e., a 2-dimensional FFT.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output.
It should be a sequence of 2 integers. This corresponds to ``n`` for ``fft(x, n)``.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used. Default is None.
axes (sequence of ints, optional): Axes over which to compute the FFT. It should be a
sequence of 2 integers. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Complex tensor. The truncated or zero-padded input, transformed along the axes indicated by `axes`,
or the last two axes if `axes` is not given.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:2, :2][1]
xp = paddle.to_tensor(x)
fft2_xp = paddle.fft.fft2(xp).numpy()
print(fft2_xp)
# [[ 2.+0.j -2.+0.j]
# [ 0.+0.j 0.+0.j]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return fftn(x, s, axes, norm, name)
def ifft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the 2-D inverse discrete Fourier Transform.
This function computes the inverse of the 2-D discrete Fourier
Transform over any number of axes in an M-D array by means of
the Fast Fourier Transform (FFT). In other words, ``ifft2(fft2(x)) == x``
to within numerical accuracy. By default, the inverse transform is
computed over the last two axes of the input array.
The input, analogously to `ifft`, should be ordered in the same way as is
returned by `fft2`, i.e., it should have the term for zero frequency
in the low-order corner of the two axes, the positive frequency terms in
the first half of these axes, the term for the Nyquist frequency in the
middle of the axes and the negative frequency terms in the second half of
both axes, in order of decreasingly negative frequency.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape (length of each transformed axis) of the output.
It should be a sequence of 2 integers. This corresponds to ``n`` for ``fft(x, n)``.
Along each axis, if the given shape is smaller than that of the input,
the input is cropped. If it is larger, the input is padded with zeros.
if `s` is not given, the shape of the input along the axes specified
by `axes` is used. Default is None.
axes (sequence of ints, optional): Axes over which to compute the FFT. It should be a
sequence of 2 integers. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Complex tensor. The truncated or zero-padded input, transformed along the axes indicated by `axes`,
or the last two axes if `axes` is not given.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:2, :2][1]
xp = paddle.to_tensor(x)
ifft2_xp = paddle.fft.ifft2(xp).numpy()
print(ifft2_xp)
# [[ 0.5+0.j -0.5+0.j]
# [ 0. +0.j 0. +0.j]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return ifftn(x, s, axes, norm, name)
def rfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
The two dimensional FFT with real tensor input.
This is really just `rfftn` with different default behavior.
For more details see `rfftn`.
Args:
x(Tensor): Input tensor, taken to be real.
s(Sequence[int]) : Shape of the FFT.
axes(Sequence[int], optional): Axes over which to compute the FFT.
norm(str, optional) : {"backward", "ortho", "forward"},
default is "backward". Indicates which direction of the
forward/backward pair of transforms is scaled and with what
normalization factor.
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor): The result of the real 2-D FFT.
Raises:
Examples:
.. code-block:: python
import paddle
import numpy as np
x = paddle.to_tensor(np.mgrid[:5, :5][0].astype(np.float32))
print(paddle.fft.rfft2(x))
# Tensor(shape=[5, 3], dtype=complex64, place=CUDAPlace(0), stop_gradient=True,
# [[ (50+0j) , (1.1920928955078125e-07+0j) , 0j ],
# [(-12.5+17.204774856567383j) , (-9.644234211236835e-08+7.006946134424652e-08j) , 0j ],
# [(-12.500000953674316+4.061495304107666j) , (3.6837697336977726e-08-1.1337477445749755e-07j), 0j ],
# [(-12.500000953674316-4.061495304107666j) , (3.6837697336977726e-08+1.1337477445749755e-07j), 0j ],
# [(-12.5-17.204774856567383j) , (-9.644234211236835e-08-7.006946134424652e-08j) , 0j ]])
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return rfftn(x, s, axes, norm, name)
def irfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Computes the inverse of `rfft2`.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape of the real output to the inverse FFT. Default is None.
axes (sequence of ints, optional): The axes over which to compute the inverse FFT. Axes
must be two-dimensional. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name` .
Returns:
Real tensor. The result of the inverse real 2-D FFT.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([[3,2,3],[2, 2, 3]]) + 1j * np.array([[3,2,3],[2, 2, 3]])).astype(np.complex128)
xp = paddle.to_tensor(x)
irfft2_xp = paddle.fft.irfft2(xp).numpy()
print(irfft2_xp)
# [[ 2.375 -1.125 0.375 0.875]
# [ 0.125 0.125 0.125 0.125]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return irfftn(x, s, axes, norm, name)
def hfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the 2-D FFT of a Hermitian complex array.
Args:
x (Tensor): The input data. It's a Tensor type.
s (sequence of ints, optional): Shape of the real output. Default is None.
axes (sequence of ints, optional): Axes over which to compute the FFT. Axes must be
two-dimensional. If not specified, the last two axes are used by default.
norm (str): Indicates which direction to scale the `forward` or `backward` transform
pair and what normalization factor to use. The parameter value must be one
of "forward" or "backward" or "ortho". Default is "backward".
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Real tensor. The real result of the 2-D Hermitian complex real FFT.
Raises:
ValueError: if `s` not be a sequence of 2 integers or None.
ValueError: if `axes` not be a sequence of 2 integers or None.
ValueError: If the input dimension is smaller than 2.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = (np.array([[3,2,3],[2, 2, 3]]) + 1j * np.array([[3,2,3],[2, 2, 3]])).astype(np.complex128)
xp = paddle.to_tensor(x)
hfft2_xp = paddle.fft.hfft2(xp).numpy()
print(hfft2_xp)
# [[19. 7. 3. -9.]
# [ 1. 1. 1. 1.]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return hfftn(x, s, axes, norm, name)
def ihfft2(x, s=None, axes=(-2, -1), norm="backward", name=None):
"""
Compute the two dimensional inverse FFT of a real spectrum.
This is really `ihfftn` with different defaults.
For more details see `ihfftn`.
Args:
x(Tensor): Input tensor
s(Sequence[int], optional): Shape of the real input to the inverse FFT.
axes(Sequance[int], optional): The axes over which to compute the
inverse fft. Default is the last two axes.
norm(str, optional): {"backward", "ortho", "forward"}. Default is
"backward".
name(str, optional): The default value is None. Normally there is no
need for user to set this property. For more information, please
refer to :ref:`api_guide_Name` .
Returns:
out(Tensor) : The result of the inverse hermitian 2-D FFT.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.mgrid[:5, :5][0].astype(np.float64)
xp = paddle.to_tensor(x)
ihfft2_xp = paddle.fft.ihfft2(xp).numpy()
print(ihfft2_xp)
# [[ 2. +0.j 0. +0.j 0. +0.j ]
# [-0.5-0.68819096j 0. +0.j 0. +0.j ]
# [-0.5-0.16245985j 0. +0.j 0. +0.j ]
# [-0.5+0.16245985j 0. +0.j 0. +0.j ]
# [-0.5+0.68819096j 0. +0.j 0. +0.j ]]
"""
_check_at_least_ndim(x, 2)
if s is not None:
if not isinstance(s, Sequence) or len(s) != 2:
raise ValueError(
"Invalid FFT argument s ({}), it should be a sequence of 2 integers.".
format(s))
if axes is not None:
if not isinstance(axes, Sequence) or len(axes) != 2:
raise ValueError(
"Invalid FFT argument axes ({}), it should be a sequence of 2 integers.".
format(axes))
return ihfftn(x, s, axes, norm, name)
# public APIs utilities
def fftfreq(n, d=1.0, dtype=None, name=None):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given input length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd
Args:
n (int): Dimension inputed.
d (scalar, optional): Sample spacing (inverse of the sampling rate). Defaults is 1.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. A tensor of length 'n' containing the sampling frequency.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
scalar_temp = 0.5
n = x.size
fftfreq_xp = paddle.fft.fftfreq(n, d=scalar_temp)
print(fftfreq_xp)
# Tensor(shape=[5], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
# [ 0. , 0.40000001, 0.80000001, -0.80000001, -0.40000001])
"""
dtype = paddle.framework.get_default_dtype()
val = 1.0 / (n * d)
pos_max = (n + 1) // 2
neg_max = n // 2
indices = paddle.arange(-neg_max, pos_max, dtype=dtype, name=name)
indices = paddle.roll(indices, -neg_max, name=name)
return indices * val
def rfftfreq(n, d=1.0, dtype=None, name=None):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned floating-point array "F" contains the center of the frequency unit,
and the unit is the number of cycles of the sampling interval (the starting point is zero).
Given input length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd
the Nyquist frequency component is considered to be positive.
Args:
n (int): Dimension inputed.
d (scalar, optional): Sample spacing (inverse of the sampling rate). Defaults is 1.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. A tensor of length ``n//2 + 1`` containing the sample frequencies.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
scalar_temp = 0.3
n = x.size
rfftfreq_xp = paddle.fft.rfftfreq(n, d=scalar_temp)
print(rfftfreq_xp)
# Tensor(shape=[3], dtype=float32, place=CUDAPlace(0), stop_gradient=True,
# [0. , 0.66666669, 1.33333337])
"""
dtype = paddle.framework.get_default_dtype()
val = 1.0 / (n * d)
pos_max = 1 + n // 2
indices = paddle.arange(0, pos_max, dtype=dtype, name=name)
return indices * val
def fftshift(x, axes=None, name=None):
"""
Shift the zero-frequency component to the center of the spectrum.
This function swaps half spaces for all the axes listed (all by default).
Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
Args:
n (int): Dimension inputed.
axes (int|tuple, optional): The axis on which to move. The default is none, which moves all axes.
Default is None.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. The shifted tensor.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
n = x.size
fftfreq_xp = paddle.fft.fftfreq(n, d=0.3)
res = paddle.fft.fftshift(fftfreq_xp).numpy()
print(res)
# [-1.3333334 -0.6666667 0. 0.6666667 1.3333334]
"""
shape = paddle.shape(x)
if axes is None:
# shift all axes
rank = paddle.rank(x).reshape([1])
axes = axes or paddle.arange(0, rank)
shifts = [size // 2 for size in shape]
elif isinstance(axes, int):
shifts = shape[axes] // 2
else:
shifts = [shape[ax] // 2 for ax in axes]
return paddle.roll(x, shifts, axes, name=name)
def ifftshift(x, axes=None, name=None):
"""
The inverse of `fftshift`. Although the even length 'x' is the same, the function of the
odd length 'x' is different. An example.
Args:
n (int): Dimension inputed.
axes (int|tuple, optional): The axis on which to move. The default is none, which moves all axes.
Default is None.
name (str, optional): The default value is None. Normally there is no need for user to set
this property. For more information, please refer to :ref:`api_guide_Name`.
Returns:
Tensor. The shifted tensor.
Examples:
.. code-block:: python
import numpy as np
import paddle
x = np.array([3, 1, 2, 2, 3], dtype=float)
n = x.size
fftfreq_xp = paddle.fft.fftfreq(n, d=0.3)
res = paddle.fft.ifftshift(fftfreq_xp).numpy()
print(res)
# [ 1.3333334 -1.3333334 -0.6666667 0. 0.6666667]
"""
shape = paddle.shape(x)
if axes is None:
# shift all axes
rank = paddle.rank(x).reshape([1])
axes = axes or paddle.arange(0, rank)
shifts = [-size // 2 for size in shape]
elif isinstance(axes, int):
shifts = -shape[axes] // 2
else:
shifts = [-shape[ax] // 2 for ax in axes]
return paddle.roll(x, shifts, axes, name=name)
# internal functions
def fft_c2c(x, n, axis, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
axis = axis if axis is not None else -1
_check_fft_axis(x, axis)
axes = [axis]
axes = _normalize_axes(x, axes)
if n is not None:
_check_fft_n(n)
s = [n]
x = _resize_fft_input(x, s, axes)
op_type = 'fft_c2c'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(dtype)
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fft_r2c(x, n, axis, norm, forward, onesided, name):
if is_interger(x):
x = paddle.cast(x, paddle.get_default_dtype())
_check_normalization(norm)
axis = axis if axis is not None else -1
_check_fft_axis(x, axis)
axes = [axis]
axes = _normalize_axes(x, axes)
if n is not None:
_check_fft_n(n)
s = [n]
x = _resize_fft_input(x, s, axes)
op_type = 'fft_r2c'
check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'onesided', onesided)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {
'axes': axes,
'normalization': norm,
'forward': forward,
'onesided': onesided,
}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_real_to_complex_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fft_c2r(x, n, axis, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
axis = axis if axis is not None else -1
_check_fft_axis(x, axis)
axes = [axis]
axes = _normalize_axes(x, axes)
if n is not None:
_check_fft_n(n)
s = [n // 2 + 1]
x = _resize_fft_input(x, s, axes)
op_type = 'fft_c2r'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
if n is not None:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'last_dim_size', n)
else:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
if n is not None:
attrs['last_dim_size'] = n
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_complex_to_real_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fftn_c2c(x, s, axes, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
if s is not None:
_check_fft_shape(x, s)
rank = x.ndim
if axes is None:
if s is None:
axes = list(range(rank))
else:
fft_ndims = len(s)
axes = list(range(rank - fft_ndims, rank))
else:
_check_fft_axes(x, axes)
axes = _normalize_axes(x, axes)
axes_argsoft = np.argsort(axes).tolist()
axes = [axes[i] for i in axes_argsoft]
if s is not None:
if len(s) != len(axes):
raise ValueError(
"Length of s ({}) and length of axes ({}) does not match.".
format(len(s), len(axes)))
s = [s[i] for i in axes_argsoft]
if s is not None:
x = _resize_fft_input(x, s, axes)
op_type = 'fft_c2c'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(dtype)
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fftn_r2c(x, s, axes, norm, forward, onesided, name):
if is_interger(x):
x = paddle.cast(x, paddle.get_default_dtype())
_check_normalization(norm)
if s is not None:
_check_fft_shape(x, s)
rank = x.ndim
if axes is None:
if s is None:
axes = list(range(rank))
else:
fft_ndims = len(s)
axes = list(range(rank - fft_ndims, rank))
else:
_check_fft_axes(x, axes)
axes = _normalize_axes(x, axes)
axes_argsoft = np.argsort(axes[:-1]).tolist()
axes = [axes[i] for i in axes_argsoft] + [axes[-1]]
if s is not None:
if len(s) != len(axes):
raise ValueError(
"Length of s ({}) and length of axes ({}) does not match.".
format(len(s), len(axes)))
s = [s[i] for i in axes_argsoft] + [s[-1]]
if s is not None:
x = _resize_fft_input(x, s, axes)
op_type = 'fft_r2c'
check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], op_type)
if in_dygraph_mode():
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'onesided', onesided)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {
'axes': axes,
'normalization': norm,
'forward': forward,
'onesided': onesided,
}
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_real_to_complex_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
def fftn_c2r(x, s, axes, norm, forward, name):
if is_interger(x):
x = paddle.cast(x, _real_to_complex_dtype(paddle.get_default_dtype()))
elif is_floating_point(x):
x = paddle.cast(x, _real_to_complex_dtype(x.dtype))
_check_normalization(norm)
if s is not None:
_check_fft_shape(x, s)
rank = x.ndim
if axes is None:
if s is None:
axes = list(range(rank))
else:
fft_ndims = len(s)
axes = list(range(rank - fft_ndims, rank))
else:
_check_fft_axes(x, axes)
axes = _normalize_axes(x, axes)
axes_argsoft = np.argsort(axes[:-1]).tolist()
axes = [axes[i] for i in axes_argsoft] + [axes[-1]]
if s is not None:
if len(s) != len(axes):
raise ValueError(
"Length of s ({}) and length of axes ({}) does not match.".
format(len(s), len(axes)))
s = [s[i] for i in axes_argsoft] + [s[-1]]
if s is not None:
fft_input_shape = list(s)
fft_input_shape[-1] = fft_input_shape[-1] // 2 + 1
x = _resize_fft_input(x, fft_input_shape, axes)
op_type = 'fft_c2r'
check_variable_and_dtype(x, 'x', ['complex64', 'complex128'], op_type)
if in_dygraph_mode():
if s:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward,
'last_dim_size', s[-1])
else:
attrs = ('axes', axes, 'normalization', norm, 'forward', forward)
out = getattr(_C_ops, op_type)(x, *attrs)
else:
inputs = {'X': [x], }
attrs = {'axes': axes, 'normalization': norm, 'forward': forward}
if s:
attrs["last_dim_size"] = s[-1]
helper = LayerHelper(op_type, **locals())
dtype = helper.input_dtype(input_param_name='x')
out = helper.create_variable_for_type_inference(
_complex_to_real_dtype(dtype))
outputs = {"Out": [out]}
helper.append_op(
type=op_type, inputs=inputs, outputs=outputs, attrs=attrs)
return out
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