/usr/include/openturns/swig/FFTImplementation_doc.i is in libopenturns-dev 1.7-3.
This file is owned by root:root, with mode 0o644.
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"Base class for Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT).
Notes
-----
Perform FFT and IFFT with array of ndim=1,2,3
"
%enddef
%feature("docstring") OT::FFTImplementation
OT_FFT_doc
// ---------------------------------------------------------------------
%define OT_FFT_transform_doc
"Perform Fast Fourier Transform (fft).
Parameters
----------
collection : :class:`~openturns.NumericalComplexCollection` or :class:`~openturns.NumericalScalarCollection`, sequence of float
Data to transform.
Returns
-------
collection : :class:`~openturns.NumericalComplexCollection`
The data in Fourier domain.
Notes
-----
The Fast Fourier Transform writes as following:
.. math::
{\\\\rm y_k} = \\\\sum_{n=0}^{N-1} x_n exp(-2 \\\\imath \\\\pi \\\\frac{kn}{N})
where :math:`x` denotes the data to be transformed, of size :math:`N`.
Examples
--------
>>> import openturns as ot
>>> fft = ot.FFT()
>>> result = fft.transform(ot.Normal(8).getRealization())
"
%enddef
%feature("docstring") OT::FFTImplementation::transform
OT_FFT_transform_doc
// ---------------------------------------------------------------------
%define OT_FFT_inverseTransform_doc
"Perform Inverse Fast Fourier Transform (fft).
Parameters
----------
collection : :class:`~openturns.NumericalComplexCollection` or :class:`~openturns.NumericalScalarCollection`, sequence of float
Data to transform.
Returns
-------
collection : :class:`~openturns.NumericalComplexCollection`
The transformed data.
Notes
-----
The Inverse Fast Fourier Transform writes as following:
.. math::
{\\\\rm y_k} = \\\\sum_{n=0}^{N-1} \\\\frac{1}{N} x_n exp(2 \\\\imath \\\\pi \\\\frac{kn}{N})
where :math:`x` denotes the data, of size :math:`N`, to be transformed.
Examples
--------
>>> import openturns as ot
>>> fft = ot.FFT()
>>> collection = ot.NumericalComplexCollection([1+1j,2-0.3j,5-.3j,6+1j,9+8j,16+8j,0.3])
>>> result = fft.inverseTransform(collection)
"
%enddef
%feature("docstring") OT::FFTImplementation::inverseTransform
OT_FFT_inverseTransform_doc
// ---------------------------------------------------------------------
%define OT_FFT_transform2D_doc
"Perform 2D FFT.
Parameters
----------
matrix : :class:`~openturns.ComplexMatrix`, :class:`~openturns.Matrix`, 2-d sequence of float
Data to transform.
Returns
-------
result : :class:`~openturns.ComplexMatrix`
The data in fourier domain.
Notes
-----
The 2D Fast Fourier Transform writes as following:
.. math::
{\\\\rm Z_{k,l}} = \\\\sum_{m=0}^{M-1}\\\\sum_{n=0}^{N-1} X_{m,n} exp(-2 \\\\imath \\\\pi \\\\frac{km}{M}) exp(-2 \\\\imath \\\\pi \\\\frac{ln}{N})
where :math:`X` denotes the data to be transformed with shape (:math:`M`,:math:`N`)
Examples
--------
>>> import openturns as ot
>>> fft = ot.FFT()
>>> x = ot.Normal(8).getSample(16)
>>> result = fft.transform2D(x)
"
%enddef
%feature("docstring") OT::FFTImplementation::transform2D
OT_FFT_transform2D_doc
// ---------------------------------------------------------------------
%define OT_FFT_inverseTransform2D_doc
"Perform 2D IFFT.
Parameters
----------
matrix : :class:`~openturns.ComplexMatrix`, :class:`~openturns.Matrix`, 2-d sequence of float
Data to transform.
Returns
-------
result : :class:`~openturns.ComplexMatrix`
The data transformed.
Notes
-----
The 2D Fast Inverse Fourier Transform writes as following:
.. math::
{\\\\rm Y_{k,l}} = \\\\frac{1}{M\\\\times N}\\\\sum_{m=0}^{M-1}\\\\sum_{n=0}^{N-1} Z_{m,n} exp(2 \\\\imath \\\\pi \\\\frac{km}{M}) exp(2 \\\\imath \\\\pi \\\\frac{ln}{N})
where :math:`Z` denotes the data to be transformed with shape (:math:`M`,:math:`N`)
Examples
--------
>>> import openturns as ot
>>> fft = ot.FFT()
>>> x = ot.Normal(8).getSample(16)
>>> result = fft.inverseTransform2D(x)
"
%enddef
%feature("docstring") OT::FFTImplementation::inverseTransform2D
OT_FFT_inverseTransform2D_doc
// ---------------------------------------------------------------------
%define OT_FFT_transform3D_doc
"Perform 3D FFT.
Parameters
----------
tensor : :class:`~openturns.ComplexTensor` or :class:`~openturns.Tensor` or 3d array
Data to transform.
Returns
-------
result : :class:`~openturns.ComplexTensor`
The data in fourier domain.
Notes
-----
The 3D Fast Fourier Transform writes as following:
.. math::
{\\\\rm Z_{k,l,r}} = \\\\sum_{m=0}^{M-1}\\\\sum_{n=0}^{N-1}\\\\sum_{p=0}^{P-1} X_{m,n,p} exp(-2 \\\\imath \\\\pi \\\\frac{km}{M}) exp(-2 \\\\imath \\\\pi \\\\frac{ln}{N}) exp(-2 \\\\imath \\\\pi \\\\frac{rp}{P})
where :math:`X` denotes the data to be transformed with shape (:math:`M`,:math:`N`, :math:`P`)
Examples
--------
>>> import openturns as ot
>>> fft = ot.FFT()
>>> x = ot.ComplexTensor(8,8,2)
>>> y = ot.Normal(8).getSample(8)
>>> x.setSheet(0,fft.transform2D(y))
>>> z = ot.Normal(8).getSample(8)
>>> x.setSheet(1,fft.transform2D(z))
>>> result = fft.transform3D(x)
"
%enddef
%feature("docstring") OT::FFTImplementation::transform3D
OT_FFT_transform3D_doc
// ---------------------------------------------------------------------
%define OT_FFT_inverseTransform3D_doc
"Perform 3D IFFT.
Parameters
----------
tensor : :class:`~openturns.ComplexTensor` or :class:`~openturns.Tensor` or 3d array
The data to be transformed.
Returns
-------
result : :class:`~openturns.ComplexTensor`
The transformed data.
Notes
-----
The 3D Inverse Fast Fourier Transform writes as following:
.. math::
{\\\\rm Y_{k,l,r}} = \\\\sum_{m=0}^{M-1}\\\\sum_{n=0}^{N-1}\\\\sum_{p=0}^{P-1} \\\\frac{1}{M\\\\times N \\\\times P} Z_{m,n,p} exp(2 \\\\imath \\\\pi \\\\frac{km}{M}) exp(2 \\\\imath \\\\pi \\\\frac{ln}{N}) exp(2 \\\\imath \\\\pi \\\\frac{rp}{P})
where :math:`Z` denotes the data to be transformed with shape (:math:`M`, :math:`N`, :math:`P`)
Examples
--------
>>> import openturns as ot
>>> fft = ot.FFT()
>>> x = ot.ComplexTensor(8,8,2)
>>> y = ot.Normal(8).getSample(8)
>>> x.setSheet(0, fft.transform2D(y))
>>> z = ot.Normal(8).getSample(8)
>>> x.setSheet(1, fft.transform2D(z))
>>> result = fft.inverseTransform3D(x)
"
%enddef
%feature("docstring") OT::FFTImplementation::inverseTransform3D
OT_FFT_inverseTransform3D_doc
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