naginterfaces.library.sum.fft_​complex_​multid_​sep

naginterfaces.library.sum.fft_complex_multid_sep(nd, x, y)[source]

fft_complex_multid_sep computes the multidimensional discrete Fourier transform of a multivariate sequence of complex data values.

For full information please refer to the NAG Library document for c06fj

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06fjf.html

Parameters
ndint, array-like, shape

must contain (the dimension of the th variable), for .

xfloat, array-like, shape

must contain the real part of the complex data value , for ; i.e., the values are stored in consecutive elements of the array according to the Fortran convention for storing multidimensional arrays.

yfloat, array-like, shape

The imaginary parts of the complex data values, stored in the same way as the real parts in the array .

Returns
xfloat, ndarray, shape

The real parts of the corresponding elements of the computed transform.

yfloat, ndarray, shape

The imaginary parts of the corresponding elements of the computed transform.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

fft_complex_multid_sep computes the multidimensional discrete Fourier transform of a multidimensional sequence of complex data values , where , and so on. Thus the individual dimensions are , and the total number of data values is .

The discrete Fourier transform is here defined (e.g., for ) by:

where , .

The extension to higher dimensions is obvious. (Note the scale factor of in this definition.)

To compute the inverse discrete Fourier transform, defined with in the above formula instead of , this function should be preceded and followed by the complex conjugation of the data values and the transform (by negating the imaginary parts stored in ).

The data values must be supplied in a pair of one-dimensional arrays (real and imaginary parts separately), in accordance with the Fortran convention for storing multidimensional data (i.e., with the first subscript varying most rapidly).

This function calls fft_complex_1d_sep() to perform one-dimensional discrete Fourier transforms by the fast Fourier transform (FFT) algorithm in Brigham (1974).

References

Brigham, E O, 1974, The Fast Fourier Transform, Prentice–Hall