naginterfaces.library.sum.fft_​complex_​3d_​sep

naginterfaces.library.sum.fft_complex_3d_sep(n1, n2, n3, x, y)[source]

fft_complex_3d_sep computes the three-dimensional discrete Fourier transform of a trivariate sequence of complex data values. This function is designed to be particularly efficient on vector processors.

For full information please refer to the NAG Library document for c06fx

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06fxf.html

Parameters
n1int

, the first dimension of the transform.

n2int

, the second dimension of the transform.

n3int

, the third dimension of the transform.

xfloat, array-like, shape

The real and imaginary parts of the complex data values must be stored in arrays and respectively. If and are regarded as three-dimensional arrays of dimension , and must contain the real and imaginary parts of .

yfloat, array-like, shape

The real and imaginary parts of the complex data values must be stored in arrays and respectively. If and are regarded as three-dimensional arrays of dimension , and must contain the real and imaginary parts of .

Returns
xfloat, ndarray, shape

The real and imaginary parts respectively of the corresponding elements of the computed transform.

yfloat, ndarray, shape

The real and imaginary parts respectively 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_3d_sep computes the three-dimensional discrete Fourier transform of a trivariate sequence of complex data values , for , for , for .

The discrete Fourier transform is here defined by

where , , .

(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 forming the complex conjugates of the data values and the transform.

This function performs, for each dimension, multiple one-dimensional discrete Fourier transforms by the fast Fourier transform (FFT) algorithm (see Brigham (1974)). It is designed to be particularly efficient on vector processors.

References

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

Temperton, C, 1983, Self-sorting mixed-radix fast Fourier transforms, J. Comput. Phys. (52), 1–23