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://support.nag.com/numeric/nl/nagdoc_30.2/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