# naginterfaces.library.sum.fft_​hermitian_​3d¶

naginterfaces.library.sum.fft_hermitian_3d(n1, n2, n3, y)[source]

fft_hermitian_3d computes the three-dimensional inverse discrete Fourier transform of a trivariate Hermitian sequence of complex data values.

For full information please refer to the NAG Library document for c06pz

https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/c06/c06pzf.html

Parameters
n1int

, the first dimension of the transform.

n2int

, the second dimension of the transform.

n3int

, the third dimension of the transform.

ycomplex, array-like, shape

The Hermitian sequence of complex input dataset , where is stored in , for , for , for .

Returns
xfloat, ndarray, shape

The real output dataset , where is stored in , for , for , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

Notes

fft_hermitian_3d computes the three-dimensional inverse discrete Fourier transform of a trivariate Hermitian sequence of complex data values , for , for , for .

The discrete Fourier transform is here defined by

where , and . (Note the scale factor of in this definition.)

Because the input data satisfies conjugate symmetry (i.e., is the complex conjugate of ), the transformed values are real.

A call of fft_real_3d() followed by a call of fft_hermitian_3d will restore the original data.

This function calls fft_realherm_1d_multi_col() and fft_complex_1d_multi_row() to perform multiple one-dimensional discrete Fourier transforms by the fast Fourier transform (FFT) algorithm in Brigham (1974) and Temperton (1983).

References

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

Temperton, C, 1983, Fast mixed-radix real Fourier transforms, J. Comput. Phys. (52), 340–350