# naginterfaces.library.sum.withdraw_​fft_​real_​1d_​multi_​rfmt¶

naginterfaces.library.sum.withdraw_fft_real_1d_multi_rfmt(m, n, x, init, trig)[source]

withdraw_fft_real_1d_multi_rfmt computes the discrete Fourier transforms of sequences, each containing real data values. This function is designed to be particularly efficient on vector processors.

Deprecated since version 27.2.0.0: withdraw_fft_real_1d_multi_rfmt will be removed in naginterfaces 30.2.0.0. Please use fft_realherm_1d_multi_row() or fft_realherm_1d_multi_col() instead. See also the Replacement Calls document.

For full information please refer to the NAG Library document for c06fp

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/c06/c06fpf.html

Parameters
mint

, the number of sequences to be transformed.

nint

, the number of real values in each sequence.

xfloat, array-like, shape

The data must be stored in as if in a two-dimensional array of dimension ; each of the sequences is stored in a row of the array. In other words, if the data values of the th sequence to be transformed are denoted by , for , the elements of the array must contain the values

initstr, length 1

Indicates whether trigonometric coefficients are to be calculated.

Calculate the required trigonometric coefficients for the given value of , and store in the array .

or

The required trigonometric coefficients are assumed to have been calculated and stored in the array in a prior call to one of withdraw_fft_real_1d_multi_rfmt or withdraw_fft_hermitian_1d_multi_rfmt(). The function performs a simple check that the current value of is consistent with the values stored in .

trigfloat, array-like, shape

If or , must contain the required trigonometric coefficients that have been previously calculated. Otherwise need not be set.

Returns
xfloat, ndarray, shape

The discrete Fourier transforms stored as if in a two-dimensional array of dimension . Each of the transforms is stored in a row of the array in Hermitian form, overwriting the corresponding original sequence. If the components of the discrete Fourier transform are written as , then for , is contained in , and for , is contained in . (See also the C06 Introduction.)

trigfloat, ndarray, shape

Contains the required coefficients (computed by the function if ).

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: , or .

(errno )

On entry, but and array incompatible.

Notes

Given sequences of real data values , for , for , withdraw_fft_real_1d_multi_rfmt simultaneously calculates the Fourier transforms of all the sequences defined by

(Note the scale factor in this definition.)

The transformed values are complex, but for each value of the form a Hermitian sequence (i.e., is the complex conjugate of ), so they are completely determined by real numbers (see also the C06 Introduction).

The discrete Fourier transform is sometimes defined using a positive sign in the exponential term:

To compute this form, this function should be followed by forming the complex conjugates of the ; that is , for .

The function uses a variant of the fast Fourier transform (FFT) algorithm (see Brigham (1974)) known as the Stockham self-sorting algorithm, which is described in Temperton (1983). Special coding is provided for the factors , , , and . This function is designed to be particularly efficient on vector processors, and it becomes especially fast as , the number of transforms to be computed in parallel, increases.

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