NAG Library Function Document
nag_sum_fft_complex_1d_multi (c06psc) computes the discrete Fourier transforms of sequences each containing complex data values.
||nag_sum_fft_complex_1d_multi (Nag_TransformDirection direct,
complex data values
, nag_sum_fft_complex_1d_multi (c06psc) simultaneously calculates the (forward
) discrete Fourier transforms of all the sequences defined by
(Note the scale factor
in this definition.) The minus sign is taken in the argument of the exponential within the summation when the forward transform is required, and the plus sign is taken when the backward transform is required.
A call of nag_sum_fft_complex_1d_multi (c06psc) with followed by a call with will restore the original data.
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 code is provided for the factors
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
direct – Nag_TransformDirectionInput
: if the forward transform as defined in Section 3
is to be computed, then direct
must be set equal to
If the backward transform is to be computed then direct
must be set equal to
n – IntegerInput
On entry: , the number of complex values in each sequence.
m – IntegerInput
On entry: , the number of sequences to be transformed.
x – ComplexInput/Output
On entry: the complex data values
stored in , for and .
On exit: is overwritten by the complex transforms.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
Dynamic memory allocation failed.
On entry, argument had an illegal value.
is an invalid value of direct
On entry, .
On entry, .
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
Some indication of accuracy can be obtained by performing a subsequent inverse transform and comparing the results with the original sequence (in exact arithmetic they would be identical).
8 Parallelism and Performance
nag_sum_fft_complex_1d_multi (c06psc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_sum_fft_complex_1d_multi (c06psc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the Users' Note
for your implementation for any additional implementation-specific information.
The time taken by nag_sum_fft_complex_1d_multi (c06psc) is approximately proportional to , but also depends on the factors of . nag_sum_fft_complex_1d_multi (c06psc) is fastest if the only prime factors of are , and , and is particularly slow if is a large prime, or has large prime factors.
This function internally allocates a workspace of Complex values.
This example reads in sequences of complex data values and prints their discrete Fourier transforms (as computed by nag_sum_fft_complex_1d_multi (c06psc) with ). Inverse transforms are then calculated using nag_sum_fft_complex_1d_multi (c06psc) with and printed out, showing that the original sequences are restored.
10.1 Program Text
Program Text (c06psce.c)
10.2 Program Data
Program Data (c06psce.d)
10.3 Program Results
Program Results (c06psce.r)