NAG Library Function Document
nag_sum_fft_complex_2d (c06puc)
1
Purpose
nag_sum_fft_complex_2d (c06puc) computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values (using complex data type).
2
Specification
#include <nag.h> |
#include <nagc06.h> |
void |
nag_sum_fft_complex_2d (Nag_TransformDirection direct,
Integer m,
Integer n,
Complex x[],
NagError *fail) |
|
3
Description
nag_sum_fft_complex_2d (c06puc) computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values
, for and .
The discrete Fourier transform is here defined by
where
and
.
(Note the scale factor of 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_2d (c06puc) with followed by a call with will restore the original data.
This function performs multiple one-dimensional discrete Fourier transforms by the fast Fourier transform (FFT) algorithm in
Brigham (1974) and
Temperton (1983).
4
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
5
Arguments
- 1:
– Nag_TransformDirectionInput
-
On entry: if the forward transform as defined in
Section 3 is to be computed,
direct must be set equal to
.
If the backward transform is to be computed,
direct must be set equal to
.
Constraint:
or .
- 2:
– IntegerInput
-
On entry: , the first dimension of the transform.
Constraint:
.
- 3:
– IntegerInput
-
On entry: , the second dimension of the transform.
Constraint:
.
- 4:
– ComplexInput/Output
-
On entry: the complex data values.
must contain , for and .
On exit: the corresponding elements of the computed transform.
- 5:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
is an invalid value of
direct.
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_INTERNAL_ERROR
-
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.
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.
See
Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
7
Accuracy
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_2d (c06puc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_sum_fft_complex_2d (c06puc) 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
x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The time taken is approximately proportional to , but also depends on the factorization of the individual dimensions and . nag_sum_fft_complex_2d (c06puc) is faster if the only prime factors are , or ; and fastest of all if they are powers of .
This function internally allocates a workspace of Complex values.
10
Example
This example reads in a bivariate sequence of complex data values and prints the two-dimensional Fourier transform. It then performs an inverse transform and prints the sequence so obtained, which may be compared to the original data values.
10.1
Program Text
Program Text (c06puce.c)
10.2
Program Data
Program Data (c06puce.d)
10.3
Program Results
Program Results (c06puce.r)