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/* fft/dft_source.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
int
FUNCTION(gsl_dft_complex,forward) (const BASE data[],
const size_t stride, const size_t n,
BASE result[])
{
gsl_fft_direction sign = gsl_fft_forward;
int status = FUNCTION(gsl_dft_complex,transform) (data, stride, n, result, sign);
return status;
}
int
FUNCTION(gsl_dft_complex,backward) (const BASE data[],
const size_t stride, const size_t n,
BASE result[])
{
gsl_fft_direction sign = gsl_fft_backward;
int status = FUNCTION(gsl_dft_complex,transform) (data, stride, n, result, sign);
return status;
}
int
FUNCTION(gsl_dft_complex,inverse) (const BASE data[],
const size_t stride, const size_t n,
BASE result[])
{
gsl_fft_direction sign = gsl_fft_backward;
int status = FUNCTION(gsl_dft_complex,transform) (data, stride, n, result, sign);
/* normalize inverse fft with 1/n */
{
const ATOMIC norm = ONE / (ATOMIC)n;
size_t i;
for (i = 0; i < n; i++)
{
REAL(result,stride,i) *= norm;
IMAG(result,stride,i) *= norm;
}
}
return status;
}
int
FUNCTION(gsl_dft_complex,transform) (const BASE data[],
const size_t stride, const size_t n,
BASE result[],
const gsl_fft_direction sign)
{
size_t i, j, exponent;
const double d_theta = 2.0 * ((int) sign) * M_PI / (double) n;
/* FIXME: check that input length == output length and give error */
for (i = 0; i < n; i++)
{
ATOMIC sum_real = 0;
ATOMIC sum_imag = 0;
exponent = 0;
for (j = 0; j < n; j++)
{
double theta = d_theta * (double) exponent;
/* sum = exp(i theta) * data[j] */
ATOMIC w_real = (ATOMIC) cos (theta);
ATOMIC w_imag = (ATOMIC) sin (theta);
ATOMIC data_real = REAL(data,stride,j);
ATOMIC data_imag = IMAG(data,stride,j);
sum_real += w_real * data_real - w_imag * data_imag;
sum_imag += w_real * data_imag + w_imag * data_real;
exponent = (exponent + i) % n;
}
REAL(result,stride,i) = sum_real;
IMAG(result,stride,i) = sum_imag;
}
return 0;
}
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