/* fft/dft_source.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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;

}