/* integration/qc25f.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.

 */

struct fn_fourier_params

{

  gsl_function *function;

  double omega;

};

static double fn_sin (double t, void *params);

static double fn_cos (double t, void *params);

static void

qc25f (gsl_function * f, double a, double b, 

       gsl_integration_qawo_table * wf, size_t level,

       double *result, double *abserr, double *resabs, double *resasc);

static void

qc25f (gsl_function * f, double a, double b, 

       gsl_integration_qawo_table * wf, size_t level,

       double *result, double *abserr, double *resabs, double *resasc)

{

  const double center = 0.5 * (a + b);

  const double half_length = 0.5 * (b - a);

  const double omega = wf->omega ;

  const double par = omega * half_length;

  if (fabs (par) < 2)

    {

      gsl_function weighted_function;

      struct fn_fourier_params fn_params;

      fn_params.function = f;

      fn_params.omega = omega;

      if (wf->sine == GSL_INTEG_SINE) 

        {

          weighted_function.function = &fn_sin;

        }

      else

        {

          weighted_function.function = &fn_cos;

        }

      weighted_function.params = &fn_params;

      gsl_integration_qk15 (&weighted_function, a, b, result, abserr,

                            resabs, resasc);

      return;

    }

  else

    {

      double *moment;

      double cheb12[13], cheb24[25];

      double result_abs, res12_cos, res12_sin, res24_cos, res24_sin;

      double est_cos, est_sin;

      double c, s;

      size_t i;

      gsl_integration_qcheb (f, a, b, cheb12, cheb24);

      if (level >= wf->n)

        {

          /* table overflow should not happen, check before calling */

          GSL_ERROR_VOID("table overflow in internal function", GSL_ESANITY);

        }

      /* obtain moments from the table */

      moment = wf->chebmo + 25 * level;

      res12_cos = cheb12[12] * moment[12];

      res12_sin = 0 ;

      for (i = 0; i < 6; i++)

        {

          size_t k = 10 - 2 * i;

          res12_cos += cheb12[k] * moment[k];

          res12_sin += cheb12[k + 1] * moment[k + 1];

        }

      res24_cos = cheb24[24] * moment[24];

      res24_sin = 0 ;

      result_abs = fabs(cheb24[24]) ;

      for (i = 0; i < 12; i++)

        {

          size_t k = 22 - 2 * i;

          res24_cos += cheb24[k] * moment[k];

          res24_sin += cheb24[k + 1] * moment[k + 1];

          result_abs += fabs(cheb24[k]) + fabs(cheb24[k+1]);

        }

      est_cos = fabs(res24_cos - res12_cos);

      est_sin = fabs(res24_sin - res12_sin);

      c = half_length * cos(center * omega);

      s = half_length * sin(center * omega);

      if (wf->sine == GSL_INTEG_SINE)

        {

          *result = c * res24_sin + s * res24_cos;

          *abserr = fabs(c * est_sin) + fabs(s * est_cos);

        }

      else

        {

          *result = c * res24_cos - s * res24_sin;

          *abserr = fabs(c * est_cos) + fabs(s * est_sin);

        }

      *resabs = result_abs * half_length;

      *resasc = GSL_DBL_MAX;

      return;

    }

}

static double

fn_sin (double x, void *params)

{

  struct fn_fourier_params *p = (struct fn_fourier_params *) params;

  gsl_function *f = p->function;

  double w = p->omega;

  double wx = w * x;

  double sinwx = sin(wx) ;

  return GSL_FN_EVAL (f, x) * sinwx;

}

static double

fn_cos (double x, void *params)

{

  struct fn_fourier_params *p = (struct fn_fourier_params *) params;

  gsl_function *f = p->function;

  double w = p->omega;

  double wx = w * x;

  double coswx = cos(wx) ;

  return GSL_FN_EVAL (f, x) * coswx ;

}