/* integration/qaws.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.

 */

#include <config.h>

#include <math.h>

#include <float.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_integration.h>

#include "initialise.c"

#include "append.c"

#include "qpsrt.c"

#include "util.c"

#include "qc25s.c"

int

gsl_integration_qaws (gsl_function * f,

                      const double a, const double b,

                      gsl_integration_qaws_table * t,

                      const double epsabs, const double epsrel,

                      const size_t limit,

                      gsl_integration_workspace * workspace,

                      double *result, double *abserr)

{

  double area, errsum;

  double result0, abserr0;

  double tolerance;

  size_t iteration = 0;

  int roundoff_type1 = 0, roundoff_type2 = 0, error_type = 0;

  /* Initialize results */

  initialise (workspace, a, b);

  *result = 0;

  *abserr = 0;

  if (limit > workspace->limit)

    {

      GSL_ERROR ("iteration limit exceeds available workspace", GSL_EINVAL) ;

    }

  if (b <= a) 

    {

      GSL_ERROR ("limits must form an ascending sequence, a < b", GSL_EINVAL) ;

    }

  if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))

    {

      GSL_ERROR ("tolerance cannot be achieved with given epsabs and epsrel",

                 GSL_EBADTOL);

    }

  /* perform the first integration */

  {

    double area1, area2;

    double error1, error2;

    int err_reliable1, err_reliable2;

    double a1 = a;

    double b1 = 0.5 * (a + b);

    double a2 = b1;

    double b2 = b;

    qc25s (f, a, b, a1, b1, t, &area1, &error1, &err_reliable1);

    qc25s (f, a, b, a2, b2, t, &area2, &error2, &err_reliable2);

    if (error1 > error2)

      {

        append_interval (workspace, a1, b1, area1, error1);

        append_interval (workspace, a2, b2, area2, error2);

      }

    else

      {

        append_interval (workspace, a2, b2, area2, error2);

        append_interval (workspace, a1, b1, area1, error1);

      }

    result0 = area1 + area2;

    abserr0 = error1 + error2;

  }

  /* Test on accuracy */

  tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (result0));

  /* Test on accuracy, use 0.01 relative error as an extra safety

     margin on the first iteration (ignored for subsequent iterations) */

  if (abserr0 < tolerance && abserr0 < 0.01 * fabs(result0))

    {

      *result = result0;

      *abserr = abserr0;

      return GSL_SUCCESS;

    }

  else if (limit == 1)

    {

      *result = result0;

      *abserr = abserr0;

      GSL_ERROR ("a maximum of one iteration was insufficient", GSL_EMAXITER);

    }

  area = result0;

  errsum = abserr0;

  iteration = 2;

  do

    {

      double a1, b1, a2, b2;

      double a_i, b_i, r_i, e_i;

      double area1 = 0, area2 = 0, area12 = 0;

      double error1 = 0, error2 = 0, error12 = 0;

      int err_reliable1, err_reliable2;

      /* Bisect the subinterval with the largest error estimate */

      retrieve (workspace, &a_i, &b_i, &r_i, &e_i);

      a1 = a_i; 

      b1 = 0.5 * (a_i + b_i);

      a2 = b1;

      b2 = b_i;

      qc25s (f, a, b, a1, b1, t, &area1, &error1, &err_reliable1);

      qc25s (f, a, b, a2, b2, t, &area2, &error2, &err_reliable2);

      area12 = area1 + area2;

      error12 = error1 + error2;

      errsum += (error12 - e_i);

      area += area12 - r_i;

      if (err_reliable1 && err_reliable2)

        {

          double delta = r_i - area12;

          if (fabs (delta) <= 1.0e-5 * fabs (area12) && error12 >= 0.99 * e_i)

            {

              roundoff_type1++;

            }

          if (iteration >= 10 && error12 > e_i)

            {

              roundoff_type2++;

            }

        }

      tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (area));

      if (errsum > tolerance)

        {

          if (roundoff_type1 >= 6 || roundoff_type2 >= 20)

            {

              error_type = 2;   /* round off error */

            }

          /* set error flag in the case of bad integrand behaviour at

             a point of the integration range */

          if (subinterval_too_small (a1, a2, b2))

            {

              error_type = 3;

            }

        }

      update (workspace, a1, b1, area1, error1, a2, b2, area2, error2);

      retrieve (workspace, &a_i, &b_i, &r_i, &e_i);

      iteration++;

    }

  while (iteration < limit && !error_type && errsum > tolerance);

  *result = sum_results (workspace);

  *abserr = errsum;

  if (errsum <= tolerance)

    {

      return GSL_SUCCESS;

    }

  else if (error_type == 2)

    {

      GSL_ERROR ("roundoff error prevents tolerance from being achieved",

                 GSL_EROUND);

    }

  else if (error_type == 3)

    {

      GSL_ERROR ("bad integrand behavior found in the integration interval",

                 GSL_ESING);

    }

  else if (iteration == limit)

    {

      GSL_ERROR ("maximum number of subdivisions reached", GSL_EMAXITER);

    }

  else

    {

      GSL_ERROR ("could not integrate function", GSL_EFAILED);

    }

}