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/* integration/qaws.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.
*/
#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 acheived 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);
}
}
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