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/* integration/romberg.c
*
* Copyright (C) 2018 Patrick Alken
*
* 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.
*/
/* the code in this module performs Romberg integration */
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_integration.h>
#define ROMBERG_PRINT_ROW(i, r) \
do { \
size_t jj; \
fprintf(stderr, "R[%zu] = ", i); \
for (jj = 0; jj <= i; ++jj) \
fprintf(stderr, "%.8e ", r[jj]); \
fprintf(stderr, "\n"); \
} while (0)
gsl_integration_romberg_workspace *
gsl_integration_romberg_alloc(const size_t n)
{
gsl_integration_romberg_workspace *w;
/* check inputs */
if (n < 1)
{
GSL_ERROR_VAL ("workspace size n must be at least 1", GSL_EDOM, 0);
}
w = calloc(1, sizeof(gsl_integration_romberg_workspace));
if (w == NULL)
{
GSL_ERROR_VAL ("unable to allocate workspace", GSL_ENOMEM, 0);
}
/* ceiling on n, since the number of points is 2^n + 1 */
w->n = GSL_MIN(n, 30);
w->work1 = malloc(w->n * sizeof(double));
if (w->work1 == NULL)
{
gsl_integration_romberg_free(w);
GSL_ERROR_VAL ("unable to allocate previous row", GSL_ENOMEM, 0);
}
w->work2 = malloc(w->n * sizeof(double));
if (w->work2 == NULL)
{
gsl_integration_romberg_free(w);
GSL_ERROR_VAL ("unable to allocate current row", GSL_ENOMEM, 0);
}
return w;
}
void
gsl_integration_romberg_free(gsl_integration_romberg_workspace * w)
{
if (w->work1)
free(w->work1);
if (w->work2)
free(w->work2);
free(w);
}
int
gsl_integration_romberg(const gsl_function * f, const double a, const double b,
const double epsabs, const double epsrel, double * result,
size_t * neval, gsl_integration_romberg_workspace * w)
{
if (epsabs < 0.0)
{
GSL_ERROR("epsabs must be non-negative", GSL_EDOM);
}
else if (epsrel < 0.0)
{
GSL_ERROR("epsrel must be non-negative", GSL_EDOM);
}
else
{
const size_t n = w->n;
double *Rp = &(w->work1[0]); /* previous row */
double *Rc = &(w->work2[0]); /* current row */
double *Rtmp;
double h = 0.5 * (b - a); /* step size */
size_t i;
/* R(0,0) */
Rp[0] = h * (GSL_FN_EVAL(f, a) + GSL_FN_EVAL(f, b));
*neval = 2;
/*ROMBERG_PRINT_ROW((size_t) 0, Rp);*/
for (i = 1; i < n; ++i)
{
size_t j;
double sum = 0.0;
double err;
double four_j; /* 4^j */
size_t two_i = 1 << i; /* 2^i */
for (j = 1; j < two_i; j += 2)
{
sum += GSL_FN_EVAL(f, a + j * h);
++(*neval);
}
/* R(i,0) */
Rc[0] = sum * h + 0.5 * Rp[0];
four_j = 4.0;
for (j = 1; j <= i; ++j)
{
Rc[j] = (four_j * Rc[j - 1] - Rp[j - 1]) / (four_j - 1.0);
four_j *= 4.0;
}
/*ROMBERG_PRINT_ROW(i, Rc);*/
/*
* compute difference between current and previous result and
* check for convergence
*/
err = fabs(Rc[i] - Rp[i - 1]);
if ((err < epsabs) || (err < epsrel * fabs(Rc[i])))
{
*result = Rc[i];
return GSL_SUCCESS;
}
/* swap Rp and Rc */
Rtmp = Rp;
Rp = Rc;
Rc = Rtmp;
h *= 0.5;
}
/* did not converge - return best guess */
*result = Rp[n - 1];
return GSL_EMAXITER;
}
}
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