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Diffstat (limited to 'gsl-1.9/integration/qawc.c')
| -rw-r--r-- | gsl-1.9/integration/qawc.c | 220 |
1 files changed, 220 insertions, 0 deletions
diff --git a/gsl-1.9/integration/qawc.c b/gsl-1.9/integration/qawc.c new file mode 100644 index 0000000..4e781d1 --- /dev/null +++ b/gsl-1.9/integration/qawc.c @@ -0,0 +1,220 @@ +/* integration/qawc.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 "set_initial.c" +#include "qpsrt.c" +#include "util.c" +#include "qc25c.c" + +int +gsl_integration_qawc (gsl_function * f, + const double a, const double b, const double c, + 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; + int err_reliable; + int sign = 1; + double lower, higher; + + /* Initialize results */ + + *result = 0; + *abserr = 0; + + if (limit > workspace->limit) + { + GSL_ERROR ("iteration limit exceeds available workspace", GSL_EINVAL) ; + } + + if (b < a) + { + lower = b ; + higher = a ; + sign = -1 ; + } + else + { + lower = a; + higher = b; + } + + initialise (workspace, lower, higher); + + 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); + } + + if (c == a || c == b) + { + GSL_ERROR ("cannot integrate with singularity on endpoint", GSL_EINVAL); + } + + /* perform the first integration */ + + qc25c (f, lower, higher, c, &result0, &abserr0, &err_reliable); + + set_initial_result (workspace, result0, abserr0); + + /* Test on accuracy, use 0.01 relative error as an extra safety + margin on the first iteration (ignored for subsequent iterations) */ + + tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (result0)); + + if (abserr0 < tolerance && abserr0 < 0.01 * fabs(result0)) + { + *result = sign * result0; + *abserr = abserr0; + + return GSL_SUCCESS; + } + else if (limit == 1) + { + *result = sign * result0; + *abserr = abserr0; + + GSL_ERROR ("a maximum of one iteration was insufficient", GSL_EMAXITER); + } + + area = result0; + errsum = abserr0; + + iteration = 1; + + 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; + + if (c > a1 && c <= b1) + { + b1 = 0.5 * (c + b2) ; + a2 = b1; + } + else if (c > b1 && c < b2) + { + b1 = 0.5 * (a1 + c) ; + a2 = b1; + } + + qc25c (f, a1, b1, c, &area1, &error1, &err_reliable1); + qc25c (f, a2, b2, c, &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 = sign * 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); + } + +} |