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Diffstat (limited to 'gsl-1.9/integration/qagp.c')
| -rw-r--r-- | gsl-1.9/integration/qagp.c | 510 |
1 files changed, 510 insertions, 0 deletions
diff --git a/gsl-1.9/integration/qagp.c b/gsl-1.9/integration/qagp.c new file mode 100644 index 0000000..fc8e039 --- /dev/null +++ b/gsl-1.9/integration/qagp.c @@ -0,0 +1,510 @@ +/* integration/qagp.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 <stdlib.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_integration.h> + +static int +qagp (const gsl_function *f, + const double *pts, const size_t npts, + const double epsabs, const double epsrel, const size_t limit, + gsl_integration_workspace * workspace, + double *result, double *abserr, + gsl_integration_rule * q); + +#include "initialise.c" +#include "qpsrt.c" +#include "util.c" +#include "append.c" +#include "reset.c" +#include "qelg.c" +#include "qpsrt2.c" +#include "ptsort.c" +#include "positivity.c" + +int +gsl_integration_qagp (const gsl_function *f, + double * pts, size_t npts, + double epsabs, double epsrel, size_t limit, + gsl_integration_workspace * workspace, + double * result, double * abserr) +{ + int status = qagp (f, pts, npts, + epsabs, epsrel, limit, + workspace, + result, abserr, + &gsl_integration_qk21) ; + + return status ; +} + + +static int +qagp (const gsl_function * f, + const double *pts, const size_t npts, + const double epsabs, const double epsrel, + const size_t limit, + gsl_integration_workspace * workspace, + double *result, double *abserr, + gsl_integration_rule * q) +{ + double area, errsum; + double res_ext, err_ext; + double result0, abserr0, resabs0; + double tolerance; + + double ertest = 0; + double error_over_large_intervals = 0; + double reseps = 0, abseps = 0, correc = 0; + size_t ktmin = 0; + int roundoff_type1 = 0, roundoff_type2 = 0, roundoff_type3 = 0; + int error_type = 0, error_type2 = 0; + + size_t iteration = 0; + + int positive_integrand = 0; + int extrapolate = 0; + int disallow_extrapolation = 0; + + struct extrapolation_table table; + + const size_t nint = npts - 1; /* number of intervals */ + + size_t *ndin = workspace->level; /* temporarily alias ndin to level */ + + size_t i; + + /* Initialize results */ + + *result = 0; + *abserr = 0; + + /* Test on validity of parameters */ + + if (limit > workspace->limit) + { + GSL_ERROR ("iteration limit exceeds available workspace", GSL_EINVAL) ; + } + + if (npts > workspace->limit) + { + GSL_ERROR ("npts exceeds size of workspace", 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); + } + + /* Check that the integration range and break points are an + ascending sequence */ + + for (i = 0; i < nint; i++) + { + if (pts[i + 1] < pts[i]) + { + GSL_ERROR ("points are not in an ascending sequence", GSL_EINVAL); + } + } + + /* Perform the first integration */ + + result0 = 0; + abserr0 = 0; + resabs0 = 0; + + initialise (workspace, 0.0, 0.0) ; + + for (i = 0; i < nint; i++) + { + double area1, error1, resabs1, resasc1; + const double a1 = pts[i]; + const double b1 = pts[i + 1]; + + q (f, a1, b1, &area1, &error1, &resabs1, &resasc1); + + result0 = result0 + area1; + abserr0 = abserr0 + error1; + resabs0 = resabs0 + resabs1; + + append_interval (workspace, a1, b1, area1, error1); + + if (error1 == resasc1 && error1 != 0.0) + { + ndin[i] = 1; + } + else + { + ndin[i] = 0; + } + } + + /* Compute the initial error estimate */ + + errsum = 0.0; + + for (i = 0; i < nint; i++) + { + if (ndin[i]) + { + workspace->elist[i] = abserr0; + } + + errsum = errsum + workspace->elist[i]; + + } + + for (i = 0; i < nint; i++) + { + workspace->level[i] = 0; + } + + /* Sort results into order of decreasing error via the indirection + array order[] */ + + sort_results (workspace); + + /* Test on accuracy */ + + tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (result0)); + + if (abserr0 <= 100 * GSL_DBL_EPSILON * resabs0 && abserr0 > tolerance) + { + *result = result0; + *abserr = abserr0; + + GSL_ERROR ("cannot reach tolerance because of roundoff error" + "on first attempt", GSL_EROUND); + } + else if (abserr0 <= tolerance) + { + *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); + } + + /* Initialization */ + + initialise_table (&table); + append_table (&table, result0); + + area = result0; + + res_ext = result0; + err_ext = GSL_DBL_MAX; + + error_over_large_intervals = errsum; + ertest = tolerance; + + positive_integrand = test_positivity (result0, resabs0); + + iteration = nint - 1; + + do + { + size_t current_level; + 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; + double resasc1, resasc2; + double resabs1, resabs2; + double last_e_i; + + /* Bisect the subinterval with the largest error estimate */ + + retrieve (workspace, &a_i, &b_i, &r_i, &e_i); + + current_level = workspace->level[workspace->i] + 1; + + a1 = a_i; + b1 = 0.5 * (a_i + b_i); + a2 = b1; + b2 = b_i; + + iteration++; + + q (f, a1, b1, &area1, &error1, &resabs1, &resasc1); + q (f, a2, b2, &area2, &error2, &resabs2, &resasc2); + + area12 = area1 + area2; + error12 = error1 + error2; + last_e_i = e_i; + + /* Improve previous approximations to the integral and test for + accuracy. + + We write these expressions in the same way as the original + QUADPACK code so that the rounding errors are the same, which + makes testing easier. */ + + errsum = errsum + error12 - e_i; + area = area + area12 - r_i; + + tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (area)); + + if (resasc1 != error1 && resasc2 != error2) + { + double delta = r_i - area12; + + if (fabs (delta) <= 1.0e-5 * fabs (area12) && error12 >= 0.99 * e_i) + { + if (!extrapolate) + { + roundoff_type1++; + } + else + { + roundoff_type2++; + } + } + + if (i > 10 && error12 > e_i) + { + roundoff_type3++; + } + } + + /* Test for roundoff and eventually set error flag */ + + if (roundoff_type1 + roundoff_type2 >= 10 || roundoff_type3 >= 20) + { + error_type = 2; /* round off error */ + } + + if (roundoff_type2 >= 5) + { + error_type2 = 1; + } + + /* 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 = 4; + } + + /* append the newly-created intervals to the list */ + + update (workspace, a1, b1, area1, error1, a2, b2, area2, error2); + + if (errsum <= tolerance) + { + goto compute_result; + } + + if (error_type) + { + break; + } + + if (iteration >= limit - 1) + { + error_type = 1; + break; + } + + if (disallow_extrapolation) + { + continue; + } + + error_over_large_intervals += -last_e_i; + + if (current_level < workspace->maximum_level) + { + error_over_large_intervals += error12; + } + + if (!extrapolate) + { + /* test whether the interval to be bisected next is the + smallest interval. */ + if (large_interval (workspace)) + continue; + + extrapolate = 1; + workspace->nrmax = 1; + } + + /* The smallest interval has the largest error. Before + bisecting decrease the sum of the errors over the larger + intervals (error_over_large_intervals) and perform + extrapolation. */ + + if (!error_type2 && error_over_large_intervals > ertest) + { + if (increase_nrmax (workspace)) + continue; + } + + /* Perform extrapolation */ + + append_table (&table, area); + + if (table.n < 3) + { + goto skip_extrapolation; + } + + qelg (&table, &reseps, &abseps); + + ktmin++; + + if (ktmin > 5 && err_ext < 0.001 * errsum) + { + error_type = 5; + } + + if (abseps < err_ext) + { + ktmin = 0; + err_ext = abseps; + res_ext = reseps; + correc = error_over_large_intervals; + ertest = GSL_MAX_DBL (epsabs, epsrel * fabs (reseps)); + if (err_ext <= ertest) + break; + } + + /* Prepare bisection of the smallest interval. */ + + if (table.n == 1) + { + disallow_extrapolation = 1; + } + + if (error_type == 5) + { + break; + } + + skip_extrapolation: + + reset_nrmax (workspace); + extrapolate = 0; + error_over_large_intervals = errsum; + + } + while (iteration < limit); + + *result = res_ext; + *abserr = err_ext; + + if (err_ext == GSL_DBL_MAX) + goto compute_result; + + if (error_type || error_type2) + { + if (error_type2) + { + err_ext += correc; + } + + if (error_type == 0) + error_type = 3; + + if (result != 0 && area != 0) + { + if (err_ext / fabs (res_ext) > errsum / fabs (area)) + goto compute_result; + } + else if (err_ext > errsum) + { + goto compute_result; + } + else if (area == 0.0) + { + goto return_error; + } + } + + /* Test on divergence. */ + + { + double max_area = GSL_MAX_DBL (fabs (res_ext), fabs (area)); + + if (!positive_integrand && max_area < 0.01 * resabs0) + goto return_error; + } + + { + double ratio = res_ext / area; + + if (ratio < 0.01 || ratio > 100 || errsum > fabs (area)) + error_type = 6; + } + + goto return_error; + +compute_result: + + *result = sum_results (workspace); + *abserr = errsum; + +return_error: + + if (error_type > 2) + error_type--; + + if (error_type == 0) + { + return GSL_SUCCESS; + } + else if (error_type == 1) + { + GSL_ERROR ("number of iterations was insufficient", GSL_EMAXITER); + } + else if (error_type == 2) + { + GSL_ERROR ("cannot reach tolerance because of roundoff error", + GSL_EROUND); + } + else if (error_type == 3) + { + GSL_ERROR ("bad integrand behavior found in the integration interval", + GSL_ESING); + } + else if (error_type == 4) + { + GSL_ERROR ("roundoff error detected in the extrapolation table", + GSL_EROUND); + } + else if (error_type == 5) + { + GSL_ERROR ("integral is divergent, or slowly convergent", + GSL_EDIVERGE); + } + else + { + GSL_ERROR ("could not integrate function", GSL_EFAILED); + } +} |