| /* integration/qag.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_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" |
| |
| static int |
| qag (const gsl_function *f, |
| const double a, const double b, |
| const double epsabs, const double epsrel, |
| const size_t limit, |
| gsl_integration_workspace * workspace, |
| double * result, double * abserr, |
| gsl_integration_rule * q) ; |
| |
| int |
| gsl_integration_qag (const gsl_function *f, |
| double a, double b, |
| double epsabs, double epsrel, size_t limit, |
| int key, |
| gsl_integration_workspace * workspace, |
| double * result, double * abserr) |
| { |
| int status ; |
| gsl_integration_rule * integration_rule = gsl_integration_qk15 ; |
| |
| if (key < GSL_INTEG_GAUSS15) |
| { |
| key = GSL_INTEG_GAUSS15 ; |
| } |
| else if (key > GSL_INTEG_GAUSS61) |
| { |
| key = GSL_INTEG_GAUSS61 ; |
| } |
| |
| switch (key) |
| { |
| case GSL_INTEG_GAUSS15: |
| integration_rule = gsl_integration_qk15 ; |
| break ; |
| case GSL_INTEG_GAUSS21: |
| integration_rule = gsl_integration_qk21 ; |
| break ; |
| case GSL_INTEG_GAUSS31: |
| integration_rule = gsl_integration_qk31 ; |
| break ; |
| case GSL_INTEG_GAUSS41: |
| integration_rule = gsl_integration_qk41 ; |
| break ; |
| case GSL_INTEG_GAUSS51: |
| integration_rule = gsl_integration_qk51 ; |
| break ; |
| case GSL_INTEG_GAUSS61: |
| integration_rule = gsl_integration_qk61 ; |
| break ; |
| default: |
| GSL_ERROR("value of key does specify a known integration rule", |
| GSL_EINVAL) ; |
| } |
| |
| status = qag (f, a, b, epsabs, epsrel, limit, |
| workspace, |
| result, abserr, |
| integration_rule) ; |
| |
| return status ; |
| } |
| |
| static int |
| qag (const gsl_function * f, |
| const double a, const double b, |
| 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 result0, abserr0, resabs0, resasc0; |
| double tolerance; |
| size_t iteration = 0; |
| int roundoff_type1 = 0, roundoff_type2 = 0, error_type = 0; |
| |
| double round_off; |
| |
| /* Initialize results */ |
| |
| initialise (workspace, a, b); |
| |
| *result = 0; |
| *abserr = 0; |
| |
| if (limit > workspace->limit) |
| { |
| GSL_ERROR ("iteration limit exceeds available 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); |
| } |
| |
| /* perform the first integration */ |
| |
| q (f, a, b, &result0, &abserr0, &resabs0, &resasc0); |
| |
| set_initial_result (workspace, result0, abserr0); |
| |
| /* Test on accuracy */ |
| |
| tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (result0)); |
| |
| /* need IEEE rounding here to match original quadpack behavior */ |
| |
| round_off = GSL_COERCE_DBL (50 * GSL_DBL_EPSILON * resabs0); |
| |
| if (abserr0 <= round_off && abserr0 > tolerance) |
| { |
| *result = result0; |
| *abserr = abserr0; |
| |
| GSL_ERROR ("cannot reach tolerance because of roundoff error " |
| "on first attempt", GSL_EROUND); |
| } |
| else if ((abserr0 <= tolerance && abserr0 != resasc0) || abserr0 == 0.0) |
| { |
| *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 = 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; |
| double resasc1, resasc2; |
| double resabs1, resabs2; |
| |
| /* 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; |
| |
| q (f, a1, b1, &area1, &error1, &resabs1, &resasc1); |
| q (f, a2, b2, &area2, &error2, &resabs2, &resasc2); |
| |
| area12 = area1 + area2; |
| error12 = error1 + error2; |
| |
| errsum += (error12 - e_i); |
| area += area12 - r_i; |
| |
| if (resasc1 != error1 && resasc2 != error2) |
| { |
| 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); |
| } |
| } |
| |
| |
