| /* integration/test.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 <stdio.h> |
| #include <math.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_integration.h> |
| #include <gsl/gsl_errno.h> |
| #include <gsl/gsl_test.h> |
| #include <gsl/gsl_ieee_utils.h> |
| |
| #include "tests.h" |
| |
| gsl_function make_function (double (* f) (double, void *), double * p); |
| |
| gsl_function make_function (double (* f) (double, void *), double * p) |
| { |
| gsl_function f_new; |
| |
| f_new.function = f ; |
| f_new.params = p ; |
| |
| return f_new; |
| } |
| |
| struct counter_params { |
| gsl_function * f; |
| int neval; |
| } ; |
| |
| double counter (double x, void * params); |
| gsl_function make_counter (gsl_function * f, struct counter_params * p); |
| |
| double |
| counter (double x, void * params) |
| { |
| struct counter_params * p = (struct counter_params *) params; |
| p->neval++ ; /* increment counter */ |
| return GSL_FN_EVAL(p->f, x); |
| } |
| |
| gsl_function make_counter (gsl_function * f, struct counter_params * p) |
| { |
| gsl_function f_new; |
| |
| p->f = f; |
| p->neval = 0 ; |
| |
| f_new.function = &counter ; |
| f_new.params = p ; |
| |
| return f_new; |
| } |
| |
| void my_error_handler (const char *reason, const char *file, |
| int line, int err); |
| |
| int main (void) |
| { |
| gsl_ieee_env_setup (); |
| gsl_set_error_handler (&my_error_handler); |
| |
| /* Test the basic Gauss-Kronrod rules with a smooth positive function. */ |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 7.716049357767090777E-02; |
| double exp_abserr = 2.990224871000550874E-06; |
| double exp_resabs = 7.716049357767090777E-02; |
| double exp_resasc = 4.434273814139995384E-02; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha) ; |
| |
| gsl_integration_qk15 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk15(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk15(f1) smooth abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk15(f1) smooth resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk15(f1) smooth resasc") ; |
| |
| gsl_integration_qk15 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qk15(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk15(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk15(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk15(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 7.716049379303084599E-02; |
| double exp_abserr = 9.424302194248481445E-08; |
| double exp_resabs = 7.716049379303084599E-02; |
| double exp_resasc = 4.434311425038358484E-02; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk21 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk21(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk21(f1) smooth abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk21(f1) smooth resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk21(f1) smooth resasc") ; |
| |
| gsl_integration_qk21 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk21(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk21(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk21(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk21(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 7.716049382494900855E-02; |
| double exp_abserr = 1.713503193600029893E-09; |
| double exp_resabs = 7.716049382494900855E-02; |
| double exp_resasc = 4.427995051868838933E-02; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk31 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk31(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk31(f1) smooth abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk31(f1) smooth resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk31(f1) smooth resasc") ; |
| |
| gsl_integration_qk31 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk31(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk31(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk31(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk31(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 7.716049382681375302E-02; |
| double exp_abserr = 9.576386660975511224E-11; |
| double exp_resabs = 7.716049382681375302E-02; |
| double exp_resasc = 4.421521169637691873E-02; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk41 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk41(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk41(f1) smooth abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk41(f1) smooth resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk41(f1) smooth resasc") ; |
| |
| gsl_integration_qk41 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk41(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk41(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk41(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk41(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 7.716049382708510540E-02; |
| double exp_abserr = 1.002079980317363772E-11; |
| double exp_resabs = 7.716049382708510540E-02; |
| double exp_resasc = 4.416474291216854892E-02; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk51 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk51(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qk51(f1) smooth abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk51(f1) smooth resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk51(f1) smooth resasc") ; |
| |
| gsl_integration_qk51 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk51(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qk51(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk51(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk51(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 7.716049382713800753E-02; |
| double exp_abserr = 1.566060362296155616E-12; |
| double exp_resabs = 7.716049382713800753E-02; |
| double exp_resasc = 4.419287685934316506E-02; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk61 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk61(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qk61(f1) smooth abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk61(f1) smooth resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk61(f1) smooth resasc") ; |
| |
| gsl_integration_qk61 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk61(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qk61(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk61(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk61(f1) reverse resasc") ; |
| } |
| |
| /* Now test the basic rules with a positive function that has a |
| singularity. This should give large values of abserr which would |
| find discrepancies in the abserr calculation. */ |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 1.555688196612745777E+01; |
| double exp_abserr = 2.350164577239293706E+01; |
| double exp_resabs = 1.555688196612745777E+01; |
| double exp_resasc = 2.350164577239293706E+01; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk15 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk15(f1) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk15(f1) singular abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk15(f1) singular resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk15(f1) singular resasc") ; |
| |
| gsl_integration_qk15 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk15(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk15(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk15(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk15(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 1.799045317938126232E+01; |
| double exp_abserr = 2.782360287710622515E+01; |
| double exp_resabs = 1.799045317938126232E+01; |
| double exp_resasc = 2.782360287710622515E+01; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk21 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk21(f1) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk21(f1) singular abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk21(f1) singular resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk21(f1) singular resasc") ; |
| |
| gsl_integration_qk21 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk21(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk21(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk21(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk21(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 2.081873305159121657E+01; |
| double exp_abserr = 3.296500137482590276E+01; |
| double exp_resabs = 2.081873305159121301E+01; |
| double exp_resasc = 3.296500137482590276E+01; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk31 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk31(f1) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk31(f1) singular abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk31(f1) singular resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk31(f1) singular resasc") ; |
| |
| gsl_integration_qk31 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk31(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk31(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk31(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk31(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 2.288677623903126701E+01; |
| double exp_abserr = 3.671538820274916048E+01; |
| double exp_resabs = 2.288677623903126701E+01; |
| double exp_resasc = 3.671538820274916048E+01; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk41 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk41(f1) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk41(f1) singular abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk41(f1) singular resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk41(f1) singular resasc") ; |
| |
| gsl_integration_qk41 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk41(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk41(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk41(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk41(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 2.449953612016972215E+01; |
| double exp_abserr = 3.967771249391228849E+01; |
| double exp_resabs = 2.449953612016972215E+01; |
| double exp_resasc = 3.967771249391228849E+01; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk51 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk51(f1) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk51(f1) singular abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk51(f1) singular resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk51(f1) singular resasc") ; |
| |
| gsl_integration_qk51 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk51(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk51(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk51(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk51(f1) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result = 2.583030240976628988E+01; |
| double exp_abserr = 4.213750493076978643E+01; |
| double exp_resabs = 2.583030240976628988E+01; |
| double exp_resasc = 4.213750493076978643E+01; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_integration_qk61 (&f, 0.0, 1.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk61(f1) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk61(f1) singular abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk61(f1) singular resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk61(f1) singular resasc") ; |
| |
| gsl_integration_qk61 (&f, 1.0, 0.0, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk61(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk61(f1) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk61(f1) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk61(f1) reverse resasc") ; |
| } |
| |
| /* Test the basic Gauss-Kronrod rules with a smooth oscillating |
| function, over an unsymmetric range. This should find any |
| discrepancies in the abscissae. */ |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result =-7.238969575483799046E-01; |
| double exp_abserr = 8.760080200939757174E-06; |
| double exp_resabs = 1.165564172429140788E+00; |
| double exp_resasc = 9.334560307787327371E-01; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_integration_qk15 (&f, 0.3, 2.71, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk15(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk15(f3) oscill abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk15(f3) oscill resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk15(f3) oscill resasc") ; |
| |
| gsl_integration_qk15 (&f, 2.71, 0.3, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk15(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk15(f3) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk15(f3) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk15(f3) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result =-7.238969575482959717E-01; |
| double exp_abserr = 7.999213141433641888E-11; |
| double exp_resabs = 1.150829032708484023E+00; |
| double exp_resasc = 9.297591249133687619E-01; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_integration_qk21 (&f, 0.3, 2.71, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk21(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qk21(f3) oscill abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk21(f3) oscill resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk21(f3) oscill resasc") ; |
| |
| gsl_integration_qk21 (&f, 2.71, 0.3, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk21(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qk21(f3) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk21(f3) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk21(f3) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result =-7.238969575482959717E-01; |
| double exp_abserr = 1.285805464427459261E-14; |
| double exp_resabs = 1.158150602093290571E+00; |
| double exp_resasc = 9.277828092501518853E-01; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_integration_qk31 (&f, 0.3, 2.71, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk31(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk31(f3) oscill abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk31(f3) oscill resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk31(f3) oscill resasc") ; |
| |
| gsl_integration_qk31 (&f, 2.71, 0.3, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk31(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk31(f3) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk31(f3) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk31(f3) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result =-7.238969575482959717E-01; |
| double exp_abserr = 1.286535726271015626E-14; |
| double exp_resabs = 1.158808363486595328E+00; |
| double exp_resasc = 9.264382258645686985E-01; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_integration_qk41 (&f, 0.3, 2.71, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk41(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk41(f3) oscill abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk41(f3) oscill resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk41(f3) oscill resasc") ; |
| |
| gsl_integration_qk41 (&f, 2.71, 0.3, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk41(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk41(f3) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk41(f3) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk41(f3) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result =-7.238969575482961938E-01; |
| double exp_abserr = 1.285290995039385778E-14; |
| double exp_resabs = 1.157687209264406381E+00; |
| double exp_resasc = 9.264666884071264263E-01; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_integration_qk51 (&f, 0.3, 2.71, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk51(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk51(f3) oscill abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk51(f3) oscill resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk51(f3) oscill resasc") ; |
| |
| gsl_integration_qk51 (&f, 2.71, 0.3, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk51(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk51(f3) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk51(f3) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk51(f3) reverse resasc") ; |
| } |
| |
| { |
| double result = 0, abserr = 0, resabs = 0, resasc = 0 ; |
| double exp_result =-7.238969575482959717E-01; |
| double exp_abserr = 1.286438572027470736E-14; |
| double exp_resabs = 1.158720854723590099E+00; |
| double exp_resasc = 9.270469641771273972E-01; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_integration_qk61 (&f, 0.3, 2.71, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,exp_result,1e-15,"qk61(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk61(f3) oscill abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk61(f3) oscill resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk61(f3) oscill resasc") ; |
| |
| gsl_integration_qk61 (&f, 2.71, 0.3, |
| &result, &abserr, &resabs, &resasc) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qk61(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qk61(f3) reverse abserr") ; |
| gsl_test_rel(resabs,exp_resabs,1e-15,"qk61(f3) reverse resabs") ; |
| gsl_test_rel(resasc,exp_resasc,1e-15,"qk61(f3) reverse resasc") ; |
| } |
| |
| /* Test the non-adaptive gaussian integrator QNG */ |
| |
| { |
| int status = 0; size_t neval = 0 ; |
| double result = 0, abserr = 0 ; |
| double exp_result = 7.716049379303083211E-02; |
| double exp_abserr = 9.424302199601294244E-08; |
| int exp_neval = 21; |
| int exp_ier = 0; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| status = gsl_integration_qng (&f, 0.0, 1.0, 1e-1, 0.0, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,exp_result,1e-15,"qng(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f1) smooth abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f1) smooth neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) smooth status") ; |
| |
| status = gsl_integration_qng (&f, 1.0, 0.0, 1e-1, 0.0, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qng(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f1) reverse abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f1) reverse neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) reverse status") ; |
| } |
| |
| { |
| int status = 0; size_t neval = 0 ; |
| double result = 0, abserr = 0 ; |
| |
| double exp_result = 7.716049382706505200E-02; |
| double exp_abserr = 2.666893044866214501E-12; |
| int exp_neval = 43; |
| int exp_ier = 0; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| status = gsl_integration_qng (&f, 0.0, 1.0, 0.0, 1e-9, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,exp_result,1e-15,"qng(f1) smooth 43pt result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qng(f1) smooth 43pt abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f1) smooth 43pt neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) smooth 43pt status") ; |
| |
| status = gsl_integration_qng (&f, 1.0, 0.0, 0.0, 1e-9, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qng(f1) reverse 43pt result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qng(f1) reverse 43pt abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f1) reverse 43pt neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) reverse 43pt status") ; |
| } |
| |
| { |
| int status; size_t neval = 0 ; |
| double result = 0, abserr = 0 ; |
| double exp_result =-7.238969575482961938E-01; |
| double exp_abserr = 1.277676889520056369E-14; |
| int exp_neval = 43; |
| int exp_ier = 0; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| status = gsl_integration_qng (&f, 0.3, 2.71, 0.0, 1e-12, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,exp_result,1e-15,"qnq(f3) oscill result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f3) oscill abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f3) oscill neval") ; |
| gsl_test_int(status,exp_ier,"qng(f3) oscill status") ; |
| |
| status = gsl_integration_qng (&f, 2.71, 0.3, 0.0, 1e-12, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qnq(f3) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f3) reverse abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f3) reverse neval") ; |
| gsl_test_int(status,exp_ier,"qng(f3) reverse status") ; |
| } |
| |
| { |
| int status = 0; size_t neval = 0 ; |
| double result = 0, abserr = 0 ; |
| |
| double exp_result = 7.716049382716029525E-02; |
| double exp_abserr = 8.566535680046930668E-16; |
| int exp_neval = 87; |
| int exp_ier = 0; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| status = gsl_integration_qng (&f, 0.0, 1.0, 0.0, 1e-13, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,exp_result,1e-15,"qng(f1) 87pt smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f1) 87pt smooth abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f1) 87pt smooth neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) 87pt smooth status") ; |
| |
| status = gsl_integration_qng (&f, 1.0, 0.0, 0.0, 1e-13, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qng(f1) 87pt reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f1) 87pt reverse abserr") ; |
| gsl_test_int((int)neval,exp_neval,"qng(f1) 87pt reverse neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) 87pt reverse status") ; |
| } |
| |
| { |
| int status = 0; size_t neval = 0 ; |
| double result = 0, abserr = 0 ; |
| |
| double exp_result = 3.222948711817264211E+01; |
| double exp_abserr = 2.782360287710622870E+01; |
| int exp_neval = 87; |
| int exp_ier = GSL_ETOL; |
| |
| double alpha = -0.9 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| status = gsl_integration_qng (&f, 0.0, 1.0, 0.0, 1e-3, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,exp_result,1e-15,"qng(f1) sing beyond 87pt result"); |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f1) sing beyond 87pt abserr"); |
| gsl_test_int((int)neval,exp_neval,"qng(f1) sing beyond 87pt neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) sing beyond 87pt status") ; |
| |
| status = gsl_integration_qng (&f, 1.0, 0.0, 0.0, 1e-3, |
| &result, &abserr, &neval) ; |
| gsl_test_rel(result,-exp_result,1e-15,"qng(f1) reverse beyond 87pt result"); |
| gsl_test_rel(abserr,exp_abserr,1e-7,"qng(f1) rev beyond 87pt abserr"); |
| gsl_test_int((int)neval,exp_neval,"qng(f1) rev beyond 87pt neval") ; |
| gsl_test_int(status,exp_ier,"qng(f1) rev beyond 87pt status") ; |
| } |
| |
| /* Test the adaptive integrator QAG */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| double exp_result = 7.716049382715854665E-02 ; |
| double exp_abserr = 6.679384885865053037E-12 ; |
| int exp_neval = 165; |
| int exp_ier = 0; |
| int exp_last = 6; |
| |
| double a[6] = { 0, 0.5, 0.25, 0.125, 0.0625, 0.03125 } ; |
| double b[6] = { 0.03125, 1, 0.5, 0.25, 0.125, 0.0625 } ; |
| double r[6] = { 3.966769831709074375E-06, 5.491842501998222409E-02, |
| 1.909827770934243926E-02, 2.776531175604360531E-03, |
| 3.280661030752063693E-04, 3.522704932261797744E-05 } ; |
| double e[6] = { 6.678528276336181873E-12, 6.097169993333454062E-16, |
| 2.120334764359736934E-16, 3.082568839745514608E-17, |
| 3.642265412331439511E-18, 3.910988124757650942E-19 } ; |
| int order[6] = { 1, 2, 3, 4, 5, 6 } ; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha) ; |
| |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qag (&fc, 0.0, 1.0, 0.0, 1e-10, w->limit, |
| GSL_INTEG_GAUSS15, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-15,"qag(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f1) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f1) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f1) smooth last") ; |
| gsl_test_int(status,exp_ier,"qag(f1) smooth status") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qag(f1) smooth alist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qag(f1) smooth blist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qag(f1) smooth rlist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-6,"qag(f1) smooth elist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qag(f1) smooth order") ; |
| |
| p.neval = 0; |
| |
| status = gsl_integration_qag (&fc, 1.0, 0.0, 0.0, 1e-10, w->limit, |
| GSL_INTEG_GAUSS15, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qag(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f1) reverse abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f1) reverse neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f1) reverse last") ; |
| gsl_test_int(status,exp_ier,"qag(f1) reverse status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test the same function using an absolute error bound and the |
| 21-point rule */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| double exp_result = 7.716049382716050342E-02 ; |
| double exp_abserr = 2.227969521869139532E-15 ; |
| int exp_neval = 315; |
| int exp_ier = 0; |
| int exp_last = 8; |
| |
| double a[8] = { 0, 0.5, 0.25, 0.125, 0.0625, 0.03125, 0.015625, |
| 0.0078125 } ; |
| double b[8] = { 0.0078125, 1, 0.5, 0.25, 0.125, 0.0625, 0.03125, |
| 0.015625 } ; |
| double r[8] = { 3.696942726831556522E-08, 5.491842501998223103E-02, |
| 1.909827770934243579E-02, 2.776531175604360097E-03, |
| 3.280661030752062609E-04, 3.522704932261797744E-05, |
| 3.579060884684503576E-06, 3.507395216921808047E-07 } ; |
| double e[8] = { 1.371316364034059572E-15, 6.097169993333454062E-16, |
| 2.120334764359736441E-16, 3.082568839745514608E-17, |
| 3.642265412331439511E-18, 3.910988124757650460E-19, |
| 3.973555800712018091E-20, 3.893990926286736620E-21 } ; |
| int order[8] = { 1, 2, 3, 4, 5, 6, 7, 8 } ; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qag (&fc, 0.0, 1.0, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS21, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-15,"qag(f1,21pt) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f1,21pt) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f1,21pt) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f1,21pt) smooth last") ; |
| gsl_test_int(status,exp_ier,"qag(f1,21pt) smooth status") ; |
| |
| for (i = 0; i < 8 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qag(f1,21pt) smooth alist") ; |
| |
| for (i = 0; i < 8 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qag(f1,21pt) smooth blist") ; |
| |
| for (i = 0; i < 8 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qag(f1,21pt) smooth rlist") ; |
| |
| for (i = 0; i < 8 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-6,"qag(f1,21pt) smooth elist") ; |
| |
| for (i = 0; i < 8 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qag(f1,21pt) smooth order"); |
| |
| |
| p.neval = 0; |
| status = gsl_integration_qag (&fc, 1.0, 0.0, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS21, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qag(f1,21pt) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f1,21pt) reverse abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f1,21pt) reverse neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f1,21pt) reverse last") ; |
| gsl_test_int(status,exp_ier,"qag(f1,21pt) reverse status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Adaptive integration of an oscillatory function which terminates because |
| of roundoff error, uses the 31-pt rule */ |
| |
| { |
| int status = 0; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| double exp_result = -7.238969575482959717E-01; |
| double exp_abserr = 1.285805464427459261E-14; |
| int exp_neval = 31; |
| int exp_ier = GSL_EROUND; |
| int exp_last = 1; |
| |
| double alpha = 1.3 ; |
| gsl_function f = make_function(&f3, &alpha); |
| |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qag (&fc, 0.3, 2.71, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS31, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-15,"qag(f3,31pt) oscill result"); |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f3,31pt) oscill abserr"); |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f3,31pt) oscill neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f3,31pt) oscill last") ; |
| gsl_test_int(status,exp_ier,"qag(f3,31pt) oscill status") ; |
| |
| p.neval = 0; |
| status = gsl_integration_qag (&fc, 2.71, 0.3, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS31, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qag(f3,31pt) reverse result"); |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f3,31pt) reverse abserr"); |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f3,31pt) reverse neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f3,31pt) reverse last") ; |
| gsl_test_int(status,exp_ier,"qag(f3,31pt) reverse status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Check the singularity detection (singularity at x=-0.1 in this example) */ |
| |
| { |
| int status = 0; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| int exp_neval = 5151; |
| int exp_ier = GSL_ESING; |
| int exp_last = 51; |
| |
| double alpha = 2.0 ; |
| gsl_function f = make_function(&f16, &alpha); |
| |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qag (&fc, -1.0, 1.0, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS51, w, |
| &result, &abserr) ; |
| |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f16,51pt) sing neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f16,51pt) sing last") ; |
| gsl_test_int(status,exp_ier,"qag(f16,51pt) sing status") ; |
| |
| p.neval = 0; |
| status = gsl_integration_qag (&fc, 1.0, -1.0, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS51, w, |
| &result, &abserr) ; |
| |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f16,51pt) rev neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f16,51pt) rev last") ; |
| gsl_test_int(status,exp_ier,"qag(f16,51pt) rev status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Check for hitting the iteration limit */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (3) ; |
| |
| double exp_result = 9.565151449233894709 ; |
| double exp_abserr = 1.570369823891028460E+01; |
| int exp_neval = 305; |
| int exp_ier = GSL_EMAXITER; |
| int exp_last = 3; |
| |
| double a[3] = { -5.000000000000000000E-01, |
| 0.000000000000000000, |
| -1.000000000000000000 } ; |
| |
| double b[3] = { 0.000000000000000000, |
| 1.000000000000000000, |
| -5.000000000000000000E-01 } ; |
| |
| double r[3] = { 9.460353469435913709, |
| 9.090909090909091161E-02, |
| 1.388888888888888812E-02 } ; |
| |
| double e[3] = { 1.570369823891028460E+01, |
| 1.009293658750142399E-15, |
| 1.541976423090495140E-16 } ; |
| |
| int order[3] = { 1, 2, 3 } ; |
| |
| double alpha = 1.0 ; |
| gsl_function f = make_function(&f16, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qag (&fc, -1.0, 1.0, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS61, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-15,"qag(f16,61pt) limit result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f16,61pt) limit abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f16,61pt) limit neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f16,61pt) limit last") ; |
| gsl_test_int(status,exp_ier,"qag(f16,61pt) limit status") ; |
| |
| for (i = 0; i < 3 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qag(f16,61pt) limit alist") ; |
| |
| for (i = 0; i < 3 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qag(f16,61pt) limit blist") ; |
| |
| for (i = 0; i < 3 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qag(f16,61pt) limit rlist") ; |
| |
| for (i = 0; i < 3 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-6,"qag(f16,61pt) limit elist") ; |
| |
| for (i = 0; i < 3 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qag(f16,61pt) limit order"); |
| |
| p.neval = 0; |
| status = gsl_integration_qag (&fc, 1.0, -1.0, 1e-14, 0.0, w->limit, |
| GSL_INTEG_GAUSS61, w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qag(f16,61pt) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qag(f16,61pt) reverse abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qag(f16,61pt) reverse neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qag(f16,61pt) reverse last") ; |
| gsl_test_int(status,exp_ier,"qag(f16,61pt) reverse status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test the adaptive integrator with extrapolation QAGS */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| double exp_result = 7.716049382715789440E-02 ; |
| double exp_abserr = 2.216394961010438404E-12 ; |
| int exp_neval = 189; |
| int exp_ier = 0; |
| int exp_last = 5; |
| |
| double a[5] = { 0, 0.5, 0.25, 0.125, 0.0625 } ; |
| double b[5] = { 0.0625, 1, 0.5, 0.25, 0.125 } ; |
| double r[5] = { 3.919381915366914693E-05, |
| 5.491842501998223103E-02, |
| 1.909827770934243579E-02, |
| 2.776531175604360097E-03, |
| 3.280661030752062609E-04 } ; |
| double e[5] = { 2.215538742580964735E-12, |
| 6.097169993333454062E-16, |
| 2.120334764359736441E-16, |
| 3.082568839745514608E-17, |
| 3.642265412331439511E-18 } ; |
| int order[5] = { 1, 2, 3, 4, 5 } ; |
| |
| double alpha = 2.6 ; |
| gsl_function f = make_function(&f1, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qags (&fc, 0.0, 1.0, 0.0, 1e-10, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-15,"qags(f1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qags(f1) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qags(f1) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qags(f1) smooth last") ; |
| gsl_test_int(status,exp_ier,"qags(f1) smooth status") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qags(f1) smooth alist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qags(f1) smooth blist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qags(f1) smooth rlist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-6,"qags(f1) smooth elist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qags(f1) smooth order") ; |
| |
| p.neval = 0; |
| status = gsl_integration_qags (&fc, 1.0, 0.0, 0.0, 1e-10, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qags(f1) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qags(f1) reverse abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qags(f1) reverse neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qags(f1) reverse last") ; |
| gsl_test_int(status,exp_ier,"qags(f1) reverse status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test f11 using an absolute error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = -5.908755278982136588E+03 ; |
| double exp_abserr = 1.299646281053874554E-10 ; |
| int exp_neval = 357; |
| int exp_ier = 0; |
| int exp_last = 9; |
| |
| double a[9] = { 1.000000000000000000E+00, |
| 5.005000000000000000E+02, |
| 2.507500000000000000E+02, |
| 1.258750000000000000E+02, |
| 6.343750000000000000E+01, |
| 3.221875000000000000E+01, |
| 1.660937500000000000E+01, |
| 8.804687500000000000E+00, |
| 4.902343750000000000E+00 } ; |
| double b[9] = { 4.902343750000000000E+00, |
| 1.000000000000000000E+03, |
| 5.005000000000000000E+02, |
| 2.507500000000000000E+02, |
| 1.258750000000000000E+02, |
| 6.343750000000000000E+01, |
| 3.221875000000000000E+01, |
| 1.660937500000000000E+01, |
| 8.804687500000000000E+00 } ; |
| double r[9] = { -3.890977835520834649E+00, |
| -3.297343675805121620E+03, |
| -1.475904154146372775E+03, |
| -6.517404019686431411E+02, |
| -2.829354222635842007E+02, |
| -1.201692001973227519E+02, |
| -4.959999906099650246E+01, |
| -1.971441499411640308E+01, |
| -7.457032710459004399E+00 } ; |
| double e[9] = { 6.448276035006137169E-11, |
| 3.660786868980994028E-11, |
| 1.638582774073219226E-11, |
| 7.235772003440423011E-12, |
| 3.141214202790722909E-12, |
| 1.334146129098576244E-12, |
| 5.506706097890446534E-13, |
| 2.188739744348345039E-13, |
| 8.278969410534525339E-14 } ; |
| int order[9] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 } ; |
| |
| double alpha = 2.0 ; |
| gsl_function f = make_function(&f11, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qags (&fc, 1.0, 1000.0, 1e-7, 0.0, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-15,"qags(f11) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-3,"qags(f11) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qags(f11) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qags(f11) smooth last") ; |
| gsl_test_int(status,exp_ier,"qags(f11) smooth status") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qags(f11) smooth alist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qags(f11) smooth blist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qags(f11) smooth rlist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-5,"qags(f11) smooth elist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qags(f11) smooth order"); |
| |
| p.neval = 0; |
| status = gsl_integration_qags (&fc, 1000.0, 1.0, 1e-7, 0.0, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-15,"qags(f11) reverse result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-3,"qags(f11) reverse abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qags(f11) reverse neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qags(f11) reverse last") ; |
| gsl_test_int(status,exp_ier,"qags(f11) reverse status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test infinite range integral f455 using a relative error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = -3.616892186127022568E-01 ; |
| double exp_abserr = 3.016716913328831851E-06; |
| int exp_neval = 285; |
| int exp_ier = 0; |
| int exp_last = 10; |
| |
| double a[10] = { 9.687500000000000000E-01, |
| 0.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 7.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 8.750000000000000000E-01, |
| 6.250000000000000000E-02, |
| 9.375000000000000000E-01, |
| 3.125000000000000000E-02 } ; |
| double b[10] = { 1.000000000000000000E+00, |
| 3.125000000000000000E-02, |
| 7.500000000000000000E-01, |
| 5.000000000000000000E-01, |
| 8.750000000000000000E-01, |
| 2.500000000000000000E-01, |
| 9.375000000000000000E-01, |
| 1.250000000000000000E-01, |
| 9.687500000000000000E-01, |
| 6.250000000000000000E-02 } ; |
| double r[10] = { -1.390003415539725340E-01, |
| 1.429785306003466313E-03, |
| -1.229943369113085765E-02, |
| 2.995321156568048898E-03, |
| -4.980050133751051655E-02, |
| 2.785385934678596704E-03, |
| -8.653752279614615461E-02, |
| 1.736218164975512294E-03, |
| -8.398745675010892142E-02, |
| 1.041689192004495576E-03 } ; |
| double e[10] = { 2.395037249893453013E-02, |
| 2.161214992172538524E-04, |
| 5.720644840858777846E-14, |
| 3.325474514168701167E-17, |
| 3.147380432198176412E-14, |
| 3.092399597147240624E-17, |
| 9.607595030230581153E-16, |
| 1.927589382528252344E-17, |
| 9.324480826368044019E-16, |
| 1.156507325466566521E-17 } ; |
| int order[10] = { 1, 2, 3, 5, 7, 9, 4, 6, 8, 10 } ; |
| |
| gsl_function f = make_function(&f455, 0); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qagiu (&fc, 0.0, 0.0, 1.0e-3, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qagiu(f455) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(f455) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qagiu(f455) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qagiu(f455) smooth last") ; |
| gsl_test_int(status,exp_ier,"qagiu(f455) smooth status") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(f455) smooth alist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(f455) smooth blist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qagiu(f455) smooth rlist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(f455) smooth elist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qagiu(f455) smooth order"); |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test infinite range integral f15 using a relative error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = 6.553600000000024738E+04; |
| double exp_abserr = 7.121667111456009280E-04; |
| int exp_neval = 285; |
| int exp_ier = 0; |
| int exp_last = 10; |
| |
| double a[10] = { 0.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02, |
| 1.562500000000000000E-02, |
| 7.812500000000000000E-03, |
| 3.906250000000000000E-03, |
| 1.953125000000000000E-03 } ; |
| double b[10] = { 1.953125000000000000E-03, |
| 1.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02, |
| 1.562500000000000000E-02, |
| 7.812500000000000000E-03, |
| 3.906250000000000000E-03 } ; |
| double r[10] = { 1.099297665754340292E+00, |
| 3.256176475185617591E-01, |
| 8.064694554185326325E+00, |
| 8.873128656118993263E+01, |
| 6.977679035845269482E+02, |
| 4.096981198511257389E+03, |
| 1.574317583220441520E+04, |
| 2.899418134793237914E+04, |
| 1.498314766425578091E+04, |
| 9.225251570832365360E+02 } ; |
| double e[10] = { 7.101865971621337814E-04, |
| 1.912660677170175771E-08, |
| 9.167763417119923333E-08, |
| 3.769501719163865578E-07, |
| 6.973493131275552509E-07, |
| 1.205653952340679711E-07, |
| 1.380003928453846583E-07, |
| 1.934652413547325474E-07, |
| 3.408933028357320364E-07, |
| 2.132473175465897029E-09 } ; |
| int order[10] = { 1, 5, 4, 9, 8, 7, 6, 3, 2, 10 } ; |
| |
| double alpha = 5.0; |
| |
| gsl_function f = make_function(&f15, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qagiu (&fc, 0.0, 0.0, 1.0e-7, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qagiu(f15) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(f15) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qagiu(f15) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qagiu(f15) smooth last") ; |
| gsl_test_int(status,exp_ier,"qagiu(f15) smooth status") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(f15) smooth alist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(f15) smooth blist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qagiu(f15) smooth rlist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(f15) smooth elist") ; |
| |
| for (i = 0; i < 10 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qagiu(f15) smooth order"); |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test infinite range integral f16 using an absolute error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = 1.000000000006713292E-04; |
| double exp_abserr = 3.084062020905636316E-09; |
| int exp_neval = 165; |
| int exp_ier = 0; |
| int exp_last = 6; |
| |
| double a[6] = { 0.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02 } ; |
| double b[6] = { 3.125000000000000000E-02, |
| 1.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02 } ; |
| double r[6] = { 7.633587786326674618E-05, |
| 9.900990099009899620E-07, |
| 1.922522349322310737E-06, |
| 3.629434715543053753E-06, |
| 6.501422186103209199E-06, |
| 1.062064387653501389E-05 } ; |
| double e[6] = { 3.084061858351569051E-09, |
| 3.112064814755089674E-17, |
| 4.543453652226561245E-17, |
| 4.908618166361344548E-17, |
| 3.014338672269481784E-17, |
| 6.795996738013555461E-18 } ; |
| int order[6] = { 1, 4, 3, 2, 5, 6 } ; |
| |
| double alpha = 1.0; |
| |
| gsl_function f = make_function(&f16, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qagiu (&fc, 99.9, 1.0e-7, 0.0, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qagiu(f16) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(f16) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qagiu(f16) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qagiu(f16) smooth last") ; |
| gsl_test_int(status,exp_ier,"qagiu(f16) smooth status") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(f16) smooth alist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(f16) smooth blist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-15,"qagiu(f16) smooth rlist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(f16) smooth elist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qagiu(f16) smooth order"); |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test infinite range integral myfn1 using an absolute error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = 2.275875794468747770E+00; |
| double exp_abserr = 7.436490118267390744E-09; |
| int exp_neval = 270; |
| int exp_ier = 0; |
| int exp_last = 5; |
| |
| double a[5] = { 1.250000000000000000E-01, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 0.000000000000000000E+00, |
| 3.750000000000000000E-01 } ; |
| double b[5] = { 2.500000000000000000E-01, |
| 1.000000000000000000E+00, |
| 3.750000000000000000E-01, |
| 1.250000000000000000E-01, |
| 5.000000000000000000E-01 } ; |
| double r[5] = { 4.639317228058405717E-04, |
| 1.691664195356748834E+00, |
| 1.146307471900291086E-01, |
| 4.379392477350953574E-20, |
| 4.691169201991640669E-01 } ; |
| double e[5] = { 3.169263960393051137E-09, |
| 4.265988974874425043E-09, |
| 1.231954072964969637E-12, |
| 8.360902986775307673E-20, |
| 5.208244060463541433E-15 } ; |
| int order[5] = { 2, 1, 3, 5, 4 } ; |
| |
| gsl_function f = make_function(&myfn1, 0); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qagi (&fc, 1.0e-7, 0.0, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qagiu(myfn1) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(myfn1) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qagiu(myfn1) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qagiu(myfn1) smooth last") ; |
| gsl_test_int(status,exp_ier,"qagiu(myfn1) smooth status") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(myfn1) smooth alist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(myfn1) smooth blist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-14,"qagiu(myfn1) smooth rlist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(myfn1) smooth elist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qagiu(myfn1) smooth order"); |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test infinite range integral myfn1 using an absolute error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = 2.718281828459044647E+00; |
| double exp_abserr = 1.588185109253204805E-10; |
| int exp_neval = 135; |
| int exp_ier = 0; |
| int exp_last = 5; |
| |
| double a[5] = { 0.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02 } ; |
| double b[5] = { 6.250000000000000000E-02, |
| 1.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01 } ; |
| double r[5] = { 8.315287189746029816E-07, |
| 1.718281828459045091E+00, |
| 8.646647167633871867E-01, |
| 1.328565310599463256E-01, |
| 2.477920647947255521E-03 } ; |
| double e[5] = { 1.533437090413525935E-10, |
| 4.117868247943567505E-12, |
| 7.802455785301941044E-13, |
| 5.395586026138397182E-13, |
| 3.713312434866150125E-14 } ; |
| int order[5] = { 1, 2, 3, 4, 5 } ; |
| |
| double alpha = 1.0 ; |
| gsl_function f = make_function(&myfn2, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qagil (&fc, 1.0, 1.0e-7, 0.0, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qagiu(myfn2) smooth result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qagiu(myfn2) smooth abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qagiu(myfn2) smooth neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qagiu(myfn2) smooth last") ; |
| gsl_test_int(status,exp_ier,"qagiu(myfn2) smooth status") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qagiu(myfn2) smooth alist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qagiu(myfn2) smooth blist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-14,"qagiu(myfn2) smooth rlist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qagiu(myfn2) smooth elist") ; |
| |
| for (i = 0; i < 5 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qagiu(myfn2) smooth order"); |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test integral f454 with integrable singular points */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = 5.274080611672716401E+01; |
| double exp_abserr = 1.755703848687062418E-04; |
| int exp_neval = 777; |
| int exp_ier = 0; |
| int exp_last = 20; |
| |
| double a[20] = { 9.687500000000000000E-01, |
| 1.401269388548935790E+00, |
| 1.414213562373095145E+00, |
| 1.000000000000000000E+00, |
| 0.000000000000000000E+00, |
| 2.207106781186547462E+00, |
| 1.810660171779821415E+00, |
| 1.207106781186547462E+00, |
| 5.000000000000000000E-01, |
| 1.103553390593273731E+00, |
| 1.612436867076458391E+00, |
| 1.310660171779821415E+00, |
| 7.500000000000000000E-01, |
| 1.051776695296636976E+00, |
| 1.513325214724776657E+00, |
| 1.362436867076458391E+00, |
| 8.750000000000000000E-01, |
| 1.463769388548935790E+00, |
| 1.388325214724776657E+00, |
| 9.375000000000000000E-01} ; |
| double b[20] = { 1.000000000000000000E+00, |
| 1.414213562373095145E+00, |
| 1.463769388548935790E+00, |
| 1.051776695296636976E+00, |
| 5.000000000000000000E-01, |
| 3.000000000000000000E+00, |
| 2.207106781186547462E+00, |
| 1.310660171779821415E+00, |
| 7.500000000000000000E-01, |
| 1.207106781186547462E+00, |
| 1.810660171779821415E+00, |
| 1.362436867076458391E+00, |
| 8.750000000000000000E-01, |
| 1.103553390593273731E+00, |
| 1.612436867076458391E+00, |
| 1.388325214724776657E+00, |
| 9.375000000000000000E-01, |
| 1.513325214724776657E+00, |
| 1.401269388548935790E+00, |
| 9.687500000000000000E-01} ; |
| double r[20] = { -1.125078814079027711E-01, |
| -1.565132123531515207E-01, |
| -4.225328513207429193E-01, |
| -1.830392049835374568E-01, |
| 6.575875041899758092E-03, |
| 4.873920540843067783E+01, |
| 6.032891565603589079E+00, |
| -2.991531901645863023E-01, |
| -7.326282608704996063E-03, |
| -2.431894410706912923E-01, |
| 5.911661670635662835E-01, |
| -2.236786562536174916E-01, |
| -5.647871991778510847E-02, |
| -1.305470403178642658E-01, |
| -1.721363984401322045E-01, |
| -1.589345454585119055E-01, |
| -7.406626263352669715E-02, |
| -2.208730668000830344E-01, |
| -1.048692749517999567E-01, |
| -6.302287584527696551E-02} ; |
| double e[20] = { 2.506431410088378817E-02, |
| 2.730454695485963826E-02, |
| 1.017446081816190118E-01, |
| 3.252808038935910834E-02, |
| 7.300687878575027348E-17, |
| 5.411138804637469780E-13, |
| 6.697855121200013106E-14, |
| 3.321267596107916554E-15, |
| 1.417509685426979386E-16, |
| 2.699945168224041491E-15, |
| 6.573952690524728748E-15, |
| 2.483331942899818875E-15, |
| 6.270397525408045936E-16, |
| 1.449363299575615261E-15, |
| 1.911097929242846383E-15, |
| 1.764527917763735212E-15, |
| 8.223007012367522077E-16, |
| 2.452183642810224359E-15, |
| 1.164282836272345215E-15, |
| 6.996944784151910810E-16} ; |
| int order[20] = { 3, 4, 2, 1, 6, 7, 11, 8, 10, 12, 18, |
| 15, 16, 14, 19, 17, 20, 13, 9, 5 } ; |
| |
| gsl_function f = make_function(&f454, 0); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| double pts[4] ; |
| |
| pts[0] = 0.0; |
| pts[1] = 1.0; |
| pts[2] = sqrt(2.0); |
| pts[3] = 3.0; |
| |
| status = gsl_integration_qagp (&fc, pts, 4, |
| 0.0, 1.0e-3, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qagp(f454) singular result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-5,"qagp(f454) singular abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qagp(f454) singular neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qagp(f454) singular last") ; |
| gsl_test_int(status,exp_ier,"qagp(f454) singular status") ; |
| |
| for (i = 0; i < 20 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qagp(f454) singular alist") ; |
| |
| for (i = 0; i < 20 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qagp(f454) singular blist") ; |
| |
| for (i = 0; i < 20 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-14,"qagp(f454) singular rlist") ; |
| |
| for (i = 0; i < 20 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qagp(f454) singular elist") ; |
| |
| for (i = 0; i < 20 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qagp(f454) singular order"); |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| |
| /* Test cauchy integration using a relative error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = -8.994400695837000137E-02; |
| double exp_abserr = 1.185290176227023727E-06; |
| int exp_neval = 215; |
| int exp_ier = 0; |
| int exp_last = 6; |
| |
| double a[6] = { -1.000000000000000000E+00, |
| 2.500000000000000000E+00, |
| 1.250000000000000000E+00, |
| 6.250000000000000000E-01, |
| -5.000000000000000000E-01, |
| -7.500000000000000000E-01} ; |
| double b[6] = { -7.500000000000000000E-01, |
| 5.000000000000000000E+00, |
| 2.500000000000000000E+00, |
| 1.250000000000000000E+00, |
| 6.250000000000000000E-01, |
| -5.000000000000000000E-01} ; |
| double r[6] = { -1.234231128040012976E-01, |
| 3.579970394639702888E-03, |
| 2.249831615049339983E-02, |
| 7.214232992127905808E-02, |
| 2.079093855884046535E-02, |
| -8.553244917962132821E-02} ; |
| double e[6] = { 1.172832717970022565E-06, |
| 9.018232896137375412E-13, |
| 1.815172652101790755E-12, |
| 1.006998195150956048E-13, |
| 1.245463873006391609E-08, |
| 1.833082948207153514E-15 } ; |
| int order[6] = { 1, 5, 3, 2, 4, 6 } ; |
| |
| double alpha = 1.0 ; |
| gsl_function f = make_function(&f459, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qawc (&fc, -1.0, 5.0, 0.0, 0.0, 1.0e-3, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qawc(f459) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qawc(f459) abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qawc(f459) neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qawc(f459) last") ; |
| gsl_test_int(status,exp_ier,"qawc(f459) status") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qawc(f459) alist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qawc(f459) blist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-14,"qawc(f459) rlist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-5,"qawc(f459) elist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qawc(f459) order"); |
| |
| p.neval = 0; |
| status = gsl_integration_qawc (&fc, 5.0, -1.0, 0.0, 0.0, 1.0e-3, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-14,"qawc(f459) rev result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qawc(f459) rev abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qawc(f459) rev neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qawc(f459) rev last") ; |
| gsl_test_int(status,exp_ier,"qawc(f459) rev status") ; |
| |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test QAWS singular integration using a relative error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_qaws_table * t |
| = gsl_integration_qaws_table_alloc (0.0, 0.0, 1, 0); |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = -1.892751853489401670E-01; |
| double exp_abserr = 1.129133712015747658E-08; |
| int exp_neval = 280; |
| int exp_ier = 0; |
| int exp_last = 8; |
| |
| double a[8] = { 0.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02, |
| 1.562500000000000000E-02, |
| 7.812500000000000000E-03} ; |
| double b[8] = { 7.812500000000000000E-03, |
| 1.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02, |
| 1.562500000000000000E-02} ; |
| double r[8] = { -4.126317299834445824E-05, |
| -1.076283950172247789E-01, |
| -6.240573216173390947E-02, |
| -1.456169844189576269E-02, |
| -3.408925115926728436E-03, |
| -8.914083918175634211E-04, |
| -2.574191402137795482E-04, |
| -8.034390712936630608E-05} ; |
| double e[8] = { 1.129099387465713953E-08, |
| 3.423394967694403596E-13, |
| 6.928428071454762659E-16, |
| 1.616673288784094320E-16, |
| 3.784667152924835070E-17, |
| 9.896621209399419425E-18, |
| 2.857926564445496100E-18, |
| 8.919965558336773736E-19} ; |
| int order[8] = { 1, 2, 3, 4, 5, 6, 7, 8 } ; |
| |
| double alpha = 1.0 ; |
| gsl_function f = make_function(&f458, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qaws (&fc, 0.0, 1.0, t, 0.0, 1.0e-7, w->limit, |
| w, |
| &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qaws(f458) ln(x-a) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qaws(f458) ln(x-a) abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qaws(f458) ln(x-a) neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qaws(f458) ln(x-a) last") ; |
| gsl_test_int(status,exp_ier,"qaws(f458) ln(x-a) status") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qaws(f458) ln(x-a) alist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qaws(f458) ln(x-a) blist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-14,"qaws(f458) ln(x-a) rlist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-4,"qaws(f458) ln(x-a) elist") ; |
| |
| for (i = 0; i < 6 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qaws(f458) ln(x-a) order"); |
| |
| /* Test without logs */ |
| |
| gsl_integration_qaws_table_set (t, -0.5, -0.3, 0, 0); |
| |
| status = gsl_integration_qaws (&fc, 0.0, 1.0, t, 0.0, 1.0e-7, w->limit, |
| w, &result, &abserr) ; |
| |
| exp_result = 9.896686656601706433E-01; |
| exp_abserr = 5.888032513201251628E-08; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qaws(f458) AB result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qaws(f458) AB abserr") ; |
| |
| /* Test with ln(x - a) */ |
| |
| gsl_integration_qaws_table_set (t, -0.5, -0.3, 1, 0); |
| |
| status = gsl_integration_qaws (&fc, 0.0, 1.0, t, 0.0, 1.0e-7, w->limit, |
| w, &result, &abserr) ; |
| |
| exp_result = -3.636679470586539620E-01; |
| exp_abserr = 2.851348775257054093E-08; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qaws(f458) AB ln(x-a) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qaws(f458) AB ln(x-a) abserr") ; |
| |
| /* Test with ln(b - x) */ |
| |
| gsl_integration_qaws_table_set (t, -0.5, -0.3, 0, 1); |
| |
| status = gsl_integration_qaws (&fc, 0.0, 1.0, t, 0.0, 1.0e-7, w->limit, |
| w, &result, &abserr) ; |
| |
| exp_result = -1.911489253363409802E+00; |
| exp_abserr = 9.854016753016499034E-09; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qaws(f458) AB ln(b-x) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qaws(f458) AB ln(b-x) abserr") ; |
| |
| /* Test with ln(x - a) ln(b - x) */ |
| |
| gsl_integration_qaws_table_set (t, -0.5, -0.3, 1, 1); |
| |
| status = gsl_integration_qaws (&fc, 0.0, 1.0, t, 0.0, 1.0e-7, w->limit, |
| w, &result, &abserr) ; |
| |
| exp_result = 3.159922862811048172E-01; |
| exp_abserr = 2.336183482198144595E-08; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qaws(f458) AB ln(x-a)ln(b-x) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-6,"qaws(f458) AB ln(x-a)ln(b-x) abserr") ; |
| |
| gsl_integration_workspace_free (w) ; |
| gsl_integration_qaws_table_free (t) ; |
| |
| } |
| |
| |
| /* Test oscillatory integration using a relative error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| gsl_integration_qawo_table * wo |
| = gsl_integration_qawo_table_alloc (10.0 * M_PI, 1.0, |
| GSL_INTEG_SINE, 1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = -1.281368483991674190E-01; |
| double exp_abserr = 6.875028324415666248E-12; |
| int exp_neval = 305; |
| int exp_ier = 0; |
| int exp_last = 9; |
| |
| double a[9] = { 0.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02, |
| 1.562500000000000000E-02, |
| 7.812500000000000000E-03, |
| 3.906250000000000000E-03 } ; |
| double b[9] = { 3.906250000000000000E-03, |
| 1.000000000000000000E+00, |
| 5.000000000000000000E-01, |
| 2.500000000000000000E-01, |
| 1.250000000000000000E-01, |
| 6.250000000000000000E-02, |
| 3.125000000000000000E-02, |
| 1.562500000000000000E-02, |
| 7.812500000000000000E-03 } ; |
| double r[9] = { -1.447193692377651136E-03, |
| 2.190541162282139478E-02, |
| -2.587726479625663753E-02, |
| 5.483209176363500886E-02, |
| -3.081695575172510582E-02, |
| -9.178321994387816929E-02, |
| -3.886716016498160953E-02, |
| -1.242306301902117854E-02, |
| -3.659495117871544145E-03} ; |
| double e[9] = { 8.326506625798146465E-07, |
| 1.302638552580516100E-13, |
| 7.259224351945759794E-15, |
| 1.249770395036711102E-14, |
| 7.832180081562836579E-16, |
| 1.018998440559284116E-15, |
| 4.315121611695628020E-16, |
| 1.379237060008662177E-16, |
| 4.062855738364339357E-17 } ; |
| int order[9] = { 1, 2, 4, 3, 6, 5, 7, 8, 9 } ; |
| |
| double alpha = 1.0 ; |
| gsl_function f = make_function(&f456, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qawo (&fc, 0.0, 0.0, 1e-7, w->limit, |
| w, wo, &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qawo(f456) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-3,"qawo(f456) abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qawo(f456) neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qawo(f456) last") ; |
| gsl_test_int(status,exp_ier,"qawo(f456) status") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->alist[i],a[i],1e-15,"qawo(f456) alist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->blist[i],b[i],1e-15,"qawo(f456) blist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-14,"qawo(f456) rlist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->elist[i],e[i],1e-3,"qawo(f456) elist") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_int((int)w->order[i],order[i]-1,"qawo(f456) order"); |
| |
| |
| /* In reverse, flip limit and sign of length */ |
| |
| gsl_integration_qawo_table_set_length (wo, -1.0); |
| |
| p.neval = 0; |
| status = gsl_integration_qawo (&fc, 1.0, 0.0, 1e-7, w->limit, |
| w, wo, &result, &abserr) ; |
| |
| gsl_test_rel(result,-exp_result,1e-14,"qawo(f456) rev result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-3,"qawo(f456) rev abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qawo(f456) rev neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qawo(f456) rev last") ; |
| gsl_test_int(status,exp_ier,"qawo(f456) rev status") ; |
| |
| |
| gsl_integration_qawo_table_free (wo) ; |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| /* Test fourier integration using an absolute error bound */ |
| |
| { |
| int status = 0, i; struct counter_params p; |
| double result = 0, abserr=0; |
| |
| gsl_integration_workspace * w = gsl_integration_workspace_alloc (1000) ; |
| gsl_integration_workspace * wc = gsl_integration_workspace_alloc (1000) ; |
| gsl_integration_qawo_table * wo |
| = gsl_integration_qawo_table_alloc (M_PI / 2.0, 1.0, |
| GSL_INTEG_COSINE, 1000) ; |
| |
| /* All results are for GSL_IEEE_MODE=double-precision */ |
| |
| double exp_result = 9.999999999279802765E-01; |
| double exp_abserr = 1.556289974669056164E-08; |
| int exp_neval = 590; |
| int exp_ier = 0; |
| int exp_last = 12; |
| |
| double r[12] = { 1.013283128125232802E+00, |
| -1.810857954748607349E-02, |
| 7.466754034900931897E-03, |
| -4.360312526786496237E-03, |
| 2.950184068216192904E-03, |
| -2.168238443073697373E-03, |
| 1.680910783140869081E-03, |
| -1.352797860944863345E-03, |
| 1.119354921991485901E-03, |
| -9.462367583691360827E-04, |
| 8.136341270731781887E-04, |
| -7.093931338504278145E-04 } ; |
| double e[12] = { 1.224798040766472695E-12, |
| 1.396565155187268456E-13, |
| 1.053844511655910310E-16, |
| 6.505213034913026604E-19, |
| 7.155734338404329264E-18, |
| 1.105886215935214523E-17, |
| 9.757819552369539906E-18, |
| 5.854691731421723944E-18, |
| 4.553649124439220312E-18, |
| 7.643625316022806260E-18, |
| 2.439454888092388058E-17, |
| 2.130457268934021451E-17 } ; |
| |
| double alpha = 1.0 ; |
| gsl_function f = make_function(&f457, &alpha); |
| gsl_function fc = make_counter(&f, &p) ; |
| |
| status = gsl_integration_qawf (&fc, 0.0, 1e-7, w->limit, |
| w, wc, wo, &result, &abserr) ; |
| |
| gsl_test_rel(result,exp_result,1e-14,"qawf(f457) result") ; |
| gsl_test_rel(abserr,exp_abserr,1e-3,"qawf(f457) abserr") ; |
| gsl_test_int((int)(p.neval),exp_neval,"qawf(f457) neval") ; |
| gsl_test_int((int)(w->size),exp_last,"qawf(f457) last") ; |
| gsl_test_int(status,exp_ier,"qawf(f457) status") ; |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->rlist[i],r[i],1e-12,"qawf(f457) rlist") ; |
| |
| /* We can only get within two orders of magnitude on the error |
| here, which is very sensitive to the floating point precision */ |
| |
| for (i = 0; i < 9 ; i++) |
| gsl_test_rel(w->elist[i],e[i],50.0,"qawf(f457) elist") ; |
| |
| |
| gsl_integration_qawo_table_free (wo) ; |
| gsl_integration_workspace_free (wc) ; |
| gsl_integration_workspace_free (w) ; |
| |
| } |
| |
| exit (gsl_test_summary()); |
| } |
| |
| void |
| my_error_handler (const char *reason, const char *file, int line, int err) |
| { |
| if (0) printf ("(caught [%s:%d: %s (%d)])\n", file, line, reason, err) ; |
| } |
| |
| |
