diff options
Diffstat (limited to 'gsl-1.9/sum/levin_utrunc.c')
-rw-r--r-- | gsl-1.9/sum/levin_utrunc.c | 202 |
1 files changed, 202 insertions, 0 deletions
diff --git a/gsl-1.9/sum/levin_utrunc.c b/gsl-1.9/sum/levin_utrunc.c new file mode 100644 index 0000000..16a3f16 --- /dev/null +++ b/gsl-1.9/sum/levin_utrunc.c @@ -0,0 +1,202 @@ +/* sum/levin_utrunc.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman, 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. + */ + +/* Author: G. Jungman */ + +#include <config.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_test.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_sum.h> + +int +gsl_sum_levin_utrunc_accel (const double *array, + const size_t array_size, + gsl_sum_levin_utrunc_workspace * w, + double *sum_accel, double *abserr_trunc) +{ + return gsl_sum_levin_utrunc_minmax (array, array_size, + 0, array_size - 1, + w, sum_accel, abserr_trunc); +} + + +int +gsl_sum_levin_utrunc_minmax (const double *array, + const size_t array_size, + const size_t min_terms, + const size_t max_terms, + gsl_sum_levin_utrunc_workspace * w, + double *sum_accel, double *abserr_trunc) +{ + if (array_size == 0) + { + *sum_accel = 0.0; + *abserr_trunc = 0.0; + w->sum_plain = 0.0; + w->terms_used = 0; + return GSL_SUCCESS; + } + else if (array_size == 1) + { + *sum_accel = array[0]; + *abserr_trunc = GSL_POSINF; + w->sum_plain = array[0]; + w->terms_used = 1; + return GSL_SUCCESS; + } + else + { + const double SMALL = 0.01; + const size_t nmax = GSL_MAX (max_terms, array_size) - 1; + double trunc_n = 0.0, trunc_nm1 = 0.0; + double actual_trunc_n = 0.0, actual_trunc_nm1 = 0.0; + double result_n = 0.0, result_nm1 = 0.0; + size_t n; + int better = 0; + int before = 0; + int converging = 0; + double least_trunc = GSL_DBL_MAX; + double result_least_trunc; + + /* Calculate specified minimum number of terms. No convergence + tests are made, and no truncation information is stored. */ + + for (n = 0; n < min_terms; n++) + { + const double t = array[n]; + + result_nm1 = result_n; + gsl_sum_levin_utrunc_step (t, n, w, &result_n); + } + + /* Assume the result after the minimum calculation is the best. */ + + result_least_trunc = result_n; + + /* Calculate up to maximum number of terms. Check truncation + condition. */ + + for (; n <= nmax; n++) + { + const double t = array[n]; + + result_nm1 = result_n; + gsl_sum_levin_utrunc_step (t, n, w, &result_n); + + /* Compute the truncation error directly */ + + actual_trunc_nm1 = actual_trunc_n; + actual_trunc_n = fabs (result_n - result_nm1); + + /* Average results to make a more reliable estimate of the + real truncation error */ + + trunc_nm1 = trunc_n; + trunc_n = 0.5 * (actual_trunc_n + actual_trunc_nm1); + + /* Determine if we are in the convergence region. */ + + better = (trunc_n < trunc_nm1 || trunc_n < SMALL * fabs (result_n)); + converging = converging || (better && before); + before = better; + + if (converging) + { + if (trunc_n < least_trunc) + { + /* Found a low truncation point in the convergence + region. Save it. */ + + least_trunc = trunc_n; + result_least_trunc = result_n; + } + + if (fabs (trunc_n / result_n) < 10.0 * GSL_MACH_EPS) + break; + } + } + + if (converging) + { + /* Stopped in the convergence region. Return result and + error estimate. */ + + *sum_accel = result_least_trunc; + *abserr_trunc = least_trunc; + w->terms_used = n; + return GSL_SUCCESS; + } + else + { + /* Never reached the convergence region. Use the last + calculated values. */ + + *sum_accel = result_n; + *abserr_trunc = trunc_n; + w->terms_used = n; + return GSL_SUCCESS; + } + } +} + +int +gsl_sum_levin_utrunc_step (const double term, + const size_t n, + gsl_sum_levin_utrunc_workspace * w, double *sum_accel) +{ + if (term == 0.0) + { + /* This is actually harmless when treated in this way. A term + which is exactly zero is simply ignored; the state is not + changed. We return GSL_EZERODIV as an indicator that this + occured. */ + + return GSL_EZERODIV; + } + else if (n == 0) + { + *sum_accel = term; + w->sum_plain = term; + w->q_den[0] = 1.0 / term; + w->q_num[0] = 1.0; + return GSL_SUCCESS; + } + else + { + double factor = 1.0; + double ratio = (double) n / (n + 1.0); + int j; + + w->sum_plain += term; + w->q_den[n] = 1.0 / (term * (n + 1.0) * (n + 1.0)); + w->q_num[n] = w->sum_plain * w->q_den[n]; + + for (j = n - 1; j >= 0; j--) + { + double c = factor * (j + 1) / (n + 1); + factor *= ratio; + w->q_den[j] = w->q_den[j + 1] - c * w->q_den[j]; + w->q_num[j] = w->q_num[j + 1] - c * w->q_num[j]; + } + + *sum_accel = w->q_num[0] / w->q_den[0]; + return GSL_SUCCESS; + } +} |