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Diffstat (limited to 'gsl-1.9/sum/gsl_sum.h')
| -rw-r--r-- | gsl-1.9/sum/gsl_sum.h | 162 |
1 files changed, 162 insertions, 0 deletions
diff --git a/gsl-1.9/sum/gsl_sum.h b/gsl-1.9/sum/gsl_sum.h new file mode 100644 index 0000000..4f7a66e --- /dev/null +++ b/gsl-1.9/sum/gsl_sum.h @@ -0,0 +1,162 @@ +/* sum/gsl_sum.h + * + * 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 */ + + +#ifndef __GSL_SUM_H__ +#define __GSL_SUM_H__ + +#include <stdlib.h> + +#undef __BEGIN_DECLS +#undef __END_DECLS +#ifdef __cplusplus +# define __BEGIN_DECLS extern "C" { +# define __END_DECLS } +#else +# define __BEGIN_DECLS /* empty */ +# define __END_DECLS /* empty */ +#endif + +__BEGIN_DECLS + +/* Workspace for Levin U Transform with error estimation, + * + * size = number of terms the workspace can handle + * sum_plain = simple sum of series + * q_num = backward diagonal of numerator; length = size + * q_den = backward diagonal of denominator; length = size + * dq_num = table of numerator derivatives; length = size**2 + * dq_den = table of denominator derivatives; length = size**2 + * dsum = derivative of sum wrt term i; length = size + */ + +typedef struct +{ + size_t size; + size_t i; /* position in array */ + size_t terms_used; /* number of calls */ + double sum_plain; + double *q_num; + double *q_den; + double *dq_num; + double *dq_den; + double *dsum; +} +gsl_sum_levin_u_workspace; + +gsl_sum_levin_u_workspace *gsl_sum_levin_u_alloc (size_t n); +void gsl_sum_levin_u_free (gsl_sum_levin_u_workspace * w); + +/* Basic Levin-u acceleration method. + * + * array = array of series elements + * n = size of array + * sum_accel = result of summation acceleration + * err = estimated error + * + * See [Fessler et al., ACM TOMS 9, 346 (1983) and TOMS-602] + */ + +int gsl_sum_levin_u_accel (const double *array, + const size_t n, + gsl_sum_levin_u_workspace * w, + double *sum_accel, double *abserr); + +/* Basic Levin-u acceleration method with constraints on the terms + * used, + * + * array = array of series elements + * n = size of array + * min_terms = minimum number of terms to sum + * max_terms = maximum number of terms to sum + * sum_accel = result of summation acceleration + * err = estimated error + * + * See [Fessler et al., ACM TOMS 9, 346 (1983) and TOMS-602] + */ + +int gsl_sum_levin_u_minmax (const double *array, + const size_t n, + const size_t min_terms, + const size_t max_terms, + gsl_sum_levin_u_workspace * w, + double *sum_accel, double *abserr); + +/* Basic Levin-u step w/o reference to the array of terms. + * We only need to specify the value of the current term + * to execute the step. See TOMS-745. + * + * sum = t0 + ... + t_{n-1} + term; term = t_{n} + * + * term = value of the series term to be added + * n = position of term in series (starting from 0) + * sum_accel = result of summation acceleration + * sum_plain = simple sum of series + */ + +int +gsl_sum_levin_u_step (const double term, + const size_t n, + const size_t nmax, + gsl_sum_levin_u_workspace * w, + double *sum_accel); + +/* The following functions perform the same calculation without + estimating the errors. They require O(N) storage instead of O(N^2). + This may be useful for summing many similar series where the size + of the error has already been estimated reliably and is not + expected to change. */ + +typedef struct +{ + size_t size; + size_t i; /* position in array */ + size_t terms_used; /* number of calls */ + double sum_plain; + double *q_num; + double *q_den; + double *dsum; +} +gsl_sum_levin_utrunc_workspace; + +gsl_sum_levin_utrunc_workspace *gsl_sum_levin_utrunc_alloc (size_t n); +void gsl_sum_levin_utrunc_free (gsl_sum_levin_utrunc_workspace * w); + +int gsl_sum_levin_utrunc_accel (const double *array, + const size_t n, + gsl_sum_levin_utrunc_workspace * w, + double *sum_accel, double *abserr_trunc); + +int gsl_sum_levin_utrunc_minmax (const double *array, + const size_t n, + const size_t min_terms, + const size_t max_terms, + gsl_sum_levin_utrunc_workspace * w, + double *sum_accel, double *abserr_trunc); + +int gsl_sum_levin_utrunc_step (const double term, + const size_t n, + gsl_sum_levin_utrunc_workspace * w, + double *sum_accel); + +__END_DECLS + +#endif /* __GSL_SUM_H__ */ |