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/* 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__ */
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