1 /* integration/jacobi.c
2 *
3 * Copyright (C) 2017 Konrad Griessinger, Patrick Alken
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20 /*
21 * The code in this module is based on IQPACK, specifically the LGPL
22 * implementation found in HERMITE_RULE:
23 * https://people.sc.fsu.edu/~jburkardt/c_src/hermite_rule/hermite_rule.html
24 */
25
26 #include <stdio.h>
27 #include <gsl/gsl_errno.h>
28 #include <gsl/gsl_math.h>
29 #include <gsl/gsl_integration.h>
30 #include <gsl/gsl_sf_gamma.h>
31
32 static int
jacobi_check(const size_t n,const gsl_integration_fixed_params * params)33 jacobi_check(const size_t n, const gsl_integration_fixed_params * params)
34 {
35 (void) n;
36
37 if (fabs(params->b - params->a) <= GSL_DBL_EPSILON)
38 {
39 GSL_ERROR("|b - a| too small", GSL_EDOM);
40 }
41 else if (params->a >= params->b)
42 {
43 GSL_ERROR("lower integration limit must be smaller than upper limit", GSL_EDOM);
44 }
45 else if (params->alpha <= -1.0 || params->beta <= -1.0)
46 {
47 GSL_ERROR("alpha and beta must be > -1", GSL_EDOM);
48 }
49 else
50 {
51 return GSL_SUCCESS;
52 }
53 }
54
55 static int
jacobi_init(const size_t n,double * diag,double * subdiag,gsl_integration_fixed_params * params)56 jacobi_init(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params)
57 {
58 const double absum = params->beta + params->alpha;
59 const double abdiff = params->beta - params->alpha;
60 const double a2b2 = absum * abdiff; /* beta^2 - alpha^2 */
61 size_t i;
62
63 /* construct the diagonal and subdiagonal elements of Jacobi matrix */
64 diag[0] = abdiff/(absum + 2.0);
65 subdiag[0] = 2.0*sqrt((params->alpha + 1.0)*(params->beta + 1.0)/(absum + 3.0))/(absum + 2.0);
66 for (i = 1; i < n; i++)
67 {
68 diag[i] = a2b2 / ( (absum + 2.0*i) * (absum + 2.0*i + 2.0) );
69 subdiag[i] = sqrt ( 4.0*(i + 1.0) * (params->alpha + i + 1.0) * (params->beta + i + 1.0) * (absum + i + 1.0) / ( pow((absum + 2.0*i + 2.0), 2.0) - 1.0 ) ) / ( absum + 2.0*i + 2.0 );
70 }
71
72 params->zemu = pow(2.0, absum + 1.0) * gsl_sf_gamma(params->alpha + 1.0) * gsl_sf_gamma(params->beta + 1.0) / gsl_sf_gamma(absum + 2.0);
73 params->shft = 0.5*(params->b + params->a);
74 params->slp = 0.5*(params->b - params->a);
75 params->al = params->alpha;
76 params->be = params->beta;
77
78 return GSL_SUCCESS;
79 }
80
81 static const gsl_integration_fixed_type jacobi_type =
82 {
83 jacobi_check,
84 jacobi_init
85 };
86
87 const gsl_integration_fixed_type *gsl_integration_fixed_jacobi = &jacobi_type;
88