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- /* specfunc/recurse.h
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
- *
- * 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 3 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 _RECURSE_H_
- #define _RECURSE_H_
- #define CONCAT(a,b) a ## _ ## b
- /* n_max >= n_min + 2
- * f[n+1] + a[n] f[n] + b[n] f[n-1] = 0
- *
- * Trivial forward recurrence.
- */
- #define GEN_RECURSE_FORWARD_SIMPLE(func) \
- int CONCAT(recurse_forward_simple, func) ( \
- const int n_max, const int n_min, \
- const double parameters[], \
- const double f_n_min, \
- const double f_n_min_p1, \
- double * f, \
- double * f_n_max \
- ) \
- { \
- int n; \
- \
- if(f == 0) { \
- double f2 = f_n_min; \
- double f1 = f_n_min_p1; \
- double f0; \
- for(n=n_min+2; n<=n_max; n++) { \
- f0 = -REC_COEFF_A(n-1,parameters) * f1 - REC_COEFF_B(n-1, parameters) * f2; \
- f2 = f1; \
- f1 = f0; \
- } \
- *f_n_max = f0; \
- } \
- else { \
- f[n_min] = f_n_min; \
- f[n_min + 1] = f_n_min_p1; \
- for(n=n_min+2; n<=n_max; n++) { \
- f[n] = -REC_COEFF_A(n-1,parameters) * f[n-1] - REC_COEFF_B(n-1, parameters) * f[n-2]; \
- } \
- *f_n_max = f[n_max]; \
- } \
- \
- return GSL_SUCCESS; \
- } \
- /* n_start >= n_max >= n_min
- * f[n+1] + a[n] f[n] + b[n] f[n-1] = 0
- *
- * Generate the minimal solution of the above recursion relation,
- * with the simplest form of the normalization condition, f[n_min] given.
- * [Gautschi, SIAM Rev. 9, 24 (1967); (3.9) with s[n]=0]
- */
- #define GEN_RECURSE_BACKWARD_MINIMAL_SIMPLE(func) \
- int CONCAT(recurse_backward_minimal_simple, func) ( \
- const int n_start, \
- const int n_max, const int n_min, \
- const double parameters[], \
- const double f_n_min, \
- double * f, \
- double * f_n_max \
- ) \
- { \
- int n; \
- double r_n = 0.; \
- double r_nm1; \
- double ratio; \
- \
- for(n=n_start; n > n_max; n--) { \
- r_nm1 = -REC_COEFF_B(n, parameters) / (REC_COEFF_A(n, parameters) + r_n); \
- r_n = r_nm1; \
- } \
- \
- if(f != 0) { \
- f[n_max] = 10.*DBL_MIN; \
- for(n=n_max; n > n_min; n--) { \
- r_nm1 = -REC_COEFF_B(n, parameters) / (REC_COEFF_A(n, parameters) + r_n); \
- f[n-1] = f[n] / r_nm1; \
- r_n = r_nm1; \
- } \
- ratio = f_n_min / f[n_min]; \
- for(n=n_min; n<=n_max; n++) { \
- f[n] *= ratio; \
- } \
- } \
- else { \
- double f_nm1; \
- double f_n = 10.*DBL_MIN; \
- *f_n_max = f_n; \
- for(n=n_max; n > n_min; n--) { \
- r_nm1 = -REC_COEFF_B(n, parameters) / (REC_COEFF_A(n, parameters) + r_n); \
- f_nm1 = f_n / r_nm1; \
- r_n = r_nm1; \
- } \
- ratio = f_n_min / f_nm1; \
- *f_n_max *= ratio; \
- } \
- \
- return GSL_SUCCESS; \
- } \
- #endif /* !_RECURSE_H_ */
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