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Diffstat (limited to 'gsl-1.9/specfunc/coupling.c')
| -rw-r--r-- | gsl-1.9/specfunc/coupling.c | 439 |
1 files changed, 439 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/coupling.c b/gsl-1.9/specfunc/coupling.c new file mode 100644 index 0000000..b7ae4d0 --- /dev/null +++ b/gsl-1.9/specfunc/coupling.c @@ -0,0 +1,439 @@ +/* specfunc/coupling.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002 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 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 <stdlib.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_sf_gamma.h> +#include <gsl/gsl_sf_coupling.h> + +#include "error.h" + +inline +static +int locMax3(const int a, const int b, const int c) +{ + int d = GSL_MAX(a, b); + return GSL_MAX(d, c); +} + +inline +static +int locMin3(const int a, const int b, const int c) +{ + int d = GSL_MIN(a, b); + return GSL_MIN(d, c); +} + +inline +static +int locMin5(const int a, const int b, const int c, const int d, const int e) +{ + int f = GSL_MIN(a, b); + int g = GSL_MIN(c, d); + int h = GSL_MIN(f, g); + return GSL_MIN(e, h); +} + + +/* See: [Thompson, Atlas for Computing Mathematical Functions] */ + +static +int +delta(int ta, int tb, int tc, gsl_sf_result * d) +{ + gsl_sf_result f1, f2, f3, f4; + int status = 0; + status += gsl_sf_fact_e((ta + tb - tc)/2, &f1); + status += gsl_sf_fact_e((ta + tc - tb)/2, &f2); + status += gsl_sf_fact_e((tb + tc - ta)/2, &f3); + status += gsl_sf_fact_e((ta + tb + tc)/2 + 1, &f4); + if(status != 0) { + OVERFLOW_ERROR(d); + } + d->val = f1.val * f2.val * f3.val / f4.val; + d->err = 4.0 * GSL_DBL_EPSILON * fabs(d->val); + return GSL_SUCCESS; +} + + +static +int +triangle_selection_fails(int two_ja, int two_jb, int two_jc) +{ + return ((two_jb < abs(two_ja - two_jc)) || (two_jb > two_ja + two_jc)); +} + + +static +int +m_selection_fails(int two_ja, int two_jb, int two_jc, + int two_ma, int two_mb, int two_mc) +{ + return ( + abs(two_ma) > two_ja + || abs(two_mb) > two_jb + || abs(two_mc) > two_jc + || GSL_IS_ODD(two_ja + two_ma) + || GSL_IS_ODD(two_jb + two_mb) + || GSL_IS_ODD(two_jc + two_mc) + || (two_ma + two_mb + two_mc) != 0 + ); +} + + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + + +int +gsl_sf_coupling_3j_e (int two_ja, int two_jb, int two_jc, + int two_ma, int two_mb, int two_mc, + gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(two_ja < 0 || two_jb < 0 || two_jc < 0) { + DOMAIN_ERROR(result); + } + else if ( triangle_selection_fails(two_ja, two_jb, two_jc) + || m_selection_fails(two_ja, two_jb, two_jc, two_ma, two_mb, two_mc) + ) { + result->val = 0.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else { + int jca = (-two_ja + two_jb + two_jc) / 2, + jcb = ( two_ja - two_jb + two_jc) / 2, + jcc = ( two_ja + two_jb - two_jc) / 2, + jmma = ( two_ja - two_ma) / 2, + jmmb = ( two_jb - two_mb) / 2, + jmmc = ( two_jc - two_mc) / 2, + jpma = ( two_ja + two_ma) / 2, + jpmb = ( two_jb + two_mb) / 2, + jpmc = ( two_jc + two_mc) / 2, + jsum = ( two_ja + two_jb + two_jc) / 2, + kmin = locMax3 (0, jpmb - jmmc, jmma - jpmc), + kmax = locMin3 (jcc, jmma, jpmb), + k, sign = GSL_IS_ODD (kmin - jpma + jmmb) ? -1 : 1, + status = 0; + double sum_pos = 0.0, sum_neg = 0.0, norm, term; + gsl_sf_result bc1, bc2, bc3, bcn1, bcn2, bcd1, bcd2, bcd3, bcd4; + + status += gsl_sf_choose_e (two_ja, jcc , &bcn1); + status += gsl_sf_choose_e (two_jb, jcc , &bcn2); + status += gsl_sf_choose_e (jsum+1, jcc , &bcd1); + status += gsl_sf_choose_e (two_ja, jmma, &bcd2); + status += gsl_sf_choose_e (two_jb, jmmb, &bcd3); + status += gsl_sf_choose_e (two_jc, jpmc, &bcd4); + + if (status != 0) { + OVERFLOW_ERROR (result); + } + + norm = sqrt (bcn1.val * bcn2.val) + / sqrt (bcd1.val * bcd2.val * bcd3.val * bcd4.val * ((double) two_jc + 1.0)); + + for (k = kmin; k <= kmax; k++) { + status += gsl_sf_choose_e (jcc, k, &bc1); + status += gsl_sf_choose_e (jcb, jmma - k, &bc2); + status += gsl_sf_choose_e (jca, jpmb - k, &bc3); + + if (status != 0) { + OVERFLOW_ERROR (result); + } + + term = bc1.val * bc2.val * bc3.val; + + if (sign < 0) { + sum_neg += norm * term; + } else { + sum_pos += norm * term; + } + + sign = -sign; + } + + result->val = sum_pos - sum_neg; + result->err = 2.0 * GSL_DBL_EPSILON * (sum_pos + sum_neg); + result->err += 2.0 * GSL_DBL_EPSILON * (kmax - kmin) * fabs(result->val); + + return GSL_SUCCESS; + } +} + +int +gsl_sf_coupling_6j_INCORRECT_e(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf, + gsl_sf_result * result) +{ + return gsl_sf_coupling_6j_e(two_ja, two_jb, two_je, two_jd, two_jc, two_jf, result); +} + + +int +gsl_sf_coupling_6j_e(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf, + gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if( two_ja < 0 || two_jb < 0 || two_jc < 0 + || two_jd < 0 || two_je < 0 || two_jf < 0 + ) { + DOMAIN_ERROR(result); + } + else if( triangle_selection_fails(two_ja, two_jb, two_jc) + || triangle_selection_fails(two_ja, two_je, two_jf) + || triangle_selection_fails(two_jb, two_jd, two_jf) + || triangle_selection_fails(two_je, two_jd, two_jc) + ) { + result->val = 0.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else { + gsl_sf_result n1; + gsl_sf_result d1, d2, d3, d4, d5, d6; + double norm; + int tk, tkmin, tkmax; + double phase; + double sum_pos = 0.0; + double sum_neg = 0.0; + double sumsq_err = 0.0; + int status = 0; + status += delta(two_ja, two_jb, two_jc, &d1); + status += delta(two_ja, two_je, two_jf, &d2); + status += delta(two_jb, two_jd, two_jf, &d3); + status += delta(two_je, two_jd, two_jc, &d4); + if(status != GSL_SUCCESS) { + OVERFLOW_ERROR(result); + } + norm = sqrt(d1.val) * sqrt(d2.val) * sqrt(d3.val) * sqrt(d4.val); + + tkmin = locMax3(0, + two_ja + two_jd - two_jc - two_jf, + two_jb + two_je - two_jc - two_jf); + + tkmax = locMin5(two_ja + two_jb + two_je + two_jd + 2, + two_ja + two_jb - two_jc, + two_je + two_jd - two_jc, + two_ja + two_je - two_jf, + two_jb + two_jd - two_jf); + + phase = GSL_IS_ODD((two_ja + two_jb + two_je + two_jd + tkmin)/2) + ? -1.0 + : 1.0; + + for(tk=tkmin; tk<=tkmax; tk += 2) { + double term; + double term_err; + gsl_sf_result den_1, den_2; + gsl_sf_result d1_a, d1_b; + status = 0; + + status += gsl_sf_fact_e((two_ja + two_jb + two_je + two_jd - tk)/2 + 1, &n1); + status += gsl_sf_fact_e(tk/2, &d1_a); + status += gsl_sf_fact_e((two_jc + two_jf - two_ja - two_jd + tk)/2, &d1_b); + status += gsl_sf_fact_e((two_jc + two_jf - two_jb - two_je + tk)/2, &d2); + status += gsl_sf_fact_e((two_ja + two_jb - two_jc - tk)/2, &d3); + status += gsl_sf_fact_e((two_je + two_jd - two_jc - tk)/2, &d4); + status += gsl_sf_fact_e((two_ja + two_je - two_jf - tk)/2, &d5); + status += gsl_sf_fact_e((two_jb + two_jd - two_jf - tk)/2, &d6); + + if(status != GSL_SUCCESS) { + OVERFLOW_ERROR(result); + } + + d1.val = d1_a.val * d1_b.val; + d1.err = d1_a.err * fabs(d1_b.val) + fabs(d1_a.val) * d1_b.err; + + den_1.val = d1.val*d2.val*d3.val; + den_1.err = d1.err * fabs(d2.val*d3.val); + den_1.err += d2.err * fabs(d1.val*d3.val); + den_1.err += d3.err * fabs(d1.val*d2.val); + + den_2.val = d4.val*d5.val*d6.val; + den_2.err = d4.err * fabs(d5.val*d6.val); + den_2.err += d5.err * fabs(d4.val*d6.val); + den_2.err += d6.err * fabs(d4.val*d5.val); + + term = phase * n1.val / den_1.val / den_2.val; + phase = -phase; + term_err = n1.err / fabs(den_1.val) / fabs(den_2.val); + term_err += fabs(term / den_1.val) * den_1.err; + term_err += fabs(term / den_2.val) * den_2.err; + + if(term >= 0.0) { + sum_pos += norm*term; + } + else { + sum_neg -= norm*term; + } + + sumsq_err += norm*norm * term_err*term_err; + } + + result->val = sum_pos - sum_neg; + result->err = 2.0 * GSL_DBL_EPSILON * (sum_pos + sum_neg); + result->err += sqrt(sumsq_err / (0.5*(tkmax-tkmin)+1.0)); + result->err += 2.0 * GSL_DBL_EPSILON * (tkmax - tkmin + 2.0) * fabs(result->val); + + return GSL_SUCCESS; + } +} + + +int +gsl_sf_coupling_RacahW_e(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf, + gsl_sf_result * result) +{ + int status = gsl_sf_coupling_6j_e(two_ja, two_jb, two_je, two_jd, two_jc, two_jf, result); + int phase_sum = (two_ja + two_jb + two_jc + two_jd)/2; + result->val *= ( GSL_IS_ODD(phase_sum) ? -1.0 : 1.0 ); + return status; +} + + +int +gsl_sf_coupling_9j_e(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf, + int two_jg, int two_jh, int two_ji, + gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if( two_ja < 0 || two_jb < 0 || two_jc < 0 + || two_jd < 0 || two_je < 0 || two_jf < 0 + || two_jg < 0 || two_jh < 0 || two_ji < 0 + ) { + DOMAIN_ERROR(result); + } + else if( triangle_selection_fails(two_ja, two_jb, two_jc) + || triangle_selection_fails(two_jd, two_je, two_jf) + || triangle_selection_fails(two_jg, two_jh, two_ji) + || triangle_selection_fails(two_ja, two_jd, two_jg) + || triangle_selection_fails(two_jb, two_je, two_jh) + || triangle_selection_fails(two_jc, two_jf, two_ji) + ) { + result->val = 0.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else { + int tk; + int tkmin = locMax3(abs(two_ja-two_ji), abs(two_jh-two_jd), abs(two_jb-two_jf)); + int tkmax = locMin3(two_ja + two_ji, two_jh + two_jd, two_jb + two_jf); + double sum_pos = 0.0; + double sum_neg = 0.0; + double sumsq_err = 0.0; + double phase; + for(tk=tkmin; tk<=tkmax; tk += 2) { + gsl_sf_result s1, s2, s3; + double term; + double term_err; + int status = 0; + + status += gsl_sf_coupling_6j_e(two_ja, two_ji, tk, two_jh, two_jd, two_jg, &s1); + status += gsl_sf_coupling_6j_e(two_jb, two_jf, tk, two_jd, two_jh, two_je, &s2); + status += gsl_sf_coupling_6j_e(two_ja, two_ji, tk, two_jf, two_jb, two_jc, &s3); + + if(status != GSL_SUCCESS) { + OVERFLOW_ERROR(result); + } + term = s1.val * s2.val * s3.val; + term_err = s1.err * fabs(s2.val*s3.val); + term_err += s2.err * fabs(s1.val*s3.val); + term_err += s3.err * fabs(s1.val*s2.val); + + if(term >= 0.0) { + sum_pos += (tk + 1) * term; + } + else { + sum_neg -= (tk + 1) * term; + } + + sumsq_err += ((tk+1) * term_err) * ((tk+1) * term_err); + } + + phase = GSL_IS_ODD(tkmin) ? -1.0 : 1.0; + + result->val = phase * (sum_pos - sum_neg); + result->err = 2.0 * GSL_DBL_EPSILON * (sum_pos + sum_neg); + result->err += sqrt(sumsq_err / (0.5*(tkmax-tkmin)+1.0)); + result->err += 2.0 * GSL_DBL_EPSILON * (tkmax-tkmin + 2.0) * fabs(result->val); + + return GSL_SUCCESS; + } +} + + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_coupling_3j(int two_ja, int two_jb, int two_jc, + int two_ma, int two_mb, int two_mc) +{ + EVAL_RESULT(gsl_sf_coupling_3j_e(two_ja, two_jb, two_jc, + two_ma, two_mb, two_mc, + &result)); +} + + +double gsl_sf_coupling_6j_INCORRECT(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf) +{ + EVAL_RESULT(gsl_sf_coupling_6j_INCORRECT_e(two_ja, two_jb, two_jc, + two_jd, two_je, two_jf, + &result)); +} + + +double gsl_sf_coupling_6j(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf) +{ + EVAL_RESULT(gsl_sf_coupling_6j_e(two_ja, two_jb, two_jc, + two_jd, two_je, two_jf, + &result)); +} + + +double gsl_sf_coupling_RacahW(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf) +{ + EVAL_RESULT(gsl_sf_coupling_RacahW_e(two_ja, two_jb, two_jc, + two_jd, two_je, two_jf, + &result)); +} + + +double gsl_sf_coupling_9j(int two_ja, int two_jb, int two_jc, + int two_jd, int two_je, int two_jf, + int two_jg, int two_jh, int two_ji) +{ + EVAL_RESULT(gsl_sf_coupling_9j_e(two_ja, two_jb, two_jc, + two_jd, two_je, two_jf, + two_jg, two_jh, two_ji, + &result)); +} |