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https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
implement spherical harmonics
This commit is contained in:
Fredrik Johansson
parent
d84efb61ca
commit
4f741bff1c
4 changed files with 275 additions and 0 deletions
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@ -169,6 +169,7 @@ void acb_hypgeom_laguerre_l(acb_t res, const acb_t n, const acb_t m, const acb_t
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void acb_hypgeom_hermite_h(acb_t res, const acb_t n, const acb_t z, long prec);
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void acb_hypgeom_chebyshev_t(acb_t res, const acb_t n, const acb_t z, long prec);
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void acb_hypgeom_chebyshev_u(acb_t res, const acb_t n, const acb_t z, long prec);
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void acb_hypgeom_spherical_y(acb_t res, long n, long m, const acb_t theta, const acb_t phi, long prec);
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#ifdef __cplusplus
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}
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93
acb_hypgeom/spherical_y.c
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93
acb_hypgeom/spherical_y.c
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@ -0,0 +1,93 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2015 Fredrik Johansson
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******************************************************************************/
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#include "acb_hypgeom.h"
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void
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acb_hypgeom_spherical_y(acb_t res, long n, long m,
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const acb_t theta, const acb_t phi, long prec)
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{
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acb_t t, u;
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if (n < 0)
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{
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if (m <= n)
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{
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acb_zero(res);
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return;
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}
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n = -1-n;
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}
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if (m > n || m < -n)
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{
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acb_zero(res);
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return;
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}
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if (n > LONG_MAX / 4)
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{
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acb_indeterminate(res);
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return;
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}
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acb_init(t);
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acb_init(u);
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acb_sin_cos(t, u, theta, prec);
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/* P_n^m(cos(theta)) */
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acb_hypgeom_legendre_p_uiui_rec(u, n, FLINT_ABS(m), u, prec);
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acb_pow_ui(t, t, FLINT_ABS(m), prec);
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acb_mul(t, t, u, prec);
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/* exp(i m phi) */
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acb_mul_onei(u, phi);
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acb_mul_si(u, u, m, prec);
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acb_exp(u, u, prec);
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if (m < 0 && m % 2)
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acb_neg(u, u);
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acb_mul(t, t, u, prec);
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/* sqrt((2n+1)/(4pi) (n-m)!/(n+m)!) */
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arb_fac_ui(acb_realref(u), n - FLINT_ABS(m), prec);
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arb_fac_ui(acb_imagref(u), n + FLINT_ABS(m), prec);
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arb_mul_ui(acb_realref(u), acb_realref(u), 2 * n + 1, prec);
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arb_div(acb_realref(u), acb_realref(u), acb_imagref(u), prec);
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arb_const_pi(acb_imagref(u), prec);
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arb_div(acb_realref(u), acb_realref(u), acb_imagref(u), prec);
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arb_mul_2exp_si(acb_realref(u), acb_realref(u), -2);
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arb_sqrt(acb_realref(u), acb_realref(u), prec);
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acb_mul_arb(t, t, acb_realref(u), prec);
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acb_set(res, t);
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acb_clear(t);
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acb_clear(u);
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}
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167
acb_hypgeom/test/t-spherical_y.c
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167
acb_hypgeom/test/t-spherical_y.c
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@ -0,0 +1,167 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2015 Fredrik Johansson
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******************************************************************************/
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#include "acb_hypgeom.h"
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/* generated with mpmath */
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static const double testdata[] = {
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0.0, 0.0,
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-0.02701626593453869896, 0.06085851132589568114,
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0.092391418427377575111, 0.29443833672801130076,
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0.65131374739365937388, 0.37063665572827331764,
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0.83847032733386007862, -0.28730577566514336534,
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-0.14750357092078405673, -0.30269451746476217073,
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-0.048646822931479694311, 0.038926542608778397121,
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0.0048197328091099892156, 0.003641138129582944611,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.027574808444335508972, 0.11025410152651193448,
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0.35400136349600893569, 0.24420566191536183849,
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0.67425312681608106523, -0.11728998324910652574,
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-0.069322941709900597259, -0.18037674817459565026,
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-0.018729775699827662658, 0.013254956213452933465,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.14771800806690767222, 0.11532328561497280466,
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0.50057392828327004059, -0.029559886614345590592,
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-0.02552211332726607337, -0.080244885187214384683,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.28209479177387814347, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.28209479177387814347, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.14771800806690767222, 0.11532328561497280466,
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0.50057392828327004059, -0.029559886614345590592,
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-0.02552211332726607337, -0.080244885187214384683,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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0.027574808444335508972, 0.11025410152651193448,
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0.35400136349600893569, 0.24420566191536183849,
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0.67425312681608106523, -0.11728998324910652574,
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-0.069322941709900597259, -0.18037674817459565026,
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-0.018729775699827662658, 0.013254956213452933465,
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0.0, 0.0,
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0.0, 0.0,
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0.0, 0.0,
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-0.02701626593453869896, 0.06085851132589568114,
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0.092391418427377575111, 0.29443833672801130076,
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0.65131374739365937388, 0.37063665572827331764,
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0.83847032733386007862, -0.28730577566514336534,
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-0.14750357092078405673, -0.30269451746476217073,
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-0.048646822931479694311, 0.038926542608778397121,
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0.0048197328091099892156, 0.003641138129582944611,
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0.0, 0.0,
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-0.033798002071615353821, 0.018033964330683617275,
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-0.071988993423855434033, 0.19195223773954952294,
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0.23381678888295549361, 0.58288246446413288682,
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1.0666048448920927459, 0.45816450098677839043,
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0.99160821344691798668, -0.56670953266315770842,
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-0.27930640165163989333, -0.44051756827083040505,
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-0.092578419347396006256, 0.086641542063743427664,
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0.015474322098595795308, 0.010316287906840124695,
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0.00051935757617903067671, -0.0014726339944978705874,
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};
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int main()
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{
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printf("spherical_y....");
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fflush(stdout);
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{
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long i, n, m;
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acb_t z, w, x, y;
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acb_init(z);
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acb_init(w);
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acb_init(x);
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acb_init(y);
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i = 0;
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arb_set_str(acb_realref(x), "0.2", 64);
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arb_set_str(acb_imagref(x), "0.3", 64);
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arb_set_str(acb_realref(y), "0.3", 64);
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arb_set_str(acb_imagref(y), "0.4", 64);
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for (n = -4; n <= 4; n++)
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{
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for (m = -4; m <= 4; m++)
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{
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acb_hypgeom_spherical_y(z, n, m, x, y, 64);
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acb_set_d_d(w, testdata[2 * i], testdata[2 * i + 1]);
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mag_set_d(arb_radref(acb_realref(w)), 1e-13);
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mag_set_d(arb_radref(acb_imagref(w)), 1e-13);
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if (!acb_overlaps(z, w))
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{
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printf("FAIL: value\n\n");
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printf("n = %ld, m = %ld\n", n, m);
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printf("z = "); acb_printd(z, 20); printf("\n\n");
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printf("w = "); acb_printd(w, 20); printf("\n\n");
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abort();
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}
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i++;
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}
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}
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acb_clear(z);
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acb_clear(w);
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acb_clear(x);
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acb_clear(y);
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}
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flint_cleanup();
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printf("PASS\n");
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return EXIT_SUCCESS;
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}
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@ -787,3 +787,17 @@ Orthogonal polynomials and functions
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For nonnegative integer *n* and *m*, uses recurrence relations to evaluate
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`(1-z^2)^{-m/2} P_n^m(z)` which is a polynomial in *z*.
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.. function:: void acb_hypgeom_spherical_y(acb_t res, long n, long m, const acb_t theta, const acb_t phi, long prec)
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Computes the spherical harmonic of degree *n*, order *m*,
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latitude angle *theta*, and longitude angle *phi*, normalized
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such that
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.. math ::
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Y_n^m(\theta, \phi) = \sqrt{\frac{2n+1}{4\pi} \frac{(n-m)!}{(n+m)!}} e^{im\phi} P_n^m(\cos(\theta)).
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The definition is extended to negative *m* and *n* by symmetry.
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This function is a polynomial in `\cos(\theta)` and `\sin(\theta)`.
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We evaluate it using :func:`acb_hypgeom_legendre_p_uiui_rec`.
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