mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
more wrappers
This commit is contained in:
fredrik
parent
aa901badda
commit
7d5a70f229
3 changed files with 479 additions and 27 deletions
46
arb_fpwrap.h
46
arb_fpwrap.h
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@ -116,6 +116,9 @@ int arb_fpwrap_cdouble_acosh(complex_double * res, complex_double x, int flags);
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int arb_fpwrap_double_atanh(double * res, double x, int flags);
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int arb_fpwrap_cdouble_atanh(complex_double * res, complex_double x, int flags);
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int arb_fpwrap_double_lambertw(double * res, double x, slong branch, int flags);
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int arb_fpwrap_cdouble_lambertw(complex_double * res, complex_double x, slong branch, int flags);
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int arb_fpwrap_double_rising(double * res, double x, double n, int flags);
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int arb_fpwrap_cdouble_rising(complex_double * res, complex_double x, complex_double n, int flags);
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@ -149,6 +152,12 @@ int arb_fpwrap_cdouble_polygamma(complex_double * res, complex_double s, complex
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int arb_fpwrap_double_polylog(double * res, double s, double z, int flags);
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int arb_fpwrap_cdouble_polylog(complex_double * res, complex_double s, complex_double z, int flags);
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int arb_fpwrap_cdouble_dirichlet_eta(complex_double * res, complex_double s, int flags);
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int arb_fpwrap_cdouble_riemann_xi(complex_double * res, complex_double s, int flags);
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int arb_fpwrap_cdouble_hardy_theta(complex_double * res, complex_double z, int flags);
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int arb_fpwrap_cdouble_hardy_z(complex_double * res, complex_double z, int flags);
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int arb_fpwrap_cdouble_zeta_zero(complex_double * res, ulong n, int flags);
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int arb_fpwrap_double_erf(double * res, double x, int flags);
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int arb_fpwrap_cdouble_erf(complex_double * res, complex_double x, int flags);
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@ -221,6 +230,11 @@ int arb_fpwrap_cdouble_airy_bi(complex_double * res, complex_double x, int flags
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int arb_fpwrap_double_airy_bi_prime(double * res, double x, int flags);
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int arb_fpwrap_cdouble_airy_bi_prime(complex_double * res, complex_double x, int flags);
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int arb_fpwrap_double_airy_ai_zero(double * res, ulong n, int flags);
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int arb_fpwrap_double_airy_ai_prime_zero(double * res, ulong n, int flags);
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int arb_fpwrap_double_airy_bi_zero(double * res, ulong n, int flags);
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int arb_fpwrap_double_airy_bi_prime_zero(double * res, ulong n, int flags);
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int arb_fpwrap_double_coulomb_f(double * res, double l, double eta, double x, int flags);
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int arb_fpwrap_cdouble_coulomb_f(complex_double * res, complex_double l, complex_double eta, complex_double x, int flags);
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@ -254,6 +268,8 @@ int arb_fpwrap_cdouble_legendre_p(complex_double * res, complex_double n, comple
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int arb_fpwrap_double_legendre_q(double * res, double n, double m, double x, int type, int flags);
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int arb_fpwrap_cdouble_legendre_q(complex_double * res, complex_double n, complex_double m, complex_double x, int type, int flags);
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int arb_fpwrap_double_legendre_root(double * res1, double * res2, ulong n, ulong k, int flags);
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int arb_fpwrap_cdouble_spherical_y(complex_double * res, slong n, slong m, complex_double x1, complex_double x2, int flags);
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int arb_fpwrap_double_hypgeom_0f1(double * res, double a, double x, int regularized, int flags);
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@ -268,13 +284,39 @@ int arb_fpwrap_cdouble_hypgeom_u(complex_double * res, complex_double a, complex
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int arb_fpwrap_double_hypgeom_2f1(double * res, double a, double b, double c, double x, int regularized, int flags);
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int arb_fpwrap_cdouble_hypgeom_2f1(complex_double * res, complex_double a, complex_double b, complex_double c, complex_double x, int regularized, int flags);
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int arb_fpwrap_double_agm1(double * res, double x, int flags);
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int arb_fpwrap_cdouble_agm1(complex_double * res, complex_double x, int flags);
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int arb_fpwrap_double_hypgeom_pfq(double * res, const double * a, slong p, const double * b, slong q, double z, int regularized, int flags);
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int arb_fpwrap_cdouble_hypgeom_pfq(complex_double * res, const complex_double * a, slong p, const complex_double * b, slong q, complex_double z, int regularized, int flags);
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int arb_fpwrap_double_agm(double * res, double x, double y, int flags);
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int arb_fpwrap_cdouble_agm(complex_double * res, complex_double x, complex_double y, int flags);
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int arb_fpwrap_cdouble_elliptic_k(complex_double * res, complex_double m, int flags);
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int arb_fpwrap_cdouble_elliptic_e(complex_double * res, complex_double m, int flags);
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int arb_fpwrap_cdouble_elliptic_pi(complex_double * res, complex_double n, complex_double m, int flags);
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int arb_fpwrap_cdouble_elliptic_f(complex_double * res, complex_double phi, complex_double m, int pi, int flags);
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int arb_fpwrap_cdouble_elliptic_e_inc(complex_double * res, complex_double phi, complex_double m, int pi, int flags);
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int arb_fpwrap_cdouble_elliptic_pi_inc(complex_double * res, complex_double n, complex_double phi, complex_double m, int pi, int flags);
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int arb_fpwrap_cdouble_elliptic_rf(complex_double * res, complex_double x, complex_double y, complex_double z, int option, int flags);
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int arb_fpwrap_cdouble_elliptic_rg(complex_double * res, complex_double x, complex_double y, complex_double z, int option, int flags);
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int arb_fpwrap_cdouble_elliptic_rj(complex_double * res, complex_double x, complex_double y, complex_double z, complex_double w, int option, int flags);
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int arb_fpwrap_cdouble_elliptic_p(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_elliptic_p_prime(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_elliptic_inv_p(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_elliptic_zeta(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_elliptic_sigma(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_jacobi_theta_1(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_jacobi_theta_2(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_jacobi_theta_3(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_jacobi_theta_4(complex_double * res, complex_double z, complex_double tau, int flags);
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int arb_fpwrap_cdouble_dedekind_eta(complex_double * res, complex_double tau, int flags);
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int arb_fpwrap_cdouble_modular_j(complex_double * res, complex_double tau, int flags);
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int arb_fpwrap_cdouble_modular_lambda(complex_double * res, complex_double tau, int flags);
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int arb_fpwrap_cdouble_modular_delta(complex_double * res, complex_double tau, int flags);
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#ifdef __cplusplus
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}
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@ -16,7 +16,21 @@
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#include "arb_fpwrap.h"
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#include "arb_hypgeom.h"
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#include "acb_hypgeom.h"
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#include "acb_dirichlet.h"
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#include "acb_elliptic.h"
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#include "acb_modular.h"
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static int
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_acb_vec_is_finite(acb_srcptr x, slong len)
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{
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slong i;
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for (i = 0; i < len; i++)
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if (!acb_is_finite(x + i))
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return 0;
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return 1;
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}
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int
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arb_accurate_enough_d(const arb_t x, int flags)
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@ -100,6 +114,22 @@ acb_accurate_enough_d(const acb_t x, int flags)
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break; \
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} \
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#define DOUBLE_CHECK_RESULT2 \
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if (arb_accurate_enough_d(arb_res1, flags) && arb_accurate_enough_d(arb_res2, flags)) \
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{ \
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*res1 = arf_get_d(arb_midref(arb_res1), ARF_RND_NEAR); \
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*res2 = arf_get_d(arb_midref(arb_res2), ARF_RND_NEAR); \
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status = FPWRAP_SUCCESS; \
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break; \
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} \
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if (wp >= double_wp_max(flags)) \
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{ \
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*res1 = D_NAN; \
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*res2 = D_NAN; \
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status = FPWRAP_UNABLE; \
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break; \
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} \
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#define CDOUBLE_CHECK_RESULT \
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if (acb_accurate_enough_d(acb_res, flags)) \
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{ \
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@ -996,22 +1026,6 @@ DEF_DOUBLE_FUN_1(dilog, arb_hypgeom_dilog)
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DEF_CDOUBLE_FUN_1(dilog, acb_hypgeom_dilog)
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static void
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_arb_agm1(arb_t res, const arb_t x, slong prec)
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{
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arb_t t;
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arb_init(t);
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arb_one(t);
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arb_agm(res, t, x, prec);
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arb_clear(t);
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}
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DEF_DOUBLE_FUN_1(agm1, _arb_agm1)
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DEF_CDOUBLE_FUN_1(agm1, acb_agm1)
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DEF_DOUBLE_FUN_2(agm, arb_agm)
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DEF_CDOUBLE_FUN_2(agm, acb_agm)
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DEF_DOUBLE_FUN_1(erf, arb_hypgeom_erf)
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DEF_CDOUBLE_FUN_1(erf, acb_hypgeom_erf)
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@ -1181,9 +1195,328 @@ DEF_CDOUBLE_FUN_3(hypgeom_u, acb_hypgeom_u)
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DEF_DOUBLE_FUN_4_INT(hypgeom_2f1, arb_hypgeom_2f1)
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DEF_CDOUBLE_FUN_4_INT(hypgeom_2f1, acb_hypgeom_2f1)
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int arb_fpwrap_double_hypgeom_pfq(double * res, const double * a, slong p, const double * b, slong q, double z, int regularized, int flags)
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{
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arb_t arb_res;
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arb_ptr t;
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slong wp;
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slong i;
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int status;
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arb_init(arb_res);
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t = _arb_vec_init(p + q + 1);
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for (i = 0; i < p; i++)
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arb_set_d(t + i, a[i]);
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for (i = 0; i < q; i++)
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arb_set_d(t + p + i, b[i]);
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arb_set_d(t + p + q, z);
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if (!_arb_vec_is_finite(t, p + q + 1))
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{
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*res = D_NAN;
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status = FPWRAP_UNABLE;
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}
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else
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{
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for (wp = WP_INITIAL; ; wp *= 2)
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{
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arb_hypgeom_pfq(arb_res, t, p, t + p, q, t + p + q, regularized, wp);
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DOUBLE_CHECK_RESULT
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}
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}
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_arb_vec_clear(t, p + q + 1);
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arb_clear(arb_res);
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return status;
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}
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int arb_fpwrap_cdouble_hypgeom_pfq(complex_double * res, const complex_double * a, slong p, const complex_double * b, slong q, complex_double z, int regularized, int flags)
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{
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acb_t acb_res;
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acb_ptr t;
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slong wp;
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slong i;
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int status;
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acb_init(acb_res);
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t = _acb_vec_init(p + q + 1);
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for (i = 0; i < p; i++)
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acb_set_d_d(t + i, a[i].real, a[i].imag);
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for (i = 0; i < q; i++)
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acb_set_d_d(t + p + i, b[i].real, b[i].imag);
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acb_set_d_d(t + p + q, z.real, z.imag);
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if (!_acb_vec_is_finite(t, p + q + 1))
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{
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res->real = D_NAN;
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res->imag = D_NAN;
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status = FPWRAP_UNABLE;
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}
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else
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{
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for (wp = WP_INITIAL; ; wp *= 2)
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{
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acb_hypgeom_pfq(acb_res, t, p, t + p, q, t + p + q, regularized, wp);
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CDOUBLE_CHECK_RESULT
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}
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}
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_acb_vec_clear(t, p + q + 1);
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acb_clear(acb_res);
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return status;
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}
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DEF_CDOUBLE_FUN_1(elliptic_k, acb_elliptic_k)
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DEF_CDOUBLE_FUN_1(elliptic_e, acb_elliptic_e)
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DEF_CDOUBLE_FUN_2(elliptic_pi, acb_elliptic_pi)
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DEF_CDOUBLE_FUN_2_INT(elliptic_f, acb_elliptic_f)
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DEF_CDOUBLE_FUN_2_INT(elliptic_e_inc, acb_elliptic_e_inc)
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DEF_CDOUBLE_FUN_3_INT(elliptic_pi_inc, acb_elliptic_pi_inc)
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DEF_CDOUBLE_FUN_3_INT(elliptic_rf, acb_elliptic_rf)
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DEF_CDOUBLE_FUN_3_INT(elliptic_rg, acb_elliptic_rg)
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DEF_CDOUBLE_FUN_4_INT(elliptic_rj, acb_elliptic_rj)
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DEF_CDOUBLE_FUN_2(elliptic_p, acb_elliptic_p)
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DEF_CDOUBLE_FUN_2(elliptic_p_prime, acb_elliptic_p_prime)
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DEF_CDOUBLE_FUN_2(elliptic_inv_p, acb_elliptic_inv_p)
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DEF_CDOUBLE_FUN_2(elliptic_zeta, acb_elliptic_zeta)
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DEF_CDOUBLE_FUN_2(elliptic_sigma, acb_elliptic_sigma)
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static void
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_acb_theta1(acb_t res, const acb_t z, const acb_t tau, slong prec)
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{
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acb_t a, b, c; acb_init(a); acb_init(b); acb_init(c);
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acb_modular_theta(res, a, b, c, z, tau, prec);
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acb_clear(a); acb_clear(b); acb_clear(c);
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}
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static void
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_acb_theta2(acb_t res, const acb_t z, const acb_t tau, slong prec)
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{
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acb_t a, b, c; acb_init(a); acb_init(b); acb_init(c);
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acb_modular_theta(a, res, b, c, z, tau, prec);
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acb_clear(a); acb_clear(b); acb_clear(c);
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}
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static void
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_acb_theta3(acb_t res, const acb_t z, const acb_t tau, slong prec)
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{
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acb_t a, b, c; acb_init(a); acb_init(b); acb_init(c);
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acb_modular_theta(a, b, res, c, z, tau, prec);
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acb_clear(a); acb_clear(b); acb_clear(c);
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}
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static void
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_acb_theta4(acb_t res, const acb_t z, const acb_t tau, slong prec)
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{
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acb_t a, b, c; acb_init(a); acb_init(b); acb_init(c);
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acb_modular_theta(a, b, c, res, z, tau, prec);
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acb_clear(a); acb_clear(b); acb_clear(c);
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}
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DEF_CDOUBLE_FUN_2(jacobi_theta_1, _acb_theta1)
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DEF_CDOUBLE_FUN_2(jacobi_theta_2, _acb_theta2)
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DEF_CDOUBLE_FUN_2(jacobi_theta_3, _acb_theta3)
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DEF_CDOUBLE_FUN_2(jacobi_theta_4, _acb_theta4)
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DEF_CDOUBLE_FUN_1(dedekind_eta, acb_modular_eta)
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DEF_CDOUBLE_FUN_1(modular_j, acb_modular_j)
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DEF_CDOUBLE_FUN_1(modular_lambda, acb_modular_lambda)
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DEF_CDOUBLE_FUN_1(modular_delta, acb_modular_delta)
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DEF_CDOUBLE_FUN_1(dirichlet_eta, acb_dirichlet_eta)
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DEF_CDOUBLE_FUN_1(riemann_xi, acb_dirichlet_xi)
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static void
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_acb_hardy_theta(acb_t res, const acb_t t, slong prec)
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{
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acb_dirichlet_hardy_theta(res, t, NULL, NULL, 1, prec);
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}
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static void
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_acb_hardy_z(acb_t res, const acb_t t, slong prec)
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{
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acb_dirichlet_hardy_z(res, t, NULL, NULL, 1, prec);
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}
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DEF_CDOUBLE_FUN_1(hardy_theta, _acb_hardy_theta)
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DEF_CDOUBLE_FUN_1(hardy_z, _acb_hardy_z)
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int arb_fpwrap_cdouble_zeta_zero(complex_double * res, ulong n, int flags)
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{
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fmpz_t t;
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acb_t acb_res;
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slong wp;
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int status;
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if (n == 0)
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{
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res->real = D_NAN;
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res->imag = D_NAN;
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return FPWRAP_UNABLE;
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}
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acb_init(acb_res);
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fmpz_init(t);
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fmpz_set_ui(t, n);
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for (wp = WP_INITIAL; ; wp *= 2)
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{
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acb_dirichlet_zeta_zero(acb_res, t, wp);
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CDOUBLE_CHECK_RESULT
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}
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acb_clear(acb_res);
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return status;
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}
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int arb_fpwrap_double_legendre_root(double * res1, double * res2, ulong n, ulong k, int flags)
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{
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arb_t arb_res1, arb_res2;
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slong wp;
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int status;
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if (k >= n)
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{
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*res1 = D_NAN;
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*res2 = D_NAN;
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return FPWRAP_UNABLE;
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}
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arb_init(arb_res1);
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arb_init(arb_res2);
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for (wp = WP_INITIAL; ; wp *= 2)
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{
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arb_hypgeom_legendre_p_ui_root(arb_res1, arb_res2, n, k, wp);
|
||||
DOUBLE_CHECK_RESULT2
|
||||
}
|
||||
|
||||
arb_clear(arb_res1);
|
||||
arb_clear(arb_res2);
|
||||
|
||||
return status;
|
||||
}
|
||||
|
||||
int _arb_fpwrap_double_airy_zero(double * res, ulong n, int which, int flags)
|
||||
{
|
||||
fmpz_t t;
|
||||
arb_t arb_res;
|
||||
slong wp;
|
||||
int status;
|
||||
|
||||
if (n == 0)
|
||||
{
|
||||
*res = D_NAN;
|
||||
return FPWRAP_UNABLE;
|
||||
}
|
||||
|
||||
arb_init(arb_res);
|
||||
fmpz_init(t);
|
||||
fmpz_set_ui(t, n);
|
||||
|
||||
for (wp = WP_INITIAL; ; wp *= 2)
|
||||
{
|
||||
if (which == 0)
|
||||
arb_hypgeom_airy_zero(arb_res, NULL, NULL, NULL, t, wp);
|
||||
else if (which == 1)
|
||||
arb_hypgeom_airy_zero(NULL, arb_res, NULL, NULL, t, wp);
|
||||
else if (which == 2)
|
||||
arb_hypgeom_airy_zero(NULL, NULL, arb_res, NULL, t, wp);
|
||||
else
|
||||
arb_hypgeom_airy_zero(NULL, NULL, NULL, arb_res, t, wp);
|
||||
|
||||
DOUBLE_CHECK_RESULT
|
||||
}
|
||||
|
||||
arb_clear(arb_res);
|
||||
fmpz_clear(t);
|
||||
|
||||
return status;
|
||||
}
|
||||
|
||||
int arb_fpwrap_double_airy_ai_zero(double * res, ulong n, int flags) { return _arb_fpwrap_double_airy_zero(res, n, 0, flags); }
|
||||
int arb_fpwrap_double_airy_ai_prime_zero(double * res, ulong n, int flags) { return _arb_fpwrap_double_airy_zero(res, n, 1, flags); }
|
||||
int arb_fpwrap_double_airy_bi_zero(double * res, ulong n, int flags) { return _arb_fpwrap_double_airy_zero(res, n, 2, flags); }
|
||||
int arb_fpwrap_double_airy_bi_prime_zero(double * res, ulong n, int flags) { return _arb_fpwrap_double_airy_zero(res, n, 3, flags); }
|
||||
|
||||
int arb_fpwrap_double_lambertw(double * res, double x, slong branch, int flags)
|
||||
{
|
||||
arb_t arb_res, arb_x;
|
||||
slong wp;
|
||||
int status;
|
||||
|
||||
arb_init(arb_res);
|
||||
arb_init(arb_x);
|
||||
|
||||
arb_set_d(arb_x, x);
|
||||
|
||||
if (!arb_is_finite(arb_x) || !(branch == 0 || branch == -1))
|
||||
{
|
||||
*res = D_NAN;
|
||||
status = FPWRAP_UNABLE;
|
||||
}
|
||||
else
|
||||
{
|
||||
for (wp = WP_INITIAL; ; wp *= 2)
|
||||
{
|
||||
arb_lambertw(arb_res, arb_x, (branch == -1), wp);
|
||||
DOUBLE_CHECK_RESULT
|
||||
}
|
||||
}
|
||||
|
||||
arb_clear(arb_x);
|
||||
arb_clear(arb_res);
|
||||
|
||||
return status;
|
||||
}
|
||||
|
||||
int arb_fpwrap_cdouble_lambertw(complex_double * res, complex_double x, slong branch, int flags)
|
||||
{
|
||||
fmpz_t t;
|
||||
acb_t acb_res, acb_x;
|
||||
slong wp;
|
||||
int status;
|
||||
|
||||
acb_init(acb_res);
|
||||
acb_init(acb_x);
|
||||
fmpz_init(t);
|
||||
|
||||
acb_set_d_d(acb_x, x.real, x.imag);
|
||||
fmpz_set_si(t, branch);
|
||||
|
||||
if (!acb_is_finite(acb_x))
|
||||
{
|
||||
res->real = D_NAN;
|
||||
res->imag = D_NAN;
|
||||
status = FPWRAP_UNABLE;
|
||||
}
|
||||
else
|
||||
{
|
||||
for (wp = WP_INITIAL; ; wp *= 2)
|
||||
{
|
||||
acb_lambertw(acb_res, acb_x, t, 0, wp);
|
||||
CDOUBLE_CHECK_RESULT
|
||||
}
|
||||
}
|
||||
|
||||
acb_clear(acb_x);
|
||||
acb_clear(acb_res);
|
||||
fmpz_clear(t);
|
||||
|
||||
return status;
|
||||
}
|
||||
|
||||
/* todo: lambertw (with branches) */
|
||||
/* todo: functions with multiple outputs */
|
||||
/* todo: airy zeros, legendre roots */
|
||||
/* todo: pfqs */
|
||||
/* todo: elliptic invariants, roots */
|
||||
/* todo: eisenstein series */
|
||||
/* todo: dirichlet functions requiring characters */
|
||||
|
||||
|
|
|
|||
|
|
@ -195,6 +195,9 @@ Elementary functions
|
|||
.. function:: int arb_fpwrap_double_atanh(double * res, double x, int flags)
|
||||
int arb_fpwrap_cdouble_atanh(complex_double * res, complex_double x, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_lambertw(double * res, double x, slong branch, int flags)
|
||||
int arb_fpwrap_cdouble_lambertw(complex_double * res, complex_double x, slong branch, int flags)
|
||||
|
||||
Gamma, zeta and related functions
|
||||
...............................................................................
|
||||
|
||||
|
|
@ -253,6 +256,16 @@ Gamma, zeta and related functions
|
|||
|
||||
Polylogarithm.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_dirichlet_eta(complex_double * res, complex_double s, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_riemann_xi(complex_double * res, complex_double s, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_hardy_theta(complex_double * res, complex_double z, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_hardy_z(complex_double * res, complex_double z, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_zeta_zero(complex_double * res, ulong n, int flags)
|
||||
|
||||
Error functions and exponential integrals
|
||||
...............................................................................
|
||||
|
||||
|
|
@ -331,6 +344,14 @@ Bessel, Airy and Coulomb functions
|
|||
.. function:: int arb_fpwrap_double_airy_bi_prime(double * res, double x, int flags)
|
||||
int arb_fpwrap_cdouble_airy_bi_prime(complex_double * res, complex_double x, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_airy_ai_zero(double * res, ulong n, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_airy_ai_prime_zero(double * res, ulong n, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_airy_bi_zero(double * res, ulong n, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_airy_bi_prime_zero(double * res, ulong n, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_coulomb_f(double * res, double l, double eta, double x, int flags)
|
||||
int arb_fpwrap_cdouble_coulomb_f(complex_double * res, complex_double l, complex_double eta, complex_double x, int flags)
|
||||
|
||||
|
|
@ -367,6 +388,12 @@ Orthogonal polynomials
|
|||
.. function:: int arb_fpwrap_double_legendre_q(double * res, double n, double m, double x, int type, int flags)
|
||||
int arb_fpwrap_cdouble_legendre_q(complex_double * res, complex_double n, complex_double m, complex_double x, int type, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_double_legendre_root(double * res1, double * res2, ulong n, ulong k, int flags)
|
||||
|
||||
Sets *res1* to the index *k* root of the Legendre polynomial `P_n(x)`,
|
||||
and simultaneously sets *res2* to the corresponding weight for
|
||||
Gauss-Legendre quadrature.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_spherical_y(complex_double * res, slong n, slong m, complex_double x1, complex_double x2, int flags)
|
||||
|
||||
Hypergeometric functions
|
||||
|
|
@ -384,19 +411,69 @@ Hypergeometric functions
|
|||
.. function:: int arb_fpwrap_double_hypgeom_2f1(double * res, double a, double b, double c, double x, int regularized, int flags)
|
||||
int arb_fpwrap_cdouble_hypgeom_2f1(complex_double * res, complex_double a, complex_double b, complex_double c, complex_double x, int regularized, int flags)
|
||||
|
||||
Elliptic integrals and elliptic functions
|
||||
.. function:: int arb_fpwrap_double_hypgeom_pfq(double * res, const double * a, slong p, const double * b, slong q, double z, int regularized, int flags);
|
||||
int arb_fpwrap_cdouble_hypgeom_pfq(complex_double * res, const complex_double * a, slong p, const complex_double * b, slong q, complex_double z, int regularized, int flags)
|
||||
|
||||
|
||||
Elliptic integrals, elliptic functions and modular forms
|
||||
...............................................................................
|
||||
|
||||
.. function:: int arb_fpwrap_double_agm1(double * res, double x, int flags)
|
||||
int arb_fpwrap_cdouble_agm1(complex_double * res, complex_double x, int flags)
|
||||
|
||||
Arithmetic-geometric mean with second variable 1.
|
||||
|
||||
.. function:: int arb_fpwrap_double_agm(double * res, double x, double y, int flags)
|
||||
int arb_fpwrap_cdouble_agm(complex_double * res, complex_double x, complex_double y, int flags)
|
||||
|
||||
Arithmetic-geometric mean.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_k(complex_double * res, complex_double m, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_e(complex_double * res, complex_double m, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_pi(complex_double * res, complex_double n, complex_double m, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_f(complex_double * res, complex_double phi, complex_double m, int pi, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_e_inc(complex_double * res, complex_double phi, complex_double m, int pi, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_pi_inc(complex_double * res, complex_double n, complex_double phi, complex_double m, int pi, int flags)
|
||||
|
||||
Complete and incomplete elliptic integrals.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_rf(complex_double * res, complex_double x, complex_double y, complex_double z, int option, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_rg(complex_double * res, complex_double x, complex_double y, complex_double z, int option, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_rj(complex_double * res, complex_double x, complex_double y, complex_double z, complex_double w, int option, int flags)
|
||||
|
||||
Carlson symmetric elliptic integrals.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_p(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_p_prime(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_inv_p(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_zeta(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_elliptic_sigma(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
Weierstrass elliptic functions.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_jacobi_theta_1(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_jacobi_theta_2(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_jacobi_theta_3(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_jacobi_theta_4(complex_double * res, complex_double z, complex_double tau, int flags)
|
||||
|
||||
Jacobi theta functions.
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_dedekind_eta(complex_double * res, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_modular_j(complex_double * res, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_modular_lambda(complex_double * res, complex_double tau, int flags)
|
||||
|
||||
.. function:: int arb_fpwrap_cdouble_modular_delta(complex_double * res, complex_double tau, int flags)
|
||||
|
||||
Interfacing from Python
|
||||
-------------------------------------------------------------------------------
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue