kopia lustrzana https://github.com/Dsplib/libdspl-2.0
798 wiersze
19 KiB
C
798 wiersze
19 KiB
C
/*
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* Copyright (c) 2015-2019 Sergey Bakhurin
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* Digital Signal Processing Library [http://dsplib.org]
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*
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* This file is part of DSPL.
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*
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* 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 3 of the License, or
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* (at your option) any later version.
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*
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* DSPL 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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*
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* You should have received a copy of the GNU General Public License
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* along with Foobar. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#include "dspl.h"
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/*****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_acd(double* w, int n, double k, double* u)
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\brief Inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ of real vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ of real vector `w`. \n
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\param[in] w Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n Size of vector `w`. \n
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\param[in] k Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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******************************************************************************/
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int DSPL_API ellip_acd(double* w, int n, double k, double* u)
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{
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double lnd[ELLIP_ITER], t;
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int i, m;
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if(!u || !w)
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return ERROR_PTR;
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if(n<1)
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return ERROR_SIZE;
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if(k < 0.0 || k>= 1.0)
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return ERROR_ELLIP_MODULE;
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ellip_landen(k,ELLIP_ITER, lnd);
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for(m = 0; m < n; m++)
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{
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u[m] = w[m];
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for(i = 1; i < ELLIP_ITER; i++)
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{
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t = lnd[i-1]*u[m];
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t *= t;
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t = 1.0 + sqrt(1.0 - t);
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u[m] = 2.0 * u[m] / (t+t*lnd[i]);
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}
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u[m] = 2.0 * acos(u[m]) / M_PI;
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}
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return RES_OK;
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}
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/*****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_acd_cmplx(complex_t* w, int n, double k, complex_t* u)
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\brief Inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ of complex vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ of complex vector `w`. \n
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\param[in] w Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n Size of vector `w`. \n
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\param[in] k Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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******************************************************************************/
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int DSPL_API ellip_acd_cmplx(complex_t* w, int n, double k, complex_t* u)
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{
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double lnd[ELLIP_ITER], t;
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complex_t tmp0, tmp1;
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int i, m;
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if(!u || !w)
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return ERROR_PTR;
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if(n<1)
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return ERROR_SIZE;
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if(k < 0.0 || k>= 1.0)
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return ERROR_ELLIP_MODULE;
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ellip_landen(k,ELLIP_ITER, lnd);
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for(m = 0; m < n; m++)
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{
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RE(u[m]) = RE(w[m]);
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IM(u[m]) = IM(w[m]);
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for(i = 1; i < ELLIP_ITER; i++)
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{
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RE(tmp0) = lnd[i-1]*RE(u[m]);
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IM(tmp0) = lnd[i-1]*IM(u[m]);
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RE(tmp1) = 1.0 - CMRE(tmp0, tmp0);
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IM(tmp1) = - CMIM(tmp0, tmp0);
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sqrt_cmplx(&tmp1, 1, &tmp0);
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RE(tmp0) += 1.0;
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RE(tmp1) = RE(tmp0) * (1.0 + lnd[i]);
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IM(tmp1) = IM(tmp0) * (1.0 + lnd[i]);
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t = 2.0 / ABSSQR(tmp1);
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RE(tmp0) = t * CMCONJRE(u[m], tmp1);
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IM(tmp0) = t * CMCONJIM(u[m], tmp1);
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RE(u[m]) = RE(tmp0);
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IM(u[m]) = IM(tmp0);
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}
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acos_cmplx(&tmp0, 1, u+m);
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t = 2.0 / M_PI;
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RE(u[m]) *= t;
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IM(u[m]) *= t;
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}
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return RES_OK;
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}
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/*****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_asn(double* w, int n, double k, double* u)
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\brief Inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$ of real vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$ of real vector `w`. \n
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\param[in] w Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n Size of vector `w`. \n
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\param[in] k Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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******************************************************************************/
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int DSPL_API ellip_asn(double* w, int n, double k, double* u)
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{
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double lnd[ELLIP_ITER], t;
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int i, m;
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if(!u || !w)
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return ERROR_PTR;
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if(n<1)
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return ERROR_SIZE;
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if(k < 0.0 || k>= 1.0)
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return ERROR_ELLIP_MODULE;
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ellip_landen(k,ELLIP_ITER, lnd);
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for(m = 0; m < n; m++)
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{
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u[m] = w[m];
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for(i = 1; i < ELLIP_ITER; i++)
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{
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t = lnd[i-1]*u[m];
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t *= t;
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t = 1.0 + sqrt(1.0 - t);
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u[m] = 2.0 * u[m] / (t+t*lnd[i]);
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}
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u[m] = 2.0 * asin(u[m]) / M_PI;
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}
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return RES_OK;
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}
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/*****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_asn_cmplx(complex_t* w, int n, double k, complex_t* u)
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\brief Inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$ of complex vector argument
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Function calculates inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$ of complex vector `w`. \n
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\param[in] w Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n Size of vector `w`. \n
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\param[in] k Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{sn}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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******************************************************************************/
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int DSPL_API ellip_asn_cmplx(complex_t* w, int n, double k, complex_t* u)
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{
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double lnd[ELLIP_ITER], t;
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complex_t tmp0, tmp1;
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int i, m;
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if(!u || !w)
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return ERROR_PTR;
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if(n<1)
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return ERROR_SIZE;
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if(k < 0.0 || k>= 1.0)
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return ERROR_ELLIP_MODULE;
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ellip_landen(k,ELLIP_ITER, lnd);
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for(m = 0; m < n; m++)
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{
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RE(u[m]) = RE(w[m]);
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IM(u[m]) = IM(w[m]);
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for(i = 1; i < ELLIP_ITER; i++)
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{
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RE(tmp0) = lnd[i-1]*RE(u[m]);
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IM(tmp0) = lnd[i-1]*IM(u[m]);
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RE(tmp1) = 1.0 - CMRE(tmp0, tmp0);
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IM(tmp1) = - CMIM(tmp0, tmp0);
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sqrt_cmplx(&tmp1, 1, &tmp0);
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RE(tmp0) += 1.0;
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RE(tmp1) = RE(tmp0) * (1.0 + lnd[i]);
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IM(tmp1) = IM(tmp0) * (1.0 + lnd[i]);
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t = 2.0 / ABSSQR(tmp1);
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RE(tmp0) = t * CMCONJRE(u[m], tmp1);
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IM(tmp0) = t * CMCONJIM(u[m], tmp1);
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RE(u[m]) = RE(tmp0);
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IM(u[m]) = IM(tmp0);
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}
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asin_cmplx(&tmp0, 1, u+m);
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t = 2.0 / M_PI;
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RE(u[m]) *= t;
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IM(u[m]) *= t;
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}
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return RES_OK;
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}
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/*****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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int ellip_cd(double* u, int n, double k, double* y)
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\brief Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$ of real vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$ of real vector `u` and
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elliptical modulus `k`. \n
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\param[in] u Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n Size of vector `u`. \n
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\param[in] k Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] y Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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******************************************************************************/
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int DSPL_API ellip_cd(double* u, int n, double k, double* y)
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{
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double lnd[ELLIP_ITER];
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int i, m;
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if(!u || !y)
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return ERROR_PTR;
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if(n<1)
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return ERROR_SIZE;
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if(k < 0.0 || k>= 1.0)
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return ERROR_ELLIP_MODULE;
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ellip_landen(k,ELLIP_ITER, lnd);
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for(m = 0; m < n; m++)
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{
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y[m] = cos(u[m] * M_PI * 0.5);
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for(i = ELLIP_ITER-1; i>0; i--)
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{
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y[m] = (1.0 + lnd[i]) / (1.0 / y[m] + lnd[i]*y[m]);
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}
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}
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return RES_OK;
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}
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/*****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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int ellip_cd_cmplx(complex_t* u, int n, double k, complex_t* y)
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\brief Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$ of complex vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$ of complex vector `u` and
|
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elliptical modulus `k`. \n
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\param[in] u Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n Size of vector `u`. \n
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\param[in] k Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
|
||
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\param[out] y Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{cd}(u K(k), k)\f$. \n
|
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Vector size is `[n x 1]`. \n
|
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Memory must be allocated. \n \n
|
||
|
||
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
|
||
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\author Sergey Bakhurin www.dsplib.org
|
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******************************************************************************/
|
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int DSPL_API ellip_cd_cmplx(complex_t* u, int n, double k, complex_t* y)
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{
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double lnd[ELLIP_ITER], t;
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int i, m;
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complex_t tmp;
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if(!u || !y)
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return ERROR_PTR;
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if(n<1)
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return ERROR_SIZE;
|
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if(k < 0.0 || k>= 1.0)
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return ERROR_ELLIP_MODULE;
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ellip_landen(k,ELLIP_ITER, lnd);
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for(m = 0; m < n; m++)
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{
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RE(tmp) = RE(u[m]) * M_PI * 0.5;
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IM(tmp) = IM(u[m]) * M_PI * 0.5;
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cos_cmplx(&tmp, 1, y+m);
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for(i = ELLIP_ITER-1; i>0; i--)
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{
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t = 1.0 / ABSSQR(y[m]);
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RE(tmp) = RE(y[m]) * t + RE(y[m]) * lnd[i];
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IM(tmp) = -IM(y[m]) * t + IM(y[m]) * lnd[i];
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t = (1.0 + lnd[i]) / ABSSQR(tmp);
|
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RE(y[m]) = RE(tmp) * t;
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IM(y[m]) = -IM(tmp) * t;
|
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|
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}
|
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}
|
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return RES_OK;
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
|
||
/*****************************************************************************
|
||
\ingroup SPEC_MATH_ELLIP_GROUP
|
||
\fn int ellip_landen(double k, int n, double* y)
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\brief Function calculates complete elliptical integral
|
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coefficients \f$ k_i \f$
|
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|
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Complete elliptical integral \f$ K(k) \f$ can be described as:
|
||
|
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\f[
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K(k) = \frac{\pi}{2} \prod_{i = 1}^{\infty}(1+k_i),
|
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\f]
|
||
|
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here \f$ k_i \f$ -- coefficients which calculated
|
||
iterative from \f$ k_0 = k\f$:
|
||
|
||
\f[
|
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k_i =
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\left(
|
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\frac{k_{i-1}}
|
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{
|
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1+\sqrt{1-k_{i-1}^2}
|
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}
|
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\right)^2
|
||
\f]
|
||
|
||
This function calculates `n` fist coefficients \f$ k_i \f$, which can
|
||
be used for Complete elliptical integral.
|
||
|
||
|
||
\param[in] k Elliptical modulus \f$ k \f$. \n
|
||
Elliptical modulus is real parameter,
|
||
which values can be from 0 to 1. \n \n
|
||
|
||
|
||
\param[in] n Number of \f$ k_i \f$ which need to calculate.\n
|
||
Parameter `n` is size of output vector `y`.\n
|
||
|
||
\param[out] y pointer to the real vector which keep \f$ k_i \f$. \n
|
||
Vector size is `[n x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
|
||
\return
|
||
`RES_OK` -- successful exit, else \ref ERROR_CODE_GROUP "error code". \n
|
||
|
||
Example:
|
||
|
||
\include ellip_landen_test.c
|
||
|
||
Result:
|
||
|
||
\verbatim
|
||
i k[i]
|
||
|
||
1 4.625e-01
|
||
2 6.009e-02
|
||
3 9.042e-04
|
||
4 2.044e-07
|
||
5 1.044e-14
|
||
6 2.727e-29
|
||
7 1.859e-58
|
||
8 8.640e-117
|
||
9 1.866e-233
|
||
10 0.000e+00
|
||
11 0.000e+00
|
||
12 0.000e+00
|
||
13 0.000e+00
|
||
\endverbatim
|
||
|
||
\note Complete elliptical integral converges enough fast
|
||
if modulus \f$ k<1 \f$. There are 10 to 20 coefficients \f$ k_i \f$
|
||
are sufficient for practical applications
|
||
to ensure complete elliptic integral precision within EPS.
|
||
|
||
\author Sergey Bakhurin www.dsplib.org
|
||
******************************************************************************/
|
||
int DSPL_API ellip_landen(double k, int n, double* y)
|
||
{
|
||
int i;
|
||
y[0] = k;
|
||
|
||
if(!y)
|
||
return ERROR_PTR;
|
||
if(n < 1)
|
||
return ERROR_SIZE;
|
||
if(k < 0.0 || k>= 1.0)
|
||
return ERROR_ELLIP_MODULE;
|
||
|
||
for(i = 1; i < n; i++)
|
||
{
|
||
y[i] = y[i-1] / (1.0 + sqrt(1.0 - y[i-1] * y[i-1]));
|
||
y[i] *= y[i];
|
||
}
|
||
|
||
return RES_OK;
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
/*****************************************************************************
|
||
* Elliptic modular equation
|
||
******************************************************************************/
|
||
int DSPL_API ellip_modulareq(double rp, double rs, int ord, double *k)
|
||
{
|
||
double ep, es, ke, kp, t, sn = 0.0;
|
||
int i, L, r;
|
||
|
||
if(rp < 0 || rp == 0)
|
||
return ERROR_FILTER_RP;
|
||
if(rs < 0 || rs == 0)
|
||
return ERROR_FILTER_RS;
|
||
if(ord < 1)
|
||
return ERROR_FILTER_ORD;
|
||
if(!k)
|
||
return ERROR_PTR;
|
||
|
||
|
||
ep = sqrt(pow(10.0, rp*0.1)-1.0);
|
||
es = sqrt(pow(10.0, rs*0.1)-1.0);
|
||
|
||
ke = ep/es;
|
||
|
||
ke = sqrt(1.0 - ke*ke);
|
||
|
||
r = ord % 2;
|
||
L = (ord-r)/2;
|
||
|
||
kp = 1.0;
|
||
for(i = 0; i < L; i++)
|
||
{
|
||
t = (double)(2*i+1) / (double)ord;
|
||
ellip_sn(&t, 1, ke, &sn);
|
||
sn*=sn;
|
||
kp *= sn*sn;
|
||
}
|
||
|
||
kp *= pow(ke, (double)ord);
|
||
*k = sqrt(1.0 - kp*kp);
|
||
|
||
return RES_OK;
|
||
|
||
}
|
||
|
||
|
||
|
||
/*****************************************************************************
|
||
* Elliptic rational function
|
||
******************************************************************************/
|
||
int DSPL_API ellip_rat(double* w, int n, int ord, double k, double* u)
|
||
{
|
||
double t, xi, w2, xi2, k2;
|
||
int i, m, r, L;
|
||
|
||
if(!u || !w)
|
||
return ERROR_PTR;
|
||
if(n<1)
|
||
return ERROR_SIZE;
|
||
if(k < 0.0 || k>= 1.0)
|
||
return ERROR_ELLIP_MODULE;
|
||
|
||
r = ord%2;
|
||
L = (ord-r)/2;
|
||
|
||
if(r)
|
||
memcpy(u, w, n*sizeof(double));
|
||
else
|
||
{
|
||
for(m = 0; m < n; m++)
|
||
{
|
||
u[m] = 1.0;
|
||
}
|
||
}
|
||
|
||
k2 = k*k;
|
||
for(i = 0; i < L; i++)
|
||
{
|
||
t = (double)(2*i+1) / (double)ord;
|
||
ellip_cd(&t, 1, k, &xi);
|
||
xi2 = xi*xi;
|
||
for(m = 0; m < n; m++)
|
||
{
|
||
w2 = w[m]*w[m];
|
||
u[m] *= (w2 - xi2) / (1.0 - w2 * k2 * xi2);
|
||
u[m] *= (1.0 - k2*xi2) / (1.0 - xi2);
|
||
}
|
||
}
|
||
return RES_OK;
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
|
||
/*****************************************************************************
|
||
\ingroup SPEC_MATH_ELLIP_GROUP
|
||
int ellip_sn(double* u, int n, double k, double* y)
|
||
\brief Jacobi elliptic function
|
||
\f$ y = \textrm{sn}(u K(k), k)\f$ of real vector argument
|
||
|
||
Function calculates Jacobi elliptic function
|
||
\f$ y = \textrm{sn}(u K(k), k)\f$ of real vector `u` and
|
||
elliptical modulus `k`. \n
|
||
|
||
\param[in] u Pointer to the argument vector \f$ u \f$. \n
|
||
Vector size is `[n x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
\param[in] n Size of vector `u`. \n
|
||
|
||
\param[in] k Elliptical modulus \f$ k \f$. \n
|
||
Elliptical modulus is real parameter,
|
||
which values can be from 0 to 1. \n \n
|
||
|
||
|
||
\param[out] y Pointer to the vector of Jacobi elliptic function
|
||
\f$ y = \textrm{sn}(u K(k), k)\f$. \n
|
||
Vector size is `[n x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
|
||
\return
|
||
`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
|
||
|
||
\author Sergey Bakhurin www.dsplib.org
|
||
******************************************************************************/
|
||
int DSPL_API ellip_sn(double* u, int n, double k, double* y)
|
||
{
|
||
double lnd[ELLIP_ITER];
|
||
int i, m;
|
||
|
||
if(!u || !y)
|
||
return ERROR_PTR;
|
||
if(n<1)
|
||
return ERROR_SIZE;
|
||
if(k < 0.0 || k>= 1.0)
|
||
return ERROR_ELLIP_MODULE;
|
||
|
||
ellip_landen(k,ELLIP_ITER, lnd);
|
||
|
||
|
||
for(m = 0; m < n; m++)
|
||
{
|
||
y[m] = sin(u[m] * M_PI * 0.5);
|
||
for(i = ELLIP_ITER-1; i>0; i--)
|
||
{
|
||
y[m] = (1.0 + lnd[i]) / (1.0 / y[m] + lnd[i]*y[m]);
|
||
}
|
||
}
|
||
return RES_OK;
|
||
}
|
||
|
||
|
||
|
||
|
||
/*****************************************************************************
|
||
\ingroup SPEC_MATH_ELLIP_GROUP
|
||
int ellip_sn_cmplx(complex_t* u, int n, double k, complex_t* y)
|
||
\brief Jacobi elliptic function
|
||
\f$ y = \textrm{sn}(u K(k), k)\f$ of complex vector argument
|
||
|
||
Function calculates Jacobi elliptic function
|
||
\f$ y = \textrm{sn}(u K(k), k)\f$ of complex vector `u` and
|
||
elliptical modulus `k`. \n
|
||
|
||
\param[in] u Pointer to the argument vector \f$ u \f$. \n
|
||
Vector size is `[n x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
\param[in] n Size of vector `u`. \n
|
||
|
||
\param[in] k Elliptical modulus \f$ k \f$. \n
|
||
Elliptical modulus is real parameter,
|
||
which values can be from 0 to 1. \n \n
|
||
|
||
|
||
\param[out] y Pointer to the vector of Jacobi elliptic function
|
||
\f$ y = \textrm{sn}(u K(k), k)\f$. \n
|
||
Vector size is `[n x 1]`. \n
|
||
Memory must be allocated. \n \n
|
||
|
||
|
||
\return
|
||
`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
|
||
|
||
\author Sergey Bakhurin www.dsplib.org
|
||
******************************************************************************/
|
||
int DSPL_API ellip_sn_cmplx(complex_t* u, int n, double k, complex_t* y)
|
||
{
|
||
double lnd[ELLIP_ITER], t;
|
||
int i, m;
|
||
complex_t tmp;
|
||
|
||
if(!u || !y)
|
||
return ERROR_PTR;
|
||
if(n<1)
|
||
return ERROR_SIZE;
|
||
if(k < 0.0 || k>= 1.0)
|
||
return ERROR_ELLIP_MODULE;
|
||
|
||
ellip_landen(k,ELLIP_ITER, lnd);
|
||
|
||
|
||
for(m = 0; m < n; m++)
|
||
{
|
||
RE(tmp) = RE(u[m]) * M_PI * 0.5;
|
||
IM(tmp) = IM(u[m]) * M_PI * 0.5;
|
||
|
||
sin_cmplx(&tmp, 1, y+m);
|
||
|
||
for(i = ELLIP_ITER-1; i>0; i--)
|
||
{
|
||
t = 1.0 / ABSSQR(y[m]);
|
||
|
||
RE(tmp) = RE(y[m]) * t + RE(y[m]) * lnd[i];
|
||
IM(tmp) = -IM(y[m]) * t + IM(y[m]) * lnd[i];
|
||
|
||
t = (1.0 + lnd[i]) / ABSSQR(tmp);
|
||
|
||
RE(y[m]) = RE(tmp) * t;
|
||
IM(y[m]) = -IM(tmp) * t;
|
||
|
||
}
|
||
}
|
||
return RES_OK;
|
||
}
|
||
|