kopia lustrzana https://github.com/Dsplib/libdspl-2.0
152 wiersze
5.0 KiB
C
152 wiersze
5.0 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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#ifdef DOXYGEN_ENGLISH
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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 \f$ u = \textrm{cd}^{-1}(w, k)\f$
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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
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Pointer to the argument vector \f$ w \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `w`. \n \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] u
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Pointer to the vector of inverse Jacobi elliptic function
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\f$ u = \textrm{cd}^{-1}(w, k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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\author Sergey Bakhurin www.dsplib.org
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***************************************************************************** */
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#endif
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#ifdef DOXYGEN_RUSSIAN
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/*! ****************************************************************************
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\ingroup SPEC_MATH_ELLIP_GROUP
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\fn int ellip_acd_cmplx(complex_t* w, int n, double k, complex_t* u)
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\brief Обратная эллиптическая функция Якоби
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ комплексного аргумента
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Функция рассчитывает значения значения обратной эллиптической функции
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\f$ u = \textrm{cd}^{-1}(w, k)\f$ для комплексного вектора `w`. \n
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Для расчета используется итерационный алгоритм на основе преобразования
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Ландена. \n
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\param[in] w
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Указатель на массив вектора переменной \f$ w \f$. \n
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Размер вектора `[n x 1]`. \n
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Память должна быть выделена. \n \n
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\param[in] n
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Размер вектора `w`. \n \n
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\param[in] k
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Значение эллиптического модуля \f$ k \f$. \n
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Эллиптический модуль -- вещественный параметр,
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принимающий значения от 0 до 1. \n \n
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\param[out] u
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Указатель на вектор значений обратной эллиптической
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функции \f$ u = \textrm{cd}^{-1}(w, k)\f$. \n
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Размер вектора `[n x 1]`. \n
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Память должна быть выделена. \n \n
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\return
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`RES_OK` Расчет произведен успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки". \n
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\author Бахурин Сергей www.dsplib.org
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***************************************************************************** */
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#endif
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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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