2021-12-29 13:31:00 +00:00
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/*
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2023-12-13 17:18:47 +00:00
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* Copyright (c) 2015-2024 Sergey Bakhurin
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2021-12-29 13:31:00 +00:00
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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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2023-12-13 17:18:47 +00:00
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2021-12-29 13:31:00 +00:00
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\brief Jacobi elliptic function \f$ y = \textrm{sn}(u K(k), k)\f$
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of real vector argument
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Function calculates Jacobi elliptic function
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\f$ y = \textrm{sn}(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
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Pointer to the argument vector \f$ u \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\param[in] n
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Size of vector `u`. \n \n
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter,
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which values can be from 0 to 1. \n \n
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\param[out] y
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Pointer to the vector of Jacobi elliptic function
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\f$ y = \textrm{sn}(u K(k), k)\f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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Example
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\include ellip_sn_test.c
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The program calculates two periods of the \f$ y = \textrm{sn}(u K(k), k)\f$
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function for different modulus values `k = 0`, `k= 0.9` и `k = 0.99`.
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Also program draws the plot of calculated elliptic functions.
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\image html ellip_sn.png
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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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\brief Эллиптическая функция Якоби
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\f$ y = \textrm{sn}(u K(k), k)\f$ вещественного аргумента
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Функция рассчитывает значения значения эллиптической функции
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\f$ y = \textrm{sn}(u K(k), k)\f$ для вещественного вектора `u` и
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эллиптического модуля `k`. \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] u
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Указатель на массив вектора переменной \f$ u \f$. \n
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Размер вектора `[n x 1]`. \n
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Память должна быть выделена. \n \n
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\param[in] n
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Размер вектора `u`. \n \n
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\param[in] k
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Значение эллиптического модуля \f$ k \f$. \n
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Эллиптический модуль -- вещественный параметр,
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принимающий значения от 0 до 1. \n \n
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\param[out] y
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Указатель на вектор значений эллиптической
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функции \f$ y = \textrm{sn}(u K(k), k)\f$. \n
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Размер вектора `[n x 1]`. \n
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Память должна быть выделена. \n \n
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\return
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`RES_OK` Расчет произведен успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки". \n
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Пример представлен в следующем листинге:
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\include ellip_sn_test.c
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Программа рассчитывает два периода эллиптической функции
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\f$ y = \textrm{sn}(u K(k), k)\f$ для `k = 0`, `k= 0.9` и `k = 0.99`,
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а также выводит графики данных функций
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\image html ellip_sn.png
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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_sn(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] = sin(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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