kopia lustrzana https://github.com/Dsplib/libdspl-2.0
198 wiersze
5.8 KiB
C
198 wiersze
5.8 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_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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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
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iterative from \f$ k_0 = k\f$:
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\f[
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k_i = \left( \frac{k_{i-1}}{1+\sqrt{1-k_{i-1}^2}}\right)^2
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\f]
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This function calculates `n` fist coefficients \f$ k_i \f$, which can
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be used for Complete elliptical integral.
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\param[in] k
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Elliptical modulus \f$ k \f$. \n
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Elliptical modulus is real parameter, which values can be from 0 to 1. \n \n
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\param[in] n
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Number of \f$ k_i \f$ which need to calculate. \n
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Parameter `n` is size of output vector `y`. \n
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\param[out] y
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pointer to the real vector which keep \f$ k_i \f$. \n
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Vector size is `[n x 1]`. \n
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Memory must be allocated. \n \n
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\return
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`RES_OK` -- successful exit, else \ref ERROR_CODE_GROUP "error code". \n
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Example:
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\include ellip_landen_test.c
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Result:
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\verbatim
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i k[i]
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1 4.625e-01
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2 6.009e-02
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3 9.042e-04
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4 2.044e-07
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5 1.044e-14
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6 2.727e-29
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7 1.859e-58
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8 8.640e-117
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9 1.866e-233
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10 0.000e+00
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11 0.000e+00
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12 0.000e+00
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13 0.000e+00
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\endverbatim
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\note Complete elliptical integral converges enough fast
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if modulus \f$ k<1 \f$. There are 10 to 20 coefficients \f$ k_i \f$
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are sufficient for practical applications
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to ensure complete elliptic integral precision within EPS.
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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_landen(double k, int n, double* y)
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\brief Расчет коэффициентов \f$ k_i \f$ ряда полного эллиптического интеграла.
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Полный эллиптический интеграл \f$ K(k) \f$ может быть представлен рядом:
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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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где \f$ k_i \f$ вычисляется итерационно при начальных условиях \f$ k_0 = k\f$:
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\f[
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k_i = \left( \frac{k_{i-1}}{1+\sqrt{1-k_{i-1}^2}}\right)^2
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\f]
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Данная функция рассчитывает ряд первых `n` значений \f$ k_i \f$, которые в
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дальнейшем могут быть использованы для расчета эллиптического интеграла и
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эллиптических функций.
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\param[in] k
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Эллиптический модуль \f$ k \f$. \n
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\param[in] n
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Размер вектора `y` соответствующих коэффициентам \f$ k_i \f$. \n \n
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\param[out] y
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Указатель на вектор значений коэффициентов \f$ k_i \f$. \n
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Размер вектора `[n x 1]`. \n
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Память должна быть выделена. \n \n
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\return
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`RES_OK` Расчет произведен успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки". \n
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Пример использования функции `ellip_landen`:
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\include ellip_landen_test.c
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Результат работы программы:
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\verbatim
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i k[i]
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1 4.625e-01
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2 6.009e-02
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3 9.042e-04
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4 2.044e-07
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5 1.044e-14
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6 2.727e-29
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7 1.859e-58
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8 8.640e-117
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9 1.866e-233
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10 0.000e+00
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11 0.000e+00
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12 0.000e+00
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13 0.000e+00
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\endverbatim
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\note
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Ряд полного эллиптического интеграла сходится при значениях
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эллиптического модуля \f$ k<1 \f$. При этом сходимость ряда достаточно
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быстрая и для практический приложений достаточно от 10 до 20 значений
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\f$ k_i \f$ для обеспечения погрешности при расчете полного
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эллиптического интеграла в пределах машинной точности.
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\author
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Бахурин Сергей
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www.dsplib.org
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***************************************************************************** */
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#endif
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int DSPL_API ellip_landen(double k, int n, double* y)
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{
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int i;
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y[0] = k;
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if(!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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for(i = 1; i < n; i++)
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{
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y[i] = y[i-1] / (1.0 + sqrt(1.0 - y[i-1] * y[i-1]));
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y[i] *= y[i];
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}
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return RES_OK;
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}
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