kopia lustrzana https://github.com/Dsplib/libdspl-2.0
187 wiersze
6.4 KiB
C
187 wiersze
6.4 KiB
C
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/*
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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 libdspl-2.0.
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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 Lesser 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 Lesser 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 <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_POLY_GROUP
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\fn int polyroots(double* a, int ord, complex_t* r, int* info)
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\brief Function calculates real polynomial roots.
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Function calculates roots of the real polynomial \f$P_N(x)\f$ order \f$N\f$
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with `a` coefficient vector size `[(N+1) x 1]`.
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\f[
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P_N(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + ... a_N x^N.
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\f]
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The roots of the polynomial are calculated as eigenvalues of the polynomial
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companion matrix. To calculate the eigenvalues,
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a subroutine of the LAPACK package is used.
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\param[in] a
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Pointer to the vector of coefficients. \n
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Vector size is `[ord+1 x 1]`. \n
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Coefficient `a[0]` corresponds to the \f$a_0\f$ polynomial coefficient. \n
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Coefficient `a[ord]` cannot be zero. \n \n
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\param[in] ord
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Polynomial order \f$N\f$. \n \n
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\param[out] r
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Pointer to the polynomial roots vector. \n
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Vector size is `[ord x 1]`. \n
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Memory must be allocated. \n
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The roots of a real polynomial can be either real or form simple
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or multiple complex conjugate pairs of roots. Therefore, the output
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root vector is of a complex data type. \n \n
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\param[out] info
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Pointer to the LAPACK subroutine error code. \n
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This code is returned by the LAPACK subroutine and translated through
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this variable for analysis.. \n\n
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\return
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`RES_OK` --- roots are calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error".
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Example:
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\include polyroots_test.c
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This program calculates the roots of the polynomial
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\f[
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P(x) = 2 + 2x + x^2
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\f]
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and prints the calculated roots.
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The result of the program:
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\verbatim
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Error code: 0x00000000
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r[0] = -1.00000 1.00000 j
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r[1] = -1.00000-1.00000 j
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\endverbatim
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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_POLY_GROUP
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\fn int polyroots(double* a, int ord, complex_t* r, int* info)
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\brief Расчет корней вещественного полинома
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Функция рассчитывает корни полинома \f$P_N(x)\f$ \f$N-\f$ого
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порядка, заданного вектором коэффициентов `a`.
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\f[
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P_N(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + ... a_N x^N.
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\f]
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Корни полинома рассчитываются как собственные числа характеристической
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матрицы полинома. Для расчета собственных чисел используется подпрограмма
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пакета LAPACK.
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\param[in] a
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Указатель на вектор вещественных коэффициентов полинома. \n
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Размер вектора `[ord+1 x 1]`. \n
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Коэффициент `a[0]` соответствует коэффициенту полинома \f$a_0\f$. \n
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Коэффициент `a[ord]` не должен быть равен нулю. \n \n
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\param[in] ord
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Порядок полинома \f$N\f$. \n \n
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\param[out] r
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Указатель на вектор комплексных корней полинома. \n
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Размер вектора `[ord x 1]`. \n
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Память должна быть выделена. \n
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Корни вещественного полинома могут быть как вещественными,
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так и образовывать простые или кратные комплексно-сопряженные пары корней.
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Поэтому выходной вектор корней имеет комплексный тип данных.
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\n \n
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\param[out] info
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Указатель наа код возврата пакета LAPACK. \n
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Данный код возвращается подпрограммой LAPACK и транслируется через данную
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переменную для возможности анализа. \n\n
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\return
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`RES_OK` --- корни полинома рассчитаны успешно. \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки".
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Пример расчета корней полинома:
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\include polyroots_test.c
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Данная программа производит расчет корней полинома
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\f[
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P(x) = 2 + 2x + x^2
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\f]
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и выводит рассчитанные корни на печать.
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Результат работы программы:
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\verbatim
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Error code: 0x00000000
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r[0] = -1.00000 1.00000 j
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r[1] = -1.00000-1.00000 j
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\endverbatim
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Получили пару комплексно-сопряженных корней полинома.
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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 polyroots(double* a, int ord, complex_t* r, int* info)
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{
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complex_t *t = NULL;
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int m;
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int err;
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if(!a || !r)
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return ERROR_PTR;
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if(ord<0)
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return ERROR_POLY_ORD;
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if(a[ord] == 0.0)
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return ERROR_POLY_AN;
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t = (complex_t*)malloc(ord * ord * sizeof(complex_t));
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if(!t)
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return ERROR_MALLOC;
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for(m = 0; m < ord-1; m++)
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{
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RE(t[m * (ord+1) + 1]) = 1.0;
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RE(t[m + ord * (ord - 1)]) = -a[m] / a[ord];
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}
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RE(t[ord * ord - 1]) = -a[ord-1] / a[ord];
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err = matrix_eig_cmplx(t, ord, r, info);
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if(t)
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free(t);
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return err;
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}
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