kopia lustrzana https://github.com/Dsplib/libdspl-2.0
178 wiersze
5.1 KiB
C
178 wiersze
5.1 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 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 cheby_poly2(double* x, int n, int ord, double* y)
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\brief Chebyshev polynomial of the second kind order `ord`
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Function calculates Chebyshev polynomial \f$ U_ord(x)\f$ of the first kind
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order `ord` for the real vector `x` (length `n`) by recurrent equation:
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\f[
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U_{ord}(x) = 2 x U_{ord-1}(x) - U_{ord-2}(x),
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\f]
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where \f$ U_0(x) = 1 \f$, \f$ U_1(x) = 2x\f$
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\param[in] x
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Pointer to the real argument vector `x`. \n
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Vector size is `[n x 1]`. \n \n
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\param[in] n
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Size of vectors `x` and `y`. \n \n
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\param[in] ord
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Chebyshev polynomial order. \n \n
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\param[out] y
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Pointer to the Chebyshev polynomial values, corresponds to the argument `x`. \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` if Chebyshev polynomial is calculated successfully. \n
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Else \ref ERROR_CODE_GROUP "code error". \n
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Example:
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\include cheby_poly2_test.c
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Text files will be created in `dat` directory: \n
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\verbatim
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cheby_poly2_ord1.txt
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cheby_poly2_ord2.txt
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cheby_poly2_ord3.txt
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cheby_poly2_ord4.txt
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\endverbatim
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GNUPLOT package will create Chebyshev polynomials plot from saved text-files:
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\image html cheby_poly2.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_POLY_GROUP
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\fn int cheby_poly2(double* x, int n, int ord, double* y)
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\brief Многочлен Чебышева второго рода порядка `ord`
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Функция производит расчет многочлена Чебышева второго рода \f$ U_{ord}(x)\f$
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для вещественного вектора `x` длины `n`на основе рекуррентной формулы
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\f[
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U_{ord}(x) = 2 x U_{ord-1}(x) - U_{ord-2}(x),
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\f]
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где \f$ U_0(x) = 1 \f$, \f$ U_1(x) = 2x\f$
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\param[in] x
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Указатель на вектор `x` аргумента полинома Чебышева второго рода. \n
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Размер вектора `[n x 1]`. \n \n
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\param[in] n
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Размер векторов `x` и `y`. \n \n
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\param[in] ord
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Порядок полинома Чебышева второго рода. \n \n
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\param[out] y
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Указатель на вектор значений полинома Чебышева,
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соответствующих аргументу `x`. \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:
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\include cheby_poly2_test.c
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В каталоге `dat` будут созданы текстовые файлы значений
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полиномов порядка 1-4: \n
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\verbatim
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cheby_poly2_ord1.txt
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cheby_poly2_ord2.txt
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cheby_poly2_ord3.txt
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cheby_poly2_ord4.txt
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\endverbatim
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Кроме того программа GNUPLOT произведет построение следующих графиков
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по сохраненным в файлах данным:
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\image html cheby_poly2.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 cheby_poly2(double* x, int n, int ord, double* y)
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{
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int k, m;
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double t[2];
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if(!x || !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(ord<0)
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return ERROR_POLY_ORD;
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if(ord==0)
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{
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for(k = 0; k < n; k++)
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{
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y[k] = 1.0;
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}
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return RES_OK;
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}
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if(ord==1)
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{
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for(k = 0; k < n; k++)
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{
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y[k] = 2.0*x[k];
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};
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return RES_OK;
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}
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for(k = 0; k < n; k++)
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{
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m = 2;
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t[1] = 2.0*x[k];
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t[0] = 1.0;
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while(m <= ord)
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{
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y[k] = 2.0 * x[k] *t[1] - t[0];
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t[0] = t[1];
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t[1] = y[k];
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m++;
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}
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}
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return RES_OK;
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}
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