kopia lustrzana https://github.com/Dsplib/libdspl-2.0
162 wiersze
5.0 KiB
C
162 wiersze
5.0 KiB
C
/*
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* Copyright (c) 2015-2024 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 "dspl.h"
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#ifdef DOXYGEN_ENGLISH
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/*! ****************************************************************************
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\ingroup SPEC_MATH_TRIG_GROUP
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\brief The inverse of the sine function the complex vector argument `x`.
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Function calculates the inverse of the sine function as: \n
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\f[
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\textrm{Arcsin}(x) = j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right)
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\f]
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\param[in] x
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Pointer to the 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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Input vector `x` and the inverse sine vector `y` size. \n\n
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\param[out] y
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Pointer to the output complex vector `y`,
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corresponds to the input vector `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 function calculated successfully.\n
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Else \ref ERROR_CODE_GROUP "code error". \n
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Example: \n
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\code{.cpp}
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complex_t x[3] = {{1.0, 2.0}, {3.0, 4.0}, {5.0, 6.0}};
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complex_t y[3];
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int k;
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asin_cmplx(x, 3, y);
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for(k = 0; k < 3; k++)
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printf("asin_cmplx(%.1f%+.1fj) = %.3f%+.3fj\n",
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RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));
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\endcode
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\n
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Output is: \n
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\verbatim
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asin_cmplx(1.0+2.0j) = 0.427+1.529j
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asin_cmplx(3.0+4.0j) = 0.634+2.306j
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asin_cmplx(5.0+6.0j) = 0.691+2.749j
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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_TRIG_GROUP
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\brief Арксинус комплексного аргумента `x`.
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Функция рассчитывает значения арксинуса комплексного аргумента,
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заданного вектором `x` длины `n`: \n
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\f[
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\textrm{Arcsin}(x) = j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right)
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\f]
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\param[in] x
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Указатель на вектор аргумента комплексного арксинуса. \n
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Размер вектора `[n x 1]`. \n \n
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\param[in] n
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Размер входного и выходного векторов `x` и `y`. \n \n
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\param[out] y
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Указатель на вектор значений комплексного арксинуса,
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соответствующего входному вектору `x`. \n
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Размер массива `[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` если значение функции рассчитано успешно . \n
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В противном случае \ref ERROR_CODE_GROUP "код ошибки": \n
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\note
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Функция может использоваться для расчета арксинуса аргумента
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большего единицы, когда вещественная функция `acos` не определена.
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Например при выполнении следующего кода
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\code{.cpp}
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complex_t x[3] = {{1.0, 2.0}, {3.0, 4.0}, {5.0, 6.0}};
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complex_t y[3];
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int k;
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asin_cmplx(x, 3, y);
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for(k = 0; k < 3; k++)
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printf("asin_cmplx(%.1f%+.1fj) = %.3f%+.3fj\n",
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RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));
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\endcode
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\n
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Результатом работы будет
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\verbatim
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asin_cmplx(1.0+2.0j) = 0.427+1.529j
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asin_cmplx(3.0+4.0j) = 0.634+2.306j
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asin_cmplx(5.0+6.0j) = 0.691+2.749j
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\endverbatim
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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 asin_cmplx(complex_t* x, int n, complex_t *y)
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{
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int k;
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complex_t tmp;
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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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for(k = 0; k < n; k++)
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{
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RE(tmp) = 1.0 - CMRE(x[k], x[k]); /* 1-x[k]^2 */
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IM(tmp) = - CMIM(x[k], x[k]); /* 1-x[k]^2 */
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sqrt_cmplx(&tmp, 1, y+k); /* sqrt(1 - x[k]^2) */
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RE(y[k]) -= IM(x[k]); /* j * x[k] + sqrt(1 - x[k]^2) */
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IM(y[k]) += RE(x[k]); /* j * x[k] + sqrt(1 - x[k]^2) */
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log_cmplx(y+k, 1, &tmp); /* log( j * x[k] + sqrt(1 - x[k]^2) ) */
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RE(y[k]) = IM(tmp); /* -j * log( j * x[k] + sqrt(1 - x[k]^2) ) */
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IM(y[k]) = -RE(tmp); /* -j * log( j * x[k] + sqrt(1 - x[k]^2) ) */
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}
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return RES_OK;
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}
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