kopia lustrzana https://github.com/Dsplib/libdspl-2.0
628 wiersze
15 KiB
C
628 wiersze
15 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 "dspl.h"
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/******************************************************************************
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\ingroup SPEC_MATH_TRIG_GROUP
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\fn int acos_cmplx(complex_t* x, int n, complex_t *y)
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\brief The inverse of the cosine function the complex vector argument `x`
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Function calculates the inverse of the cosine function as: \n
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\f[
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\textrm{Arccos}(x) = \frac{\pi}{2} - \textrm{Arcsin}(x) =
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\frac{\pi}{2} -j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right)
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\f]
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\param[in] x 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 Input vector `x` and the inverse cosine vector `y` size. \n \n
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\param[out] y 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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acos_cmplx(x, 3, y);
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for(k = 0; k < 3; k++)
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printf("acos_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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acos_cmplx(1.0+2.0j) = 1.144-1.529j
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acos_cmplx(3.0+4.0j) = 0.937-2.306j
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acos_cmplx(5.0+6.0j) = 0.880-2.749j
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\endverbatim
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\author
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Sergey Bakhurin www.dsplib.org
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*******************************************************************************/
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int DSPL_API acos_cmplx(complex_t* x, int n, complex_t *y)
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{
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int k, res;
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double pi2 = 0.5 * M_PI;
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res = asin_cmplx(x, n, y);
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if(res != RES_OK)
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return res;
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for(k = 0; k < n; k++)
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{
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RE(y[k]) = pi2 - RE(y[k]);
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IM(y[k]) = - IM(y[k]);
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}
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return RES_OK;
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}
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/******************************************************************************
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\ingroup SPEC_MATH_TRIG_GROUP
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\fn int asin_cmplx(complex_t* x, int n, complex_t *y)
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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 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 Input vector `x` and the inverse sine vector `y` size. \n \n
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\param[out] y 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
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Sergey Bakhurin www.dsplib.org
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*******************************************************************************/
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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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/******************************************************************************
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\ingroup TYPES_GROUP
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\fn int cmplx2re(complex_t* x, int n, double* re, double* im)
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\brief Separate complex vector to the real and image vectors
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Function fills `re` and `im` vectors corresponds to real and image
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parts of the input complex array `x`. \n
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\param[in] x Pointer to the real complex vector. \n
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Vector size is `[n x 1]`. \n \n
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\param[in] n Size of the input complex vector `x` and real and image
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vectors `re` and `im`. \n \n
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\param[out] re Pointer to the real part vector. \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[out] im Pointer to the image part vector. \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 converts complex vector 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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double re[3], im[3];
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cmplx2re(x, 3, re, im);
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\endcode
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Vectors `re` and `im` will contains:
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\verbatim
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re[0] = 1.0; im[0] = 2.0;
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re[1] = 3.0; im[1] = 4.0;
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re[2] = 5.0; im[2] = 6.0;
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\endverbatim
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\author Sergey Bakhurin. www.dsplib.org
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*******************************************************************************/
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int DSPL_API cmplx2re(complex_t* x, int n, double* re, double* im)
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{
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int k;
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if(!x)
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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(re)
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{
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for(k = 0; k < n; k++)
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re[k] = RE(x[k]);
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}
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if(im)
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{
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for(k = 0; k < n; k++)
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im[k] = IM(x[k]);
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}
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return RES_OK;
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}
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/******************************************************************************
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\ingroup SPEC_MATH_TRIG_GROUP
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\fn int cos_cmplx(complex_t* x, int n, complex_t *y)
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\brief The cosine function the complex vector argument `x`
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Function calculates the cosine function as: \n
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\f[
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\textrm{cos}(x) = \frac{\exp(jx) + \exp(-jx)}{2}
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\f]
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\param[in] x 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 Input vector `x` and the cosine vector `y` size. \n \n
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\param[out] y 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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cos_cmplx(x, 3, y);
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for(k = 0; k < 3; k++)
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printf("cos_cmplx(%.1f%+.1fj) = %9.3f%+9.3fj\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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cos_cmplx(1.0+2.0j) = 2.033 -3.052j
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cos_cmplx(3.0+4.0j) = -27.035 -3.851j
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cos_cmplx(5.0+6.0j) = 57.219 +193.428j
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\endverbatim
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\author
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Sergey Bakhurin www.dsplib.org
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*******************************************************************************/
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int DSPL_API cos_cmplx(complex_t* x, int n, complex_t *y)
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{
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int k;
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double ep, em, sx, cx;
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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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ep = exp( IM(x[k]));
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em = exp(-IM(x[k]));
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sx = 0.5 * sin(RE(x[k]));
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cx = 0.5 * cos(RE(x[k]));
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RE(y[k]) = cx * (em + ep);
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IM(y[k]) = sx * (em - ep);
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}
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return RES_OK;
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}
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/******************************************************************************
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\ingroup SPEC_MATH_COMMON_GROUP
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\fn int log_cmplx(complex_t* x, int n, complex_t *y)
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\brief The logarithm function the complex vector argument `x`
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Function calculates the logarithm function as: \n
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\f[
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\textrm{Ln}(x) = j \varphi + \ln(|x|),
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\f]
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here \f$\varphi\f$ - the complex number phase.
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\param[in] x 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 Input vector `x` and the logarithm vector `y` size. \n \n
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\param[out] y 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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log_cmplx(x, 3, y);
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for(k = 0; k < 3; k++)
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printf("log_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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log_cmplx(1.0+2.0j) = 0.805+1.107j
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log_cmplx(3.0+4.0j) = 1.609+0.927j
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log_cmplx(5.0+6.0j) = 2.055+0.876j
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\endverbatim
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\author
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Sergey Bakhurin www.dsplib.org
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*******************************************************************************/
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int DSPL_API log_cmplx(complex_t* x, int n, complex_t *y)
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{
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int k;
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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(y[k]) = 0.5 * log(ABSSQR(x[k]));
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IM(y[k]) = atan2(IM(x[k]), RE(x[k]));
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}
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return RES_OK;
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}
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/******************************************************************************
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\ingroup TYPES_GROUP
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\fn int re2cmplx(double* x, int n, complex_t *y)
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\brief Convert real array to the complex array.
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Function copies the vector `x` to the real part of vector `y`.
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Image part of the vector `y` sets as zero. \n
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So complex vector contains data: \n
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`y[i] = x[i] + j0, here i = 0,1,2 ... n-1`
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\param[in] x Pointer to the real vector `x`. \n
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Vector size is `[n x 1]`. \n \n
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\param[in] n Size of the real vector `x` and complex vector `y`. \n \n
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\param[out] y Pointer to the complex vector `y`. \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 returns successfully. \n
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Else \ref ERROR_CODE_GROUP "code error": \n
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Например при выполнении следующего кода
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\code{.cpp}
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double x[3] = {1.0, 2.0, 3.0};
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complex_t y[3];
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re2cmplx(x, 3, y);
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\endcode
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Vector `y` will keep:
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\verbatim
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y[0] = 1+0j;
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y[1] = 2+0j;
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y[2] = 3+0j.
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\endverbatim
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\author Sergey Bakhurin. www.dsplib.org
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*******************************************************************************/
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int DSPL_API re2cmplx(double* x, int n, complex_t* y)
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{
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int k;
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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(y[k]) = x[k];
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IM(y[k]) = 0.0;
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}
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return RES_OK;
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}
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/******************************************************************************
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\ingroup SPEC_MATH_TRIG_GROUP
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\fn int sin_cmplx(complex_t* x, int n, complex_t *y)
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\brief The sine function the complex vector argument `x`
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Function calculates the sine function as: \n
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\f[
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\textrm{cos}(x) = \frac{\exp(jx) - \exp(-jx)}{2j}
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\f]
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\param[in] x 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 Input vector `x` and the sine vector `y` size. \n \n
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\param[out] y 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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sin_cmplx(x, 3, y);
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for(k = 0; k < 3; k++)
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printf("sin_cmplx(%.1f%+.1fj) = %9.3f%+9.3fj\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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sin_cmplx(1.0+2.0j) = 3.166 +1.960j
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sin_cmplx(3.0+4.0j) = 3.854 -27.017j
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sin_cmplx(5.0+6.0j) = -193.430 +57.218j
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\endverbatim
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\author
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Sergey Bakhurin www.dsplib.org
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*******************************************************************************/
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int DSPL_API sin_cmplx(complex_t* x, int n, complex_t *y)
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{
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int k;
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double ep, em, sx, cx;
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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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|
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for(k = 0; k < n; k++)
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|
{
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ep = exp( IM(x[k]));
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em = exp(-IM(x[k]));
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sx = 0.5 * sin(RE(x[k]));
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cx = 0.5 * cos(RE(x[k]));
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RE(y[k]) = sx * (em + ep);
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|
IM(y[k]) = cx * (ep - em);
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|
}
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|
return RES_OK;
|
|
}
|
|
|
|
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/******************************************************************************
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|
\ingroup SPEC_MATH_COMMON_GROUP
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\fn int sqrt_cmplx(complex_t* x, int n, complex_t *y)
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|
\brief Square root of the complex vector argguument `x`.
|
|
|
|
Function calculates square root value of vector `x` length `n`: \n
|
|
\f[
|
|
y(k) = \sqrt{x(k)}, \qquad k = 0 \ldots n-1.
|
|
\f]
|
|
|
|
|
|
\param[in] x Pointer to the input complex vector `x`. \n
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|
Vector size is `[n x 1]`. \n \n
|
|
|
|
\param[in] n Size of input and output vectors `x` and `y`. \n \n
|
|
|
|
|
|
\param[out] y Pointer to the square root vector `y`. \n
|
|
Vector size is `[n x 1]`. \n
|
|
Memory must be allocated. \n \n
|
|
|
|
\return `RES_OK` if function is calculated successfully. \n
|
|
Else \ref ERROR_CODE_GROUP "code error". \n
|
|
|
|
Example
|
|
\code{.cpp}
|
|
complex_t x[3] = {{1.0, 2.0}, {3.0, 4.0}, {5.0, 6.0}};
|
|
complex_t y[3]
|
|
int k;
|
|
|
|
sqrt_cmplx(x, 3, y);
|
|
|
|
for(k = 0; k < 3; k++)
|
|
printf("sqrt_cmplx(%.1f%+.1fj) = %.3f%+.3fj\n",
|
|
RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));
|
|
|
|
\endcode
|
|
\n
|
|
|
|
Результатом работы будет
|
|
|
|
\verbatim
|
|
sqrt_cmplx(1.0+2.0j) = 1.272+0.786j
|
|
sqrt_cmplx(3.0+4.0j) = 2.000+1.000j
|
|
sqrt_cmplx(5.0+6.0j) = 2.531+1.185j
|
|
\endverbatim
|
|
|
|
\author Sergey Bakhurin www.dsplib.org
|
|
*******************************************************************************/
|
|
int DSPL_API sqrt_cmplx(complex_t* x, int n, complex_t *y)
|
|
{
|
|
int k;
|
|
double r, zr, at;
|
|
complex_t t;
|
|
if(!x || !y)
|
|
return ERROR_PTR;
|
|
if(n < 1)
|
|
return ERROR_SIZE;
|
|
|
|
for(k = 0; k < n; k++)
|
|
{
|
|
r = ABS(x[k]);
|
|
if(r == 0.0)
|
|
{
|
|
RE(y[k]) = 0.0;
|
|
IM(y[k]) = 0.0;
|
|
}
|
|
else
|
|
{
|
|
RE(t) = RE(x[k]) + r;
|
|
IM(t) = IM(x[k]);
|
|
at = ABS(t);
|
|
if(at == 0.0)
|
|
{
|
|
RE(y[k]) = 0.0;
|
|
IM(y[k]) = sqrt(r);
|
|
}
|
|
else
|
|
{
|
|
zr = 1.0 / ABS(t);
|
|
r = sqrt(r);
|
|
RE(y[k]) = RE(t) * zr * r;
|
|
IM(y[k]) = IM(t) * zr * r;
|
|
}
|
|
}
|
|
}
|
|
return RES_OK;
|
|
}
|
|
|