Basic math functions of the real and complex arguments.

Functions
int DSPL_API	log_cmplx (complex_t *x, int n, complex_t *y)
	The logarithm function the complex vector argument x. More...
int DSPL_API	sinc (double *x, int n, double a, double *y)
	Function \( \textrm{sinc}(x,a) = \frac{\sin(ax)}{ax}\) for the real vector x. More...
int DSPL_API	sqrt_cmplx (complex_t *x, int n, complex_t *y)
	Square root of the complex vector argguument x. More...
int DSPL_API	polyroots (double *a, int ord, complex_t *r, int *info)
	Function calculates real polynomial roots. More...

Detailed Description

Function Documentation

log_cmplx()

int log_cmplx	(	complex_t *	x,
		int	n,
		complex_t *	y
	)

The logarithm function the complex vector argument x.

---

Function calculates the logarithm function as:

\[ \textrm{Ln}(x) = j \varphi + \ln(|x|), \]

here \(\varphi\) - the complex number phase.

Parameters

[in]	x	Pointer to the argument vector x. Vector size is [n x 1].
[in]	n	Input vector x and the logarithm vector y size.
[out]	y	Pointer to the output complex vector y, corresponds to the input vector x. Vector size is [n x 1]. Memory must be allocated.

Returns

RES_OK if function calculated successfully.
Else code error.
Example:

complex_t x[3] = {{1.0, 2.0}, {3.0, 4.0}, {5.0, 6.0}};
complex_t y[3];
int k;
 
log_cmplx(x, 3, y);    
 
for(k = 0; k < 3; k++)
    printf("log_cmplx(%.1f%+.1fj) = %.3f%+.3fj\n", 
           RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));

Output is:

log_cmplx(1.0+2.0j) = 0.805+1.107j
log_cmplx(3.0+4.0j) = 1.609+0.927j
log_cmplx(5.0+6.0j) = 2.055+0.876j

Author

Sergey Bakhurin www.dsplib.org

Definition at line 718 of file math.c.

Referenced by asin_cmplx().

polyroots()

int polyroots	(	double *	a,
		int	ord,
		complex_t *	r,
		int *	info
	)

Function calculates real polynomial roots.

---

Function calculates roots of the real polynomial \(P_N(x)\) order \(N\) with a coefficient vector size [(N+1) x 1].

\[ P_N(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + ... a_N x^N. \]

The roots of the polynomial are calculated as eigenvalues of the polynomial companion matrix. To calculate the eigenvalues, a subroutine of the LAPACK package is used.

Parameters

[in]	a	Pointer to the vector of coefficients. Vector size is [ord+1 x 1]. Coefficient a[0] corresponds to the \(a_0\) polynomial coefficient. Coefficient a[ord] cannot be zero.
[in]	ord	Polynomial order \(N\).
[out]	r	Pointer to the polynomial roots vector. Vector size is [ord x 1]. Memory must be allocated. The roots of a real polynomial can be either real or form simple or multiple complex conjugate pairs of roots. Therefore, the output root vector is of a complex data type.
[out]	info	Pointer to the LAPACK subroutine error code. This code is returned by the LAPACK subroutine and translated through this variable for analysis..

Returns

RES_OK — roots are calculated successfully.

Else code error.

Example:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dspl.h"
 
#define N  2
 
int main(int argc, char* argv[])
{
    void* hdspl;                     /* DSPL handle           */
    double a[N+1] = {2.0, 2.0, 1.0}; /* P(x) = 2 + 2x + x^2   */
    complex_t r[N] = {0};            /* roots                 */
    int err, n, info;
    hdspl = dspl_load();            /* Load DSPL functions    */
    if(!hdspl)
    {
        printf("libdspl loading error!\n");
        return -1;
    }
 
 
    /* roots calculation */
    err = polyroots(a, N, r, &info);
    printf("Error code: 0x%.8x\n", err);
 
    /* print roots */
    for(n = 0; n < N; n++)
        printf("r[%d] = % -8.5f% -8.5f j\n", n, RE(r[n]), IM(r[n]));
 
    /* free dspl handle  */
    dspl_free(hdspl);
    return 0;
}
 

This program calculates the roots of the polynomial

\[ P(x) = 2 + 2x + x^2 \]

and prints the calculated roots. The result of the program:

Error code: 0x00000000
r[0] = -1.00000 1.00000 j
r[1] = -1.00000-1.00000 j

Author

Sergey Bakhurin. www.dsplib.org

Definition at line 199 of file polyval.c.

sinc()

int sinc	(	double *	x,
		int	n,
		double	a,
		double *	y
	)

Function \( \textrm{sinc}(x,a) = \frac{\sin(ax)}{ax}\) for the real vector x.

---

Parameters

[in]	x	Pointer to the input vector \( x \). Vector size is [n x 1].
[in]	n	Input and output vectors size.
[in]	a	Function parameter \( \textrm{sinc}(x,a) = \frac{\sin(ax)}{ax}\).
[out]	y	Pointer to the sinc function output vector. Vector size is [n x 1]. Memory must be allocated.

Returns

RES_OK if function calculated successfully.
Else code error.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 936 of file math.c.

sqrt_cmplx()

int sqrt_cmplx	(	complex_t *	x,
		int	n,
		complex_t *	y
	)

Square root of the complex vector argguument x.

---

Function calculates square root value of vector x length n:

\[ y(k) = \sqrt{x(k)}, \qquad k = 0 \ldots n-1. \]

Parameters

[in]	x	Pointer to the input complex vector x. Vector size is [n x 1].
[in]	n	Size of input and output vectors x and y.
[out]	y	Pointer to the square root vector y. Vector size is [n x 1]. Memory must be allocated.

Returns

RES_OK if function is calculated successfully.
Else code error.
Example

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]));

Result:

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

Author

Sergey Bakhurin www.dsplib.org

Definition at line 1307 of file math.c.

Referenced by asin_cmplx(), ellip_acd_cmplx(), and ellip_asn_cmplx().