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...

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().

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().