Trigonometric and hyperbolic of functions the real and complex arguments.

Functions
int DSPL_API	acos_cmplx (complex_t *x, int n, complex_t *y)
	The inverse of the cosine function the complex vector argument x. More...
int DSPL_API	asin_cmplx (complex_t *x, int n, complex_t *y)
	The inverse of the sine function the complex vector argument x. More...
int DSPL_API	cos_cmplx (complex_t *x, int n, complex_t *y)
	The cosine function the complex vector argument x. More...
int DSPL_API	sin_cmplx (complex_t *x, int n, complex_t *y)
	The sine function the complex vector argument x. More...

Detailed Description

Function Documentation

acos_cmplx()

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

The inverse of the cosine function the complex vector argument x.

---

Function calculates the inverse of the cosine function as:

\[ \textrm{Arccos}(x) = \frac{\pi}{2} - \textrm{Arcsin}(x) = \frac{\pi}{2} -j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right) \]

Parameters

[in]	x	Pointer to the argument vector x. Vector size is [n x 1].
[in]	n	Input vector x and the inverse cosine 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;
 
acos_cmplx(x, 3, y);
 
for(k = 0; k < 3; k++)
    printf("acos_cmplx(%.1f%+.1fj) = %.3f%+.3fj\n", 
            RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));

Output is:

acos_cmplx(1.0+2.0j) = 1.144-1.529j
acos_cmplx(3.0+4.0j) = 0.937-2.306j
acos_cmplx(5.0+6.0j) = 0.880-2.749j

Author

Sergey Bakhurin www.dsplib.org

Definition at line 141 of file acos_cmplx.c.

Referenced by ellip_acd_cmplx().

asin_cmplx()

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

The inverse of the sine function the complex vector argument x.

---

Function calculates the inverse of the sine function as:

\[ \textrm{Arcsin}(x) = j \textrm{Ln}\left( j x + \sqrt{1 - x^2} \right) \]

Parameters

[in]	x	Pointer to the argument vector x. Vector size is [n x 1].
[in]	n	Input vector x and the inverse sine 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;
 
asin_cmplx(x, 3, y);    
for(k = 0; k < 3; k++)
    printf("asin_cmplx(%.1f%+.1fj) = %.3f%+.3fj\n", 
            RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));

Output is:

asin_cmplx(1.0+2.0j) = 0.427+1.529j
asin_cmplx(3.0+4.0j) = 0.634+2.306j
asin_cmplx(5.0+6.0j) = 0.691+2.749j

Author

Sergey Bakhurin www.dsplib.org

Definition at line 138 of file asin_cmplx.c.

Referenced by acos_cmplx(), and ellip_asn_cmplx().

cos_cmplx()

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

The cosine function the complex vector argument x.

---

Function calculates the cosine function as:

\[ \textrm{cos}(x) = \frac{\exp(jx) + \exp(-jx)}{2} \]

Parameters

[in]	x	Pointer to the argument vector x. Vector size is [n x 1].
[in]	n	Input vector x and the cosine 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;
 
cos_cmplx(x, 3, y);
 
for(k = 0; k < 3; k++)
    printf("cos_cmplx(%.1f%+.1fj) = %9.3f%+9.3fj\n", 
            RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));

Output is:

cos_cmplx(1.0+2.0j) =       2.033   -3.052j
cos_cmplx(3.0+4.0j) =     -27.035   -3.851j
cos_cmplx(5.0+6.0j) =      57.219 +193.428j

Author

Sergey Bakhurin www.dsplib.org

Definition at line 136 of file cos_cmplx.c.

Referenced by ellip_cd_cmplx().

sin_cmplx()

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

The sine function the complex vector argument x.

---

Function calculates the sine function as:

\[ \textrm{cos}(x) = \frac{\exp(jx) - \exp(-jx)}{2j} \]

Parameters

[in]	x	Pointer to the argument vector x. Vector size is [n x 1].
[in]	n	Input vector x and the sine 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;
 
sin_cmplx(x, 3, y);
 
for(k = 0; k < 3; k++)
    printf("sin_cmplx(%.1f%+.1fj) = %9.3f%+9.3fj\n", 
            RE(x[k]), IM(x[k]), RE(y[k]), IM(y[k]));

Output is:

sin_cmplx(1.0+2.0j) =       3.166  +1.960j
sin_cmplx(3.0+4.0j) =       3.854 -27.017j
sin_cmplx(5.0+6.0j) =    -193.430 +57.218j

Author

Sergey Bakhurin www.dsplib.org

Definition at line 136 of file sin_cmplx.c.

Referenced by ellip_sn_cmplx().