Functions
int DSPL_API	array_scale_lin (double x, int n, double xmin, double xmax, double dx, double h, double y)
	Vector `x` linear transformation. More...

int DSPL_API	concat (void a, size_t na, void b, size_t nb, void *c)
	Concatenate arrays `a` and `b` More...

int DSPL_API	decimate (double x, int n, int d, double y, int *cnt)
	Real vector decimation. More...

int DSPL_API	decimate_cmplx (complex_t x, int n, int d, complex_t y, int *cnt)
	Complex vector decimation. More...

int DSPL_API	flipip (double *x, int n)
	Flip real vector `x` in place. More...

int DSPL_API	flipip_cmplx (complex_t *x, int n)
	Flip complex vector `x` in place. More...

int DSPL_API	linspace (double x0, double x1, int n, int type, double *x)
	Function fills a vector with `n` linearly spaced elements between `x0` and `x1`. More...

int DSPL_API	logspace (double x0, double x1, int n, int type, double *x)
	Function fills a vector with `n` logarithmically spaced elements between \(10^{x_0}\) and \(10^{x_1}\). More...

int DSPL_API	ones (double *x, int n)
	Function fills all real vector `x` by ones values. More...

int DSPL_API	sum (double x, int n, double s)

int DSPL_API	verif (double x, double y, size_t n, double eps, double *err)
	Real arrays verification. More...

int DSPL_API	verif_cmplx (complex_t x, complex_t y, size_t n, double eps, double *err)
	Complex arrays verification. More...

Detailed Description

Function Documentation

◆ array_scale_lin()

int array_scale_lin	(	double *	x,
		int	n,
		double	xmin,
		double	xmax,
		double	dx,
		double	h,
		double *	y
	)

Vector x linear transformation.

Function transforms values \(x(i)\), \(i = 0,1,\ldots n\) to the \(y(i)\), accordint to equation:

\[ y(i) = k_x x(i) + d_x, \qquad k_x = \frac{h}{x_{\textrm{max}} - x_{\textrm{min}}}. \]

All values of the vector x between \(x_{\textrm{min}}\) and \(x_{\textrm{max}}\), transforms to the vector y between \(d_x\) and \(h + d_x\). Parameter \(d_x\) sets mean shift of the vector y.

This function is convenient for translating values of different dimensions. For example it can be used to transfer the values of the vector x to the graph of the height ofh, where the height can be set in the number of pixels, in centimeters, etc.

Parameters

[in]	x	Pointer to the input vector `x`. Vector size is `[n x 1]`.
[in]	n	Size of vector `x`.
[in]	xmin	Parameter \(x_{\textrm{min}}\).
[in]	xmax	Parameter \(x_{\textrm{min}}\). Value `xmax` must be more than `xmin`.
[in]	dx	Displacement after transformation. This parameter must have output vector `y` dimensions (pixels, centimeters).
[in]	h	Height of vector `y` after transforming between `dx` and `h+dx`.
[out]	y	Pointer to the output vector `y`. Vector size is `[n x 1]`. Memory must be allocated.

Note: Pointer y can be equal to x. Velues of vector x will be rewritten in this case.

Returns: RES_OK if function returns successfully.
Else code error.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 171 of file array_scale_lin.c.

◆ concat()

int concat	(	void *	a,
		size_t	na,
		void *	b,
		size_t	nb,
		void *	c
	)

Concatenate arrays a and b

Let's arrays a and b are vectors:
a = [a(0), a(1), ... a(na-1)],
b = [b(0), b(1), ... b(nb-1)],
concatenation of these arrays will be array c size na+nb:
c = [a(0), a(1), ... a(na-1), b(0), b(1), ... b(nb-1)].

Parameters

[in]	a	Pointer to the first array `a`. Array `a` size is `na` bytes.
[in]	na	Array `a` size (bytes).
[in]	b	Pointer to the second array `b`. Array `b` size is `nb` bytes.
[in]	nb	Array `a` size (bytes).
[out]	c	Pointer to the concatenation result array `c`. Array `c` size is `na + nb` bytes. Memory must be allocated.

Returns: RES_OK if function returns successfully.
Else code error.

Function uses pointer type void* and can be useful for an arrays concatenation with different types.
For example two double arrays concatenation:

double a[3] = {1.0, 2.0, 3.0};
double b[2] = {4.0, 5.0};
double c[5];
 
concat((void*)a, 3*sizeof(double), (void*)b, 2*sizeof(double), (void*)c);

Vector c keeps follow data:

c = [1.0, 2.0, 3.0, 4.0, 5.0]

Author: Sergey Bakhurin www.dsplib.org

Definition at line 146 of file concat.c.

◆ decimate()

int decimate	(	double *	x,
		int	n,
		int	d,
		double *	y,
		int *	cnt
	)

Real vector decimation.

Function d times decimates real vector x.
Output vector y keeps values corresponds to: y(k) = x(k*d), k = 0...n/d-1

Parameters

[in]	x	Pointer to the input real vector `x`. Vector `x` size is `[n x 1]`.
[in]	n	Size of input vector `x`.
[in]	d	Decimation coefficient. Each d-th vector will be copy from vector `x` to the output vector `y`.
[out]	y	Pointer to the output decimated vector `y`. Output vector size is `[n/d x 1]` will be copy to the address `cnt`.
[out]	cnt	Address which will keep decimated vector `y` size. Pointer can be `NULL`, vector `y` will not return in this case.

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

Two-times decimation example:

double x[10] = {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0};
double y[5];
int d = 2;
int cnt;
 
decimate(x, 10, d, y, &cnt);

As result variable cnt will be written value 5 and vector y will keep array:

c = [0.0, 2.0, 4.0, 6.0, 8.0]

Author: Sergey Bakhurin www.dsplib.org

Definition at line 140 of file decimate.c.

◆ decimate_cmplx()

int decimate_cmplx	(	complex_t *	x,
		int	n,
		int	d,
		complex_t *	y,
		int *	cnt
	)

Complex vector decimation.

Function d times decimates a complex vector x.
Output vector y keeps values corresponds to: y(k) = x(k*d), k = 0...n/d-1

Parameters

[in]	x	Pointer to the input complex vector `x`. Vector `x` size is `[n x 1]`.
[in]	n	Size of input vector `x`.
[in]	d	Decimation coefficient. Each d-th vector will be copy from vector `x` to the output vector `y`.
[out]	y	Pointer to the output decimated vector `y`. Output vector size is `[n/d x 1]` will be copy to the address `cnt`. Memory must be allocated.
[out]	cnt	Address which will keep decimated vector `y` size. Pointer can be `NULL`, vector `y` will not return in this case.

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

Two-times complex vector decimation example:

compex_t x[10] = {{0.0, 0.0}, {1.0, 1.0}, {2.0, 2.0}, {3.0, 3.0}, {4.0, 4.0},
{5.0, 5.0}, {6.0, 6.0}, {7.0, 7.0}, {8.0, 8.0}, {9.0, 9.0}};
compex_t y[5];
int d = 2;
int cnt;
 
decimate_cmplx(x, 10, d, y, &cnt);

As result variable cnt will be written value 5 and vector y will keep array:

c = [0.0+0.0j, 2.0+2.0j, 4.0+4.0j, 6.0+6.0j, 8.0+8.0j]

Author: Sergey Bakhurin www.dsplib.org

Definition at line 144 of file decimate_cmplx.c.

◆ flipip()

int flipip	(	double *	x,
		int	n
	)

Flip real vector x in place.

Function flips real vector x length n in the memory.
For example real vector x length 6:

x = [0, 1, 2, 3, 4, 5]

After flipping it will be as follow:

x = [5, 4, 3, 2, 1, 0]

Parameters

[in,out]	x	Pointer to the real vector `x`. Vector size is `[n x 1]`. Flipped vector will be on the same address.
[in]	n	Length of the vector `x`.

Returns: RES_OK if function returns successfully.
Else error code.

Example:

double x[5] = {0.0, 1.0, 2.0, 3.0, 4.0};
int i;
for(i = 0; i < 5; i++)
    printf("%6.1f    ", x[i]);
flipip(x, 5);
printf("\n");
for(i = 0; i < 5; i++)
    printf("%6.1f    ", x[i]);

Program result:

     0.0         1.0         2.0         3.0         4.0
     4.0         3.0         2.0         1.0         0.0

Author: Sergey Bakhurin www.dsplib.org

Definition at line 133 of file flipip.c.

◆ flipip_cmplx()

int flipip_cmplx	(	complex_t *	x,
		int	n
	)

Flip complex vector x in place.

Function flips complex vector x length n in the memory
For example complex vector x length 6:

x = [0+0j, 1+1j, 2+2j, 3+3j, 4+4j, 5+5j]

After flipping it will be as follow:

x = [5+5j, 4+4j, 3+3j, 2+2j, 1+1j, 0+0j]

Parameters

[in,out]	x	Pointer to the complex vector `x`. Vector size is `[n x 1]`. Flipped vector will be on the same address.
[in]	n	Length of the vector `x`.

Returns: RES_OK if function returns successfully.
Else error code.

Example:

complex_t y[5] = {{0.0, 0.0}, {1.0, 1.0}, {2.0, 2.0}, {3.0, 3.0}, {4.0, 4.0}};
for(i = 0; i < 5; i++)
    printf("%6.1f%+.1fj    ", RE(y[i]), IM(y[i]));
flipip_cmplx(y, 5);
printf("\n");
for(i = 0; i < 5; i++)
    printf("%6.1f%+.1fj    ", RE(y[i]), IM(y[i]));

Program result:

0.0+0.0j         1.0+1.0j         2.0+2.0j         3.0+3.0j         4.0+4.0j
4.0+4.0j         3.0+3.0j         2.0+2.0j         1.0+1.0j         0.0+0.0j

Author: Sergey Bakhurin www.dsplib.org

Definition at line 132 of file flipip_cmplx.c.

◆ linspace()

int linspace	(	double	x0,
		double	x1,
		int	n,
		int	type,
		double *	x
	)

Function fills a vector with n linearly spaced elements between x0 and x1.

Function supports two kinds of filling according to type parameter:
Symmetric fill (parameter type=DSPL_SYMMETRIC):
\(x(k) = x_0 + k \cdot dx\), \(dx = \frac{x_1 - x_0}{n-1}\), \(k = 0 \ldots n-1.\)

Periodic fill (parameter type=DSPL_PERIODIC):
\(x(k) = x_0 + k \cdot dx\), \(dx = \frac{x_1 - x_0}{n}\), \(k = 0 \ldots n-1.\)

Parameters

[in]	x0	Start point \(x_0\).
[in]	x1	End point \(x_1\).
[in]	n	Number of points `x` (size of vector `x`).
[in]	type	Fill type: `DSPL_SYMMETRIC` — symmetric, `DSPL_PERIODIC` — periodic.
[in,out]	x	Pointer to the output linearly spaced vector `x`. Vector size is `[n x 1]`. Memory must be allocated.

Returns: RES_OK if function returns successfully.
Else error code.

Note

Difference between symmetric and periodic filling we can understand from the follow examples.
Example 1. Periodic fill. double x[5]; linspace(0, 5, 5, DSPL_PERIODIC, x); Values in the vector x are:

0,    1,    2,    3,    4

Example 2. Symmetric fill.

double x[5];

linspace(0, 5, 5, DSPL_SYMMETRIC, x);

linspace

int DSPL_API linspace(double x0, double x1, int n, int type, double *x)

Function fills a vector with n linearly spaced elements between x0 and x1.

Definition: linspace.c:169

Values in the vector x are:

0,    1.25,    2.5,    3.75,    5

Author: Sergey Bakhurin www.dsplib.org

Definition at line 169 of file linspace.c.

◆ logspace()

int logspace	(	double	x0,
		double	x1,
		int	n,
		int	type,
		double *	x
	)

Function fills a vector with n logarithmically spaced elements between \(10^{x_0}\) and \(10^{x_1}\).

Function supports two kinds of filling according to type parameter:
Symmetric fill (parameter type=DSPL_SYMMETRIC):
\(x(k) = 10^{x_0} \cdot dx^k\), here \(dx = \sqrt[n-1]{10^{x_1 - x_0}}\), \(k = 0 \ldots n-1.\)

Periodic fill (parameter type=DSPL_PERIODIC):
\(x(k) = 10^{x_0} \cdot dx^k\), here \(dx = \sqrt[n]{10^{x_1 - x_0}}\), \(k = 0 \ldots n-1.\)

Parameters

[in]	x0	Start exponent value \(x_0\).
[in]	x1	End exponent value \(x_1\).
[in]	n	Number of points `x` (size of vector `x`).
[in]	type	Fill type: `DSPL_SYMMETRIC` — symmetric, `DSPL_PERIODIC` — periodic.
[in,out]	x	Pointer to the output logarithmically spaced vector `x` . Vector size is `[n x 1]`. Memory must be allocated.

Returns: RES_OK if function returns successfully.
Else error code.

Note: Difference between symmetric and periodic filling we can understand from the follow examples.
Example 1. Periodic fill.
double x[5];

logspace(-2, 3, 5, DSPL_PERIODIC, x);

logspace
int DSPL_API logspace(double x0, double x1, int n, int type, double *x)
Function fills a vector with n logarithmically spaced elements between and .
Definition: logspace.c:178

Values in the vector x are:

0.01,    0.1,    1,    10,    100

Example 2. Symmetric fill.

double x[5];

logspace(-2, 3, 5, DSPL_SYMMETRIC, x);

Values in the vector x are:

0.01    0.178    3.162    56.234    1000

Author: Sergey Bakhurin www.dsplib.org

Definition at line 178 of file logspace.c.

◆ ones()

int ones	(	double *	x,
		int	n
	)

Function fills all real vector x by ones values.

Parameters

[in,out]	x	Pointer to the vector `x`. Vector size is `[n x 1]`. All elements on this vector will be set to one.
[in]	n	Size of vector `x`.

Returns: RES_OK if function returns successfully.
Else error code.

Example:

double y[5] = {0};
int i;
ones(y, 5);
for(i = 0; i < 5; i++)
    printf("%6.1f%    ", y[i]);

Vector y values are:

    1.0    1.0    1.0    1.0    1.0

Author: Sergey Bakhurin www.dsplib.org

Definition at line 103 of file ones.c.

◆ sum()

int sum	(	double *	x,
		int	n,
		double *	s
	)

Author: Sergey Bakhurin www.dsplib.org

Definition at line 43 of file sum.c.

Referenced by mean(), mean_cmplx(), stat_std(), and stat_std_cmplx().

◆ verif()

int verif	(	double *	x,
		double *	y,
		size_t	n,
		double	eps,
		double *	err
	)

Real arrays verification.

Function calculates a maximum relative error between two real arrays x and y (both length equals n):

\[ e = \max \left( \frac{|x(k) - y(k)| }{ |x(k)|} \right), \quad if \quad |x(k)| > 0, \]

or

\[ e = \max(|x(k) - y(k)| ), ~\qquad if \quad~|x(k)| = 0, \]

This function can be used for algorithms verification if vector x is user algorithm result and vector y – reference vector.

Parameters

[in]	x	Pointer to the first vector `x`. Vector size is `[n x 1]`.
[in]	y	Pointer to the second vector `y`. Vector size is `[n x 1]`.
[in]	n	Size of vectors `x` and `y`.
[in]	eps	Relative error threshold. If error less than `eps`, then function returns `DSPL_VERIF_SUCCESS`, else `DSPL_VERIF_FAILED`.
[in,out]	err	Pointer to the variable which keep maximum relative error. Pointer can be `NULL`, maximum error will not be returned in this case.

Returns: DSPL_VERIF_SUCCESS if maximum relative error less than eps.
Otherwise DSPL_VERIF_FAILED.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 130 of file verif.c.

◆ verif_cmplx()

int verif_cmplx	(	complex_t *	x,
		complex_t *	y,
		size_t	n,
		double	eps,
		double *	err
	)

Complex arrays verification.

Function calculates a maximum relative error between two complex arrays x and y (both length equals n):

\[ e = \max \left( \frac{|x(k) - y(k)| }{ |x(k)|} \right), \quad if \quad |x(k)| > 0, \]

or

\[ e = \max(|x(k) - y(k)| ), ~\qquad if \quad~|x(k)| = 0, \]

Return DSPL_VERIF_SUCCESS if maximum relative error \( e\) less than eps. Else returns DSPL_VERIF_FAILED.
This function can be used for algorithms verification if vector x is user algorithm result and vector y – reference vector.

Parameters

[in]	x	Pointer to the first vector `x`. Vector size is `[n x 1]`.
[in]	y	Pointer to the second vector `y`. Vector size is `[n x 1]`.
[in]	n	Size of vectors `x` and `y`.
[in]	eps	Relative error threshold. If error less than `eps`, then function returns `DSPL_VERIF_SUCCESS`, else `DSPL_VERIF_FAILED`.
[in,out]	err	Pointer to the variable which keep maximum relative error. Pointer can be `NULL`, maximum error will not be returned in this case.

Returns: DSPL_VERIF_SUCCESS if maximum relative error less than eps.
Otherwise DSPL_VERIF_FAILED.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 141 of file verif_cmplx.c.

Functions

Detailed Description

Function Documentation

◆ array_scale_lin()

◆ concat()

◆ decimate()

◆ decimate_cmplx()

◆ flipip()

◆ flipip_cmplx()

◆ linspace()

◆ logspace()

◆ ones()

◆ sum()

◆ verif()

◆ verif_cmplx()