include/lwpr_math.h File Reference

Prototypes for some rather simple vector and matrix operations. More...

Functions
double	lwpr_math_norm2 (const double *x, int n)
	Computes the square norm of a vector of doubles.
double	lwpr_math_dot_product (const double a, const double b, int n)
	Computes the dot product between two vectors of doubles.
void	lwpr_math_scalar_vector (double y, double a, const double x, int n)
	Multiplies a vector by a scalar and stores the result in another vector.
void	lwpr_math_add_scalar_vector (double y, double a, const double x, int n)
	Multiplies a vector by a scalar and adds the result to another vector.
void	lwpr_math_scale_add_scalar_vector (double b, double y, double a, const double x, int n)
	Multiplies a vector by a scalar and adds the result to another vector, which is scaled before the addition.
int	lwpr_math_cholesky (int N, int Ns, double R, const double A)
	Computes the Cholesky decomposition of a matrix.

Detailed Description

Prototypes for some rather simple vector and matrix operations.

Function Documentation

void lwpr_math_add_scalar_vector	(	double *	y,
		double	a,
		const double *	x,
		int	n
	)

Multiplies a vector by a scalar and adds the result to another vector.

Parameters:

`[in,out]`	y	Output vector, must point to an array of n doubles
`[in]`	a	Scalar multiplier
`[in]`	x	Input vector, must point to an array of n doubles
`[in]`	n	Length of the vectors

Computes

$\mathbf{y} \leftarrow \mathbf{y} + a\mathbf{x}\quad\Leftrightarrow\quad y_i \leftarrow y_i + a x_i \quad i=1\dots n$

Referenced by LWPR_ReceptiveFieldObject::slope().

int lwpr_math_cholesky	(	int	N,
		int	Ns,
		double *	R,
		const double *	A
	)

Computes the Cholesky decomposition of a matrix.

Parameters:

`[in]`	N	Number of columns and rows of the matrix
`[in]`	Ns	Stride parameter, i.e. offset between the first element of adjacent columns
`[in,out]`	R	Upper triangular Cholesky factor. Also serves as input matrix if A==NULL
`[in]`	A	Matrix to decompose. May be NULL, in which case the decomposition of R is done in place.

Returns:

1 in case of succes
0 in case of failure (e.g. input matrix is not positive definite)

Given a positive definite matrix A, this function computes an upper triangular matrix R such that

$\mathbf{R}^T\mathbf{R} = \mathbf{A}.$

Since the decomposition is done in place, you can also call

   lwpr_math_cholesky(n,n,R,NULL);

if you can afford to overwrite the original contents of the matrix.

double lwpr_math_dot_product	(	const double *	a,
		const double *	b,
		int	n
	)

Computes the dot product between two vectors of doubles.

Parameters:

`[in]`	a	First input vector, must point to an array of n doubles
`[in]`	b	Second input vector, must point to an array of n doubles
`[in]`	n	Length of the vectors

Returns:: The dot product
$\mathbf{a}\cdot\mathbf{b} = \sum_{i=1}^n a_i b_i$

Referenced by LWPR_ReceptiveFieldObject::slope().

double lwpr_math_norm2	(	const double *	x,
		int	n
	)

Computes the square norm of a vector of doubles.

Parameters:

`[in]`	x	Input vector, must point to an array of n doubles
`[in]`	n	Length of the vector

Returns:: The square norm
$\|\mathbf{x}\|^2 = \sum_{i=1}^n x_i^2$

void lwpr_math_scalar_vector	(	double *	y,
		double	a,
		const double *	x,
		int	n
	)

Multiplies a vector by a scalar and stores the result in another vector.

Parameters:

`[out]`	y	Output vector, must point to an array of n doubles
`[in]`	a	Scalar multiplier
`[in]`	x	Input vector, must point to an array of n doubles
`[in]`	n	Length of the vectors

Computes

$\mathbf{y} \leftarrow a\mathbf{x}\quad\Leftrightarrow\quad y_i \leftarrow a x_i \quad i=1\dots n$

Referenced by LWPR_ReceptiveFieldObject::slope().

void lwpr_math_scale_add_scalar_vector	(	double	b,
		double *	y,
		double	a,
		const double *	x,
		int	n
	)

Multiplies a vector by a scalar and adds the result to another vector, which is scaled before the addition.

Parameters:

`[in]`	b	Scalar multiplier for y before the addition
`[in,out]`	y	Output vector, must point to an array of n doubles
`[in]`	a	Scalar multiplier for x
`[in]`	x	Input vector, must point to an array of n doubles
`[in]`	n	Length of the vectors

Computes

$\mathbf{y} \leftarrow b\mathbf{y} + a\mathbf{x}\quad\Leftrightarrow\quad y_i \leftarrow b y_i + a x_i \quad i=1\dots n$

include/lwpr_math.h File Reference

Functions

Detailed Description

Function Documentation