ml::LinearAlgebra Namespace Reference

Linear algebra helper functions. More...

Functions
double	xAx_symmetric (const Eigen::MatrixXd &A, Eigen::Ref< const Eigen::VectorXd > x)
	Calculates x^T A x for a symmetric matrix A. More...
void	xxT (const Eigen::VectorXd &x, Eigen::MatrixXd &dest)
	Calculates x * x^T and places it in dest. More...
void	add_a_xxT (const Eigen::VectorXd &x, Eigen::MatrixXd &dest, double a)
	Adds a * x * x^T to A. More...

Detailed Description

Linear algebra helper functions.

Function Documentation

xAx_symmetric()

double ml::LinearAlgebra::xAx_symmetric	(	const Eigen::MatrixXd &	A,
		Eigen::Ref< const Eigen::VectorXd >	x
	)

Calculates x^T A x for a symmetric matrix A.

Parameters

A	Symmetric square matrix.
x	Vector.

Returns

Value of \( \vec{x}^T A \vec{x} \).

Exceptions

std::invalid_argument

If A is not square or x.size() != A.rows().

xxT()

void ml::LinearAlgebra::xxT	(	const Eigen::VectorXd &	x,
		Eigen::MatrixXd &	dest
	)

Calculates x * x^T and places it in dest.

Parameters

[in]	x	Vector of length N.
[out]	dest	Output matrix, resized if necessary. Assumed to be non-aliasing with x.

add_a_xxT()

void ml::LinearAlgebra::add_a_xxT	(	const Eigen::VectorXd &	x,
		Eigen::MatrixXd &	dest,
		double	a
	)

Adds a * x * x^T to A.

Parameters

[in]	x	Vector of length N.
[out]	A	Existing N x N matrix.

Exceptions

std::invalid_argument

If A is not square or x.size() != A.rows().