Matrix.cpp File Reference

#include "Matrix.h"
#include <gsl/gsl_errno.h>

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Functions
std::ostream &	operator<< (std::ostream &os, RealMatrix A)
RealMatrix	eye (std::size_t n)
	Returns the identity matrix of size n.
RealMatrix	diag (const gsl_vector *X)
	Builds a diagonal matrix from a GSL vector.
RealMatrix	nearest_psd (RealMatrix R, double thr)
	Projects a matrix to the nearest positive semi-definite correlation-like matrix.
RealMatrix	cholesky_L (RealMatrix R)
	Returns the lower-triangular Cholesky factor of a PSD matrix.
RealMatrix	block_diag (const std::vector< RealMatrix > &blocks)
	Builds a block-diagonal matrix from several square blocks.

Function Documentation

block_diag()

RealMatrix block_diag

(

const std::vector< RealMatrix > &

blocks

)

Builds a block-diagonal matrix from several square blocks.

Parameters

blocks

List of square matrices.

Returns

Block-diagonal concatenation of all input matrices.

Exceptions

std::invalid_argument

if one input block is not square.

Definition at line 529 of file Matrix.cpp.

cholesky_L()

RealMatrix cholesky_L

(

RealMatrix

R

)

Returns the lower-triangular Cholesky factor of a PSD matrix.

If R = L L^T, this function returns L.

Parameters

R	Input matrix.

Returns

Lower-triangular Cholesky factor.

Exceptions

std::invalid_argument	if the matrix is not square.
std::runtime_error	if Cholesky decomposition fails.

Definition at line 508 of file Matrix.cpp.

diag()

RealMatrix diag

(

const gsl_vector *

X

)

Builds a diagonal matrix from a GSL vector.

Parameters

X	Input vector.

Returns

Square diagonal matrix whose diagonal entries are the values of X.

Definition at line 464 of file Matrix.cpp.

eye()

RealMatrix eye

(

std::size_t

n

)

Returns the identity matrix of size n.

Parameters

n	Matrix dimension.

Returns

n × n identity matrix.

Definition at line 453 of file Matrix.cpp.

nearest_psd()

RealMatrix nearest_psd	(	RealMatrix	R,
		double	thr = 1e-12
	)

Projects a matrix to the nearest positive semi-definite correlation-like matrix.

Algorithm:

• symmetrize the input,
• diagonalize it,
• clip eigenvalues below thr,
• reconstruct the matrix,
• renormalize the diagonal to 1,
• symmetrize again.

This is especially useful for repairing numerically inconsistent correlation matrices.

Parameters

R	Input matrix.
thr	Lower bound applied to eigenvalues during clipping.

Returns

Positive semi-definite, unit-diagonal repaired matrix.

Exceptions

std::invalid_argument

if the matrix is not square.

Definition at line 475 of file Matrix.cpp.

operator<<()

std::ostream & operator<<	(	std::ostream &	os,
		RealMatrix	A
	)

Prints the matrix in a nested bracket form.

Parameters

os	Output stream.
A	Matrix to print.

Returns

Output stream.

Definition at line 439 of file Matrix.cpp.