#include "MatrixTools.hh"
#include <iostream.h>

Functions
void	CopyMatrix (double LHS_Matrix, double RHS_Matrix, int dim)
	Matrix Assignment LHS_Matrix = RHS_Matrix.
void	DenseMatrixProduct (double A, double B, double **R, bool Transpose_B, bool R_is_symmetric, int dim)
void	DenseMatrixSimilarityProduct (double A, double B, double R, double Work, bool Transpose_A, bool R_is_symmetric, int dim)
void	DenseMatrixScale (double **A, int dim, double scale)
	Multiply all elements of the dim x dim double matrix A by the double scale.
void	CopyLowerToUpperHalf (double **A, int dim)
void	SymmetrizeMatrix (double **A, int dim)
	Replaces A with 0.5*(A+A') where A' is the transpose of the real matrix A.
void	TransposeMatrix (double **A, int dim)
	If input[i][j] = A_ij then output[i][j]= A_ji.
void	ZeroMatrix (double **A, int dim)
	Sets all entries of Matrix A to 0.
void	DenseMatrixFilter (double *A, int dim, double filter)
	Filters the matrix A with filter.
void	WriteMatrix (double *A, int dim, ofstream F, double scaling)
	Writes the Matrix scaling*A of size dim x dim to the file F.
void	ReadMatrix (double *A, int dim, ifstream F, double scaling)
void	DenseMatrixVectorProduct (double Out, double A, double In, int dim)
void	DenseVectorMatrixProduct (double Out, double In, double **A, int dim)
void	AddToPrincipalDiag (double **A, int dim, double add)
	Adds the double add to the principal diagonal of Matrix A.
void	AddVectorToPrincipalDiag (double *A, double V, double ScalarMultiple, int dim)
double	ScalarProductNormalized (cplx aa, cplx bb, int len)
double	VectorAngle (cplx aa, cplx bb, int len)
void	SchmidtOrthogonalizer (cplx *vec, int num, int len, double alpha)
void	SchmidtOrthogonalizer (cplx *vec, int num, int len, double alpha, int k1=1)
double	InfNormMatrix (double **A, int dim)
double	OneNormMatrix (double **A, int dim)
double	InnerProduct (double V, double W, int Length)
	Returns the standard inner product of two real vectors.

Function Documentation

void AddToPrincipalDiag	(	double **	A,
		int	dim,
		double	add
	)

Adds the double add to the principal diagonal of Matrix A.

Referenced by NoiseCovariance::AmplifyCovarianceMatrix(), NoiseCovariance::ComputeCovarianceMatrixAWGN(), NoiseCovariance::InitializeCovarianceMatrix(), NoiseCovariance::PropagateAnalyticCWSignalNoLossNoDispersion(), and ChiSquareReceiver::TestEigDecomposition().

void AddVectorToPrincipalDiag	(	double **	A,
		double *	V,
		double	ScalarMultiple,
		int	dim
	)

Adds the array ScalarMultiple*V, where V is a vector to the principal diagonal of Matrix A.

Referenced by ChiSquareReceiver::TestEigDecomposition().

void CopyLowerToUpperHalf	(	double **	A,
		int	dim
	)

Copies the lower half of the matrix A to the upper half, so that the resulting matrix is symmetric.

A: real matrix of dimension dim x dim indices run from 0 to dim-1 A[row][column]

Referenced by DenseMatrixProduct().

void CopyMatrix	(	double **	LHS_Matrix,
		double **	RHS_Matrix,
		int	dim
	)

Matrix Assignment LHS_Matrix = RHS_Matrix.

Referenced by NoiseCovariance::operator=(), and ChiSquareReceiver::SymmetricEig().

void DenseMatrixFilter	(	double **	A,
		int	dim,
		double *	filter
	)

Filters the matrix A with filter.

If A[i][j] is the (i,j) entry of A, and filter[i] is the i-th element of filter, then the filtering of A is defined to be

A_new[i][j] = A_old[i][j]*filter[i]*filter[j]

where * is regular multiplication of numbers.

void DenseMatrixProduct	(	double **	A,
		double **	B,
		double **	R,
		bool	Transpose_B,
		bool	R_is_symmetric,
		int	dim
	)

Computes the matrix product R = A * B or R = A * B^T depending on whether the flag Transpose_B is 0 or 1.

A,B, and R are all real matrices of dimension dim x dim where indices run from 0 to dim-1. It is assumed that all matrices are double 2D arrays with M[i][j] being the (row,col) = (i,j) of the Matrix M.

References CopyLowerToUpperHalf().

Referenced by ChiSquareReceiver::ComputeKLModes(), DenseMatrixSimilarityProduct(), ChiSquareReceiver::TestEigDecomposition(), and NoiseCovariance::UpdateCovMatrixODE().

void DenseMatrixScale	(	double **	A,
		int	dim,
		double	scale
	)

Multiply all elements of the dim x dim double matrix A by the double scale.

A is a real matrix of dimension dim x dim where indices run from 0 to dim-1. A is a double 2D array with A[i][j] being the (row,col) = (i,j) of the Matrix A.

Referenced by NoiseCovariance::AmplifyCovarianceMatrix(), ChiSquareReceiver::GetReducedNoiseFreeSigAndDiagonalizeCovMatrix(), and NoiseCovariance::LumpedLossCovarianceMatrix().

void DenseMatrixSimilarityProduct	(	double **	A,
		double **	B,
		double **	R,
		double **	Work,
		bool	Transpose_A,
		bool	R_is_symmetric,
		int	dim
	)

Computes the matrix product R = A*B*A^T or R = A^T*B*A depending on whether the flag Transpose_A is 0 or 1, respectively

A,B,R, and Work are all real matrices of dimension dim x dim where indices run from 0 to dim-1. It is assumed that all matrices are double 2D arrays with M[i][j] being the (row,col) = (i,j) of the Matrix M.

References DenseMatrixProduct(), and TransposeMatrix().

Referenced by ChiSquareReceiver::ComputeKLModes(), and ChiSquareReceiver::TestEigDecomposition().

void DenseMatrixVectorProduct	(	double *	Out,
		double **	A,
		double *	In,
		int	dim
	)

Computes the matrix-vector product Out = A*In where In and Out are vectors and A is square of size dim x dim

Referenced by ChiSquareReceiver::ComputeKLModes().

void DenseVectorMatrixProduct	(	double *	Out,
		double *	In,
		double **	A,
		int	dim
	)

Computes the matrix-vector product Out = In*A where In and Out are vectors and A is square of size dim x dim

double InfNormMatrix	(	double **	A,
		int	dim
	)

The infinity norm of a square matrix A is the largest row sum of the matrix whose entries are the absolute values of A

Referenced by OneNormMatrix(), and ChiSquareReceiver::TestEigDecomposition().

double InnerProduct	(	double *	V,
		double *	W,
		int	Length
	)

Returns the standard inner product of two real vectors.

Referenced by ChiSquareReceiver::ComputeKLModes(), ReduPolarizer::PolarizeOptSignal(), Polarizer::PolarizeOptSignal(), and GaussianReceiver::ReceiveSignalDGD_NoisePartiallyPolarized().

double OneNormMatrix	(	double **	A,
		int	dim
	)

The one norm of a square matrix A is the largest column sum of the matrix whose entries are the absolute values of A

References InfNormMatrix(), and TransposeMatrix().

void ReadMatrix	(	double **	A,
		int	dim,
		ifstream *	F,
		double	scaling
	)

Reads in the Matrix scaling*A of size dim x dim from the file F that was previously written using WriteMatrix

The i-th row of the file contains the i-th row of A

Referenced by NoiseCovariance::ReadFileNoiseFreeSignalAndCovarianceMatrix().

double ScalarProductNormalized	(	cplx *	aa,
		cplx *	bb,
		int	len
	)

Returns the double (aa,bb)/(bb,bb) for aa, bb complex vectors of length len where (aa,bb) := Re[conj(aa) * bb] = Re(aa)*Re(bb) + Im(aa)*Im(bb)

Referenced by SchmidtOrthogonalizer().

void SchmidtOrthogonalizer	(	cplx **	vec,
		int	num,
		int	len,
		double *	alpha
	)

Performs Gram-Schmidt orthogonalization of num vectors of length len where vec[i][] is the i-th vector i.e., vec is a cplx array of dim num x len alpha[] must be a double array of length (num^2-num)/2 Can start orthogonalization proceedure with the k1-th vector instead of the 1-st vector if you like. (k1 is an optional argument). Uses the inner product (aa,bb) := Re[conj(aa) * bb] = Re(aa)*Re(bb) + Im(aa)*Im(bb)

Input: Set of num vectors of length len that span a linear space

Output: Orthogonalized set of num vectors in vec. vec[0][] is untouched, the component of vec[1][] that is parallel to vec[0][] is removed from vec[1][], then the component of vec[2][] that is parallel to vec[0][] is removed from vec[2][], then the component of vec[2][] that is parallel to vec[1][] is removed etc...

Method: Schmidt's orthogonalization procedure, see "Taschenbuch der Mathematik", p. 147 alpha[] must be a double array of length (num^2-num)/2 that will contain the normalized scalar products (a_2,b_1)/(b_1,b_1), (a_3,b_1)/(b_1,b_1), (a_3,b_2)/(b_2,b_2), (a_4,b_1)/(b_1,b_1), (a_4,b_2)/(b_2,b_2), (a_4,b_3)/(b_3,b_3),...

vec[][]: cplx array of dim num x len k1: optional argument, start index (index of b_i to start with)

Successfully tested 25 Feb 2001 R.H. for vectors of length 3: vec[0][0] = 2.0; vec[0][1] = 3.0; vec[0][2] = -1.0; vec[1][0] = -5.0; vec[1][1] = 7.0; vec[1][2] = -3.0; vec[2][0] = 1.0; vec[2][1] = 2.0; vec[2][2] = 9.0; schmidt_orthogonalizer(vec, 3, 3, alpha);

References SchmidtOrthogonalizer().

Referenced by NoiseCovariance::ComputeColumnPropagator(), and SchmidtOrthogonalizer().

void SchmidtOrthogonalizer	(	cplx **	vec,
		int	num,
		int	len,
		double *	alpha,
		int	k1 = `1`
	)

References ScalarProductNormalized().

void SymmetrizeMatrix	(	double **	A,
		int	dim
	)

Replaces A with 0.5*(A+A') where A' is the transpose of the real matrix A.

Referenced by ChiSquareReceiver::ComputeKLModes(), and ChiSquareReceiver::GetReducedNoiseFreeSigAndDiagonalizeCovMatrix().

void TransposeMatrix	(	double **	A,
		int	dim
	)

If input[i][j] = A_ij then output[i][j]= A_ji.

Referenced by ChiSquareReceiver::ComputeKLModes(), DenseMatrixSimilarityProduct(), OneNormMatrix(), and ChiSquareReceiver::SymmetricEig().

double VectorAngle	(	cplx *	aa,
		cplx *	bb,
		int	len
	)

Returns the angle between complex vectors aa and bb of length len using the inner product (aa,bb) := Re[conj(aa) * bb] = Re(aa)*Re(bb) + Im(aa)*Im(bb)

Computes acos((aa,bb)/(|bb|*|aa|)) for aa, bb complex vectors of length len where (aa,bb) := Re[conj(aa) * bb] = Re(aa)*Re(bb) + Im(aa)*Im(bb)

References sqrt().

void WriteMatrix	(	double **	A,
		int	dim,
		ofstream *	F,
		double	scaling
	)

Writes the Matrix scaling*A of size dim x dim to the file F.

The i-th row of the file contains the i-th row of A

Referenced by NoiseCovariance::WriteFileNoiseFreeSignalAndCovarianceMatrix(), and ChiSquareReceiver::WriteFileSquareMatrix().

void ZeroMatrix	(	double **	A,
		int	dim
	)

Sets all entries of Matrix A to 0.

A: real matrix of dimension dim x dim indices run from 0 to dim-1

Referenced by NoiseCovariance::AllocateMemory(), NoiseCovariance::ComputeCovarianceMatrixAWGN(), NoiseCovariance::InitializeCovarianceMatrix(), NoiseCovariance::PropagateAnalyticCWSignalNoLossNoDispersion(), and NoiseCovariance::ResetVolatileParameters().

MatrixTools.cc File Reference

Functions

Function Documentation