edu.northwestern.at.utils.math.matrix
Class Matrices

java.lang.Object
  edu.northwestern.at.utils.math.matrix.Matrices

public class Matrices
extends java.lang.Object

Matrices: Perform operations on matrices.

Constructor Summary

protected

Matrices()

Method Summary

static Matrix	abs(Matrix a)
static Matrix	add(Matrix a, double scalar)
static Matrix	add(Matrix a, Matrix b)
static int[]	bandwidth(Matrix matrix)
static Matrix	blkdiag(java.util.ArrayList matrices)
static Matrix[]	chol(Matrix m)
static double	cond(Matrix m)
static Matrix	corr(Matrix matrix) Get correlation matrix.
static Matrix	cos(Matrix a)
static Matrix	cov(Matrix matrix) Get covariance matrix.
static Matrix	create(java.lang.String src) Creation
static Matrix	cumprod(Matrix m)
static Matrix	cumsum(Matrix m)
static double	det(Matrix m)
static Matrix	diag(Matrix m)
static Matrix	diagEm(Matrix m, int offset)
static Matrix	diagEx(Matrix m, int offset)
static Matrix	divide(double scalar, Matrix a)
static Matrix	divide(Matrix a, double scalar)
static Matrix	divide(Matrix a, Matrix b)
static double	dotprod(Matrix a, Matrix b)
static Matrix[]	eig(Matrix m)
static Matrix	exp(Matrix a)
static Matrix	eye(int rows, int cols)
static Matrix	hdp(Matrix a, Matrix b)
static Matrix	horzcat(Matrix a, Matrix b)
static Matrix	inv(Matrix m)
static Matrix	kron(Matrix a, Matrix b)
static int	length(Matrix m)
static Matrix	load(java.lang.String fileName) Load matrix from an ASCII file.
static Matrix	log(Matrix a)
static Matrix[]	lu(Matrix m) Decompositions
static Matrix	maxCol(Matrix m)
static double	maxElem(Matrix m)
static Matrix	meanCol(Matrix m)
static double	meanElem(Matrix m)
static Matrix	minCol(Matrix m)
static double	minElem(Matrix m)
static Matrix	multiply(Matrix a, double scalar)
static Matrix	multiply(Matrix a, Matrix b)
static Matrix	multiplyEBE(Matrix a, Matrix b)
static Matrix	neg(Matrix a) Operators
static double	norm_1(Matrix m)
static double	norm(Matrix m)
static double	normFro(Matrix m)
static double	normInf(Matrix m)
static Matrix	nullSpace(Matrix a) Found basis of the null space for a matrix.
static Matrix	ones(int size)
static Matrix	ones(int rows, int cols)
static Matrix	orthBasis(Matrix a) Found orthonormal basis for a matrix.
static Matrix	pow(Matrix a, int s)
static Matrix	powElem(Matrix a, double s)
static Matrix	powElem(Matrix a, Matrix b)
static Matrix	prodCol(Matrix m)
static double	prodElem(Matrix m)
static Matrix[]	qr(Matrix m)
static Matrix	rand(int rows, int cols)
static int	rank(Matrix m) Methods
static void	rankOrderColumns(Matrix matrix) Rank order columns of a matrix.
static void	save(java.lang.String fileName, Matrix matrix) Save matrix in an ASCII file.
static Matrix	sin(Matrix a)
static Matrix	solve(Matrix a, Matrix b)
static Matrix	sqrt(Matrix a)
static Matrix[]	standardize(Matrix matrix) Standardize columns of a matrix.
static Matrix	subtract(double scalar, Matrix a)
static Matrix	subtract(Matrix a, double scalar)
static Matrix	subtract(Matrix a, Matrix b)
static Matrix	sumCol(Matrix m)
static double	sumElem(Matrix m)
static Matrix[]	svd(Matrix m)
static Matrix	t(Matrix m)
static double	trace(Matrix m)
static Matrix	transpose(Matrix m)
static Matrix	tril(Matrix m, int offset)
static Matrix	triu(Matrix m, int offset)
static Matrix	vertcat(Matrix a, Matrix b)
static Matrix	zeroise(Matrix m)
static Matrix	zeroize(Matrix m)
static Matrix	zeros(int size)
static Matrix	zeros(int rows, int cols)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Matrices

protected Matrices()

Method Detail

bandwidth

public static int[] bandwidth(Matrix matrix)

create

public static Matrix create(java.lang.String src)

Creation

rand

public static Matrix rand(int rows,
                          int cols)

zeros

public static Matrix zeros(int rows,
                           int cols)

zeros

public static Matrix zeros(int size)

ones

public static Matrix ones(int rows,
                          int cols)

ones

public static Matrix ones(int size)

eye

public static Matrix eye(int rows,
                         int cols)

neg

public static Matrix neg(Matrix a)

Operators

sin

public static Matrix sin(Matrix a)

cos

public static Matrix cos(Matrix a)

exp

public static Matrix exp(Matrix a)

log

public static Matrix log(Matrix a)

sqrt

public static Matrix sqrt(Matrix a)

abs

public static Matrix abs(Matrix a)

powElem

public static Matrix powElem(Matrix a,
                             double s)

powElem

public static Matrix powElem(Matrix a,
                             Matrix b)

pow

public static Matrix pow(Matrix a,
                         int s)

add

public static Matrix add(Matrix a,
                         Matrix b)

add

public static Matrix add(Matrix a,
                         double scalar)

subtract

public static Matrix subtract(Matrix a,
                              Matrix b)

subtract

public static Matrix subtract(Matrix a,
                              double scalar)

subtract

public static Matrix subtract(double scalar,
                              Matrix a)

dotprod

public static double dotprod(Matrix a,
                             Matrix b)

multiply

public static Matrix multiply(Matrix a,
                              Matrix b)

multiplyEBE

public static Matrix multiplyEBE(Matrix a,
                                 Matrix b)

multiply

public static Matrix multiply(Matrix a,
                              double scalar)

kron

public static Matrix kron(Matrix a,
                          Matrix b)

hdp

public static Matrix hdp(Matrix a,
                         Matrix b)

solve

public static Matrix solve(Matrix a,
                           Matrix b)

divide

public static Matrix divide(Matrix a,
                            Matrix b)

divide

public static Matrix divide(Matrix a,
                            double scalar)

divide

public static Matrix divide(double scalar,
                            Matrix a)

t

public static Matrix t(Matrix m)

transpose

public static Matrix transpose(Matrix m)

inv

public static Matrix inv(Matrix m)

horzcat

public static Matrix horzcat(Matrix a,
                             Matrix b)

vertcat

public static Matrix vertcat(Matrix a,
                             Matrix b)

blkdiag

public static Matrix blkdiag(java.util.ArrayList matrices)

rank

public static int rank(Matrix m)

Methods

det

public static double det(Matrix m)

trace

public static double trace(Matrix m)

norm

public static double norm(Matrix m)

norm_1

public static double norm_1(Matrix m)

normInf

public static double normInf(Matrix m)

normFro

public static double normFro(Matrix m)

cond

public static double cond(Matrix m)

diag

public static Matrix diag(Matrix m)

diagEx

public static Matrix diagEx(Matrix m,
                            int offset)

diagEm

public static Matrix diagEm(Matrix m,
                            int offset)

length

public static int length(Matrix m)

sumElem

public static double sumElem(Matrix m)

sumCol

public static Matrix sumCol(Matrix m)

prodElem

public static double prodElem(Matrix m)

prodCol

public static Matrix prodCol(Matrix m)

maxElem

public static double maxElem(Matrix m)

maxCol

public static Matrix maxCol(Matrix m)

minElem

public static double minElem(Matrix m)

minCol

public static Matrix minCol(Matrix m)

meanElem

public static double meanElem(Matrix m)

meanCol

public static Matrix meanCol(Matrix m)

cumprod

public static Matrix cumprod(Matrix m)

cumsum

public static Matrix cumsum(Matrix m)

triu

public static Matrix triu(Matrix m,
                          int offset)

tril

public static Matrix tril(Matrix m,
                          int offset)

zeroize

public static Matrix zeroize(Matrix m)

zeroise

public static Matrix zeroise(Matrix m)

lu

public static Matrix[] lu(Matrix m)

Decompositions

qr

public static Matrix[] qr(Matrix m)

eig

public static Matrix[] eig(Matrix m)

chol

public static Matrix[] chol(Matrix m)

svd

public static Matrix[] svd(Matrix m)

save

public static void save(java.lang.String fileName,
                        Matrix matrix)

Save matrix in an ASCII file.

Parameters:

fileName - The filename to save to.

matrix - The matrix to save.

load

public static Matrix load(java.lang.String fileName)

Load matrix from an ASCII file.

Parameters:

fileName - The filename of the file containing the matrix.

Returns:

Matrix read from file.

corr

public static Matrix corr(Matrix matrix)

Get correlation matrix.

Parameters:

matrix - The matrix.

Returns:

Correlation matrix of columns in matrix.

cov

public static Matrix cov(Matrix matrix)

Get covariance matrix.

Parameters:

matrix - The matrix.

Returns:

Covariance matrix of columns in matrix.

standardize

public static Matrix[] standardize(Matrix matrix)

Standardize columns of a matrix.

Parameters:

matrix - The matrix whose columns should be standardized to mean=0 and standard deviation=1.

Returns:

Input matrix is standardized. Two-element array returned with first entry the row vector of column means and the second entry the row vector of column standard deviations.

rankOrderColumns

public static void rankOrderColumns(Matrix matrix)

Rank order columns of a matrix.

Parameters:

matrix - The matrix whose columns should be converted to rank order.

nullSpace

public static Matrix nullSpace(Matrix a)

Found basis of the null space for a matrix.

Parameters:

a - Matrix whose null space is to be found.

Returns:

Basis of the null space for a.

orthBasis

public static Matrix orthBasis(Matrix a)

Found orthonormal basis for a matrix.

Parameters:

a - Matrix whose orthonmal basis is to be found.

Returns:

Orthonormal basis for a.