Package edu.cmu.tetrad.util

Class MatrixUtils

java.lang.Object

edu.cmu.tetrad.util.MatrixUtils

public final class MatrixUtils
extends Object

Class Matrix includes several public static functions performing matrix operations. These function include: determinant, GJinverse, inverse, multiple, difference, transpose, trace, duplicate, minor, identity, mprint, impliedCovar, SEMimpliedCovar.

Version:

$Id: $Id

Author:

Tianjiao Chu, josephramsey, Kevin V. Bui

Method Summary

Modifier and Type	Method	Description
static double[][]	asRow(double[] v)	asRow.
static Matrix	cholesky(Matrix covar)	cholesky.
static double[]	concatenate(double[][] vectors)	Concatenates the vectors rows[i], i = 0...rows.length, into a single vector.
static Matrix	convertCovToCorr(Matrix m)	Converts a covariance matrix to a correlation matrix in place; the same matrix is returned for convenience, but m is modified in the process.
static double[][]	convertLowerTriangleToSymmetric(double[][] arr)	Converts a matrix in lower triangular form to a symmetric matrix in square form.
static double[][]	copyOf(double[][] arr)	copyOf.
static int[]	copyOf(int[] arr, int length)	copyOf.
static double	determinant(double[][] m)	determinant.
static double[][]	directProduct(double[][] ma, double[][] mb)	Computes the direct (Kronecker) outerProduct.
static boolean	equals(double[][] ma, double[][] mb)	Tests two matrices for equality.
static boolean	equals(double[][] ma, double[][] mb, double tolerance)	Tests to see whether two matrices are equal within the given tolerance.
static boolean	equals(double[] va, double[] vb)	Tests two vectors for equality.
static boolean	equals(double[] va, double[] vb, double tolerance)	Tests to see whether two vectors are equal within the given tolerance.
static boolean	hasDimensions(double[][] m, int i, int j)	hasDimensions.
static org.ejml.simple.SimpleMatrix	identity(int size)	identity.
static Matrix	impliedCovar(Matrix edgeCoef, Matrix errCovar)
static double	innerProduct(double[] ma, double[] mb)	innerProduct.
static double[][]	inverse(double[][] m)	Calculates the inverse of a given matrix.
static double[][]	invVech(double[] vech)	invVech.
static boolean	isPositiveDefinite(Matrix matrix)	Return true if the given matrix is symmetric positive definite--that is, if it would make a valid covariance matrix.
static boolean	isSquare(double[][] m)	isSquare.
static boolean	isSymmetric(double[][] m, double tolerance)	isSymmetric.
static double[][]	outerProduct(double[] ma, double[] mb)	outerProduct.
static double[]	product(double[][] ma, double[] mb)	product.
static double[][]	product(double[][] ma, double[][] mb)	product.
static double[]	product(double[] ma, double[][] mb)	product.
static Vector	product(Vector ma, Matrix mb)	product.
static double[][]	repmat(double[][] mat, int n)	Make a n repeat copy of the rows and columns of the matrix mat.
static double[][]	repmat(double[][] mat, int nRow, int mColumn)	Make a repeat copy of matrix mat.
static double[]	scalarProduct(double scalar, double[] m)	scalarProduct.
static double[][]	scalarProduct(double scalar, double[][] m)	Multiplies the given matrix through by the given scalar.
static double[][]	submatrix(double[][] m, int rem)	A copy of the original (square) matrix with the stated index row/column removed
static double[][]	subtract(double[][] ma, double[][] mb)	subtract.
static double[]	subtract(double[] ma, double[] mb)	subtract.
static double[][]	sum(double[][] ma, double[][] mb)	sum.
static double[]	sum(double[] ma, double[] mb)	sum.
static int	sum0ToN(int n)	sum0ToN.
static String	toString(boolean[][] m)	Copies the given array, starting each line with a tab character..
static String	toString(double[] m)	toString.
static String	toString(double[][] m)	Copies the given array, using a standard scientific notation number formatter and beginning each line with a tab character.
static String	toString(double[][] m, List<String> variables)	toString.
static String	toString(double[] m, NumberFormat nf)	toString.
static String	toString(int[] m)	toString.
static String	toString(int[][] m)	toString.
static String	toString(int[][] m, List<String> variables)	toString.
static String	toStringSquare(double[][] m, NumberFormat nf, List<String> variables)	toStringSquare.
static String	toStringSquare(double[][] m, List<String> variables)	toStringSquare.
static String	toStringSquare(int[][] m, List<String> variables)	toStringSquare.
static double	trace(double[][] m)	trace.
static double[][]	transpose(double[][] m)	transpose.
static org.apache.commons.math3.linear.RealMatrix	transposeWithoutCopy(org.apache.commons.math3.linear.RealMatrix apacheData)	transposeWithoutCopy.
static double[][]	vec(double[][] m)	vec.
static double[][]	vech(double[][] m)	vech.
static double[][]	vechToVecLeft(int n)	The matrix which, when postmultiplied by vech, return vec.
static double[][]	zeros(int rows, int cols)	zeros.

Methods inherited from class java.lang.Object

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

Method Details

repmat

public static double[][] repmat(double[][] mat,
 int nRow,
 int mColumn)

Make a repeat copy of matrix mat.

Parameters:

mat - matrix to copy

nRow - number of repeat copy of row

mColumn - number of repeat copy of column

Returns:

an array of objects

repmat

public static double[][] repmat(double[][] mat,
 int n)

Make a n repeat copy of the rows and columns of the matrix mat.

Parameters:

mat - an array of objects

n - number of repeat copy

Returns:

an array of objects

equals

public static boolean equals(double[][] ma,
 double[][] mb)

Tests two matrices for equality.

Parameters:

ma - The first 2D matrix to check.

mb - The second 2D matrix to check.

Returns:

True iff the first and second matrices are equal.

equals

public static boolean equals(double[] va,
 double[] vb)

Tests two vectors for equality.

Parameters:

va - The first 1D matrix to check.

vb - The second 1D matrix to check.

Returns:

True iff the first and second matrices are equal.

equals

public static boolean equals(double[][] ma,
 double[][] mb,
 double tolerance)

Tests to see whether two matrices are equal within the given tolerance. If any two corresponding elements differ by more than the given tolerance, false is returned.

Parameters:

ma - The first 2D matrix to check.

mb - The second 2D matrix to check.

tolerance - A double >= 0.

Returns:

Ibid.

equals

public static boolean equals(double[] va,
 double[] vb,
 double tolerance)

Tests to see whether two vectors are equal within the given tolerance. If any two corresponding elements differ by more than the given tolerance, false is returned.

Parameters:

va - The first matrix to check.

vb - The second matrix to check.

tolerance - A double >= 0.

Returns:

Ibid.

isSquare

public static boolean isSquare(double[][] m)

isSquare.

Parameters:

m - A 2D double matrix.

Returns:

Ibid.

isSymmetric

public static boolean isSymmetric(double[][] m,
 double tolerance)

isSymmetric.

Parameters:

m - The matrix to check.

tolerance - A double >= 0.

Returns:

Ibid.

determinant

public static double determinant(double[][] m)

determinant.

Parameters:

m - The matrix whose determinant is sought. Must be square.

Returns:

Ibid.

submatrix

public static double[][] submatrix(double[][] m,
 int rem)

A copy of the original (square) matrix with the stated index row/column removed

Parameters:

m - an array of objects

rem - a int

Returns:

an array of objects

inverse

public static double[][] inverse(double[][] m)

Calculates the inverse of a given matrix.

Parameters:

m - the input matrix to calculate the inverse of

Returns:

the inverse of the input matrix as a 2D array of doubles

product

public static double[][] product(double[][] ma,
 double[][] mb)

product.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

the outerProduct of ma and mb. The dimensions of ma and mb must be compatible for multiplication.

product

public static double[] product(double[] ma,
 double[][] mb)

product.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

product

public static Vector product(Vector ma,
 Matrix mb)

product.

Parameters:

ma - a Vector object

mb - a Matrix object

Returns:

a Vector object

product

public static double[] product(double[][] ma,
 double[] mb)

product.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

outerProduct

public static double[][] outerProduct(double[] ma,
 double[] mb)

outerProduct.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

innerProduct

public static double innerProduct(double[] ma,
 double[] mb)

innerProduct.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

a double

transpose

public static double[][] transpose(double[][] m)

transpose.

Parameters:

m - an array of objects

Returns:

the transpose of the given matrix.

trace

public static double trace(double[][] m)

trace.

Parameters:

m - an array of objects

Returns:

the trace of the given (square) m.

identity

public static org.ejml.simple.SimpleMatrix identity(int size)

identity.

Parameters:

size - a int

Returns:

the identity matrix of the given order.

sum

public static double[][] sum(double[][] ma,
 double[][] mb)

sum.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

the sum of ma and mb.

sum

public static double[] sum(double[] ma,
 double[] mb)

sum.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

subtract

public static double[][] subtract(double[][] ma,
 double[][] mb)

subtract.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

subtract

public static double[] subtract(double[] ma,
 double[] mb)

subtract.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

directProduct

public static double[][] directProduct(double[][] ma,
 double[][] mb)

Computes the direct (Kronecker) outerProduct.

Parameters:

ma - an array of objects

mb - an array of objects

Returns:

an array of objects

scalarProduct

public static double[][] scalarProduct(double scalar,
 double[][] m)

Multiplies the given matrix through by the given scalar.

Parameters:

scalar - a double

m - an array of objects

Returns:

an array of objects

scalarProduct

public static double[] scalarProduct(double scalar,
 double[] m)

scalarProduct.

Parameters:

scalar - a double

m - an array of objects

Returns:

an array of objects

concatenate

public static double[] concatenate(double[][] vectors)

Concatenates the vectors rows[i], i = 0...rows.length, into a single vector.

Parameters:

vectors - an array of objects

Returns:

an array of objects

asRow

public static double[][] asRow(double[] v)

asRow.

Parameters:

v - an array of objects

Returns:

the vector as a 1 x n row matrix.

impliedCovar

public static Matrix impliedCovar(Matrix edgeCoef,
 Matrix errCovar)

vech

public static double[][] vech(double[][] m)

vech.

Parameters:

m - an array of objects

Returns:

vech of the given array. (This is what you get when you stack all of the elements of m in the lower triangular of m to form a vector. The elements are stacked in columns left to right, top to bottom.)

invVech

public static double[][] invVech(double[] vech)

invVech.

Parameters:

vech - an array of objects

Returns:

the symmetric matrix for which the given array is the vech.

vec

public static double[][] vec(double[][] m)

vec.

Parameters:

m - an array of objects

Returns:

vech of the given array. (This is what you get when you stack all of the elements of m to form a vector. The elements are stacked in columns left to right, top to bottom.)

sum0ToN

public static int sum0ToN(int n)

sum0ToN.

Parameters:

n - a int

Returns:

the sum of integers from 0 up to n.

vechToVecLeft

public static double[][] vechToVecLeft(int n)

The matrix which, when postmultiplied by vech, return vec.

Parameters:

n - the size of the square matrix that vec and vech come from.

Returns:

an array of objects

hasDimensions

public static boolean hasDimensions(double[][] m,
 int i,
 int j)

hasDimensions.

Parameters:

m - an array of objects

i - a int

j - a int

Returns:

true just in case the given matrix has the given dimensions --that is, just in case m.length == i and m[0].length == j.

zeros

public static double[][] zeros(int rows,
 int cols)

zeros.

Parameters:

rows - a int

cols - a int

Returns:

an array of objects

isPositiveDefinite

public static boolean isPositiveDefinite(Matrix matrix)

Return true if the given matrix is symmetric positive definite--that is, if it would make a valid covariance matrix.

Parameters:

matrix - a Matrix object

Returns:

a boolean

cholesky

public static Matrix cholesky(Matrix covar)

cholesky.

Parameters:

covar - a Matrix object

Returns:

a Matrix object

convertCovToCorr

public static Matrix convertCovToCorr(Matrix m)

Converts a covariance matrix to a correlation matrix in place; the same matrix is returned for convenience, but m is modified in the process.

Parameters:

m - a Matrix object

Returns:

a Matrix object

convertLowerTriangleToSymmetric

public static double[][] convertLowerTriangleToSymmetric(double[][] arr)

Converts a matrix in lower triangular form to a symmetric matrix in square form. The lower triangular matrix need not contain matrix elements to represent elements in the upper triangle.

Parameters:

arr - an array of objects

Returns:

an array of objects

toString

public static String toString(double[][] m)

Copies the given array, using a standard scientific notation number formatter and beginning each line with a tab character. The number format is DecimalFormat(" 0.0000;-0.0000").

Parameters:

m - an array of objects

Returns:

a String object

toString

public static String toString(double[][] m,
 List<String> variables)

toString.

Parameters:

m - an array of objects

variables - a List object

Returns:

a String object

toStringSquare

public static String toStringSquare(double[][] m,
 List<String> variables)

toStringSquare.

Parameters:

m - an array of objects

variables - a List object

Returns:

a String object

toStringSquare

public static String toStringSquare(double[][] m,
 NumberFormat nf,
 List<String> variables)

toStringSquare.

Parameters:

m - an array of objects

nf - a NumberFormat object

variables - a List object

Returns:

a String object

toString

public static String toString(int[] m)

toString.

Parameters:

m - an array of objects

Returns:

a String object

toString

public static String toString(int[][] m,
 List<String> variables)

toString.

Parameters:

m - an array of objects

variables - a List object

Returns:

a String object

toStringSquare

public static String toStringSquare(int[][] m,
 List<String> variables)

toStringSquare.

Parameters:

m - an array of objects

variables - a List object

Returns:

a String object

toString

public static String toString(double[] m)

toString.

Parameters:

m - an array of objects

Returns:

a String object

toString

public static String toString(double[] m,
 NumberFormat nf)

toString.

Parameters:

m - an array of objects

nf - a NumberFormat object

Returns:

a String object

toString

public static String toString(int[][] m)

toString.

Parameters:

m - an array of objects

Returns:

a String object

toString

public static String toString(boolean[][] m)

Copies the given array, starting each line with a tab character..

Parameters:

m - an array of objects

Returns:

a String object

copyOf

public static int[] copyOf(int[] arr,
 int length)

copyOf.

Parameters:

arr - an array of objects

length - a int

Returns:

an array of objects

copyOf

public static double[][] copyOf(double[][] arr)

copyOf.

Parameters:

arr - an array of objects

Returns:

an array of objects

transposeWithoutCopy

public static org.apache.commons.math3.linear.RealMatrix transposeWithoutCopy(org.apache.commons.math3.linear.RealMatrix apacheData)

transposeWithoutCopy.

Parameters:

apacheData - a RealMatrix object

Returns:

a RealMatrix object