fr.lip6.jkernelmachines.util.algebra

Class MatrixOperations

java.lang.Object

fr.lip6.jkernelmachines.util.algebra.MatrixOperations

public class MatrixOperations
extends java.lang.Object

This class provides basic linear algebra operations on matrices.

Author:

picard

Field Summary

Fields

Modifier and Type	Field and Description
static double	num_prec

Constructor Summary

Constructors

Constructor and Description
MatrixOperations()

Method Summary

Modifier and Type	Method and Description
static double[][][]	eig_jacobi(double[][] m, boolean prec) Performs the eigen decomposition of a symmetric matrix: A = Q * L * Q' with Q orthonormal and L diagonal
static double[][][]	eig_qr(double[][] A) Performs the eigen decomposition of a symmetric matrix: A = Q * L * Q' with Q orthonormal and L diagonal
static double[][][]	eig(double[][] A) Performs the eigen decomposition of a symmetric matrix: A = Q * L * Q' with Q orthonormal and L diagonal
static double[][]	givensRoti(double[][] matrix, double[][] G, int i, int j) Performs the Givens rotation that nullifies component (i,j) of a matrix, accumulated on previous Rotation matrices
static double[][]	inv(double[][] A) Compute the inverse matrix
static boolean	is_tri(double[][] A)
static boolean	isSquare(double[][] A) Tests if a matrix is square
static boolean	isSymmetric(double[][] A) Checks if a matrix is symmetric
static boolean	isTriDiagonal(double[][] A)
static double[][][]	lancsos_iteration(double[][] m)
static double[][]	mul(double[][] A, double[][] B) Performs the matrix multiplication between two double matrices C = A * B
static double[][]	muli(double[][] C, double[][] A, double[][] B) Performs the matrix multiplication between two double matrices C = A * B
static void	print(double[][] A) outputs the matrix on System.out
static double[][][]	qr(double[][] A) Performs the QR decomposition of a symmetric matrix, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R
static void	qri_givens(double[][] Q, double[][] R, double[][] m) Performs the in place QR decomposition of a symmetric matrix using Givens rotation matrices, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R
static void	qri_gramschmidt(double[][] Q, double[][] R, double[][] A) Performs the in place QR decomposition of a symmetric matrix, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R
static void	qri(double[][] Q, double[][] R, double[][] A) Performs the in place QR decomposition of a symmetric matrix, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R
static double[][]	trans(double[][] A) Computes the transposed matrix of a matrix
static double[][]	transi(double[][] A) Computes the transposed matrix of a symmetric matrix in place
static double[][]	transi(double[][] C, double[][] A) Computes the transposed matrix of a matrix in place
static double[][]	transMul(double[][] A, double[][] B) Computes the transpose multiplication between two matrices : C = A' * B
static double[][]	transMuli(double[][] C, double[][] A, double[][] B) Computes the transpose multiplication between two matrices : C = A' * B
static double[][][]	tri_givens(double[][] m, boolean prec)
static double[][][]	tri_householder(double[][] m)
static double[][][]	tri_lancsos(double[][] m)
static double[][][]	tri(double[][] m) Performs the trigonalization of a symmetric matrix: A = Q * T * Q' with Q orthonormal and T tridiagonal

Methods inherited from class java.lang.Object

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

Field Detail

num_prec

public static final double num_prec

See Also:

Constant Field Values

Constructor Detail

MatrixOperations

public MatrixOperations()

Method Detail

isSquare

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

Tests if a matrix is square

Parameters:

A - the input matrix

Returns:

true if A is n*n, false else

isSymmetric

public static boolean isSymmetric(double[][] A)

Checks if a matrix is symmetric

Parameters:

A - the matrix

Returns:

true if A is symmetric, false else

isTriDiagonal

public static boolean isTriDiagonal(double[][] A)

trans

public static double[][] trans(double[][] A)

Computes the transposed matrix of a matrix

Parameters:

A - the input matrix

Returns:

a newly allocated matrix containing the transpose of A

transi

public static double[][] transi(double[][] A)

Computes the transposed matrix of a symmetric matrix in place

Parameters:

A - the input matrix to transpose

Returns:

A transpose

transi

public static double[][] transi(double[][] C,
                                double[][] A)

Computes the transposed matrix of a matrix in place

Parameters:

C - the output matrix

A - the input matrix

Returns:

a newly allocated matrix containing the transpose of A

mul

public static double[][] mul(double[][] A,
                             double[][] B)
                      throws java.lang.ArithmeticException

Performs the matrix multiplication between two double matrices C = A * B

Parameters:

A - first matrix

B - second matrix

Returns:

a newly allocated matrix C

Throws:

java.lang.ArithmeticException

muli

public static double[][] muli(double[][] C,
                              double[][] A,
                              double[][] B)
                       throws java.lang.ArithmeticException

Performs the matrix multiplication between two double matrices C = A * B

Parameters:

A - first matrix

B - second matrix

C - the result matrix

Returns:

matrix C

Throws:

java.lang.ArithmeticException

transMul

public static double[][] transMul(double[][] A,
                                  double[][] B)

Computes the transpose multiplication between two matrices : C = A' * B

Parameters:

A - first matrix

B - second matrix

Returns:

C = A' * B

transMuli

public static double[][] transMuli(double[][] C,
                                   double[][] A,
                                   double[][] B)

Computes the transpose multiplication between two matrices : C = A' * B

Parameters:

A - first matrix

B - second matrix

Returns:

C = A' * B

givensRoti

public static double[][] givensRoti(double[][] matrix,
                                    double[][] G,
                                    int i,
                                    int j)

Performs the Givens rotation that nullifies component (i,j) of a matrix, accumulated on previous Rotation matrices

Parameters:

matrix - the input/output matrix

G - the input/output rotation matrix

i - component one the lines

j - component on the columns

Returns:

matrix

qr

public static double[][][] qr(double[][] A)

Performs the QR decomposition of a symmetric matrix, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R

Parameters:

A - input matrix

Returns:

an newly allocated array of two matrices containing {Q, R}

qri

public static void qri(double[][] Q,
                       double[][] R,
                       double[][] A)

Performs the in place QR decomposition of a symmetric matrix, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R

Parameters:

Q - output matrix Q

R - output matrix R

A - input matrix A

qri_givens

public static void qri_givens(double[][] Q,
                              double[][] R,
                              double[][] m)

Performs the in place QR decomposition of a symmetric matrix using Givens rotation matrices, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R

Parameters:

Q - output matrix Q

R - output matrix R

m - input matrix m

qri_gramschmidt

public static void qri_gramschmidt(double[][] Q,
                                   double[][] R,
                                   double[][] A)

Performs the in place QR decomposition of a symmetric matrix, such that Q is orthonormal and R is an upper triangular matrix: A = Q*R

Parameters:

Q - output matrix Q

R - output matrix R

A - input matrix A

inv

public static double[][] inv(double[][] A)

Compute the inverse matrix

Parameters:

A - input matrix

Returns:

the inverse of A if possible

eig

public static double[][][] eig(double[][] A)

Performs the eigen decomposition of a symmetric matrix: A = Q * L * Q' with Q orthonormal and L diagonal

Parameters:

A - input matrix

Returns:

an array of two matrices containing {Q, L}

eig_jacobi

public static final double[][][] eig_jacobi(double[][] m,
                                            boolean prec)

Performs the eigen decomposition of a symmetric matrix: A = Q * L * Q' with Q orthonormal and L diagonal

Parameters:

m - input matrix

Returns:

an array of two matrices containing {Q, L}

eig_qr

public static double[][][] eig_qr(double[][] A)

Performs the eigen decomposition of a symmetric matrix: A = Q * L * Q' with Q orthonormal and L diagonal

Parameters:

A - input matrix

Returns:

an array of two matrices containing {Q, L}

tri

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

Performs the trigonalization of a symmetric matrix: A = Q * T * Q' with Q orthonormal and T tridiagonal

Parameters:

m - input matrix

Returns:

an array of two matrices containing {Q, L}

tri_householder

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

tri_lancsos

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

lancsos_iteration

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

tri_givens

public static double[][][] tri_givens(double[][] m,
                                      boolean prec)

print

public static void print(double[][] A)

outputs the matrix on System.out

Parameters:

A -

is_tri

public static boolean is_tri(double[][] A)