This class implements a few methods for matrix calculations when the matrix entries are in double. More...

Public Member Functions
	DMatrix (int r, int c)
	Creates a new DMatrix with r rows and c columns.
	DMatrix (double[][] data, int r, int c)
	Creates a new DMatrix with r rows and c columns using the data in data.
	DMatrix (DMatrix that)
	Copy constructor.
String	toString ()
	Creates a String containing all the data of the DMatrix.
int	numRows ()
	Returns the number of rows of the DMatrix.
int	numColumns ()
	Returns the number of columns of the DMatrix.
double	get (int row, int column)
	Returns the matrix element in the specified row and column.
void	set (int row, int column, double value)
	Sets the value of the element in the specified row and column.
DMatrix	transpose ()
	Returns the transposed matrix.

Static Public Member Functions
static void	CholeskyDecompose (double[][] M, double[][] L)
	Given a symmetric positive-definite matrix \(M\), performs the Cholesky decomposition of \(M\) and returns the result as a lower triangular matrix \(L\), such that \(M = L L^T\).
static DoubleMatrix2D	CholeskyDecompose (DoubleMatrix2D M)
	Given a symmetric positive-definite matrix \(M\), performs the Cholesky decomposition of \(M\) and returns the result as a lower triangular matrix \(L\), such that \(M = L L^T\).
static void	PCADecompose (double[][] M, double[][] A, double[] lambda)
	Computes the principal components decomposition \(M\) =.
static DoubleMatrix2D	PCADecompose (DoubleMatrix2D M, double[] lambda)
	Computes the principal components decomposition \(M\) =.
static double[]	solveLU (double[][] A, double[] b)
	Solves the matrix equation \(Ax = b\) using LU decomposition.
static void	solveTriangular (DoubleMatrix2D U, DoubleMatrix2D B, DoubleMatrix2D X)
	Solve the triangular matrix equation \(UX = B\) for \(X\).
static double[][]	exp (double[][] A)
	Similar to #exp(final DoubleMatrix2D).
static DoubleMatrix2D	exp (final DoubleMatrix2D A)
	Returns \(e^A\), the exponential of the square matrix \(A\).
static DoubleMatrix2D	expBidiagonal (final DoubleMatrix2D A)
	Returns \(e^A\), the exponential of the bidiagonal square matrix.
static DoubleMatrix1D	expBidiagonal (final DoubleMatrix2D A, final DoubleMatrix1D b)
	Computes \(c = e^A b\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\).
static DoubleMatrix2D	expmiBidiagonal (final DoubleMatrix2D A)
	Computes \(e^A - I\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\).
static DoubleMatrix1D	expmiBidiagonal (final DoubleMatrix2D A, final DoubleMatrix1D b)
	Computes \(c = (e^A - I)b\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\).
static void	copy (double[][] M, double[][] R)
	Copies the matrix \(M\) into \(R\).
static String	toString (double[][] M)
	Returns matrix \(M\) as a string.

Static Package Functions
static void	multBand (final DoubleMatrix2D A, int sa, final DoubleMatrix2D B, int sb, DoubleMatrix2D C)
	Matrix multiplication \(C = AB\).
static void	multBand (DoubleMatrix2D A, int sa, double h)
	Multiplication of the matrix \(A\) by the scalar \(h\).
static void	addMultBand (double g, DoubleMatrix2D A, int sa, double h, final DoubleMatrix2D B, int sb)
	Addition of the matrices \(gA + hB\) after multiplication with the scalars \(g\) and \(h\).

Detailed Description

This class implements a few methods for matrix calculations when the matrix entries are in double.

Definition at line 38 of file DMatrix.java.

Constructor & Destructor Documentation

◆ DMatrix() [1/3]

umontreal.ssj.util.DMatrix.DMatrix	(	int	r,
		int	c )

Creates a new DMatrix with r rows and c columns.

Parameters

r	the number of rows
c	the number of columns

Definition at line 268 of file DMatrix.java.

◆ DMatrix() [2/3]

umontreal.ssj.util.DMatrix.DMatrix	(	double	data[][],
		int	r,
		int	c )

Creates a new DMatrix with r rows and c columns using the data in data.

Parameters

data	the data of the new DMatrix
r	the number of rows
c	the number of columns

Definition at line 282 of file DMatrix.java.

◆ DMatrix() [3/3]

umontreal.ssj.util.DMatrix.DMatrix ( DMatrix that )

Copy constructor.

Parameters

that	the DMatrix to copy

Definition at line 294 of file DMatrix.java.

Member Function Documentation

◆ addMultBand()

void umontreal.ssj.util.DMatrix.addMultBand	(	double	g,
		DoubleMatrix2D	A,
		int	sa,
		double	h,
		final DoubleMatrix2D	B,
		int	sb )

staticpackage

Addition of the matrices \(gA + hB\) after multiplication with the scalars \(g\) and \(h\).

\(A\) is a square banded upper triangular matrix. It has a non-zero diagonal, sa superdiagonals, and thus a bandwidth of sa + 1. Similarly for \(B\) which has a bandwidth of sb + 1. The result is put back in \(A\).

Parameters

g	coefficient multiplying A
A	input and output matrix
sa	number of superdiagonals of A
h	coefficient multiplying B
B	input matrix
sb	number of superdiagonals of B

Definition at line 812 of file DMatrix.java.

◆ CholeskyDecompose() [1/2]

void umontreal.ssj.util.DMatrix.CholeskyDecompose	(	double	M[][],
		double	L[][] )

static

Given a symmetric positive-definite matrix \(M\), performs the Cholesky decomposition of \(M\) and returns the result as a lower triangular matrix \(L\), such that \(M = L L^T\).

Parameters

M	the input matrix
L	the Cholesky lower triangular matrix

Definition at line 306 of file DMatrix.java.

◆ CholeskyDecompose() [2/2]

DoubleMatrix2D umontreal.ssj.util.DMatrix.CholeskyDecompose ( DoubleMatrix2D M )

static

Given a symmetric positive-definite matrix \(M\), performs the Cholesky decomposition of \(M\) and returns the result as a lower triangular matrix \(L\), such that \(M = L L^T\).

Parameters

M	the input matrix

Returns: the Cholesky lower triangular matrix

Definition at line 328 of file DMatrix.java.

◆ copy()

void umontreal.ssj.util.DMatrix.copy	(	double	M[][],
		double	R[][] )

static

Copies the matrix \(M\) into \(R\).

Parameters

M	original matrix
R	output matrix

Definition at line 833 of file DMatrix.java.

◆ exp() [1/2]

double[][] umontreal.ssj.util.DMatrix.exp ( double A[][] )

static

Similar to #exp(final DoubleMatrix2D).

Parameters

A	input matrix

Returns: the exponential of \(A\)

Definition at line 436 of file DMatrix.java.

◆ exp() [2/2]

DoubleMatrix2D umontreal.ssj.util.DMatrix.exp ( final DoubleMatrix2D A )

static

Returns \(e^A\), the exponential of the square matrix \(A\).

The scaling and squaring method [82] is used with Padé approximants to compute the exponential.

Parameters

A	input matrix

Returns: the exponential of \(A\)

Definition at line 450 of file DMatrix.java.

◆ expBidiagonal() [1/2]

DoubleMatrix2D umontreal.ssj.util.DMatrix.expBidiagonal ( final DoubleMatrix2D A )

static

Returns \(e^A\), the exponential of the bidiagonal square matrix.

\(A\). The only non-zero elements of \(A\) are on the diagonal and on the first superdiagonal. This method is faster than #exp(final DoubleMatrix2D) because of the special form of \(A\).

Parameters

A	bidiagonal matrix

Returns: \(e^A\)

Definition at line 554 of file DMatrix.java.

◆ expBidiagonal() [2/2]

DoubleMatrix1D umontreal.ssj.util.DMatrix.expBidiagonal	(	final DoubleMatrix2D	A,
		final DoubleMatrix1D	b )

static

Computes \(c = e^A b\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\).

The only non-zero elements of

\(A\) are on the diagonal and on the first superdiagonal. Uses the scaling and squaring method [82] with Padé approximants. Returns \(c\).

Parameters

A	bidiagonal matrix
b	vector

Returns: \(c\)

Definition at line 646 of file DMatrix.java.

◆ expmiBidiagonal() [1/2]

DoubleMatrix2D umontreal.ssj.util.DMatrix.expmiBidiagonal ( final DoubleMatrix2D A )

static

Computes \(e^A - I\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\).

The only non-zero elements of

\(A\) are on the diagonal and on the first superdiagonal. Uses the scaling and squaring method [209], [82] with Padé approximants. Returns \(e^A - I\).

Parameters

A	bidiagonal matrix

Returns: \((e^A - I)b\)

Definition at line 663 of file DMatrix.java.

◆ expmiBidiagonal() [2/2]

DoubleMatrix1D umontreal.ssj.util.DMatrix.expmiBidiagonal	(	final DoubleMatrix2D	A,
		final DoubleMatrix1D	b )

static

Computes \(c = (e^A - I)b\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\).

The only non-zero elements of \(A\) are on the diagonal and on the first superdiagonal. Uses the scaling and squaring method [209], [82] with a Taylor expansion. Returns \(c\).

Parameters

A	bidiagonal matrix
b	vector

Returns: \(c\)

Definition at line 708 of file DMatrix.java.

◆ get()

double umontreal.ssj.util.DMatrix.get	(	int	row,
		int	column )

Returns the matrix element in the specified row and column.

Parameters

row	the row of the selected element
column	the column of the selected element

Returns: the value of the element

Exceptions

IndexOutOfBoundsException if the selected element would be outside the DMatrix

Definition at line 903 of file DMatrix.java.

◆ multBand() [1/2]

void umontreal.ssj.util.DMatrix.multBand	(	DoubleMatrix2D	A,
		int	sa,
		double	h )

staticpackage

Multiplication of the matrix \(A\) by the scalar \(h\).

\(A\) is a square banded upper triangular matrix. It has a non-zero diagonal, sa superdiagonals, and thus a bandwidth of sa + 1. The result of the multiplication is put back in \(A\).

Parameters

A	input and output matrix
sa	number of superdiagonals of A
h	scalar

Definition at line 786 of file DMatrix.java.

◆ multBand() [2/2]

void umontreal.ssj.util.DMatrix.multBand	(	final DoubleMatrix2D	A,
		int	sa,
		final DoubleMatrix2D	B,
		int	sb,
		DoubleMatrix2D	C )

staticpackage

Matrix multiplication \(C = AB\).

All three matrices are square, banded, and upper triangular. \(A\) has a non-zero diagonal, sa non-zero superdiagonals, and thus a bandwidth of sa + 1. The non-zero elements of

\(A_{ij}\) are those for which \(j - s_a \le i \le j\). Similarly for \(B\) which has a bandwidth of sb + 1. The resulting matrix \(C\) has sa + sb non-zero superdiagonals, and a bandwidth of sa + sb + 1.

Parameters

A	input matrix
sa	number of superdiagonals of A
B	input matrix
sb	number of superdiagonals of B
C	result

Definition at line 772 of file DMatrix.java.

◆ numColumns()

int umontreal.ssj.util.DMatrix.numColumns ( )

Returns the number of columns of the DMatrix.

Returns: the number of columns

Definition at line 889 of file DMatrix.java.

◆ numRows()

int umontreal.ssj.util.DMatrix.numRows ( )

Returns the number of rows of the DMatrix.

Returns: the number of rows

Definition at line 880 of file DMatrix.java.

◆ PCADecompose() [1/2]

void umontreal.ssj.util.DMatrix.PCADecompose	(	double	M[][],
		double	A[][],
		double[]	lambda )

static

Computes the principal components decomposition \(M\) =.

\(U\Lambda U^{\mathsf{t}}\) by using the singular value decomposition of matrix \(M\). Puts the eigenvalues, which are the diagonal elements of matrix \(\Lambda\), sorted by decreasing size, in vector lambda, and puts matrix \(A = U\sqrt{\Lambda}\) in A.

Parameters

M	input matrix
A	matrix square root of M
lambda	the eigenvalues

Definition at line 345 of file DMatrix.java.

◆ PCADecompose() [2/2]

DoubleMatrix2D umontreal.ssj.util.DMatrix.PCADecompose	(	DoubleMatrix2D	M,
		double[]	lambda )

static

Computes the principal components decomposition \(M\) =.

\(U\Lambda U^{\mathsf{t}}\) by using the singular value decomposition of matrix \(M\). Puts the eigenvalues, which are the diagonal elements of matrix \(\Lambda\), sorted by decreasing size, in vector lambda. Returns matrix \(A = U\sqrt{\Lambda}\).

Parameters

M	input matrix
lambda	the eigenvalues

Returns: matrix square root of M

Definition at line 367 of file DMatrix.java.

◆ set()

void umontreal.ssj.util.DMatrix.set	(	int	row,
		int	column,
		double	value )

Sets the value of the element in the specified row and column.

Parameters

row	the row of the selected element
column	the column of the selected element
value	the new value of the element

Exceptions

IndexOutOfBoundsException if the selected element would be outside the DMatrix

Definition at line 919 of file DMatrix.java.

◆ solveLU()

double[] umontreal.ssj.util.DMatrix.solveLU	(	double	A[][],
		double[]	b )

static

Solves the matrix equation \(Ax = b\) using LU decomposition.

\(A\) is a square matrix, \(b\) and \(x\) are vectors. Returns the solution \(x\).

Parameters

A	square matrix
b	right side vector

Returns: the solution vector

Definition at line 396 of file DMatrix.java.

◆ solveTriangular()

void umontreal.ssj.util.DMatrix.solveTriangular	(	DoubleMatrix2D	U,
		DoubleMatrix2D	B,
		DoubleMatrix2D	X )

static

Solve the triangular matrix equation \(UX = B\) for \(X\).

\(U\) is a square upper triangular matrix. \(B\) and \(X\) must have the same number of columns.

Parameters

U	input matrix
B	right-hand side matrix
X	output matrix

Definition at line 414 of file DMatrix.java.

◆ toString() [1/2]

String umontreal.ssj.util.DMatrix.toString ( )

Creates a String containing all the data of the DMatrix.

The result is displayed in matrix form, with each row on a line.

Returns: the content of the DMatrix

Definition at line 871 of file DMatrix.java.

◆ toString() [2/2]

String umontreal.ssj.util.DMatrix.toString ( double M[][] )

static

Returns matrix \(M\) as a string.

It is displayed in matrix form, with each row on a line.

Returns: the content of \(M\)

Definition at line 847 of file DMatrix.java.

◆ transpose()

DMatrix umontreal.ssj.util.DMatrix.transpose ( )

Returns the transposed matrix.

The rows and columns are interchanged.

Returns: the transposed matrix

Definition at line 931 of file DMatrix.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/util/DMatrix.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Static Package Functions

Detailed Description

Constructor & Destructor Documentation

◆ DMatrix() [1/3]

◆ DMatrix() [2/3]

◆ DMatrix() [3/3]

Member Function Documentation

◆ addMultBand()

◆ CholeskyDecompose() [1/2]

◆ CholeskyDecompose() [2/2]

◆ copy()

◆ exp() [1/2]

◆ exp() [2/2]

◆ expBidiagonal() [1/2]

◆ expBidiagonal() [2/2]

◆ expmiBidiagonal() [1/2]

◆ expmiBidiagonal() [2/2]

◆ get()

◆ multBand() [1/2]

◆ multBand() [2/2]

◆ numColumns()

◆ numRows()

◆ PCADecompose() [1/2]

◆ PCADecompose() [2/2]

◆ set()

◆ solveLU()

◆ solveTriangular()

◆ toString() [1/2]

◆ toString() [2/2]

◆ transpose()