This class implements a few methods for matrix calculations with double numbers. More...

Public Member Functions
	DMatrix (int r, int c)
	Creates a new `DMatrix` with `r` rows and `c` columns. More...

	DMatrix (double[][] data, int r, int c)
	Creates a new `DMatrix` with `r` rows and `c` columns using the data in `data`. More...

	DMatrix (DMatrix that)
	Copy constructor. More...

String	toString ()
	Creates a String containing all the data of the `DMatrix`. More...

int	numRows ()
	Returns the number of rows of the `DMatrix`. More...

int	numColumns ()
	Returns the number of columns of the `DMatrix`. More...

double	get (int row, int column)
	Returns the matrix element in the specified row and column. More...

void	set (int row, int column, double value)
	Sets the value of the element in the specified row and column. More...

DMatrix	transpose ()
	Returns the transposed matrix. More...

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 \(M = L L^T\). More...

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 \(M = L L^T\). More...

static void	PCADecompose (double[][] M, double[][] A, double[] lambda)
	Computes the principal components decomposition \(M\) = \(U\Lambda U^{\mathsf{t}}\) by using the singular value decomposition of matrix \(M\). More...

static DoubleMatrix2D	PCADecompose (DoubleMatrix2D M, double[] lambda)
	Computes the principal components decomposition \(M\) = \(U\Lambda U^{\mathsf{t}}\) by using the singular value decomposition of matrix \(M\). More...

static double []	solveLU (double[][] A, double[] b)
	Solves the matrix equation \(Ax = b\) using LU decomposition. More...

static void	solveTriangular (DoubleMatrix2D U, DoubleMatrix2D B, DoubleMatrix2D X)
	Solve the triangular matrix equation \(UX = B\) for \(X\). More...

static double [][]	exp (double[][] A)
	Similar to #exp(final DoubleMatrix2D). More...

static DoubleMatrix2D	exp (final DoubleMatrix2D A)
	Returns \(e^A\), the exponential of the square matrix \(A\). More...

static DoubleMatrix2D	expBidiagonal (final DoubleMatrix2D A)
	Returns \(e^A\), the exponential of the bidiagonal square matrix \(A\). More...

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 \(A\). More...

static DoubleMatrix2D	expmiBidiagonal (final DoubleMatrix2D A)
	Computes \(e^A - I\), where \(e^A\) is the exponential of the bidiagonal square matrix \(A\). More...

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 \(A\). More...

static void	copy (double[][] M, double[][] R)
	Copies the matrix \(M\) into \(R\). More...

static String	toString (double[][] M)
	Returns matrix \(M\) as a string. More...

Static Package Functions
static void	addMultTriang (final DoubleMatrix2D A, DoubleMatrix1D b, double h)

static void	multBand (final DoubleMatrix2D A, int sa, final DoubleMatrix2D B, int sb, DoubleMatrix2D C)
	Matrix multiplication \(C = AB\). More...

static void	multBand (DoubleMatrix2D A, int sa, double h)
	Multiplication of the matrix \(A\) by the scalar \(h\). More...

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 \(h\). More...

Package Attributes
int	c

Detailed Description

This class implements a few methods for matrix calculations with double numbers.

Constructor & Destructor Documentation

◆ DMatrix() [1/3]

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

◆ DMatrix() [2/3]

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

◆ DMatrix() [3/3]

DMatrix ( DMatrix that )

Copy constructor.

Parameters

that	the `DMatrix` to copy

Member Function Documentation

◆ addMultBand()

static void 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

◆ CholeskyDecompose() [1/2]

static void 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

◆ CholeskyDecompose() [2/2]

static DoubleMatrix2D 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

◆ copy()

static void copy	(	double	M[][],
		double	R[][]
	)

static

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

Parameters

M	original matrix
R	output matrix

◆ exp() [1/2]

static double [][] exp ( double A[][] )

static

Similar to #exp(final DoubleMatrix2D).

Parameters

A	input matrix

Returns: the exponential of \(A\)

◆ exp() [2/2]

static DoubleMatrix2D exp ( final DoubleMatrix2D A )

static

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

The scaling and squaring method [85] is used with Padé approximants to compute the exponential.

Parameters

A	input matrix

Returns: the exponential of \(A\)

◆ expBidiagonal() [1/2]

static DoubleMatrix2D 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: \(e^A\)

◆ expBidiagonal() [2/2]

static DoubleMatrix1D 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 [85] with Padé approximants. Returns \(c\).

Parameters

A	bidiagonal matrix
b	vector

Returns: \(c\)

◆ expmiBidiagonal() [1/2]

static DoubleMatrix2D 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 [217], [85] with Padé approximants. Returns \(e^A - I\).

Parameters

A	bidiagonal matrix

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

◆ expmiBidiagonal() [2/2]

static DoubleMatrix1D 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 [217], [85] with a Taylor expansion. Returns \(c\).

Parameters

A	bidiagonal matrix
b	vector

Returns: \(c\)

◆ get()

double 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

◆ multBand() [1/2]

static void 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

◆ multBand() [2/2]

static void 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

◆ numColumns()

int numColumns ( )

Returns the number of columns of the DMatrix.

Returns: the number of columns

◆ numRows()

int numRows ( )

Returns the number of rows of the DMatrix.

Returns: the number of rows

◆ PCADecompose() [1/2]

static void 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

◆ PCADecompose() [2/2]

static DoubleMatrix2D 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

◆ set()

void 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

◆ solveLU()

static double [] 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

◆ solveTriangular()

static void 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

◆ toString() [1/2]

static String 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 \(M\)

◆ toString() [2/2]

String 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

◆ transpose()

DMatrix transpose ( )

Returns the transposed matrix.

The rows and columns are interchanged.

Returns: the transposed matrix

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

DMatrix.java

Public Member Functions

Static Public Member Functions

Static Package Functions

Package Attributes

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()