Inheritance diagram for Jama.Matrix:

Collaboration diagram for Jama.Matrix:

Public Member Functions
	Matrix (int m, int n)

	Matrix (int m, int n, double s)

int	getNumRows ()

int	getNumColumns ()

	Matrix (double[][] A)

	Matrix (double[][] A, int m, int n)

	Matrix (double vals[], int m)

Matrix	copy ()

Object	clone ()

double[][]	getArray ()

double[][]	getArrayCopy ()

double[]	getColumnPackedCopy ()

double[]	getRowPackedCopy ()

int	getRowDimension ()

int	getColumnDimension ()

double	get (int i, int j)

double[]	getRow (int i)

double[]	getColumn (int j)

Matrix	getMatrix (int i0, int i1, int j0, int j1)

Matrix	getMatrix (int[] r, int[] c)

Matrix	getMatrix (int i0, int i1, int[] c)

Matrix	getMatrix (int[] r, int j0, int j1)

void	set (int i, int j, double s)

void	setMatrix (int i0, int i1, int j0, int j1, Matrix X)

void	setMatrix (int[] r, int[] c, Matrix X)

void	setMatrix (int[] r, int j0, int j1, Matrix X)

void	setMatrix (int i0, int i1, int[] c, Matrix X)

Matrix	transpose ()

double	norm1 ()

double	norm2 ()

double	normInf ()

double	normF ()

Matrix	uminus ()

Matrix	plus (Matrix B)

Matrix	plusEquals (Matrix B)

Matrix	minus (Matrix B)

Matrix	minusEquals (Matrix B)

Matrix	arrayTimes (Matrix B)

Matrix	arrayTimesEquals (Matrix B)

Matrix	arrayRightDivide (Matrix B)

Matrix	arrayRightDivideEquals (Matrix B)

Matrix	arrayLeftDivide (Matrix B)

Matrix	arrayLeftDivideEquals (Matrix B)

Matrix	times (double s)

Matrix	timesEquals (double s)

Matrix	times (Matrix B)

LUDecomposition	lu ()

QRDecomposition	qr ()

CholeskyDecomposition	chol ()

SingularValueDecomposition	svd ()

EigenvalueDecomposition	eig ()

Matrix	solve (Matrix B)

Matrix	solveTranspose (Matrix B)

Matrix	inverse ()

double	det ()

int	rank ()

double	cond ()

double	trace ()

void	print (int w, int d)

void	print (PrintWriter output, int w, int d)

void	print (NumberFormat format, int width)

void	print (PrintWriter output, NumberFormat format, int width)

boolean	isSymmetric ()

boolean	isDiagonal ()

void	quantileNormalizeColumns ()

Matrix	sortColumnsKeepingIndex (Matrix index)

Matrix	sortColumns ()

void	setColumn (int column, double[] vals)

boolean	setRow (int row, double[] vals)

boolean	setRow (int row, int[] vals)

String	toString ()

void	write (String save, double[] observed) throws IOException

Static Public Member Functions
static Matrix	constructWithCopy (double[][] A)

static Matrix	random (int m, int n)

static Matrix	identity (int m, int n)

static Matrix	read (BufferedReader input) throws java.io.IOException

Detailed Description

Jama = Java Matrix class.

The Java Matrix Class provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various "gets" and "sets" provide access to submatrices and matrix elements. Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix Class involve real matrices. Complex matrices may be handled in a future version.

Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:

Cholesky Decomposition of symmetric, positive definite matrices.
LU Decomposition of rectangular matrices.
QR Decomposition of rectangular matrices.
Singular Value Decomposition of rectangular matrices.
Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.

Example of use:

Solve a linear system A x = b and compute the residual norm, ||b - A x||.

      double[][] vals = {{1.,2.,3},{4.,5.,6.},{7.,8.,10.}};
      Matrix A = new Matrix(vals);
      Matrix b = Matrix.random(3,1);
      Matrix x = A.solve(b);
      Matrix r = A.times(x).minus(b);
      double rnorm = r.normInf();

Author: The MathWorks, Inc. and the National Institute of Standards and Technology.

Version: 5 August 1998

Constructor & Destructor Documentation

Jama.Matrix.Matrix	(	int	m,
		int	n
	)

Construct an m-by-n matrix of zeros.

Parameters

m	Number of rows.
n	Number of colums.

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Jama.Matrix.Matrix	(	int	m,
		int	n,
		double	s
	)

Construct an m-by-n constant matrix.

Parameters

m	Number of rows.
n	Number of colums.
s	Fill the matrix with this scalar value.

Jama.Matrix.Matrix ( double A[][] )

Construct a matrix from a 2-D array.

Parameters

A	Two-dimensional array of doubles.

Exceptions

IllegalArgumentException All rows must have the same length

See also: constructWithCopy

Jama.Matrix.Matrix	(	double	A[][],
		int	m,
		int	n
	)

Construct a matrix quickly without checking arguments.

Parameters

A	Two-dimensional array of doubles.
m	Number of rows.
n	Number of colums.

Jama.Matrix.Matrix	(	double	vals[],
		int	m
	)

Construct a matrix from a one-dimensional packed array

Parameters

vals	One-dimensional array of doubles, packed by columns (ala Fortran).
m	Number of rows.

Exceptions

IllegalArgumentException Array length must be a multiple of m.

Member Function Documentation

Matrix Jama.Matrix.arrayLeftDivide ( Matrix B )

Element-by-element left division, C = A.

Parameters

B	another matrix

Returns: A.

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Matrix Jama.Matrix.arrayLeftDivideEquals ( Matrix B )

Element-by-element left division in place, A = A.

Parameters

B	another matrix

Returns: A.

Matrix Jama.Matrix.arrayRightDivide ( Matrix B )

Element-by-element right division, C = A./B

Parameters

B	another matrix

Returns: A./B

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Matrix Jama.Matrix.arrayRightDivideEquals ( Matrix B )

Element-by-element right division in place, A = A./B

Parameters

B	another matrix

Returns: A./B

Matrix Jama.Matrix.arrayTimes ( Matrix B )

Element-by-element multiplication, C = A.*B

Parameters

B	another matrix

Returns: A.*B

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Matrix Jama.Matrix.arrayTimesEquals ( Matrix B )

Element-by-element multiplication in place, A = A.*B

Parameters

B	another matrix

Returns: A.*B

CholeskyDecomposition Jama.Matrix.chol ( )

Cholesky Decomposition

Returns: CholeskyDecomposition

See also: CholeskyDecomposition

Object Jama.Matrix.clone ( )

Clone the Matrix object.

double Jama.Matrix.cond ( )

Matrix condition (2 norm)

Returns: ratio of largest to smallest singular value.

static Matrix Jama.Matrix.constructWithCopy ( double A[][] )

static

Construct a matrix from a copy of a 2-D array.

Parameters

A	Two-dimensional array of doubles.

Exceptions

IllegalArgumentException All rows must have the same length

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Matrix Jama.Matrix.copy ( )

Make a deep copy of a matrix

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double Jama.Matrix.det ( )

Matrix determinant

Returns: determinant

EigenvalueDecomposition Jama.Matrix.eig ( )

Eigenvalue Decomposition

Returns: EigenvalueDecomposition

See also: EigenvalueDecomposition

double Jama.Matrix.get	(	int	i,
		int	j
	)

Get a single element.

Parameters

i	Row index.
j	Column index.

Returns: A(i,j)

Exceptions

ArrayIndexOutOfBoundsException

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double [][] Jama.Matrix.getArray ( )

Access the internal two-dimensional array.

Returns: Pointer to the two-dimensional array of matrix elements.

double [][] Jama.Matrix.getArrayCopy ( )

Copy the internal two-dimensional array.

Returns: Two-dimensional array copy of matrix elements.

double [] Jama.Matrix.getColumn ( int j )

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int Jama.Matrix.getColumnDimension ( )

Get column dimension.

Returns: n, the number of columns.

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double [] Jama.Matrix.getColumnPackedCopy ( )

Make a one-dimensional column packed copy of the internal array.

Returns: Matrix elements packed in a one-dimensional array by columns.

Matrix Jama.Matrix.getMatrix	(	int	i0,
		int	i1,
		int	j0,
		int	j1
	)

Get a submatrix.

Parameters

i0	Initial row index
i1	Final row index
j0	Initial column index
j1	Final column index

Returns: A(i0:i1,j0:j1)

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

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Matrix Jama.Matrix.getMatrix	(	int[]	r,
		int[]	c
	)

Get a submatrix.

Parameters

r	Array of row indices.
c	Array of column indices.

Returns: A(r(:),c(:))

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

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Matrix Jama.Matrix.getMatrix	(	int	i0,
		int	i1,
		int[]	c
	)

Get a submatrix.

Parameters

i0	Initial row index
i1	Final row index
c	Array of column indices.

Returns: A(i0:i1,c(:))

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

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Matrix Jama.Matrix.getMatrix	(	int[]	r,
		int	j0,
		int	j1
	)

Get a submatrix.

Parameters

r	Array of row indices.
i0	Initial column index
i1	Final column index

Returns: A(r(:),j0:j1)

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

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int Jama.Matrix.getNumColumns ( )

int Jama.Matrix.getNumRows ( )

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double [] Jama.Matrix.getRow ( int i )

int Jama.Matrix.getRowDimension ( )

Get row dimension.

Returns: m, the number of rows.

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double [] Jama.Matrix.getRowPackedCopy ( )

Make a one-dimensional row packed copy of the internal array.

Returns: Matrix elements packed in a one-dimensional array by rows.

static Matrix Jama.Matrix.identity	(	int	m,
		int	n
	)

static

Generate identity matrix

Parameters

m	Number of rows.
n	Number of colums.

Returns: An m-by-n matrix with ones on the diagonal and zeros elsewhere.

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Matrix Jama.Matrix.inverse ( )

Matrix inverse or pseudoinverse

Returns: inverse(A) if A is square, pseudoinverse otherwise.

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boolean Jama.Matrix.isDiagonal ( )

boolean Jama.Matrix.isSymmetric ( )

LUDecomposition Jama.Matrix.lu ( )

LU Decomposition

Returns: LUDecomposition

See also: LUDecomposition

Matrix Jama.Matrix.minus ( Matrix B )

C = A - B

Parameters

B	another matrix

Returns: A - B

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Matrix Jama.Matrix.minusEquals ( Matrix B )

A = A - B

Parameters

B	another matrix

Returns: A - B

double Jama.Matrix.norm1 ( )

One norm

Returns: maximum column sum.

double Jama.Matrix.norm2 ( )

Two norm

Returns: maximum singular value.

double Jama.Matrix.normF ( )

Frobenius norm

Returns: sqrt of sum of squares of all elements.

double Jama.Matrix.normInf ( )

Infinity norm

Returns: maximum row sum.

Matrix Jama.Matrix.plus ( Matrix B )

C = A + B

Parameters

B	another matrix

Returns: A + B

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Matrix Jama.Matrix.plusEquals ( Matrix B )

A = A + B

Parameters

B	another matrix

Returns: A + B

void Jama.Matrix.print	(	int	w,
		int	d
	)

Print the matrix to stdout. Line the elements up in columns with a Fortran-like 'Fw.d' style format.

Parameters

w	Column width.
d	Number of digits after the decimal.

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void Jama.Matrix.print	(	PrintWriter	output,
		int	w,
		int	d
	)

Print the matrix to the output stream. Line the elements up in columns with a Fortran-like 'Fw.d' style format.

Parameters

output	Output stream.
w	Column width.
d	Number of digits after the decimal.

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void Jama.Matrix.print	(	NumberFormat	format,
		int	width
	)

Print the matrix to stdout. Line the elements up in columns. Use the format object, and right justify within columns of width characters. Note that is the matrix is to be read back in, you probably will want to use a NumberFormat that is set to US Locale.

Parameters

format	A Formatting object for individual elements.
width	Field width for each column.

See also: java.text.DecimalFormat::setDecimalFormatSymbols

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void Jama.Matrix.print	(	PrintWriter	output,
		NumberFormat	format,
		int	width
	)

Print the matrix to the output stream. Line the elements up in columns. Use the format object, and right justify within columns of width characters. Note that is the matrix is to be read back in, you probably will want to use a NumberFormat that is set to US Locale.

Parameters

output	the output stream.
format	A formatting object to format the matrix elements
width	Column width.

See also: java.text.DecimalFormat::setDecimalFormatSymbols

QRDecomposition Jama.Matrix.qr ( )

QR Decomposition

Returns: QRDecomposition

See also: QRDecomposition

void Jama.Matrix.quantileNormalizeColumns ( )

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static Matrix Jama.Matrix.random	(	int	m,
		int	n
	)

static

Generate matrix with random elements

Parameters

m	Number of rows.
n	Number of colums.

Returns: An m-by-n matrix with uniformly distributed random elements.

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int Jama.Matrix.rank ( )

Matrix rank

Returns: effective numerical rank, obtained from SVD.

static Matrix Jama.Matrix.read ( BufferedReader input ) throws java.io.IOException

static

Read a matrix from a stream. The format is the same the print method, so printed matrices can be read back in (provided they were printed using US Locale). Elements are separated by whitespace, all the elements for each row appear on a single line, the last row is followed by a blank line.

Parameters

input the input stream.

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void Jama.Matrix.set	(	int	i,
		int	j,
		double	s
	)

Set a single element.

Parameters

i	Row index.
j	Column index.
s	A(i,j).

Exceptions

ArrayIndexOutOfBoundsException

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void Jama.Matrix.setColumn	(	int	column,
		double[]	vals
	)

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void Jama.Matrix.setMatrix	(	int	i0,
		int	i1,
		int	j0,
		int	j1,
		Matrix	X
	)

Set a submatrix.

Parameters

i0	Initial row index
i1	Final row index
j0	Initial column index
j1	Final column index
X	A(i0:i1,j0:j1)

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

void Jama.Matrix.setMatrix	(	int[]	r,
		int[]	c,
		Matrix	X
	)

Set a submatrix.

Parameters

r	Array of row indices.
c	Array of column indices.
X	A(r(:),c(:))

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

void Jama.Matrix.setMatrix	(	int[]	r,
		int	j0,
		int	j1,
		Matrix	X
	)

Set a submatrix.

Parameters

r	Array of row indices.
j0	Initial column index
j1	Final column index
X	A(r(:),j0:j1)

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

void Jama.Matrix.setMatrix	(	int	i0,
		int	i1,
		int[]	c,
		Matrix	X
	)

Set a submatrix.

Parameters

i0	Initial row index
i1	Final row index
c	Array of column indices.
X	A(i0:i1,c(:))

Exceptions

ArrayIndexOutOfBoundsException Submatrix indices

boolean Jama.Matrix.setRow	(	int	row,
		double[]	vals
	)

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boolean Jama.Matrix.setRow	(	int	row,
		int[]	vals
	)

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Matrix Jama.Matrix.solve ( Matrix B )

Solve A*X = B

Parameters

B	right hand side

Returns: solution if A is square, least squares solution otherwise

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Matrix Jama.Matrix.solveTranspose ( Matrix B )

Solve X*A = B, which is also A'*X' = B'

Parameters

B	right hand side

Returns: solution if A is square, least squares solution otherwise.

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Matrix Jama.Matrix.sortColumns ( )

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Matrix Jama.Matrix.sortColumnsKeepingIndex ( Matrix index )

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SingularValueDecomposition Jama.Matrix.svd ( )

Singular Value Decomposition

Returns: SingularValueDecomposition

See also: SingularValueDecomposition

Matrix Jama.Matrix.times ( double s )

Multiply a matrix by a scalar, C = s*A

Parameters

s scalar

Returns: s*A

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Matrix Jama.Matrix.times ( Matrix B )

Linear algebraic matrix multiplication, A * B

Parameters

B	another matrix

Returns: Matrix product, A * B

Exceptions

IllegalArgumentException Matrix inner dimensions must agree.

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Matrix Jama.Matrix.timesEquals ( double s )

Multiply a matrix by a scalar in place, A = s*A

Parameters

s scalar

Returns: replace A by s*A

String Jama.Matrix.toString ( )

double Jama.Matrix.trace ( )

Matrix trace.

Returns: sum of the diagonal elements.

Matrix Jama.Matrix.transpose ( )

Matrix transpose.

Returns: A'

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Matrix Jama.Matrix.uminus ( )

Unary minus

Returns: -A

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void Jama.Matrix.write	(	String	save,
		double[]	observed
	)		throws IOException

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

java/Jama/Matrix.java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation