mpv2
Class JamaMatrix

java.lang.Object
  mpv2.AllMatrices
      mpv2.JamaMatrix

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable

public class JamaMatrix
extends AllMatrices
implements java.lang.Cloneable, java.io.Serializable

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.}};
      JamaMatrix A = new JamaMatrix(vals);
      JamaMatrix b = JamaMatrix.random(3,1);
      JamaMatrix x = A.solve(b);
      JamaMatrix r = A.times(x).minus(b);
      double rnorm = r.normInf();

See Also:

Serialized Form

Field Summary

Fields inherited from class mpv2.AllMatrices

K, N

Constructor Summary

JamaMatrix(AllMatrices B)
Construct a new matrix from another matrix (of any kind) if argument B is an object of class JamaMatrix this is the same as (deep) copy (or clone).

JamaMatrix(double[][] A)
Construct a matrix from a 2-D array.

JamaMatrix(double[][] A, int m, int n)
Construct a matrix quickly without checking arguments.

JamaMatrix(double[] vals, int m)
Construct a matrix from a one-dimensional packed array

JamaMatrix(int m, int n)
Construct an m-by-n matrix of zeros.

JamaMatrix(int m, int n, double s)
Construct an m-by-n constant matrix.

Method Summary

JamaMatrix	arrayLeftDivide(JamaMatrix B) Element-by-element left division, C = A.
JamaMatrix	arrayLeftDivideEquals(JamaMatrix B) Element-by-element left division in place, A = A.
JamaMatrix	arrayRightDivide(JamaMatrix B) Element-by-element right division, C = A.
JamaMatrix	arrayRightDivideEquals(JamaMatrix B) Element-by-element right division in place, A = A.
JamaMatrix	arrayTimes(JamaMatrix B) Element-by-element multiplication, C = A.
JamaMatrix	arrayTimesEquals(JamaMatrix B) Element-by-element multiplication in place, A = A.
CholeskyDecomposition	chol() Cholesky Decomposition
java.lang.Object	clone() Clone the JamaMatrix object.
double	cond() Matrix condition (2 norm)
static JamaMatrix	constructWithCopy(double[][] A) Construct a matrix from a copy of a 2-D array.
JamaMatrix	copy() Make a deep copy of a matrix
double	det() Matrix determinant
EigenvalueDecomposition	eig() Eigenvalue Decomposition
double	get(int i, int j) Get a single element.
void	getAll(double[] vals) Get all entries of the matrix into argument vals in a column-packed way.
double[][]	getArray() Access the internal two-dimensional array.
double[][]	getArrayCopy() Copy the internal two-dimensional array.
int	getColumnDimension() Get column dimension.
double[]	getColumnPackedCopy() Make a one-dimensional column packed copy of the internal array.
JamaMatrix	getMatrix(int[] r, int[] c) Get a submatrix.
JamaMatrix	getMatrix(int[] r, int j0, int j1) Get a submatrix.
JamaMatrix	getMatrix(int i0, int i1, int[] c) Get a submatrix.
JamaMatrix	getMatrix(int i0, int i1, int j0, int j1) Get a submatrix.
void	getRow(int rowNumber, double[] x) Get a row of the matrix into argument x.
int	getRowDimension() Get row dimension.
double[]	getRowPackedCopy() Make a one-dimensional row packed copy of the internal array.
static JamaMatrix	identity(int m, int n) Generate identity matrix
JamaMatrix	inverse() Matrix inverse or pseudoinverse
LUDecomposition	lu() LU Decomposition
JamaMatrix	minus(JamaMatrix B) C = A - B
JamaMatrix	minusEquals(JamaMatrix B) A = A - B
double	norm1() One norm
double	norm2() Two norm
double	normF() Frobenius norm
double	normInf() Infinity norm
JamaMatrix	plus(JamaMatrix B) C = A + B
JamaMatrix	plusEquals(JamaMatrix B) A = A + B
void	print(int w, int d) Print the matrix to stdout.
void	print(java.text.NumberFormat format, int width) Print the matrix to stdout.
void	print(java.io.PrintWriter output, int w, int d) Print the matrix to the output stream.
void	print(java.io.PrintWriter output, java.text.NumberFormat format, int width) Print the matrix to the output stream.
QRDecomposition	qr() QR Decomposition
static JamaMatrix	random(int m, int n) Generate matrix with random elements
int	rank() Matrix rank
static JamaMatrix	read(java.io.BufferedReader input) Read a matrix from a stream.
void	set(int i, int j, double s) Set a single element.
void	setAll(double[] vals) Set all entries of the matrix to the supplied new values.
void	setMatrix(int[] r, int[] c, JamaMatrix X) Set a submatrix.
void	setMatrix(int[] r, int j0, int j1, JamaMatrix X) Set a submatrix.
void	setMatrix(int i0, int i1, int[] c, JamaMatrix X) Set a submatrix.
void	setMatrix(int i0, int i1, int j0, int j1, JamaMatrix X) Set a submatrix.
void	setRow(int rowNumber, double[] x) Copy an array (x) into a row of the matrix.
JamaMatrix	solve(JamaMatrix B) Solve A*X = B
JamaMatrix	solveTranspose(JamaMatrix B) Solve X*A = B, which is also A'*X' = B'
SingularValueDecomposition	svd() Singular Value Decomposition
JamaMatrix	times(double s) Multiply a matrix by a scalar, C = s*A
JamaMatrix	times(JamaMatrix B) Linear algebraic matrix multiplication, A * B
JamaMatrix	timesEquals(double s) Multiply a matrix by a scalar in place, A = s*A
double	trace() Matrix trace.
JamaMatrix	transpose() JamaMatrix transpose.
JamaMatrix	uminus() Unary minus

Methods inherited from class mpv2.AllMatrices

addColumn, columnNorm0, columnNorm1, columnNorm2, columnNormInf, eqConstant, eqCopy, eqCopy, eqCopy, eqCopy, eqCopy, eqDifference, eqEProduct, eqEQuotient, eqIdentity, eqInverse, eqIProduct, eqNegate, eqOnes, eqPermuteColumns, eqPermuteRows, eqProduct, eqProduct, eqRandom, eqScaleColumns, eqScaleRows, eqSum, eqTProduct, eqTranspose, eqZeros, getAll, getColumn, getColumn, getK, getN, getRow, getSubMatrix, getSubMatrix, getSubMatrix, getSubMatrix, getValue, innerProduct, lup, pluseqOuterProduct, setColumn, setValue, sumAll, times, times, times, times, transposeTimes, transposeTimes, transposeTimes, transposeTimes

Methods inherited from class java.lang.Object

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

Constructor Detail

JamaMatrix

public JamaMatrix(int m,
                  int n)

Construct an m-by-n matrix of zeros.

Parameters:

m - Number of rows.

n - Number of colums.

JamaMatrix

public JamaMatrix(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.

JamaMatrix

public JamaMatrix(double[][] A)

Construct a matrix from a 2-D array.

Parameters:

A - Two-dimensional array of doubles.

Throws:

java.lang.IllegalArgumentException - All rows must have the same length

See Also:

constructWithCopy(double[][])

JamaMatrix

public JamaMatrix(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.

JamaMatrix

public JamaMatrix(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.

Throws:

java.lang.IllegalArgumentException - Array length must be a multiple of m.

JamaMatrix

public JamaMatrix(AllMatrices B)

Construct a new matrix from another matrix (of any kind) if argument B is an object of class JamaMatrix this is the same as (deep) copy (or clone). Note that argument B may be another kind of matrix, ex. an object of class SparseMatrix or BandMatrix or any subclass of AllMatrices

Parameters:

B - a matrix of any kind, class is a subclass of AllMatrices

See Also:

copy()

Method Detail

getRow

public void getRow(int rowNumber,
                   double[] x)

Get a row of the matrix into argument x.

Overrides:

getRow in class AllMatrices

Parameters:

rowNumber - number of the row in the matrix.

x - is set to the given row of matrix.

Throws:

java.lang.IllegalArgumentException

getAll

public void getAll(double[] vals)

Get all entries of the matrix into argument vals in a column-packed way.

Overrides:

getAll in class AllMatrices

Parameters:

vals - an one-dimensional array where the values are copied into

Throws:

java.lang.IllegalArgumentException

setRow

public void setRow(int rowNumber,
                   double[] x)

Copy an array (x) into a row of the matrix. Legal range of the integer argument is 0 <= n < N.

Overrides:

setRow in class AllMatrices

Parameters:

rowNumber - number of the row in the matrix A.

x - the given row of matrix A.

Throws:

java.lang.IllegalArgumentException

setAll

public void setAll(double[] vals)

Set all entries of the matrix to the supplied new values. If argument is wrong length an IllegalArgumentException is thrown.

Overrides:

setAll in class AllMatrices

Parameters:

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

Throws:

java.lang.IllegalArgumentException

constructWithCopy

public static JamaMatrix constructWithCopy(double[][] A)

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

Parameters:

A - Two-dimensional array of doubles.

Throws:

java.lang.IllegalArgumentException - All rows must have the same length

copy

public JamaMatrix copy()

Make a deep copy of a matrix

clone

public java.lang.Object clone()

Clone the JamaMatrix object.

Overrides:

clone in class java.lang.Object

getArray

public double[][] getArray()

Access the internal two-dimensional array.

Returns:

Pointer to the two-dimensional array of matrix elements.

getArrayCopy

public double[][] getArrayCopy()

Copy the internal two-dimensional array.

Returns:

Two-dimensional array copy of matrix elements.

getColumnPackedCopy

public double[] getColumnPackedCopy()

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

Returns:

JamaMatrix elements packed in a one-dimensional array by columns.

getRowPackedCopy

public double[] getRowPackedCopy()

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

Returns:

JamaMatrix elements packed in a one-dimensional array by rows.

getRowDimension

public int getRowDimension()

Get row dimension.

Overrides:

getRowDimension in class AllMatrices

Returns:

m, the number of rows.

getColumnDimension

public int getColumnDimension()

Get column dimension.

Overrides:

getColumnDimension in class AllMatrices

Returns:

n, the number of columns.

get

public double get(int i,
                  int j)

Get a single element.

Specified by:

get in class AllMatrices

Parameters:

i - Row index.

j - Column index.

Returns:

A(i,j)

Throws:

java.lang.ArrayIndexOutOfBoundsException

getMatrix

public JamaMatrix 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)

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

public JamaMatrix getMatrix(int[] r,
                            int[] c)

Get a submatrix.

Parameters:

r - Array of row indices.

c - Array of column indices.

Returns:

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

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

public JamaMatrix 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(:))

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

public JamaMatrix getMatrix(int[] r,
                            int j0,
                            int j1)

Get a submatrix.

Parameters:

r - Array of row indices.

j0 - Initial column index

j1 - Final column index

Returns:

A(r(:),j0:j1)

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

set

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

Set a single element.

Specified by:

set in class AllMatrices

Parameters:

i - Row index.

j - Column index.

s - A(i,j).

Throws:

java.lang.ArrayIndexOutOfBoundsException

setMatrix

public void setMatrix(int i0,
                      int i1,
                      int j0,
                      int j1,
                      JamaMatrix 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)

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(int[] r,
                      int[] c,
                      JamaMatrix X)

Set a submatrix.

Parameters:

r - Array of row indices.

c - Array of column indices.

X - A(r(:),c(:))

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

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

Set a submatrix.

Parameters:

r - Array of row indices.

j0 - Initial column index

j1 - Final column index

X - A(r(:),j0:j1)

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

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

Set a submatrix.

Parameters:

i0 - Initial row index

i1 - Final row index

c - Array of column indices.

X - A(i0:i1,c(:))

Throws:

java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

transpose

public JamaMatrix transpose()

JamaMatrix transpose.

Returns:

A'

norm1

public double norm1()

One norm

Overrides:

norm1 in class AllMatrices

Returns:

maximum column sum.

norm2

public double norm2()

Two norm

Overrides:

norm2 in class AllMatrices

Returns:

maximum singular value.

normInf

public double normInf()

Infinity norm

Overrides:

normInf in class AllMatrices

Returns:

maximum row sum.

normF

public double normF()

Frobenius norm

Overrides:

normF in class AllMatrices

Returns:

sqrt of sum of squares of all elements.

uminus

public JamaMatrix uminus()

Unary minus

Returns:

-A

plus

public JamaMatrix plus(JamaMatrix B)

C = A + B

Parameters:

B - another matrix

Returns:

A + B

plusEquals

public JamaMatrix plusEquals(JamaMatrix B)

A = A + B

Parameters:

B - another matrix

Returns:

A + B

minus

public JamaMatrix minus(JamaMatrix B)

C = A - B

Parameters:

B - another matrix

Returns:

A - B

minusEquals

public JamaMatrix minusEquals(JamaMatrix B)

A = A - B

Parameters:

B - another matrix

Returns:

A - B

arrayTimes

public JamaMatrix arrayTimes(JamaMatrix B)

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

Parameters:

B - another matrix

Returns:

A.*B

arrayTimesEquals

public JamaMatrix arrayTimesEquals(JamaMatrix B)

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

Parameters:

B - another matrix

Returns:

A.*B

arrayRightDivide

public JamaMatrix arrayRightDivide(JamaMatrix B)

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

Parameters:

B - another matrix

Returns:

A./B

arrayRightDivideEquals

public JamaMatrix arrayRightDivideEquals(JamaMatrix B)

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

Parameters:

B - another matrix

Returns:

A./B

arrayLeftDivide

public JamaMatrix arrayLeftDivide(JamaMatrix B)

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

Parameters:

B - another matrix

Returns:

A.\B

arrayLeftDivideEquals

public JamaMatrix arrayLeftDivideEquals(JamaMatrix B)

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

Parameters:

B - another matrix

Returns:

A.\B

times

public JamaMatrix times(double s)

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

Parameters:

s - scalar

Returns:

s*A

timesEquals

public JamaMatrix timesEquals(double s)

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

Parameters:

s - scalar

Returns:

replace A by s*A

times

public JamaMatrix times(JamaMatrix B)

Linear algebraic matrix multiplication, A * B

Parameters:

B - another matrix

Returns:

JamaMatrix product, A * B

Throws:

java.lang.IllegalArgumentException - Matrix inner dimensions must agree.

lu

public LUDecomposition lu()

LU Decomposition

Overrides:

lu in class AllMatrices

Returns:

LUDecomposition

See Also:

LUDecomposition

qr

public QRDecomposition qr()

QR Decomposition

Overrides:

qr in class AllMatrices

Returns:

QRDecomposition

See Also:

QRDecomposition

chol

public CholeskyDecomposition chol()

Cholesky Decomposition

Overrides:

chol in class AllMatrices

Returns:

CholeskyDecomposition

See Also:

CholeskyDecomposition

svd

public SingularValueDecomposition svd()

Singular Value Decomposition

Overrides:

svd in class AllMatrices

Returns:

SingularValueDecomposition

See Also:

SingularValueDecomposition

eig

public EigenvalueDecomposition eig()

Eigenvalue Decomposition

Overrides:

eig in class AllMatrices

Returns:

EigenvalueDecomposition

See Also:

EigenvalueDecomposition

solve

public JamaMatrix solve(JamaMatrix B)

Solve A*X = B

Parameters:

B - right hand side

Returns:

solution if A is square, least squares solution otherwise

solveTranspose

public JamaMatrix solveTranspose(JamaMatrix 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.

inverse

public JamaMatrix inverse()

Matrix inverse or pseudoinverse

Returns:

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

det

public double det()

Matrix determinant

Overrides:

det in class AllMatrices

Returns:

determinant

rank

public int rank()

Matrix rank

Overrides:

rank in class AllMatrices

Returns:

effective numerical rank, obtained from SVD.

cond

public double cond()

Matrix condition (2 norm)

Overrides:

cond in class AllMatrices

Returns:

ratio of largest to smallest singular value.

trace

public double trace()

Matrix trace.

Overrides:

trace in class AllMatrices

Returns:

sum of the diagonal elements.

random

public static JamaMatrix random(int m,
                                int n)

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.

identity

public static JamaMatrix identity(int m,
                                  int n)

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.

print

public void print(int w,
                  int d)

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

Overrides:

print in class AllMatrices

Parameters:

w - Column width.

d - Number of digits after the decimal.

print

public void print(java.io.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.

Overrides:

print in class AllMatrices

Parameters:

output - Output stream.

w - Column width.

d - Number of digits after the decimal.

print

public void print(java.text.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.

Overrides:

print in class AllMatrices

Parameters:

format - A Formatting object for individual elements.

width - Field width for each column.

See Also:

DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)

print

public void print(java.io.PrintWriter output,
                  java.text.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.

Overrides:

print in class AllMatrices

Parameters:

output - the output stream.

format - A formatting object to format the matrix elements

width - Column width.

See Also:

DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)

read

public static JamaMatrix read(java.io.BufferedReader input)
                       throws java.io.IOException

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.

Throws:

java.io.IOException