JSci.maths

Class DoubleDiagonalMatrix

java.lang.Object

JSci.maths.Matrix

JSci.maths.DoubleMatrix

JSci.maths.DoubleSquareMatrix

JSci.maths.DoubleTridiagonalMatrix

JSci.maths.DoubleDiagonalMatrix

All Implemented Interfaces:

java.io.Serializable, Algebra.Member, Module.Member, VectorSpace.Member, Ring.Member, AbelianGroup.Member, Member

public final class DoubleDiagonalMatrix
extends DoubleTridiagonalMatrix

The DoubleDiagonalMatrix class encapsulates diagonal matrices containing doubles. Uses compressed diagonal storage.

Version:

2.2

Author:

Mark Hale

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected static int	DIAGONAL Storage format identifier.

Fields inherited from class JSci.maths.DoubleTridiagonalMatrix

diag, ldiag, TRIDIAGONAL, udiag

Fields inherited from class JSci.maths.DoubleSquareMatrix

LU, LUpivot

Fields inherited from class JSci.maths.DoubleMatrix

ARRAY_2D, matrix

Fields inherited from class JSci.maths.Matrix

CLASS_SPECIFIC, numCols, numRows, storageFormat

Constructor Summary

Constructors

Modifier	Constructor and Description
	DoubleDiagonalMatrix(double[] array) Constructs a matrix by wrapping an array containing the diagonal elements.
	DoubleDiagonalMatrix(double[][] array) Constructs a matrix from an array.
	DoubleDiagonalMatrix(int size) Constructs an empty matrix.
protected	DoubleDiagonalMatrix(int size, int storeID) Constructs a matrix.

Method Summary

Methods

Modifier and Type	Method and Description
DoubleDiagonalMatrix	add(DoubleDiagonalMatrix m) Returns the addition of this matrix and another.
DoubleMatrix	add(DoubleMatrix m) Returns the addition of this matrix and another.
DoubleSquareMatrix	add(DoubleSquareMatrix m) Returns the addition of this matrix and another.
DoubleTridiagonalMatrix	add(DoubleTridiagonalMatrix m) Returns the addition of this matrix and another.
DoubleSquareMatrix[]	choleskyDecompose() Returns the Cholesky decomposition of this matrix.
double	det() Returns the determinant.
boolean	equals(java.lang.Object m) Compares two double diagonal matrices for equality.
double	frobeniusNorm() Returns the Frobenius (l2) norm.
double	getElement(int i, int j) Returns an element of the matrix.
static DoubleDiagonalMatrix	identity(int size) Creates an identity matrix.
double	infNorm() Returns the l-norm.
DoubleSquareMatrix	inverse() Returns the inverse of this matrix.
boolean	isSymmetric() Returns true if this matrix is symmetric.
boolean	isUnitary() Returns true if this matrix is unitary.
DoubleSquareMatrix[]	luDecompose(int[] pivot) Returns the LU decomposition of this matrix.
DoubleMatrix	mapElements(Mapping f) Applies a function on all the matrix elements.
DoubleDiagonalMatrix	multiply(DoubleDiagonalMatrix m) Returns the multiplication of this matrix and another.
DoubleMatrix	multiply(DoubleMatrix m) Returns the multiplication of this matrix and another.
DoubleSquareMatrix	multiply(DoubleSquareMatrix m) Returns the multiplication of this matrix and another.
DoubleSquareMatrix	multiply(DoubleTridiagonalMatrix m) Returns the multiplication of this matrix and another.
DoubleVector	multiply(DoubleVector v) Returns the multiplication of a vector by this matrix.
double	operatorNorm() Returns the operator norm.
DoubleMatrix	scalarMultiply(double x) Returns the multiplication of this matrix by a scalar.
double	scalarProduct(DoubleDiagonalMatrix m) Returns the scalar product of this matrix and another.
double	scalarProduct(DoubleMatrix m) Returns the scalar product of this matrix and another.
double	scalarProduct(DoubleSquareMatrix m) Returns the scalar product of this matrix and another.
double	scalarProduct(DoubleTridiagonalMatrix m) Returns the scalar product of this matrix and another.
void	setElement(int i, int j, double x) Sets the value of an element of the matrix.
DoubleSquareMatrix[]	singularValueDecompose() Returns the singular value decomposition of this matrix.
DoubleDiagonalMatrix	subtract(DoubleDiagonalMatrix m) Returns the subtraction of this matrix by another.
DoubleMatrix	subtract(DoubleMatrix m) Returns the subtraction of this matrix and another.
DoubleSquareMatrix	subtract(DoubleSquareMatrix m) Returns the subtraction of this matrix and another.
DoubleTridiagonalMatrix	subtract(DoubleTridiagonalMatrix m) Returns the subtraction of this matrix and another.
ComplexMatrix	toComplexMatrix() Converts this matrix to a complex matrix.
IntegerMatrix	toIntegerMatrix() Converts this matrix to an integer matrix.
double	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.DoubleTridiagonalMatrix

toString

Methods inherited from class JSci.maths.DoubleSquareMatrix

polarDecompose

Methods inherited from class JSci.maths.DoubleMatrix

add, directSum, finalize, hashCode, multiply, negate, scalarDivide, scalarDivide, scalarMultiply, subtract, tensorProduct

Methods inherited from class JSci.maths.Matrix

columns, getInvalidElementMsg, rows

Methods inherited from class java.lang.Object

clone, getClass, notify, notifyAll, wait, wait, wait

Field Detail

DIAGONAL

protected static final int DIAGONAL

Storage format identifier.

See Also:

Constant Field Values

Constructor Detail

DoubleDiagonalMatrix

protected DoubleDiagonalMatrix(int size,
                    int storeID)

Constructs a matrix.

DoubleDiagonalMatrix

public DoubleDiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

DoubleDiagonalMatrix

public DoubleDiagonalMatrix(double[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

DoubleDiagonalMatrix

public DoubleDiagonalMatrix(double[] array)

Constructs a matrix by wrapping an array containing the diagonal elements.

Parameters:

array - an assigned value

Method Detail

identity

public static DoubleDiagonalMatrix identity(int size)

Creates an identity matrix.

Parameters:

size - the number of rows/columns

equals

public boolean equals(java.lang.Object m)

Compares two double diagonal matrices for equality.

Overrides:

equals in class DoubleTridiagonalMatrix

Parameters:

m - a double diagonal matrix

toIntegerMatrix

public IntegerMatrix toIntegerMatrix()

Converts this matrix to an integer matrix.

Overrides:

toIntegerMatrix in class DoubleTridiagonalMatrix

Returns:

an integer diagonal matrix

toComplexMatrix

public ComplexMatrix toComplexMatrix()

Converts this matrix to a complex matrix.

Overrides:

toComplexMatrix in class DoubleTridiagonalMatrix

Returns:

a complex diagonal matrix

getElement

public double getElement(int i,
                int j)

Returns an element of the matrix.

Overrides:

getElement in class DoubleTridiagonalMatrix

Parameters:

i - row index of the element

j - column index of the element

Throws:

MatrixDimensionException - If attempting to access an invalid element.

setElement

public void setElement(int i,
              int j,
              double x)

Sets the value of an element of the matrix.

Overrides:

setElement in class DoubleTridiagonalMatrix

Parameters:

i - row index of the element

j - column index of the element

x - a number

Throws:

MatrixDimensionException - If attempting to access an invalid element.

isSymmetric

public boolean isSymmetric()

Returns true if this matrix is symmetric.

Overrides:

isSymmetric in class DoubleTridiagonalMatrix

isUnitary

public boolean isUnitary()

Returns true if this matrix is unitary.

Overrides:

isUnitary in class DoubleSquareMatrix

det

public double det()

Returns the determinant.

Overrides:

det in class DoubleSquareMatrix

trace

public double trace()

Returns the trace.

Overrides:

trace in class DoubleTridiagonalMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class DoubleTridiagonalMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class DoubleTridiagonalMatrix

operatorNorm

public double operatorNorm()

Returns the operator norm.

Overrides:

operatorNorm in class DoubleTridiagonalMatrix

add

public DoubleMatrix add(DoubleMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class DoubleTridiagonalMatrix

Parameters:

m - a double matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public DoubleSquareMatrix add(DoubleSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class DoubleTridiagonalMatrix

Parameters:

m - a double square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public DoubleTridiagonalMatrix add(DoubleTridiagonalMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class DoubleTridiagonalMatrix

Parameters:

m - a double tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public DoubleDiagonalMatrix add(DoubleDiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a double diagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public DoubleMatrix subtract(DoubleMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class DoubleTridiagonalMatrix

Parameters:

m - a double matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public DoubleSquareMatrix subtract(DoubleSquareMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class DoubleTridiagonalMatrix

Parameters:

m - a double square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public DoubleTridiagonalMatrix subtract(DoubleTridiagonalMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class DoubleTridiagonalMatrix

Parameters:

m - a double tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public DoubleDiagonalMatrix subtract(DoubleDiagonalMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - a double diagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarMultiply

public DoubleMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class DoubleTridiagonalMatrix

Parameters:

x - a double.

Returns:

a double diagonal matrix.

scalarProduct

public double scalarProduct(DoubleMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class DoubleTridiagonalMatrix

Parameters:

m - a double matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarProduct

public double scalarProduct(DoubleSquareMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class DoubleTridiagonalMatrix

Parameters:

m - a double square matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarProduct

public double scalarProduct(DoubleTridiagonalMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class DoubleTridiagonalMatrix

Parameters:

m - a double tridiagonal matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarProduct

public double scalarProduct(DoubleDiagonalMatrix m)

Returns the scalar product of this matrix and another.

Parameters:

m - a double diagonal matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public DoubleVector multiply(DoubleVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class DoubleTridiagonalMatrix

Parameters:

v - a double vector.

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public DoubleMatrix multiply(DoubleMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class DoubleTridiagonalMatrix

Parameters:

m - a double matrix

Returns:

a DoubleMatrix or a DoubleSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public DoubleSquareMatrix multiply(DoubleSquareMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class DoubleTridiagonalMatrix

Parameters:

m - a double square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public DoubleSquareMatrix multiply(DoubleTridiagonalMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class DoubleTridiagonalMatrix

Parameters:

m - a double tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public DoubleDiagonalMatrix multiply(DoubleDiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a double diagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

inverse

public DoubleSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class DoubleSquareMatrix

Returns:

a double diagonal matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class DoubleTridiagonalMatrix

Returns:

a double diagonal matrix

luDecompose

public DoubleSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class DoubleTridiagonalMatrix

Parameters:

pivot - an empty array of length rows()+1 to hold the pivot information (null if not interested). The last array element will contain the parity.

Returns:

an array with [0] containing the L-matrix and [1] containing the U-matrix.

choleskyDecompose

public DoubleSquareMatrix[] choleskyDecompose()

Returns the Cholesky decomposition of this matrix. Matrix must be symmetric and positive definite.

Overrides:

choleskyDecompose in class DoubleTridiagonalMatrix

Returns:

an array with [0] containing the L-matrix and [1] containing the U-matrix.

singularValueDecompose

public DoubleSquareMatrix[] singularValueDecompose()

Returns the singular value decomposition of this matrix.

Overrides:

singularValueDecompose in class DoubleTridiagonalMatrix

Returns:

an array with [0] containing the U-matrix, [1] containing the S-matrix and [2] containing the V-matrix.

mapElements

public DoubleMatrix mapElements(Mapping f)

Applies a function on all the matrix elements.

Overrides:

mapElements in class DoubleTridiagonalMatrix

Parameters:

f - a user-defined function

Returns:

a double diagonal matrix