JSci.maths

Class DoubleTridiagonalMatrix

java.lang.Object

JSci.maths.Matrix

JSci.maths.DoubleMatrix

JSci.maths.DoubleSquareMatrix

JSci.maths.DoubleTridiagonalMatrix

All Implemented Interfaces:

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

Direct Known Subclasses:

DoubleDiagonalMatrix

public class DoubleTridiagonalMatrix
extends DoubleSquareMatrix

The DoubleTridiagonalMatrix class provides an object for encapsulating tridiagonal 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 double[]	diag
protected double[]	ldiag Tridiagonal data.
protected static int	TRIDIAGONAL Storage format identifier.
protected double[]	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
	DoubleTridiagonalMatrix(double[][] array) Constructs a matrix from an array.
	DoubleTridiagonalMatrix(int size) Constructs an empty matrix.
protected	DoubleTridiagonalMatrix(int size, int storeID) Constructs a matrix.

Method Summary

Methods

Modifier and Type	Method and Description
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.
boolean	equals(java.lang.Object m) Compares two double tridiagonal matrices for equality.
double	frobeniusNorm() Returns the Frobenius (l2) norm.
double	getElement(int i, int j) Returns an element of the matrix.
double	infNorm() Returns the l-norm.
boolean	isSymmetric() Returns true if this matrix is symmetric.
DoubleSquareMatrix[]	luDecompose(int[] pivot) Returns the LU decomposition of this matrix.
DoubleMatrix	mapElements(Mapping f) Applies a function on all the matrix elements.
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(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.
DoubleMatrix	subtract(DoubleMatrix m) Returns the subtraction of this matrix and another.
DoubleSquareMatrix	subtract(DoubleSquareMatrix m) Returns the subtraction of this matrix by 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.
java.lang.String	toString() Returns a string representing this matrix.
double	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.DoubleSquareMatrix

det, inverse, isUnitary, 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

TRIDIAGONAL

protected static final int TRIDIAGONAL

Storage format identifier.

See Also:

Constant Field Values

ldiag

protected double[] ldiag

Tridiagonal data.

diag

protected double[] diag

udiag

protected double[] udiag

Constructor Detail

DoubleTridiagonalMatrix

protected DoubleTridiagonalMatrix(int size,
                       int storeID)

Constructs a matrix.

DoubleTridiagonalMatrix

public DoubleTridiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

DoubleTridiagonalMatrix

public DoubleTridiagonalMatrix(double[][] array)

Constructs a matrix from an array. Any non-tridiagonal elements in the array are ignored.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

Method Detail

equals

public boolean equals(java.lang.Object m)

Compares two double tridiagonal matrices for equality.

Overrides:

equals in class DoubleMatrix

Parameters:

m - a double tridiagonal matrix

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class DoubleMatrix

toIntegerMatrix

public IntegerMatrix toIntegerMatrix()

Converts this matrix to an integer matrix.

Overrides:

toIntegerMatrix in class DoubleMatrix

Returns:

an integer tridiagonal matrix.

toComplexMatrix

public ComplexMatrix toComplexMatrix()

Converts this matrix to a complex matrix.

Overrides:

toComplexMatrix in class DoubleMatrix

Returns:

a complex tridiagonal matrix.

getElement

public double getElement(int i,
                int j)

Returns an element of the matrix.

Overrides:

getElement in class DoubleMatrix

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 DoubleMatrix

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 DoubleSquareMatrix

trace

public double trace()

Returns the trace.

Overrides:

trace in class DoubleSquareMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class DoubleMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class DoubleMatrix

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

Overrides:

operatorNorm in class DoubleSquareMatrix

Throws:

MaximumIterationsExceededException - If it takes more than 50 iterations to determine an eigenvalue.

add

public DoubleMatrix add(DoubleMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class DoubleSquareMatrix

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 DoubleSquareMatrix

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.

Parameters:

m - a double tridiagonal 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 DoubleSquareMatrix

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 by another.

Overrides:

subtract in class DoubleSquareMatrix

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.

Parameters:

m - a double tridiagonal 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 DoubleSquareMatrix

Parameters:

x - a double.

Returns:

a double tridiagonal matrix.

scalarProduct

public double scalarProduct(DoubleMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class DoubleSquareMatrix

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 DoubleSquareMatrix

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.

Parameters:

m - a double tridiagonal 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 DoubleSquareMatrix

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 DoubleMatrix

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 DoubleSquareMatrix

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.

Parameters:

m - a double tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class DoubleSquareMatrix

Returns:

a double tridiagonal matrix

luDecompose

public DoubleSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class DoubleSquareMatrix

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 DoubleSquareMatrix

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. Based on the code from JAMA (public domain).

Overrides:

singularValueDecompose in class DoubleSquareMatrix

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 DoubleSquareMatrix

Parameters:

f - a user-defined function

Returns:

a double tridiagonal matrix