JSci.maths

Class IntegerTridiagonalMatrix

java.lang.Object

JSci.maths.Matrix

JSci.maths.IntegerMatrix

JSci.maths.IntegerSquareMatrix

JSci.maths.IntegerTridiagonalMatrix

All Implemented Interfaces:

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

Direct Known Subclasses:

IntegerDiagonalMatrix

public class IntegerTridiagonalMatrix
extends IntegerSquareMatrix

The IntegerTridiagonalMatrix class provides an object for encapsulating tridiagonal matrices containing integers. Uses compressed diagonal storage.

Version:

2.2

Author:

Mark Hale

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected int[]	diag
protected int[]	ldiag Tridiagonal data.
protected static int	TRIDIAGONAL Storage format identifier.
protected int[]	udiag

Fields inherited from class JSci.maths.IntegerSquareMatrix

LU, LUpivot

Fields inherited from class JSci.maths.IntegerMatrix

ARRAY_2D, matrix

Fields inherited from class JSci.maths.Matrix

CLASS_SPECIFIC, numCols, numRows, storageFormat

Constructor Summary

Constructors

Modifier	Constructor and Description
	IntegerTridiagonalMatrix(int size) Constructs an empty matrix.
	IntegerTridiagonalMatrix(int[][] array) Constructs a matrix from an array.
protected	IntegerTridiagonalMatrix(int size, int storeID) Constructs a matrix.

Method Summary

Methods

Modifier and Type	Method and Description
IntegerMatrix	add(IntegerMatrix m) Returns the addition of this matrix and another.
IntegerSquareMatrix	add(IntegerSquareMatrix m) Returns the addition of this matrix and another.
IntegerTridiagonalMatrix	add(IntegerTridiagonalMatrix 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 integer tridiagonal matrices for equality.
double	frobeniusNorm() Returns the Frobenius (l2) norm.
int	getElement(int i, int j) Returns an element of the matrix.
int	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.
IntegerMatrix	multiply(IntegerMatrix m) Returns the multiplication of this matrix and another.
IntegerSquareMatrix	multiply(IntegerSquareMatrix m) Returns the multiplication of this matrix and another.
IntegerSquareMatrix	multiply(IntegerTridiagonalMatrix m) Returns the multiplication of this matrix and another.
IntegerVector	multiply(IntegerVector v) Returns the multiplication of a vector by this matrix.
IntegerMatrix	scalarMultiply(int x) Returns the multiplication of this matrix by a scalar.
void	setElement(int i, int j, int x) Sets the value of an element of the matrix.
IntegerMatrix	subtract(IntegerMatrix m) Returns the subtraction of this matrix and another.
IntegerSquareMatrix	subtract(IntegerSquareMatrix m) Returns the subtraction of this matrix by another.
IntegerTridiagonalMatrix	subtract(IntegerTridiagonalMatrix m) Returns the subtraction of this matrix by another.
ComplexMatrix	toComplexMatrix() Converts this matrix to a complex matrix.
DoubleMatrix	toDoubleMatrix() Converts this matrix to a double matrix.
java.lang.String	toString() Returns a string representing this matrix.
int	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.IntegerSquareMatrix

choleskyDecomposition, det, isUnitary

Methods inherited from class JSci.maths.IntegerMatrix

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

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 int[] ldiag

Tridiagonal data.

diag

protected int[] diag

udiag

protected int[] udiag

Constructor Detail

IntegerTridiagonalMatrix

protected IntegerTridiagonalMatrix(int size,
                        int storeID)

Constructs a matrix.

IntegerTridiagonalMatrix

public IntegerTridiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

IntegerTridiagonalMatrix

public IntegerTridiagonalMatrix(int[][] 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 integer tridiagonal matrices for equality.

Overrides:

equals in class IntegerMatrix

Parameters:

m - a integer tridiagonal matrix

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class IntegerMatrix

toDoubleMatrix

public DoubleMatrix toDoubleMatrix()

Converts this matrix to a double matrix.

Overrides:

toDoubleMatrix in class IntegerMatrix

Returns:

a double tridiagonal matrix

toComplexMatrix

public ComplexMatrix toComplexMatrix()

Converts this matrix to a complex matrix.

Overrides:

toComplexMatrix in class IntegerMatrix

Returns:

a complex tridiagonal matrix

getElement

public int getElement(int i,
             int j)

Returns an element of the matrix.

Overrides:

getElement in class IntegerMatrix

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,
              int x)

Sets the value of an element of the matrix.

Overrides:

setElement in class IntegerMatrix

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 IntegerSquareMatrix

trace

public int trace()

Returns the trace.

Overrides:

trace in class IntegerSquareMatrix

infNorm

public int infNorm()

Returns the l-norm.

Overrides:

infNorm in class IntegerMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class IntegerMatrix

add

public IntegerMatrix add(IntegerMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class IntegerSquareMatrix

Parameters:

m - an integer matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public IntegerSquareMatrix add(IntegerSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class IntegerSquareMatrix

Parameters:

m - an integer square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public IntegerTridiagonalMatrix add(IntegerTridiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - an integer tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public IntegerMatrix subtract(IntegerMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class IntegerSquareMatrix

Parameters:

m - an integer matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public IntegerSquareMatrix subtract(IntegerSquareMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class IntegerSquareMatrix

Parameters:

m - an integer square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public IntegerTridiagonalMatrix subtract(IntegerTridiagonalMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - an integer tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarMultiply

public IntegerMatrix scalarMultiply(int x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class IntegerSquareMatrix

Parameters:

x - an integer

Returns:

an integer tridiagonal matrix

multiply

public IntegerVector multiply(IntegerVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class IntegerSquareMatrix

Parameters:

v - an integer vector

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public IntegerMatrix multiply(IntegerMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class IntegerMatrix

Parameters:

m - an integer matrix

Returns:

an IntegerMatrix or a IntegerSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public IntegerSquareMatrix multiply(IntegerSquareMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class IntegerSquareMatrix

Parameters:

m - an integer square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public IntegerSquareMatrix multiply(IntegerTridiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - an integer tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class IntegerSquareMatrix

Returns:

an integer tridiagonal matrix

luDecompose

public DoubleSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class IntegerSquareMatrix

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.

Returns:

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