JSci.maths

Class IntegerDiagonalMatrix

java.lang.Object

JSci.maths.Matrix

JSci.maths.IntegerMatrix

JSci.maths.IntegerSquareMatrix

JSci.maths.IntegerTridiagonalMatrix

JSci.maths.IntegerDiagonalMatrix

All Implemented Interfaces:

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

public final class IntegerDiagonalMatrix
extends IntegerTridiagonalMatrix

The IntegerDiagonalMatrix class provides an object for encapsulating diagonal 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 static int	DIAGONAL Storage format identifier.

Fields inherited from class JSci.maths.IntegerTridiagonalMatrix

diag, ldiag, TRIDIAGONAL, 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
	IntegerDiagonalMatrix(int size) Constructs an empty matrix.
	IntegerDiagonalMatrix(int[] array) Constructs a matrix by wrapping an array containing the diagonal elements.
	IntegerDiagonalMatrix(int[][] array) Constructs a matrix from an array.
protected	IntegerDiagonalMatrix(int size, int storeID) Constructs a matrix.

Method Summary

Methods

Modifier and Type	Method and Description
IntegerDiagonalMatrix	add(IntegerDiagonalMatrix m) Returns the addition of this matrix and another.
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.
int	det() Returns the determinant.
boolean	equals(java.lang.Object m) Compares two integer diagonal matrices for equality.
double	frobeniusNorm() Returns the Frobenius (l2) norm.
int	getElement(int i, int j) Returns an element of the matrix.
static IntegerDiagonalMatrix	identity(int size) Creates an identity matrix.
int	infNorm() Returns the l-norm.
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.
IntegerDiagonalMatrix	multiply(IntegerDiagonalMatrix m) Returns the multiplication of this matrix and another.
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.
IntegerDiagonalMatrix	subtract(IntegerDiagonalMatrix m) Returns the subtraction of this matrix by another.
IntegerMatrix	subtract(IntegerMatrix m) Returns the subtraction of this matrix and another.
IntegerSquareMatrix	subtract(IntegerSquareMatrix m) Returns the subtraction of this matrix and another.
IntegerTridiagonalMatrix	subtract(IntegerTridiagonalMatrix m) Returns the subtraction of this matrix and another.
ComplexMatrix	toComplexMatrix() Converts this matrix to a complex matrix.
DoubleMatrix	toDoubleMatrix() Converts this matrix to a double matrix.
int	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.IntegerTridiagonalMatrix

toString

Methods inherited from class JSci.maths.IntegerSquareMatrix

choleskyDecomposition

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

DIAGONAL

protected static final int DIAGONAL

Storage format identifier.

See Also:

Constant Field Values

Constructor Detail

IntegerDiagonalMatrix

protected IntegerDiagonalMatrix(int size,
                     int storeID)

Constructs a matrix.

IntegerDiagonalMatrix

public IntegerDiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

IntegerDiagonalMatrix

public IntegerDiagonalMatrix(int[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

IntegerDiagonalMatrix

public IntegerDiagonalMatrix(int[] array)

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

Parameters:

array - an assigned value

Method Detail

identity

public static IntegerDiagonalMatrix identity(int size)

Creates an identity matrix.

Parameters:

size - the number of rows/columns

equals

public boolean equals(java.lang.Object m)

Compares two integer diagonal matrices for equality.

Overrides:

equals in class IntegerTridiagonalMatrix

Parameters:

m - a integer diagonal matrix

toDoubleMatrix

public DoubleMatrix toDoubleMatrix()

Converts this matrix to a double matrix.

Overrides:

toDoubleMatrix in class IntegerTridiagonalMatrix

Returns:

a double diagonal matrix

toComplexMatrix

public ComplexMatrix toComplexMatrix()

Converts this matrix to a complex matrix.

Overrides:

toComplexMatrix in class IntegerTridiagonalMatrix

Returns:

a complex diagonal matrix

getElement

public int getElement(int i,
             int j)

Returns an element of the matrix.

Overrides:

getElement in class IntegerTridiagonalMatrix

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 IntegerTridiagonalMatrix

Parameters:

i - row index of the element

j - column index of the element

x - an integer

Throws:

MatrixDimensionException - If attempting to access an invalid element.

isSymmetric

public boolean isSymmetric()

Returns true if this matrix is symmetric.

Overrides:

isSymmetric in class IntegerTridiagonalMatrix

isUnitary

public boolean isUnitary()

Returns true if this matrix is unitary.

Overrides:

isUnitary in class IntegerSquareMatrix

det

public int det()

Returns the determinant.

Overrides:

det in class IntegerSquareMatrix

trace

public int trace()

Returns the trace.

Overrides:

trace in class IntegerTridiagonalMatrix

infNorm

public int infNorm()

Returns the l-norm.

Overrides:

infNorm in class IntegerTridiagonalMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class IntegerTridiagonalMatrix

add

public IntegerMatrix add(IntegerMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class IntegerTridiagonalMatrix

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 IntegerTridiagonalMatrix

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.

Overrides:

add in class IntegerTridiagonalMatrix

Parameters:

m - an integer tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public IntegerDiagonalMatrix add(IntegerDiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - an integer diagonal 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 IntegerTridiagonalMatrix

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 and another.

Overrides:

subtract in class IntegerTridiagonalMatrix

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 and another.

Overrides:

subtract in class IntegerTridiagonalMatrix

Parameters:

m - an integer tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public IntegerDiagonalMatrix subtract(IntegerDiagonalMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - an integer diagonal 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 IntegerTridiagonalMatrix

Parameters:

x - an integer

Returns:

an integer diagonal matrix

multiply

public IntegerVector multiply(IntegerVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class IntegerTridiagonalMatrix

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 IntegerTridiagonalMatrix

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 IntegerTridiagonalMatrix

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.

Overrides:

multiply in class IntegerTridiagonalMatrix

Parameters:

m - an integer tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public IntegerDiagonalMatrix multiply(IntegerDiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - an integer diagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class IntegerTridiagonalMatrix

Returns:

an integer diagonal matrix

luDecompose

public DoubleSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class IntegerTridiagonalMatrix

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 IntegerTridiagonalMatrix

Returns:

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