JSci.maths

Class ComplexTridiagonalMatrix

java.lang.Object

JSci.maths.Matrix

JSci.maths.ComplexMatrix

JSci.maths.ComplexSquareMatrix

JSci.maths.ComplexTridiagonalMatrix

All Implemented Interfaces:

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

Direct Known Subclasses:

ComplexDiagonalMatrix

public class ComplexTridiagonalMatrix
extends ComplexSquareMatrix

The ComplexTridiagonalMatrix class provides an object for encapsulating tridiagonal matrices containing complex numbers. 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[]	diagIm
protected double[]	diagRe
protected double[]	ldiagIm Tridiagonal data.
protected double[]	ldiagRe Tridiagonal data.
protected static int	TRIDIAGONAL Storage format identifier.
protected double[]	udiagIm
protected double[]	udiagRe

Fields inherited from class JSci.maths.ComplexSquareMatrix

LU, LUpivot

Fields inherited from class JSci.maths.ComplexMatrix

ARRAY_2D, matrixIm, matrixRe

Fields inherited from class JSci.maths.Matrix

CLASS_SPECIFIC, numCols, numRows, storageFormat

Constructor Summary

Constructors

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

Method Summary

Methods

Modifier and Type	Method and Description
ComplexMatrix	add(ComplexMatrix m) Returns the addition of this matrix and another.
ComplexSquareMatrix	add(ComplexSquareMatrix m) Returns the addition of this matrix and another.
ComplexTridiagonalMatrix	add(ComplexTridiagonalMatrix m) Returns the addition of this matrix and another.
ComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
boolean	equals(java.lang.Object m) Compares two complex tridiagonal matrices for equality.
double	frobeniusNorm() Returns the Frobenius (l2) norm.
Complex	getElement(int i, int j) Returns an element of the matrix.
ComplexMatrix	hermitianAdjoint() Returns the hermitian adjoint of this matrix.
DoubleMatrix	imag() Returns the imaginary part of this complex matrix.
double	infNorm() Returns the l-norm.
ComplexSquareMatrix[]	luDecompose(int[] pivot) Returns the LU decomposition of this matrix.
ComplexMatrix	mapElements(ComplexMapping f) Applies a function on all the matrix elements.
ComplexMatrix	multiply(ComplexMatrix m) Returns the multiplication of this matrix and another.
ComplexSquareMatrix	multiply(ComplexSquareMatrix m) Returns the multiplication of this matrix and another.
ComplexSquareMatrix	multiply(ComplexTridiagonalMatrix m) Returns the multiplication of this matrix and another.
ComplexVector	multiply(ComplexVector v) Returns the multiplication of a vector by this matrix.
double	operatorNorm() Returns the operator norm.
DoubleMatrix	real() Returns the real part of this complex matrix.
ComplexMatrix	scalarMultiply(Complex z) Returns the multiplication of this matrix by a scalar.
ComplexMatrix	scalarMultiply(double x) Returns the multiplication of this matrix by a scalar.
void	setElement(int i, int j, Complex z) Sets the value of an element of the matrix.
void	setElement(int i, int j, double x, double y) Sets the value of an element of the matrix.
ComplexMatrix	subtract(ComplexMatrix m) Returns the subtraction of this matrix and another.
ComplexSquareMatrix	subtract(ComplexSquareMatrix m) Returns the subtraction of this matrix by another.
ComplexTridiagonalMatrix	subtract(ComplexTridiagonalMatrix m) Returns the subtraction of this matrix and another.
java.lang.String	toString() Returns a string representing this matrix.
Complex	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.ComplexSquareMatrix

det, inverse, involution, isHermitian, isUnitary, norm, polarDecompose

Methods inherited from class JSci.maths.ComplexMatrix

add, directSum, finalize, hashCode, multiply, negate, scalarDivide, 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

Methods inherited from interface JSci.maths.fields.Ring.Member

multiply

Methods inherited from interface JSci.maths.algebras.VectorSpace.Member

scalarDivide

Methods inherited from interface JSci.maths.algebras.Module.Member

scalarMultiply

Field Detail

TRIDIAGONAL

protected static final int TRIDIAGONAL

Storage format identifier.

See Also:

Constant Field Values

ldiagRe

protected double[] ldiagRe

Tridiagonal data.

ldiagIm

protected double[] ldiagIm

Tridiagonal data.

diagRe

protected double[] diagRe

diagIm

protected double[] diagIm

udiagRe

protected double[] udiagRe

udiagIm

protected double[] udiagIm

Constructor Detail

ComplexTridiagonalMatrix

protected ComplexTridiagonalMatrix(int size,
                        int storeID)

Constructs a matrix.

ComplexTridiagonalMatrix

public ComplexTridiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

ComplexTridiagonalMatrix

public ComplexTridiagonalMatrix(Complex[][] 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 complex tridiagonal matrices for equality.

Overrides:

equals in class ComplexMatrix

Parameters:

m - a complex tridiagonal matrix

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class ComplexMatrix

real

public DoubleMatrix real()

Returns the real part of this complex matrix.

Overrides:

real in class ComplexMatrix

Returns:

a double tridiagonal matrix

imag

public DoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class ComplexMatrix

Returns:

a double tridiagonal matrix

getElement

public Complex getElement(int i,
                 int j)

Returns an element of the matrix.

Overrides:

getElement in class ComplexMatrix

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,
              Complex z)

Sets the value of an element of the matrix. Should only be used to initialise this matrix.

Overrides:

setElement in class ComplexMatrix

Parameters:

i - row index of the element

j - column index of the element

z - a complex number

Throws:

MatrixDimensionException - If attempting to access an invalid element.

setElement

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

Sets the value of an element of the matrix. Should only be used to initialise this matrix.

Overrides:

setElement in class ComplexMatrix

Parameters:

i - row index of the element

j - column index of the element

x - the real part of a complex number

y - the imaginary part of a complex number

Throws:

MatrixDimensionException - If attempting to access an invalid element.

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class ComplexSquareMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class ComplexMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class ComplexMatrix

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

Overrides:

operatorNorm in class ComplexSquareMatrix

Throws:

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

add

public ComplexMatrix add(ComplexMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class ComplexSquareMatrix

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public ComplexSquareMatrix add(ComplexSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class ComplexSquareMatrix

Parameters:

m - a complex square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public ComplexTridiagonalMatrix add(ComplexTridiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexMatrix subtract(ComplexMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class ComplexSquareMatrix

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexSquareMatrix subtract(ComplexSquareMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class ComplexSquareMatrix

Parameters:

m - a complex square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexTridiagonalMatrix subtract(ComplexTridiagonalMatrix m)

Returns the subtraction of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarMultiply

public ComplexMatrix scalarMultiply(Complex z)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class ComplexSquareMatrix

Parameters:

z - a complex number

Returns:

a complex tridiagonal matrix

scalarMultiply

public ComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class ComplexSquareMatrix

Parameters:

x - a double

Returns:

a complex tridiagonal matrix

multiply

public ComplexVector multiply(ComplexVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class ComplexSquareMatrix

Parameters:

v - a complex vector

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public ComplexMatrix multiply(ComplexMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class ComplexMatrix

Parameters:

m - a complex matrix

Returns:

a ComplexMatrix or a ComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public ComplexSquareMatrix multiply(ComplexSquareMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class ComplexSquareMatrix

Parameters:

m - a complex square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public ComplexSquareMatrix multiply(ComplexTridiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

hermitianAdjoint

public ComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class ComplexSquareMatrix

Returns:

a complex tridiagonal matrix

conjugate

public ComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class ComplexSquareMatrix

Returns:

a complex tridiagonal matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class ComplexSquareMatrix

Returns:

a complex tridiagonal matrix

luDecompose

public ComplexSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class ComplexSquareMatrix

Returns:

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

mapElements

public ComplexMatrix mapElements(ComplexMapping f)

Applies a function on all the matrix elements.

Overrides:

mapElements in class ComplexSquareMatrix

Parameters:

f - a user-defined function

Returns:

a complex tridiagonal matrix