JSci.maths

Class ComplexDiagonalMatrix

java.lang.Object

JSci.maths.Matrix

JSci.maths.ComplexMatrix

JSci.maths.ComplexSquareMatrix

JSci.maths.ComplexTridiagonalMatrix

JSci.maths.ComplexDiagonalMatrix

All Implemented Interfaces:

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

public final class ComplexDiagonalMatrix
extends ComplexTridiagonalMatrix

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

Fields inherited from class JSci.maths.ComplexTridiagonalMatrix

diagIm, diagRe, ldiagIm, ldiagRe, TRIDIAGONAL, udiagIm, 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
	ComplexDiagonalMatrix(Complex[] array) Constructs a matrix from an array containing the diagonal elements.
	ComplexDiagonalMatrix(Complex[][] array) Constructs a matrix from an array.
	ComplexDiagonalMatrix(double[] arrayRe, double[] arrayIm) Constructs a matrix by wrapping two arrays containing the diagonal elements.
	ComplexDiagonalMatrix(int size) Constructs an empty matrix.
protected	ComplexDiagonalMatrix(int size, int storeID) Constructs a matrix.

Method Summary

Methods

Modifier and Type	Method and Description
ComplexDiagonalMatrix	add(ComplexDiagonalMatrix m) Returns the addition of this matrix and another.
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.
Complex	det() Returns the determinant.
boolean	equals(java.lang.Object m) Compares two complex diagonal 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.
static ComplexDiagonalMatrix	identity(int size) Creates an identity matrix.
DoubleMatrix	imag() Returns the imaginary part of this complex matrix.
double	infNorm() Returns the l-norm.
ComplexSquareMatrix	inverse() Returns the inverse of this matrix.
boolean	isHermitian() Returns true if this matrix is hermitian.
boolean	isUnitary() Returns true if this matrix is unitary.
ComplexSquareMatrix[]	luDecompose(int[] pivot) Returns the LU decomposition of this matrix.
ComplexMatrix	mapElements(ComplexMapping f) Applies a function on all the matrix elements.
ComplexDiagonalMatrix	multiply(ComplexDiagonalMatrix m) Returns the multiplication of this matrix and another.
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.
ComplexDiagonalMatrix	subtract(ComplexDiagonalMatrix m) Returns the subtraction of this matrix by another.
ComplexMatrix	subtract(ComplexMatrix m) Returns the subtraction of this matrix by another.
ComplexSquareMatrix	subtract(ComplexSquareMatrix m) Returns the subtraction of this matrix by another.
ComplexTridiagonalMatrix	subtract(ComplexTridiagonalMatrix m) Returns the subtraction of this matrix by another.
Complex	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.ComplexTridiagonalMatrix

toString

Methods inherited from class JSci.maths.ComplexSquareMatrix

involution, 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

DIAGONAL

protected static final int DIAGONAL

Storage format identifier.

See Also:

Constant Field Values

Constructor Detail

ComplexDiagonalMatrix

protected ComplexDiagonalMatrix(int size,
                     int storeID)

Constructs a matrix.

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(Complex[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(double[] arrayRe,
                     double[] arrayIm)

Constructs a matrix by wrapping two arrays containing the diagonal elements.

Parameters:

arrayRe - an array of real values

arrayIm - an array of imaginary values

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(Complex[] array)

Constructs a matrix from an array containing the diagonal elements.

Parameters:

array - an assigned value

Method Detail

identity

public static ComplexDiagonalMatrix identity(int size)

Creates an identity matrix.

Parameters:

size - the number of rows/columns

equals

public boolean equals(java.lang.Object m)

Compares two complex diagonal matrices for equality.

Overrides:

equals in class ComplexTridiagonalMatrix

Parameters:

m - a complex diagonal matrix

real

public DoubleMatrix real()

Returns the real part of this complex matrix.

Overrides:

real in class ComplexTridiagonalMatrix

Returns:

a double diagonal matrix

imag

public DoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class ComplexTridiagonalMatrix

Returns:

a double diagonal matrix

getElement

public Complex getElement(int i,
                 int j)

Returns an element of the matrix.

Overrides:

getElement in class ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

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.

isHermitian

public boolean isHermitian()

Returns true if this matrix is hermitian.

Overrides:

isHermitian in class ComplexSquareMatrix

isUnitary

public boolean isUnitary()

Returns true if this matrix is unitary.

Overrides:

isUnitary in class ComplexSquareMatrix

det

public Complex det()

Returns the determinant.

Overrides:

det in class ComplexSquareMatrix

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class ComplexTridiagonalMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class ComplexTridiagonalMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class ComplexTridiagonalMatrix

operatorNorm

public double operatorNorm()

Returns the operator norm.

Overrides:

operatorNorm in class ComplexTridiagonalMatrix

add

public ComplexMatrix add(ComplexMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

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.

Overrides:

add in class ComplexTridiagonalMatrix

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public ComplexDiagonalMatrix add(ComplexDiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a complex diagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexMatrix subtract(ComplexMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

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 by another.

Overrides:

subtract in class ComplexTridiagonalMatrix

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexDiagonalMatrix subtract(ComplexDiagonalMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - a complex diagonal 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 ComplexTridiagonalMatrix

Parameters:

z - a complex number

Returns:

a complex diagonal matrix

scalarMultiply

public ComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class ComplexTridiagonalMatrix

Parameters:

x - a double

Returns:

a complex diagonal matrix

multiply

public ComplexVector multiply(ComplexVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

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.

Overrides:

multiply in class ComplexTridiagonalMatrix

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public ComplexDiagonalMatrix multiply(ComplexDiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex diagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

inverse

public ComplexSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class ComplexSquareMatrix

Returns:

a complex diagonal matrix

hermitianAdjoint

public ComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class ComplexTridiagonalMatrix

Returns:

a complex diagonal matrix

conjugate

public ComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class ComplexTridiagonalMatrix

Returns:

a complex diagonal matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class ComplexTridiagonalMatrix

Returns:

a complex diagonal matrix

luDecompose

public ComplexSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class ComplexTridiagonalMatrix

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 ComplexTridiagonalMatrix

Parameters:

f - a user-defined function

Returns:

a complex diagonal matrix