jsci.maths.matrices

Class ComplexDiagonalMatrix

java.lang.Object

jsci.maths.matrices.Matrix

jsci.maths.matrices.AbstractComplexMatrix

jsci.maths.matrices.AbstractComplexSquareMatrix

jsci.maths.matrices.ComplexDiagonalMatrix

All Implemented Interfaces:

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

public class ComplexDiagonalMatrix
extends AbstractComplexSquareMatrix
implements DiagonalMatrix

The ComplexDiagonalMatrix class provides an object for encapsulating diagonal matrices containing complex numbers. Uses compressed diagonal storage.

See Also:

Serialized Form

Constructor Summary

Constructors

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.

Method Summary

Modifier and Type	Method and Description
AbstractComplexSquareMatrix	add(AbstractComplexSquareMatrix m) Returns the addition of this matrix and another.
ComplexDiagonalMatrix	add(ComplexDiagonalMatrix m) Returns the addition of this matrix and another.
ComplexSquareMatrix	add(ComplexSquareMatrix m)
ComplexTridiagonalMatrix	add(ComplexTridiagonalMatrix m) Returns the addition of this matrix and another.
AbstractComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
Complex	det() Returns the determinant.
boolean	equals(AbstractComplexMatrix m, double tol) 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.
double	getImagElement(int i, int j) Returns the imag part of an element of the matrix.
double	getRealElement(int i, int j) Returns the real part of an element of the matrix.
AbstractComplexMatrix	hermitianAdjoint() Returns the hermitian adjoint of this matrix.
static ComplexDiagonalMatrix	identity(int size) Creates an identity matrix.
AbstractDoubleMatrix	imag() Returns the imaginary part of this complex matrix.
double	infNorm() Returns the l-norm.
AbstractComplexSquareMatrix	inverse() Returns the inverse of this matrix.
AbstractComplexSquareMatrix[]	luDecompose() Returns the LU decomposition of this matrix.
AbstractComplexSquareMatrix[]	luDecompose(int[] pivot) Returns the LU decomposition of this matrix.
AbstractComplexMatrix	mapElements(ComplexMapping f) Applies a function on all the matrix elements.
AbstractComplexSquareMatrix	multiply(AbstractComplexSquareMatrix m) Returns the multiplication of this matrix and another.
AbstractComplexVector	multiply(AbstractComplexVector v) Returns the multiplication of a vector by this matrix.
ComplexDiagonalMatrix	multiply(ComplexDiagonalMatrix m) Returns the multiplication of this matrix and another.
ComplexSquareMatrix	multiply(ComplexSquareMatrix m) Returns the multiplication of this matrix and another.
ComplexTridiagonalMatrix	multiply(ComplexTridiagonalMatrix m) Returns the multiplication of this matrix and another.
double	operatorNorm() Returns the operator norm.
AbstractDoubleMatrix	real() Returns the real part of this complex matrix.
AbstractComplexMatrix	scalarMultiply(Complex z) Returns the multiplication of this matrix by a scalar.
AbstractComplexMatrix	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.
AbstractComplexSquareMatrix	subtract(AbstractComplexSquareMatrix m) Returns the subtraction of this matrix by another.
ComplexDiagonalMatrix	subtract(ComplexDiagonalMatrix m) Returns the subtraction of this matrix by another.
ComplexSquareMatrix	subtract(ComplexSquareMatrix m)
ComplexTridiagonalMatrix	subtract(ComplexTridiagonalMatrix m)
Complex	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class jsci.maths.matrices.AbstractComplexSquareMatrix

add, directSum, involution, isHermitian, isUnitary, negate, norm, polarDecompose, scalarDivide, scalarDivide, scalarProduct, scalarProduct, subtract, tensor

Methods inherited from class jsci.maths.matrices.AbstractComplexMatrix

add, directSum, equals, equals, getSet, hashCode, multiply, multiply, scalarDivide, scalarMultiply, subtract, tensor, toString

Methods inherited from class jsci.maths.matrices.Matrix

columns, rows

Methods inherited from class java.lang.Object

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

Constructor Detail

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(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(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(AbstractComplexMatrix m,
                      double tol)

Compares two complex diagonal matrices for equality.

Overrides:

equals in class AbstractComplexMatrix

Parameters:

m - a complex diagonal matrix

real

public AbstractDoubleMatrix real()

Returns the real part of this complex matrix.

Overrides:

real in class AbstractComplexSquareMatrix

Returns:

a double diagonal matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class AbstractComplexSquareMatrix

Returns:

a double diagonal matrix

getElement

public Complex getElement(int i,
                          int j)

Returns an element of the matrix.

Specified by:

getElement in class AbstractComplexMatrix

Parameters:

i - row index of the element

j - column index of the element

Throws:

MatrixDimensionException - If attempting to access an invalid element.

getRealElement

public double getRealElement(int i,
                             int j)

Description copied from class: AbstractComplexMatrix

Returns the real part of an element of the matrix.

Specified by:

getRealElement in class AbstractComplexMatrix

Parameters:

i - row index of the element

j - column index of the element

getImagElement

public double getImagElement(int i,
                             int j)

Description copied from class: AbstractComplexMatrix

Returns the imag part of an element of the matrix.

Specified by:

getImagElement in class AbstractComplexMatrix

Parameters:

i - row index of the element

j - column index of the 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.

Specified by:

setElement in class AbstractComplexMatrix

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.

Specified by:

setElement in class AbstractComplexMatrix

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.

det

public Complex det()

Returns the determinant.

Overrides:

det in class AbstractComplexSquareMatrix

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class AbstractComplexSquareMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractComplexMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class AbstractComplexMatrix

operatorNorm

public double operatorNorm()

Returns the operator norm.

Overrides:

operatorNorm in class AbstractComplexSquareMatrix

add

public AbstractComplexSquareMatrix add(AbstractComplexSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class AbstractComplexSquareMatrix

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public ComplexSquareMatrix add(ComplexSquareMatrix m)

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.

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 AbstractComplexSquareMatrix subtract(AbstractComplexSquareMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class AbstractComplexSquareMatrix

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexSquareMatrix subtract(ComplexSquareMatrix m)

subtract

public ComplexTridiagonalMatrix subtract(ComplexTridiagonalMatrix m)

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 AbstractComplexMatrix scalarMultiply(Complex z)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class AbstractComplexSquareMatrix

Parameters:

z - a complex number

Returns:

a complex diagonal matrix

scalarMultiply

public AbstractComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class AbstractComplexSquareMatrix

Parameters:

x - a double

Returns:

a complex diagonal matrix

multiply

public AbstractComplexVector multiply(AbstractComplexVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class AbstractComplexMatrix

Parameters:

v - a complex vector

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public AbstractComplexSquareMatrix multiply(AbstractComplexSquareMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class AbstractComplexSquareMatrix

Parameters:

m - a complex matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public ComplexSquareMatrix multiply(ComplexSquareMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex square matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public ComplexTridiagonalMatrix 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.

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 AbstractComplexSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class AbstractComplexSquareMatrix

Returns:

a complex diagonal matrix

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class AbstractComplexSquareMatrix

Returns:

a complex diagonal matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class AbstractComplexSquareMatrix

Returns:

a complex diagonal matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractComplexSquareMatrix

Returns:

a complex diagonal matrix

luDecompose

public AbstractComplexSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class AbstractComplexSquareMatrix

Returns:

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

luDecompose

public AbstractComplexSquareMatrix[] luDecompose()

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class AbstractComplexSquareMatrix

Returns:

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

mapElements

public AbstractComplexMatrix mapElements(ComplexMapping f)

Applies a function on all the matrix elements.

Overrides:

mapElements in class AbstractComplexSquareMatrix

Parameters:

f - a user-defined function

Returns:

a complex diagonal matrix