jsci.maths.matrices

Class ComplexSquareMatrix

java.lang.Object

jsci.maths.matrices.Matrix

jsci.maths.matrices.AbstractComplexMatrix

jsci.maths.matrices.AbstractComplexSquareMatrix

jsci.maths.matrices.ComplexSquareMatrix

All Implemented Interfaces:

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

Direct Known Subclasses:

GammaMatrix

public class ComplexSquareMatrix
extends AbstractComplexSquareMatrix

The ComplexSquareMatrix class provides an object for encapsulating square matrices containing complex numbers.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ComplexSquareMatrix(AbstractComplexVector[] array) Constructs a matrix from an array of vectors.
ComplexSquareMatrix(Complex[][] array) Constructs a matrix from an array.
ComplexSquareMatrix(double[][] arrayRe, double[][] arrayIm) Constructs a matrix by wrapping two arrays.
ComplexSquareMatrix(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.
ComplexSquareMatrix	add(ComplexSquareMatrix m)
AbstractComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
Complex	det() Returns the determinant.
AbstractComplexSquareMatrix	directSum(AbstractComplexSquareMatrix m) Returns the direct sum of this matrix and another.
boolean	equals(AbstractComplexMatrix m, double tol) Compares two complex matrices for equality.
double	frobeniusNorm() Returns the Frobenius or Hilbert-Schmidt (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.
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.
ComplexSquareMatrix	multiply(ComplexSquareMatrix m)
AbelianGroup.Member	negate() Returns the negative of this matrix.
AbstractComplexSquareMatrix[]	polarDecompose() Returns the polar decomposition of this matrix.
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.
ComplexSquareMatrix	subtract(ComplexSquareMatrix m)
AbstractComplexSquareMatrix	tensor(AbstractComplexSquareMatrix m) Returns the tensor product 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.matrices.AbstractComplexSquareMatrix

add, involution, isHermitian, isUnitary, norm, operatorNorm, scalarDivide, scalarDivide, scalarProduct, scalarProduct, subtract

Methods inherited from class jsci.maths.matrices.AbstractComplexMatrix

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

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

ComplexSquareMatrix

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

Constructs a matrix by wrapping two arrays.

Parameters:

arrayRe - an array of real values

arrayIm - an array of imaginary values

Throws:

MatrixDimensionException - If the array is not square.

ComplexSquareMatrix

public ComplexSquareMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

ComplexSquareMatrix

public ComplexSquareMatrix(Complex[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

ComplexSquareMatrix

public ComplexSquareMatrix(AbstractComplexVector[] array)

Constructs a matrix from an array of vectors. The vectors form columns in the matrix.

Parameters:

array - an assigned value.

Throws:

MatrixDimensionException - If the array is not square.

Method Detail

equals

public boolean equals(AbstractComplexMatrix m,
                      double tol)

Compares two complex matrices for equality.

Overrides:

equals in class AbstractComplexMatrix

Parameters:

m - a complex matrix

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class AbstractComplexMatrix

real

public AbstractDoubleMatrix real()

Returns the real part of this complex matrix.

Overrides:

real in class AbstractComplexSquareMatrix

Returns:

a double square matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class AbstractComplexSquareMatrix

Returns:

a double square 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.

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractComplexMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius or Hilbert-Schmidt (l²) norm.

Overrides:

frobeniusNorm in class AbstractComplexMatrix

det

public Complex det()

Returns the determinant.

Overrides:

det in class AbstractComplexSquareMatrix

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class AbstractComplexSquareMatrix

negate

public AbelianGroup.Member negate()

Returns the negative of this matrix.

Specified by:

negate in interface AbelianGroup.Member

Overrides:

negate 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)

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)

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 square 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 square 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 square matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are incompatible.

multiply

public ComplexSquareMatrix multiply(ComplexSquareMatrix m)

directSum

public AbstractComplexSquareMatrix directSum(AbstractComplexSquareMatrix m)

Returns the direct sum of this matrix and another.

Overrides:

directSum in class AbstractComplexSquareMatrix

tensor

public AbstractComplexSquareMatrix tensor(AbstractComplexSquareMatrix m)

Returns the tensor product of this matrix and another.

Overrides:

tensor in class AbstractComplexSquareMatrix

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class AbstractComplexSquareMatrix

Returns:

a complex square matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class AbstractComplexSquareMatrix

Returns:

a complex square matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractComplexSquareMatrix

Returns:

a complex square matrix

inverse

public AbstractComplexSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class AbstractComplexSquareMatrix

Returns:

a complex square matrix

luDecompose

public final 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. Warning: no pivoting.

Overrides:

luDecompose in class AbstractComplexSquareMatrix

Returns:

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

polarDecompose

public AbstractComplexSquareMatrix[] polarDecompose()

Returns the polar decomposition of this matrix.

Overrides:

polarDecompose in class AbstractComplexSquareMatrix

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 square matrix