JSci.maths
Class ComplexSquareMatrix

java.lang.Object
  JSci.maths.Matrix
      JSci.maths.ComplexMatrix
          JSci.maths.ComplexSquareMatrix

All Implemented Interfaces:

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

Direct Known Subclasses:

ComplexTridiagonalMatrix, GammaMatrix

public class ComplexSquareMatrix
extends ComplexMatrix
implements CStarAlgebra.Member

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

Version:

2.2

Author:

Mark Hale

See Also:

Serialized Form

Field Summary

protected ComplexSquareMatrix[]	LU
protected int[]	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

	ComplexSquareMatrix(Complex[][] array) Constructs a matrix from an array.
	ComplexSquareMatrix(ComplexVector[] array) Constructs a matrix from an array of vectors.
	ComplexSquareMatrix(double[][] arrayRe, double[][] arrayIm) Constructs a matrix by wrapping two arrays.
	ComplexSquareMatrix(int size) Constructs an empty matrix.
protected	ComplexSquareMatrix(int size, int storeID) Constructs a matrix.

Method Summary

ComplexMatrix	add(ComplexMatrix m) Returns the addition of this matrix and another.
ComplexSquareMatrix	add(ComplexSquareMatrix m) Returns the addition of this matrix and another.
ComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
Complex	det() Returns the determinant.
ComplexMatrix	hermitianAdjoint() Returns the hermitian adjoint of this matrix.
ComplexSquareMatrix	inverse() Returns the inverse of this matrix.
CStarAlgebra.Member	involution() Returns the involution 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.
ComplexSquareMatrix	multiply(ComplexSquareMatrix m) Returns the multiplication of this matrix and another.
ComplexVector	multiply(ComplexVector v) Returns the multiplication of a vector by this matrix.
double	norm() Returns the C* norm.
double	operatorNorm() Returns the operator norm.
ComplexSquareMatrix[]	polarDecompose() Returns the polar decomposition of this 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.
ComplexMatrix	subtract(ComplexMatrix m) Returns the subtraction of this matrix by another.
ComplexSquareMatrix	subtract(ComplexSquareMatrix 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.ComplexMatrix

add, directSum, equals, finalize, frobeniusNorm, getElement, hashCode, imag, infNorm, multiply, multiply, negate, real, scalarDivide, scalarDivide, scalarDivide, scalarMultiply, setElement, setElement, subtract, tensorProduct, toString

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

LU

protected transient ComplexSquareMatrix[] LU

LUpivot

protected transient int[] LUpivot

Constructor Detail

ComplexSquareMatrix

protected ComplexSquareMatrix(int size,
                              int storeID)

Constructs a matrix.

ComplexSquareMatrix

public ComplexSquareMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

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(Complex[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

ComplexSquareMatrix

public ComplexSquareMatrix(ComplexVector[] 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

isHermitian

public boolean isHermitian()

Returns true if this matrix is hermitian.

isUnitary

public boolean isUnitary()

Returns true if this matrix is unitary.

det

public Complex det()

Returns the determinant.

trace

public Complex trace()

Returns the trace.

norm

public double norm()

Returns the C^* norm.

Specified by:

norm in interface BanachSpace.Member

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

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 ComplexMatrix

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.

Parameters:

m - a complex square 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 ComplexMatrix

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.

Parameters:

m - a complex square 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 ComplexMatrix

Parameters:

z - a complex number

Returns:

a complex square matrix

scalarMultiply

public ComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class ComplexMatrix

Parameters:

x - a double

Returns:

a complex square matrix

multiply

public ComplexVector multiply(ComplexVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class ComplexMatrix

Parameters:

v - a complex vector

Throws:

DimensionException - If the matrix and vector are incompatible.

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 incompatible.

involution

public CStarAlgebra.Member involution()

Returns the involution of this matrix.

Specified by:

involution in interface CStarAlgebra.Member

hermitianAdjoint

public ComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class ComplexMatrix

Returns:

a complex square matrix

conjugate

public ComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class ComplexMatrix

Returns:

a complex square matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class ComplexMatrix

Returns:

a complex square matrix

inverse

public ComplexSquareMatrix inverse()

Returns the inverse of this matrix.

Returns:

a complex square matrix

luDecompose

public ComplexSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Returns:

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

polarDecompose

public ComplexSquareMatrix[] polarDecompose()

Returns the polar decomposition of this matrix.

mapElements

public ComplexMatrix mapElements(ComplexMapping f)

Applies a function on all the matrix elements.

Overrides:

mapElements in class ComplexMatrix

Parameters:

f - a user-defined function

Returns:

a complex square matrix