JSci.maths.matrices
Class ComplexMatrix

java.lang.Object
  JSci.maths.matrices.Matrix
      JSci.maths.matrices.AbstractComplexMatrix
          JSci.maths.matrices.ComplexMatrix

All Implemented Interfaces:

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

public class ComplexMatrix
extends AbstractComplexMatrix

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

See Also:

Serialized Form

Field Summary

protected double[][]	matrixIm Arrays containing the elements of the matrix.
protected double[][]	matrixRe Arrays containing the elements of the matrix.

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

ComplexMatrix(Complex[][] array)
Constructs a matrix from an array.

ComplexMatrix(ComplexVector[] array)
Constructs a matrix from an array of vectors (columns).

ComplexMatrix(double[][] arrayRe, double[][] arrayIm)
Constructs a matrix by wrapping two arrays.

ComplexMatrix(int rows, int cols)
Constructs an empty matrix.

Method Summary

AbstractComplexMatrix	add(AbstractComplexMatrix m) Returns the addition of this matrix and another.
ComplexMatrix	add(ComplexMatrix m)
AbstractComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
AbstractComplexMatrix	directSum(AbstractComplexMatrix 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.
int	hashCode() Returns a hashcode for this 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.
AbstractComplexMatrix	mapElements(ComplexMapping f) Applies a function on all the matrix elements.
AbstractComplexMatrix	multiply(AbstractComplexMatrix m) Returns the multiplication of this matrix and another.
AbstractComplexVector	multiply(AbstractComplexVector v) Returns the multiplication of a vector by this matrix.
AbstractComplexMatrix	multiply(ComplexMatrix m)
AbelianGroup.Member	negate() Returns the negative of this matrix.
AbstractDoubleMatrix	real() Returns the real part of this complex matrix.
AbstractComplexMatrix	scalarDivide(Complex z) Returns the division of this matrix by a scalar.
AbstractComplexMatrix	scalarDivide(double x) Returns the division of this matrix by a scalar.
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.
AbstractComplexMatrix	subtract(AbstractComplexMatrix m) Returns the subtraction of this matrix by another.
ComplexMatrix	subtract(ComplexMatrix m)
AbstractComplexMatrix	tensor(AbstractComplexMatrix m) Returns the tensor product of this matrix and another.
java.lang.String	toString() Returns a string representing this matrix.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.matrices.AbstractComplexMatrix

add, equals, equals, getSet, multiply, scalarDivide, scalarMultiply, scalarProduct, subtract

Methods inherited from class JSci.maths.matrices.Matrix

columns, getInvalidElementMsg, rows

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

matrixRe

protected double[][] matrixRe

Arrays containing the elements of the matrix.

matrixIm

protected double[][] matrixIm

Arrays containing the elements of the matrix.

Constructor Detail

ComplexMatrix

public ComplexMatrix(int rows,
                     int cols)

Constructs an empty matrix.

Parameters:

rows - the number of rows

cols - the number of columns

ComplexMatrix

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

Constructs a matrix by wrapping two arrays.

Parameters:

arrayRe - an array of real values

arrayIm - an array of imaginary values

ComplexMatrix

public ComplexMatrix(Complex[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

ComplexMatrix

public ComplexMatrix(ComplexVector[] array)

Constructs a matrix from an array of vectors (columns).

Parameters:

array - an assigned value

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

hashCode

public int hashCode()

Returns a hashcode for this matrix.

Overrides:

hashCode in class AbstractComplexMatrix

real

public AbstractDoubleMatrix real()

Returns the real part of this complex matrix.

Overrides:

real in class AbstractComplexMatrix

Returns:

a double matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class AbstractComplexMatrix

Returns:

a double 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

PlanetMath references:

FrobeniusMatrixNorm

negate

public AbelianGroup.Member negate()

Returns the negative of this matrix.

Specified by:

negate in interface AbelianGroup.Member

Overrides:

negate in class AbstractComplexMatrix

add

public AbstractComplexMatrix add(AbstractComplexMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class AbstractComplexMatrix

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public ComplexMatrix add(ComplexMatrix m)

subtract

public AbstractComplexMatrix subtract(AbstractComplexMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class AbstractComplexMatrix

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexMatrix subtract(ComplexMatrix m)

scalarMultiply

public AbstractComplexMatrix scalarMultiply(Complex z)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class AbstractComplexMatrix

Parameters:

z - a complex number

Returns:

a complex matrix

scalarMultiply

public AbstractComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class AbstractComplexMatrix

Parameters:

x - a double

Returns:

a complex matrix

scalarDivide

public AbstractComplexMatrix scalarDivide(Complex z)

Returns the division of this matrix by a scalar.

Overrides:

scalarDivide in class AbstractComplexMatrix

Parameters:

z - a complex number

Returns:

a complex matrix

scalarDivide

public AbstractComplexMatrix scalarDivide(double x)

Returns the division of this matrix by a scalar.

Overrides:

scalarDivide in class AbstractComplexMatrix

Parameters:

x - a double

Returns:

a complex 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 AbstractComplexMatrix multiply(AbstractComplexMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class AbstractComplexMatrix

Parameters:

m - a complex matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are incompatible.

multiply

public AbstractComplexMatrix multiply(ComplexMatrix m)

directSum

public AbstractComplexMatrix directSum(AbstractComplexMatrix m)

Returns the direct sum of this matrix and another.

Overrides:

directSum in class AbstractComplexMatrix

tensor

public AbstractComplexMatrix tensor(AbstractComplexMatrix m)

Returns the tensor product of this matrix and another.

Overrides:

tensor in class AbstractComplexMatrix

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class AbstractComplexMatrix

Returns:

a complex matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class AbstractComplexMatrix

Returns:

a complex matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractComplexMatrix

Returns:

a complex matrix

mapElements

public AbstractComplexMatrix mapElements(ComplexMapping f)

Applies a function on all the matrix elements.

Overrides:

mapElements in class AbstractComplexMatrix

Parameters:

f - a user-defined function

Returns:

a complex matrix