JSci.maths.matrices
Class AbstractComplexMatrix

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

All Implemented Interfaces:

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

Direct Known Subclasses:

AbstractComplexSquareMatrix, ComplexMatrix

public abstract class AbstractComplexMatrix
extends Matrix

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

See Also:

Serialized Form

Field Summary

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

protected

AbstractComplexMatrix(int rows, int cols) Constructs a matrix.

Method Summary

AbelianGroup.Member	add(AbelianGroup.Member m) Returns the addition of this matrix and another.
AbstractComplexMatrix	add(AbstractComplexMatrix m) Returns the addition of this matrix and another.
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) Compares two complex matrices for equality.
boolean	equals(AbstractComplexMatrix m, double tol)
boolean	equals(java.lang.Object obj) Compares two complex matrices for equality.
double	frobeniusNorm() Returns the Frobenius or Hilbert-Schmidt (l2) norm.
abstract Complex	getElement(int i, int j) Returns an element of the matrix.
abstract double	getImagElement(int i, int j) Returns the imag part of an element of the matrix.
abstract double	getRealElement(int i, int j) Returns the real part of an element of the matrix.
java.lang.Object	getSet()
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.
Ring.Member	multiply(Ring.Member m) Returns the multiplication of this matrix and another.
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.
VectorSpace.Member	scalarDivide(Field.Member 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.
Module.Member	scalarMultiply(Ring.Member x) Returns the multiplication of this matrix by a scalar.
Complex	scalarProduct(AbstractComplexMatrix m) Returns the scalar product of this matrix and another.
abstract void	setElement(int i, int j, Complex z) Sets the value of an element of the matrix.
abstract void	setElement(int i, int j, double x, double y) Sets the value of an element of the matrix.
AbelianGroup.Member	subtract(AbelianGroup.Member m) Returns the subtraction of this matrix by another.
AbstractComplexMatrix	subtract(AbstractComplexMatrix m) Returns the subtraction of this matrix by another.
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.Matrix

columns, getInvalidElementMsg, rows

Methods inherited from class java.lang.Object

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

Constructor Detail

AbstractComplexMatrix

protected AbstractComplexMatrix(int rows,
                                int cols)

Constructs a matrix.

Method Detail

equals

public final boolean equals(java.lang.Object obj)

Compares two complex matrices for equality.

Overrides:

equals in class java.lang.Object

Parameters:

obj - a complex matrix

equals

public final boolean equals(AbstractComplexMatrix m)

Compares two complex matrices for equality. Two matrices are considered to be equal if the Frobenius norm of their difference is within the zero tolerance.

Parameters:

m - a complex matrix

equals

public boolean equals(AbstractComplexMatrix m,
                      double tol)

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class java.lang.Object

hashCode

public int hashCode()

Returns a hashcode for this matrix.

Overrides:

hashCode in class java.lang.Object

real

public AbstractDoubleMatrix real()

Returns the real part of this complex matrix.

Returns:

a double matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Returns:

a double matrix

getElement

public abstract Complex getElement(int i,
                                   int j)

Returns an element of the matrix.

Parameters:

i - row index of the element

j - column index of the element

Throws:

MatrixDimensionException - If attempting to access an invalid element.

getRealElement

public abstract double getRealElement(int i,
                                      int j)

Returns the real part of an element of the matrix.

Parameters:

i - row index of the element

j - column index of the element

Throws:

MatrixDimensionException - If attempting to access an invalid element.

getImagElement

public abstract double getImagElement(int i,
                                      int j)

Returns the imag part of an element of the matrix.

Parameters:

i - row index of the element

j - column index of the element

Throws:

MatrixDimensionException - If attempting to access an invalid element.

setElement

public abstract 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.

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 abstract 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.

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.

getSet

public java.lang.Object getSet()

infNorm

public double infNorm()

Returns the l-norm.

frobeniusNorm

public double frobeniusNorm()

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

PlanetMath references:

FrobeniusMatrixNorm

negate

public AbelianGroup.Member negate()

Returns the negative of this matrix.

add

public final AbelianGroup.Member add(AbelianGroup.Member m)

Returns the addition of this matrix and another.

Parameters:

m - a group member

add

public AbstractComplexMatrix add(AbstractComplexMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public final AbelianGroup.Member subtract(AbelianGroup.Member m)

Returns the subtraction of this matrix by another.

Parameters:

m - a group member

subtract

public AbstractComplexMatrix subtract(AbstractComplexMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - a complex matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarMultiply

public final Module.Member scalarMultiply(Ring.Member x)

Returns the multiplication of this matrix by a scalar.

Parameters:

x - a ring member

scalarMultiply

public AbstractComplexMatrix scalarMultiply(Complex z)

Returns the multiplication of this matrix by a scalar.

Parameters:

z - a complex number

Returns:

a complex matrix

scalarMultiply

public AbstractComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Parameters:

x - a double

Returns:

a complex matrix

scalarDivide

public final VectorSpace.Member scalarDivide(Field.Member x)

Returns the division of this matrix by a scalar.

Parameters:

x - a field member

scalarDivide

public AbstractComplexMatrix scalarDivide(Complex z)

Returns the division of this matrix by a scalar.

Parameters:

z - a complex number

Returns:

a complex matrix

scalarDivide

public AbstractComplexMatrix scalarDivide(double x)

Returns the division of this matrix by a scalar.

Parameters:

x - a double

Returns:

a complex matrix

scalarProduct

public Complex scalarProduct(AbstractComplexMatrix m)

Returns the scalar product of this matrix and another.

Parameters:

m - a complex matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public AbstractComplexVector multiply(AbstractComplexVector v)

Returns the multiplication of a vector by this matrix.

Parameters:

v - a complex vector

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public final Ring.Member multiply(Ring.Member m)

Returns the multiplication of this matrix and another.

Parameters:

m - a ring member

multiply

public AbstractComplexMatrix multiply(AbstractComplexMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are incompatible.

directSum

public AbstractComplexMatrix directSum(AbstractComplexMatrix m)

Returns the direct sum of this matrix and another.

tensor

public AbstractComplexMatrix tensor(AbstractComplexMatrix m)

Returns the tensor product of this matrix and another.

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Returns:

a complex matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Returns:

a complex matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Specified by:

transpose in class Matrix

Returns:

a complex matrix

mapElements

public AbstractComplexMatrix mapElements(ComplexMapping f)

Applies a function on all the matrix elements.

Parameters:

f - a user-defined function

Returns:

a complex matrix