jsci.maths.matrices

Class AbstractComplexSquareMatrix

java.lang.Object

jsci.maths.matrices.Matrix

jsci.maths.matrices.AbstractComplexMatrix

jsci.maths.matrices.AbstractComplexSquareMatrix

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:

ComplexDiagonalMatrix, ComplexSquareMatrix, ComplexTridiagonalMatrix

public abstract class AbstractComplexSquareMatrix
extends AbstractComplexMatrix
implements CStarAlgebra.Member, SquareMatrix

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

See Also:

Serialized Form

Method Summary

Modifier and Type	Method and Description
AbstractComplexMatrix	add(AbstractComplexMatrix m) Returns the addition of this matrix and another.
AbstractComplexSquareMatrix	add(AbstractComplexSquareMatrix m) Returns the addition of this matrix and another.
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.
AbstractComplexMatrix	hermitianAdjoint() Returns the hermitian adjoint of this matrix.
AbstractDoubleMatrix	imag() Returns the imaginary part of this complex matrix.
AbstractComplexSquareMatrix	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.
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.
AbelianGroup.Member	negate() Returns the negative of this matrix.
double	norm() Returns the C* norm.
double	operatorNorm() Returns the operator norm.
AbstractComplexSquareMatrix[]	polarDecompose() Returns the polar decomposition 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.
Complex	scalarProduct(AbstractComplexMatrix m) Returns the scalar product of this matrix and another.
Complex	scalarProduct(AbstractComplexSquareMatrix m) Returns the scalar product of this matrix and another.
AbstractComplexMatrix	subtract(AbstractComplexMatrix m) Returns the subtraction of this matrix and another.
AbstractComplexSquareMatrix	subtract(AbstractComplexSquareMatrix m) Returns the subtraction of this matrix by another.
AbstractComplexSquareMatrix	tensor(AbstractComplexSquareMatrix m) Returns the tensor product of this matrix and another.
Complex	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class jsci.maths.matrices.AbstractComplexMatrix

add, directSum, equals, equals, equals, frobeniusNorm, getElement, getImagElement, getRealElement, getSet, hashCode, infNorm, multiply, multiply, multiply, scalarDivide, scalarMultiply, setElement, setElement, 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

Method Detail

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

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.

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 final AbstractComplexMatrix add(AbstractComplexMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class AbstractComplexMatrix

Parameters:

m - a complex square matrix

Throws:

MatrixDimensionException - If the matrices are not square or different sizes.

add

public AbstractComplexSquareMatrix add(AbstractComplexSquareMatrix 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 final AbstractComplexMatrix subtract(AbstractComplexMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class AbstractComplexMatrix

Parameters:

m - a complex square matrix

Throws:

MatrixDimensionException - If the matrices are not square or different sizes.

subtract

public AbstractComplexSquareMatrix subtract(AbstractComplexSquareMatrix 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 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 square 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 square 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 square 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 square matrix

scalarProduct

public final Complex scalarProduct(AbstractComplexMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class AbstractComplexMatrix

Parameters:

m - a Complex square matrix.

Throws:

MatrixDimensionException - If the matrices are not square or different sizes.

scalarProduct

public Complex scalarProduct(AbstractComplexSquareMatrix m)

Returns the scalar product of this matrix and another.

Parameters:

m - a complex square matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public AbstractComplexSquareMatrix multiply(AbstractComplexSquareMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex square matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are incompatible.

directSum

public AbstractComplexSquareMatrix directSum(AbstractComplexSquareMatrix m)

Returns the direct sum of this matrix and another.

tensor

public AbstractComplexSquareMatrix tensor(AbstractComplexSquareMatrix m)

Returns the tensor product of this matrix and another.

involution

public final CStarAlgebra.Member involution()

Returns the involution of this matrix.

Specified by:

involution in interface CStarAlgebra.Member

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class AbstractComplexMatrix

Returns:

a complex square matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class AbstractComplexMatrix

Returns:

a complex square matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractComplexMatrix

Returns:

a complex square matrix

inverse

public AbstractComplexSquareMatrix inverse()

Returns the inverse of this matrix.

Returns:

a complex square matrix

luDecompose

public AbstractComplexSquareMatrix[] 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.

luDecompose

public AbstractComplexSquareMatrix[] luDecompose()

Returns the LU decomposition of this matrix. Warning: no pivoting.

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.

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 square matrix