JSci.maths.matrices
Class ComplexTridiagonalMatrix

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

All Implemented Interfaces:

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

public class ComplexTridiagonalMatrix
extends AbstractComplexSquareMatrix
implements TridiagonalMatrix

The ComplexTridiagonalMatrix class provides an object for encapsulating tridiagonal matrices containing complex numbers. Uses compressed diagonal storage.

See Also:

Serialized Form

Field Summary

protected double[]	diagIm
protected double[]	diagRe
protected double[]	ldiagIm Tridiagonal data.
protected double[]	ldiagRe Tridiagonal data.
protected double[]	udiagIm
protected double[]	udiagRe

Fields inherited from class JSci.maths.matrices.AbstractComplexSquareMatrix

luCache

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

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

ComplexTridiagonalMatrix(int size)
Constructs an empty matrix.

Method Summary

AbstractComplexSquareMatrix	add(AbstractComplexSquareMatrix m) Returns the addition of this matrix and another.
ComplexSquareMatrix	add(ComplexSquareMatrix m)
ComplexTridiagonalMatrix	add(ComplexTridiagonalMatrix m)
AbstractComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
boolean	equals(AbstractComplexMatrix m, double tol) Compares two complex matrices for equality.
double	frobeniusNorm() Returns the Frobenius (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.
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)
ComplexSquareMatrix	multiply(ComplexTridiagonalMatrix m) Returns the multiplication of this matrix and another.
double	operatorNorm() Returns the operator norm.
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 and another.
ComplexSquareMatrix	subtract(ComplexSquareMatrix m)
ComplexTridiagonalMatrix	subtract(ComplexTridiagonalMatrix m) Returns the subtraction 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, det, directSum, inverse, involution, isHermitian, isUnitary, luDecompose_cache, luDecompose, luDecompose, negate, norm, polarDecompose, scalarDivide, scalarDivide, scalarProduct, scalarProduct, subtract, tensor

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, getInvalidElementMsg, rows

Methods inherited from class java.lang.Object

clone, finalize, 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

ldiagRe

protected final double[] ldiagRe

Tridiagonal data.

ldiagIm

protected final double[] ldiagIm

Tridiagonal data.

diagRe

protected final double[] diagRe

diagIm

protected final double[] diagIm

udiagRe

protected final double[] udiagRe

udiagIm

protected final double[] udiagIm

Constructor Detail

ComplexTridiagonalMatrix

public ComplexTridiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

ComplexTridiagonalMatrix

public ComplexTridiagonalMatrix(Complex[][] array)

Constructs a matrix from an array. Any non-tridiagonal elements in the array are ignored.

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 tridiagonal matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class AbstractComplexSquareMatrix

Returns:

a double tridiagonal 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.

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class AbstractComplexSquareMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractComplexMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class AbstractComplexMatrix

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

Overrides:

operatorNorm in class AbstractComplexSquareMatrix

Throws:

MaximumIterationsExceededException - If it takes more than 50 iterations to determine an eigenvalue.

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)

add

public ComplexTridiagonalMatrix add(ComplexTridiagonalMatrix m)

subtract

public AbstractComplexSquareMatrix subtract(AbstractComplexSquareMatrix m)

Returns the subtraction of this matrix and 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)

subtract

public ComplexTridiagonalMatrix subtract(ComplexTridiagonalMatrix m)

Returns the subtraction of this matrix and another.

Parameters:

m - a complex tridiagonal 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 AbstractComplexSquareMatrix

Parameters:

z - a complex number

Returns:

a complex tridiagonal 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 tridiagonal 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 matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are different sizes.

multiply

public ComplexSquareMatrix multiply(ComplexSquareMatrix m)

multiply

public ComplexSquareMatrix multiply(ComplexTridiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class AbstractComplexSquareMatrix

Returns:

a complex tridiagonal matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class AbstractComplexSquareMatrix

Returns:

a complex tridiagonal matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractComplexSquareMatrix

Returns:

a complex tridiagonal matrix

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 tridiagonal matrix