org.jscience.mathematics.algebraic.matrices
Class ComplexTridiagonalMatrix

java.lang.Object
  org.jscience.mathematics.algebraic.AbstractHypermatrix
      org.jscience.mathematics.algebraic.AbstractMatrix
          org.jscience.mathematics.algebraic.matrices.AbstractComplexMatrix
              org.jscience.mathematics.algebraic.matrices.AbstractComplexSquareMatrix
                  org.jscience.mathematics.algebraic.matrices.ComplexTridiagonalMatrix

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, BandedMatrix, Ring.Member, AbelianGroup.Member, Hypermatrix, Matrix, Module.Member, VectorSpace.Member, SquareMatrix, TridiagonalMatrix, Member

public class ComplexTridiagonalMatrix
extends AbstractComplexSquareMatrix
implements java.lang.Cloneable, java.io.Serializable, 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 DOCUMENT ME!
protected double[]	diagRe DOCUMENT ME!
protected double[]	ldiagIm Tridiagonal data.
protected double[]	ldiagRe Tridiagonal data.
protected double[]	udiagIm DOCUMENT ME!
protected double[]	udiagRe DOCUMENT ME!

Fields inherited from class org.jscience.mathematics.algebraic.matrices.AbstractComplexSquareMatrix

LU, LUpivot

Constructor Summary

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

ComplexTridiagonalMatrix(ComplexTridiagonalMatrix mat)
Copy constructor.

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) DOCUMENT ME!
ComplexTridiagonalMatrix	add(ComplexTridiagonalMatrix m) DOCUMENT ME!
java.lang.Object	clone() Clone matrix into a new matrix.
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.
double	getImagElement(int i, int j) DOCUMENT ME!
int	getK1() DOCUMENT ME!
int	getK2() DOCUMENT ME!
Complex	getPrimitiveElement(int i, int j) Returns an element of the matrix.
double	getRealElement(int i, int j) DOCUMENT ME!
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.
boolean	isSymmetric() Returns true if this matrix is symmetric.
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.
AbstractComplexVector	multiply(AbstractComplexVector v) Returns the multiplication of a vector by this matrix.
ComplexSquareMatrix	multiply(ComplexSquareMatrix m) DOCUMENT ME!
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	setAllElements(Complex r) Sets the value of all elements of the matrix.
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) DOCUMENT ME!
ComplexTridiagonalMatrix	subtract(ComplexTridiagonalMatrix m) Returns the subtraction of this matrix and another.
Complex[][]	toPrimitiveArray() Projects the matrix to an array.
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 org.jscience.mathematics.algebraic.matrices.AbstractComplexSquareMatrix

add, det, directSum, inverse, involution, isHermitian, isUnitary, negate, norm, polarDecompose, scalarDivide, scalarDivide, scalarProduct, scalarProduct, subtract, tensorProduct

Methods inherited from class org.jscience.mathematics.algebraic.matrices.AbstractComplexMatrix

abs, add, directSum, equals, equals, getColumn, getElement, getMatrixAsColumns, getMatrixAsRows, getRow, getSet, getSubMatrix, hashCode, horizontalAxisSymmetry, mass, multiply, multiply, read, reverse, scalarDivide, scalarMultiply, setColumn, setRow, setSubMatrix, subtract, tensorProduct, verticalAxisSymmetry

Methods inherited from class org.jscience.mathematics.algebraic.AbstractMatrix

getElement, getInvalidElementMsg, numColumns, numRows, print, print, print, print, toArray, toArray

Methods inherited from class org.jscience.mathematics.algebraic.AbstractHypermatrix

getDimensions, numDimensions, numElements, numElements, toArray

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.jscience.mathematics.algebraic.Matrix

getColumn, getElement, getRow, numColumns, numRows, toArray

Methods inherited from interface org.jscience.mathematics.algebraic.Hypermatrix

getDimensions, getElement, numDimensions, numElements, numElements, toArray, toArray

Methods inherited from interface org.jscience.mathematics.algebraic.fields.Ring.Member

multiply

Methods inherited from interface org.jscience.mathematics.algebraic.modules.VectorSpace.Member

scalarDivide

Methods inherited from interface org.jscience.mathematics.algebraic.modules.Module.Member

scalarMultiply

Field Detail

ldiagRe

protected final double[] ldiagRe

Tridiagonal data.

ldiagIm

protected final double[] ldiagIm

Tridiagonal data.

diagRe

protected final double[] diagRe

DOCUMENT ME!

diagIm

protected final double[] diagIm

DOCUMENT ME!

udiagRe

protected final double[] udiagRe

DOCUMENT ME!

udiagIm

protected final double[] udiagIm

DOCUMENT ME!

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:

IllegalDimensionException - If the array is not square.

ComplexTridiagonalMatrix

public ComplexTridiagonalMatrix(ComplexTridiagonalMatrix mat)

Copy constructor.

Parameters:

mat - 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

tol - DOCUMENT ME!

Returns:

DOCUMENT ME!

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class AbstractComplexMatrix

Returns:

DOCUMENT ME!

getK1

public int getK1()

DOCUMENT ME!

Specified by:

getK1 in interface BandedMatrix

Returns:

DOCUMENT ME!

getK2

public int getK2()

DOCUMENT ME!

Specified by:

getK2 in interface BandedMatrix

Returns:

DOCUMENT ME!

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

getPrimitiveElement

public Complex getPrimitiveElement(int i,
                                   int j)

Returns an element of the matrix.

Specified by:

getPrimitiveElement in class AbstractComplexMatrix

Parameters:

i - row index of the element

j - column index of the element

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If attempting to access an invalid element.

getRealElement

public double getRealElement(int i,
                             int j)

DOCUMENT ME!

Overrides:

getRealElement in class AbstractComplexMatrix

Parameters:

i - DOCUMENT ME!

j - DOCUMENT ME!

Returns:

DOCUMENT ME!

getImagElement

public double getImagElement(int i,
                             int j)

DOCUMENT ME!

Overrides:

getImagElement in class AbstractComplexMatrix

Parameters:

i - DOCUMENT ME!

j - DOCUMENT ME!

Returns:

DOCUMENT ME!

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:

IllegalDimensionException - 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.

Overrides:

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:

IllegalDimensionException - If attempting to access an invalid element.

setAllElements

public void setAllElements(Complex r)

Sets the value of all elements of the matrix. This method will throw an error unless the paramter is Complex.ZERO. This is because you need a SquareMatrix to set all the contents of the matrix to a value. You should think about using a ComplexSquareMatrix.

Overrides:

setAllElements in class AbstractComplexMatrix

Parameters:

r - a Complex element

Throws:

java.lang.IllegalArgumentException - DOCUMENT ME!

isSymmetric

public boolean isSymmetric()

Returns true if this matrix is symmetric.

Specified by:

isSymmetric in interface SquareMatrix

Overrides:

isSymmetric in class AbstractComplexSquareMatrix

Returns:

DOCUMENT ME!

trace

public Complex trace()

Returns the trace.

Overrides:

trace in class AbstractComplexSquareMatrix

Returns:

DOCUMENT ME!

Throws:

java.lang.ArithmeticException - DOCUMENT ME!

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractComplexMatrix

Returns:

DOCUMENT ME!

Throws:

java.lang.ArithmeticException - DOCUMENT ME!

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class AbstractComplexMatrix

Returns:

DOCUMENT ME!

Throws:

java.lang.ArithmeticException - DOCUMENT ME!

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

Overrides:

operatorNorm in class AbstractComplexSquareMatrix

Returns:

DOCUMENT ME!

Throws:

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

java.lang.ArithmeticException - DOCUMENT ME!

add

public AbstractComplexSquareMatrix add(AbstractComplexSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class AbstractComplexSquareMatrix

Parameters:

m - a complex matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

add

public ComplexSquareMatrix add(ComplexSquareMatrix m)

DOCUMENT ME!

Parameters:

m - DOCUMENT ME!

Returns:

DOCUMENT ME!

add

public ComplexTridiagonalMatrix add(ComplexTridiagonalMatrix m)

DOCUMENT ME!

Parameters:

m - DOCUMENT ME!

Returns:

DOCUMENT ME!

subtract

public AbstractComplexSquareMatrix subtract(AbstractComplexSquareMatrix m)

Returns the subtraction of this matrix and another.

Overrides:

subtract in class AbstractComplexSquareMatrix

Parameters:

m - a complex matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

subtract

public ComplexSquareMatrix subtract(ComplexSquareMatrix m)

DOCUMENT ME!

Parameters:

m - DOCUMENT ME!

Returns:

DOCUMENT ME!

subtract

public ComplexTridiagonalMatrix subtract(ComplexTridiagonalMatrix m)

Returns the subtraction of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - 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

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - 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:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

multiply

public ComplexSquareMatrix multiply(ComplexSquareMatrix m)

DOCUMENT ME!

Parameters:

m - DOCUMENT ME!

Returns:

DOCUMENT ME!

multiply

public ComplexSquareMatrix multiply(ComplexTridiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - 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.

Specified by:

transpose in interface Matrix

Overrides:

transpose in class AbstractComplexSquareMatrix

Returns:

a complex tridiagonal matrix

luDecompose

public AbstractComplexSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class AbstractComplexSquareMatrix

Parameters:

pivot - DOCUMENT ME!

Returns:

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

clone

public java.lang.Object clone()

Clone matrix into a new matrix.

Overrides:

clone in class java.lang.Object

Returns:

the cloned matrix.

toPrimitiveArray

public Complex[][] toPrimitiveArray()

Projects the matrix to an array.

Overrides:

toPrimitiveArray in class AbstractComplexMatrix

Returns:

an double array.