org.jscience.mathematics.algebraic.matrices
Class ComplexDiagonalMatrix

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.ComplexDiagonalMatrix

All Implemented Interfaces:

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

public class ComplexDiagonalMatrix
extends AbstractComplexSquareMatrix
implements java.lang.Cloneable, java.io.Serializable, DiagonalMatrix

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

See Also:

Serialized Form

Field Summary

protected double[]	diagIm Arrays containing the elements of the matrix.
protected double[]	diagRe Arrays containing the elements of the matrix.

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

LU, LUpivot

Constructor Summary

ComplexDiagonalMatrix(Complex[] array)
Constructs a matrix from an array containing the diagonal elements.

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

ComplexDiagonalMatrix(ComplexDiagonalMatrix mat)
Copy constructor.

ComplexDiagonalMatrix(double[] arrayRe, double[] arrayIm)
Constructs a matrix by wrapping two arrays containing the diagonal elements.

ComplexDiagonalMatrix(int size)
Constructs an empty matrix.

Method Summary

AbstractComplexSquareMatrix	add(AbstractComplexSquareMatrix m) Returns the addition of this matrix and another.
ComplexDiagonalMatrix	add(ComplexDiagonalMatrix m) Returns the addition of this matrix and another.
ComplexSquareMatrix	add(ComplexSquareMatrix m) DOCUMENT ME!
ComplexTridiagonalMatrix	add(ComplexTridiagonalMatrix m) Returns the addition of this matrix and another.
java.lang.Object	clone() Clone matrix into a new matrix.
AbstractComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
Complex	det() Returns the determinant.
boolean	equals(AbstractComplexMatrix m, double tol) Compares two complex diagonal 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.
static ComplexDiagonalMatrix	identity(int size) Creates an identity matrix.
AbstractDoubleMatrix	imag() Returns the imaginary part of this complex matrix.
double	infNorm() Returns the l-norm.
AbstractComplexSquareMatrix	inverse() Returns the inverse of this matrix.
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.
ComplexDiagonalMatrix	multiply(ComplexDiagonalMatrix m) Returns the multiplication of this matrix and another.
ComplexSquareMatrix	multiply(ComplexSquareMatrix m) Returns the multiplication of this matrix and another.
ComplexTridiagonalMatrix	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 by another.
ComplexDiagonalMatrix	subtract(ComplexDiagonalMatrix m) Returns the subtraction of this matrix by another.
ComplexSquareMatrix	subtract(ComplexSquareMatrix m) DOCUMENT ME!
ComplexTridiagonalMatrix	subtract(ComplexTridiagonalMatrix m) DOCUMENT ME!
Complex[][]	toPrimitiveArray() Projects the matrix to an array.
Complex	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

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

add, directSum, 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, toString, 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

diagRe

protected final double[] diagRe

Arrays containing the elements of the matrix.

diagIm

protected final double[] diagIm

Arrays containing the elements of the matrix.

Constructor Detail

ComplexDiagonalMatrix

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

Constructs a matrix by wrapping two arrays containing the diagonal elements.

Parameters:

arrayRe - an array of real values

arrayIm - an array of imaginary values

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(Complex[][] array)

Constructs a matrix from an array.

Parameters:

array - an assigned value

Throws:

IllegalDimensionException - If the array is not square.

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(Complex[] array)

Constructs a matrix from an array containing the diagonal elements.

Parameters:

array - an assigned value

ComplexDiagonalMatrix

public ComplexDiagonalMatrix(ComplexDiagonalMatrix mat)

Copy constructor.

Parameters:

mat - an assigned value

Method Detail

identity

public static ComplexDiagonalMatrix identity(int size)

Creates an identity matrix.

Parameters:

size - the number of rows/columns

Returns:

DOCUMENT ME!

equals

public boolean equals(AbstractComplexMatrix m,
                      double tol)

Compares two complex diagonal matrices for equality.

Overrides:

equals in class AbstractComplexMatrix

Parameters:

m - a complex diagonal matrix

tol - DOCUMENT ME!

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 diagonal matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Overrides:

imag in class AbstractComplexSquareMatrix

Returns:

a double diagonal 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!

det

public Complex det()

Returns the determinant.

Overrides:

det in class AbstractComplexSquareMatrix

Returns:

DOCUMENT ME!

Throws:

java.lang.ArithmeticException - 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()

Returns the operator norm.

Overrides:

operatorNorm in class AbstractComplexSquareMatrix

Returns:

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)

Returns the addition of this matrix and another.

Parameters:

m - a complex tridiagonal matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

add

public ComplexDiagonalMatrix add(ComplexDiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a complex diagonal matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

subtract

public AbstractComplexSquareMatrix subtract(AbstractComplexSquareMatrix m)

Returns the subtraction of this matrix by 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)

DOCUMENT ME!

Parameters:

m - DOCUMENT ME!

Returns:

DOCUMENT ME!

subtract

public ComplexDiagonalMatrix subtract(ComplexDiagonalMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - a complex diagonal 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 diagonal 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 diagonal 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)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex square matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

multiply

public ComplexTridiagonalMatrix 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.

multiply

public ComplexDiagonalMatrix multiply(ComplexDiagonalMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex diagonal matrix

Returns:

DOCUMENT ME!

Throws:

IllegalDimensionException - If the matrices are different sizes.

inverse

public AbstractComplexSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class AbstractComplexSquareMatrix

Returns:

a complex diagonal matrix

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Overrides:

hermitianAdjoint in class AbstractComplexSquareMatrix

Returns:

a complex diagonal matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Overrides:

conjugate in class AbstractComplexSquareMatrix

Returns:

a complex diagonal 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 diagonal 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 Complex array.