JSci.maths.matrices
Class ComplexDiagonalMatrix

java.lang.Object
  extended byJSci.maths.matrices.Matrix
      extended byJSci.maths.matrices.AbstractComplexMatrix
          extended byJSci.maths.matrices.AbstractComplexSquareMatrix
              extended byJSci.maths.matrices.ComplexDiagonalMatrix
All Implemented Interfaces:
AbelianGroup.Member, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, DiagonalMatrix, Member, Module.Member, Ring.Member, java.io.Serializable, SquareMatrix, TridiagonalMatrix, VectorSpace.Member

public class ComplexDiagonalMatrix
extends AbstractComplexSquareMatrix
implements 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 JSci.maths.matrices.AbstractComplexSquareMatrix
LU, LUpivot
 
Fields inherited from class JSci.maths.matrices.Matrix
numCols, numRows
 
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(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)
           
 ComplexTridiagonalMatrix add(ComplexTridiagonalMatrix m)
          Returns the addition of this matrix and another.
 AbstractComplexMatrix conjugate()
          Returns the complex conjugate of this matrix.
 Complex det()
          Returns the determinant.
 boolean equals(AbstractComplexMatrix m)
          Compares two complex diagonal 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.
static ComplexDiagonalMatrix identity(int size)
          Creates an identity matrix.
 AbstractDoubleMatrix imag()
          Returns the imaginary part of this complex matrix.
 double infNorm()
          Returns the linfinity-norm.
 AbstractComplexSquareMatrix inverse()
          Returns the inverse 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.
 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 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)
           
 ComplexTridiagonalMatrix subtract(ComplexTridiagonalMatrix m)
           
 Complex trace()
          Returns the trace.
 Matrix transpose()
          Returns the transpose of this matrix.
 
Methods inherited from class JSci.maths.matrices.AbstractComplexSquareMatrix
add, directSum, involution, isHermitian, isUnitary, negate, norm, polarDecompose, scalarDivide, scalarDivide, scalarProduct, scalarProduct, subtract, tensor
 
Methods inherited from class JSci.maths.matrices.AbstractComplexMatrix
add, directSum, equals, hashCode, multiply, multiply, scalarDivide, scalarMultiply, subtract, tensor, toString
 
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.algebras.VectorSpace.Member
scalarDivide
 
Methods inherited from interface JSci.maths.algebras.Module.Member
scalarMultiply
 
Methods inherited from interface JSci.maths.groups.AbelianGroup.Member
add, subtract
 
Methods inherited from interface JSci.maths.fields.Ring.Member
multiply
 

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:
MatrixDimensionException - 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
Method Detail

identity

public static ComplexDiagonalMatrix identity(int size)
Creates an identity matrix.

Parameters:
size - the number of rows/columns

equals

public boolean equals(AbstractComplexMatrix m)
Compares two complex diagonal matrices for equality.

Overrides:
equals in class AbstractComplexMatrix
Parameters:
m - a complex diagonal matrix

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

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.

det

public Complex det()
Returns the determinant.

Overrides:
det in class AbstractComplexSquareMatrix

trace

public Complex trace()
Returns the trace.

Overrides:
trace in class AbstractComplexSquareMatrix

infNorm

public double infNorm()
Returns the linfinity-norm.

Overrides:
infNorm in class AbstractComplexMatrix

frobeniusNorm

public double frobeniusNorm()
Returns the Frobenius (l2) norm.

Overrides:
frobeniusNorm in class AbstractComplexMatrix

operatorNorm

public double operatorNorm()
Returns the operator norm.

Overrides:
operatorNorm in class AbstractComplexSquareMatrix

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)
Returns the addition of this matrix and another.

Parameters:
m - a complex tridiagonal matrix
Throws:
MatrixDimensionException - 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
Throws:
MatrixDimensionException - 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
Throws:
MatrixDimensionException - If the matrices are different sizes.

subtract

public ComplexSquareMatrix subtract(ComplexSquareMatrix m)

subtract

public ComplexTridiagonalMatrix subtract(ComplexTridiagonalMatrix m)

subtract

public ComplexDiagonalMatrix subtract(ComplexDiagonalMatrix m)
Returns the subtraction of this matrix by another.

Parameters:
m - a complex diagonal 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 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
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)
Returns the multiplication of this matrix and another.

Parameters:
m - a complex square matrix
Throws:
MatrixDimensionException - 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
Throws:
MatrixDimensionException - 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
Throws:
MatrixDimensionException - 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.

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
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 AbstractComplexSquareMatrix
Parameters:
f - a user-defined function
Returns:
a complex diagonal matrix