org.jscience.mathematics.algebraic.matrices
Class AbstractComplexMatrix

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

All Implemented Interfaces:

java.io.Serializable, Algebra.Member, Ring.Member, AbelianGroup.Member, Hypermatrix, Matrix, Module.Member, VectorSpace.Member, Member

Direct Known Subclasses:

AbstractComplexSquareMatrix, ComplexMatrix, ComplexSparseMatrix

public abstract class AbstractComplexMatrix
extends AbstractMatrix

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

See Also:

Serialized Form

Constructor Summary

protected

AbstractComplexMatrix(int rows, int cols) Constructs a matrix.

Method Summary

AbstractDoubleMatrix	abs() Applies the abs function on all the matrix components.
AbelianGroup.Member	add(AbelianGroup.Member m) Returns the addition of this matrix and another.
AbstractComplexMatrix	add(AbstractComplexMatrix m) Returns the addition of this matrix and another.
AbstractComplexMatrix	conjugate() Returns the complex conjugate of this matrix.
AbstractComplexMatrix	directSum(AbstractComplexMatrix m) Returns the direct sum of this matrix and another.
boolean	equals(AbstractComplexMatrix m) Compares two complex matrices for equality.
boolean	equals(AbstractComplexMatrix m, double tol)
boolean	equals(java.lang.Object obj) Compares two complex matrices for equality.
double	frobeniusNorm() Returns the Frobenius or Hilbert-Schmidt (l2) norm.
AbstractComplexVector	getColumn(int j) Returns the ith column.
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.
Complex[]	getMatrixAsColumns() Make a one-dimensional column packed copy of the internal array.
Complex[]	getMatrixAsRows() Make a one-dimensional row packed copy of the internal array.
abstract Complex	getPrimitiveElement(int i, int j) Returns an element of the matrix.
double	getRealElement(int i, int j) Returns the real part of an element of the matrix.
AbstractComplexVector	getRow(int i) Returns the ith row.
java.lang.Object	getSet()
AbstractComplexMatrix	getSubMatrix(int k1, int k2, int k3, int k4) Computes a sub matrix from the parameters index.
int	hashCode() Returns a hashcode for this NON EMPTY matrix.
AbstractComplexMatrix	hermitianAdjoint() Returns the hermitian adjoint of this matrix.
AbstractComplexMatrix	horizontalAxisSymmetry() Invert matrix elements order from the top to the bottom.
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.
Complex	mass() Gets the mass of the matrix components.
AbstractComplexMatrix	multiply(AbstractComplexMatrix m) Returns the multiplication of this matrix and another.
AbstractComplexVector	multiply(AbstractComplexVector v) Returns the multiplication of a vector by this matrix.
Ring.Member	multiply(Ring.Member m) Returns the multiplication of this matrix and another.
AbelianGroup.Member	negate() Returns the negative of this matrix.
static AbstractComplexMatrix	read(java.io.BufferedReader input) Read a matrix from a stream.
AbstractDoubleMatrix	real() Returns the real part of this complex matrix.
AbstractComplexMatrix	reverse() Invert matrix elements order from the top to the bottom, from the right to the left.
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.
VectorSpace.Member	scalarDivide(Field.Member 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.
Module.Member	scalarMultiply(Ring.Member x) Returns the multiplication of this matrix by a scalar.
Complex	scalarProduct(AbstractComplexMatrix m) Returns the scalar product of this matrix and another.
void	setAllElements(Complex m) Sets the value of all elements of the matrix.
void	setColumn(int j, AbstractComplexVector v) Returns the ith column.
abstract 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.
void	setRow(int i, AbstractComplexVector v) Returns the ith row.
AbstractComplexMatrix	setSubMatrix(int k, int l, AbstractComplexMatrix m) Set a sub matrix.
AbelianGroup.Member	subtract(AbelianGroup.Member m) Returns the subtraction of this matrix by another.
AbstractComplexMatrix	subtract(AbstractComplexMatrix m) Returns the subtraction of this matrix by another.
AbstractComplexMatrix	tensorProduct(AbstractComplexMatrix m) Returns the tensor product of this matrix and another.
Complex[][]	toPrimitiveArray() Projects the matrix to an array.
java.lang.String	toString() Returns a string representing this matrix.
Matrix	transpose() Returns the transpose of this matrix.
AbstractComplexMatrix	verticalAxisSymmetry() Invert matrix elements order from the right to the left.

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

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

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

getDimensions, numDimensions, numElements, numElements, toArray

Constructor Detail

AbstractComplexMatrix

protected AbstractComplexMatrix(int rows,
                                int cols)

Constructs a matrix.

Method Detail

equals

public boolean equals(java.lang.Object obj)

Compares two complex matrices for equality.

Overrides:

equals in class java.lang.Object

Parameters:

obj - a complex matrix

equals

public boolean equals(AbstractComplexMatrix m)

Compares two complex matrices for equality. Two matrices are considered to be equal if the Frobenius norm of their difference is within the zero tolerance.

Parameters:

m - a complex matrix

equals

public boolean equals(AbstractComplexMatrix m,
                      double tol)

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class java.lang.Object

hashCode

public int hashCode()

Returns a hashcode for this NON EMPTY matrix.

Overrides:

hashCode in class java.lang.Object

real

public AbstractDoubleMatrix real()

Returns the real part of this complex matrix.

Returns:

a double matrix

imag

public AbstractDoubleMatrix imag()

Returns the imaginary part of this complex matrix.

Returns:

a double matrix

getPrimitiveElement

public abstract Complex getPrimitiveElement(int i,
                                            int j)

Returns an element of the matrix.

Parameters:

i - row index of the element

j - column index of the element

Throws:

IllegalDimensionException - If attempting to access an invalid element.

getElement

public Complex getElement(int i,
                          int j)

Returns an element of the matrix.

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)

Returns the real part of an element of the matrix.

Parameters:

i - row index of the element

j - column index of the element

Throws:

IllegalDimensionException - If attempting to access an invalid element.

getImagElement

public double getImagElement(int i,
                             int j)

Returns the imag part of an element of the matrix.

Parameters:

i - row index of the element

j - column index of the element

Throws:

IllegalDimensionException - If attempting to access an invalid element.

getRow

public AbstractComplexVector getRow(int i)

Returns the ith row.

Parameters:

i - DOCUMENT ME!

Returns:

DOCUMENT ME!

getColumn

public AbstractComplexVector getColumn(int j)

Returns the ith column.

Parameters:

j - DOCUMENT ME!

Returns:

DOCUMENT ME!

setRow

public void setRow(int i,
                   AbstractComplexVector v)

Returns the ith row.

setColumn

public void setColumn(int j,
                      AbstractComplexVector v)

Returns the ith column.

setElement

public abstract 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.

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.

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 m)

Sets the value of all elements of the matrix.

Parameters:

m - a complex element

getSet

public final java.lang.Object getSet()

infNorm

public double infNorm()

Returns the l-norm.

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius or Hilbert-Schmidt (l²) norm.

abs

public AbstractDoubleMatrix abs()

Applies the abs function on all the matrix components.

mass

public Complex mass()

Gets the mass of the matrix components.

Returns:

the mass.

negate

public AbelianGroup.Member negate()

Returns the negative of this matrix.

Returns:

DOCUMENT ME!

add

public final AbelianGroup.Member add(AbelianGroup.Member m)

Returns the addition of this matrix and another.

Parameters:

m - a group member

Returns:

DOCUMENT ME!

add

public AbstractComplexMatrix add(AbstractComplexMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a complex matrix

Throws:

IllegalDimensionException - If the matrices are different sizes.

subtract

public final AbelianGroup.Member subtract(AbelianGroup.Member m)

Returns the subtraction of this matrix by another.

Parameters:

m - a group member

Returns:

DOCUMENT ME!

subtract

public AbstractComplexMatrix subtract(AbstractComplexMatrix m)

Returns the subtraction of this matrix by another.

Parameters:

m - a complex matrix

Throws:

IllegalDimensionException - If the matrices are different sizes.

scalarMultiply

public final Module.Member scalarMultiply(Ring.Member x)

Returns the multiplication of this matrix by a scalar.

Parameters:

x - a ring member

Returns:

DOCUMENT ME!

scalarMultiply

public AbstractComplexMatrix scalarMultiply(Complex z)

Returns the multiplication of this matrix by a scalar.

Parameters:

z - a complex number

Returns:

a complex matrix

scalarMultiply

public AbstractComplexMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Parameters:

x - a double

Returns:

a complex matrix

scalarDivide

public final VectorSpace.Member scalarDivide(Field.Member x)

Returns the division of this matrix by a scalar.

Parameters:

x - a field member

Returns:

DOCUMENT ME!

scalarDivide

public AbstractComplexMatrix scalarDivide(Complex z)

Returns the division of this matrix by a scalar.

Parameters:

z - a complex number

Returns:

a complex matrix

scalarDivide

public AbstractComplexMatrix scalarDivide(double x)

Returns the division of this matrix by a scalar.

Parameters:

x - a double

Returns:

a complex matrix

scalarProduct

public Complex scalarProduct(AbstractComplexMatrix m)

Returns the scalar product of this matrix and another.

Parameters:

m - a complex matrix.

Throws:

IllegalDimensionException - If the matrices are different sizes.

multiply

public AbstractComplexVector multiply(AbstractComplexVector v)

Returns the multiplication of a vector by this matrix.

Parameters:

v - a complex vector

Throws:

IllegalDimensionException - If the matrix and vector are incompatible.

multiply

public final Ring.Member multiply(Ring.Member m)

Returns the multiplication of this matrix and another.

Parameters:

m - a ring member

Returns:

DOCUMENT ME!

multiply

public AbstractComplexMatrix multiply(AbstractComplexMatrix m)

Returns the multiplication of this matrix and another.

Parameters:

m - a complex matrix

Returns:

an AbstractComplexMatrix or an AbstractComplexSquareMatrix as appropriate

Throws:

IllegalDimensionException - If the matrices are incompatible.

directSum

public AbstractComplexMatrix directSum(AbstractComplexMatrix m)

Returns the direct sum of this matrix and another.

tensorProduct

public AbstractComplexMatrix tensorProduct(AbstractComplexMatrix m)

Returns the tensor product of this matrix and another.

hermitianAdjoint

public AbstractComplexMatrix hermitianAdjoint()

Returns the hermitian adjoint of this matrix.

Returns:

a complex matrix

conjugate

public AbstractComplexMatrix conjugate()

Returns the complex conjugate of this matrix.

Returns:

a complex matrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Returns:

a complex matrix

horizontalAxisSymmetry

public AbstractComplexMatrix horizontalAxisSymmetry()

Invert matrix elements order from the top to the bottom.

verticalAxisSymmetry

public AbstractComplexMatrix verticalAxisSymmetry()

Invert matrix elements order from the right to the left.

reverse

public AbstractComplexMatrix reverse()

Invert matrix elements order from the top to the bottom, from the right to the left.

getSubMatrix

public AbstractComplexMatrix getSubMatrix(int k1,
                                          int k2,
                                          int k3,
                                          int k4)

Computes a sub matrix from the parameters index. If k1<0 k1 elements are added at the beginning of the returned matrix If k2>numRows() k2-numRows() elements are added at the end of the returned matrix Finally, if k1>k2 the vector is returned inverted. If k3<0 k3 elements are added at the beginning of the returned matrix If k4>numColumns() k2-numColumns() elements are added at the end of the returned matrix Finally, if k3>k4 the matrix is returned inverted.

Parameters:

k1 - the beginning rows index

k2 - the finishing rows index

k3 - the beginning columns index

k4 - the finishing columns index

Returns:

the sub matrix.

setSubMatrix

public AbstractComplexMatrix setSubMatrix(int k,
                                          int l,
                                          AbstractComplexMatrix m)

Set a sub matrix. If k<0 k elements are added at the beginning of the returned matrix If k+v.numRows()>numRows() k+v.numRows()-numRows() elements are added at the end of the returned matrix If l<0 l elements are added at the beginning of the returned matrix If l+v.numColumns()>numColumns() l+v.numColumns()-numColumns() elements are added at the end of the returned matrix

Parameters:

k - Initial row index to offset the patching matrix

l - Initial column index to offset the patching matrix

m - the patching matrix

mapElements

public AbstractComplexMatrix mapElements(ComplexMapping f)

Applies a function on all the matrix elements.

Parameters:

f - a user-defined function

Returns:

a complex matrix

toPrimitiveArray

public Complex[][] toPrimitiveArray()

Projects the matrix to an array.

Returns:

an Complex array.

getMatrixAsRows

public Complex[] getMatrixAsRows()

Make a one-dimensional row packed copy of the internal array. Useful to iterate over the elements with an org.jscience.util.ArrayIterator

Returns:

Matrix elements packed in a one-dimensional array by rows.

getMatrixAsColumns

public Complex[] getMatrixAsColumns()

Make a one-dimensional column packed copy of the internal array. Useful to iterate over the elements with an org.jscience.util.ArrayIterator

Returns:

Matrix elements packed in a one-dimensional array by columns.

read

public static AbstractComplexMatrix read(java.io.BufferedReader input)
                                  throws java.io.IOException

Read a matrix from a stream. The format is the same the print method, so printed matrices can be read back in (provided they were printed using US Locale). Elements are separated by whitespace, all the elements for each row appear on a single line, the last row is followed by a blank line.

Parameters:

input - the input stream.

Throws:

java.io.IOException