JSci.maths.matrices
Class DoubleSquareMatrix

java.lang.Object
  JSci.maths.matrices.Matrix
      JSci.maths.matrices.AbstractDoubleMatrix
          JSci.maths.matrices.AbstractDoubleSquareMatrix
              JSci.maths.matrices.DoubleSquareMatrix

All Implemented Interfaces:

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

public class DoubleSquareMatrix
extends AbstractDoubleSquareMatrix

The DoubleSquareMatrix class provides an object for encapsulating double square matrices.

See Also:

Serialized Form

Field Summary

protected double[][]

matrix Array containing the elements of the matrix.

Fields inherited from class JSci.maths.matrices.AbstractDoubleSquareMatrix

luCache

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

DoubleSquareMatrix(AbstractDoubleVector[] array)
Constructs a matrix from an array of vectors (columns).

DoubleSquareMatrix(double[][] array)
Constructs a matrix by wrapping an array.

DoubleSquareMatrix(int size)
Constructs an empty matrix.

Method Summary

AbstractDoubleSquareMatrix	add(AbstractDoubleSquareMatrix m) Returns the addition of this matrix and another.
DoubleSquareMatrix	add(DoubleSquareMatrix m)
AbstractDoubleSquareMatrix[]	choleskyDecompose() Returns the Cholesky decomposition of this matrix.
double	det() Returns the determinant.
AbstractDoubleSquareMatrix	directSum(AbstractDoubleSquareMatrix m) Returns the direct sum of this matrix and another.
boolean	equals(AbstractDoubleMatrix m, double tol) Compares two ${nativeTyp} matrices for equality.
double	frobeniusNorm() Returns the Frobenius or Hilbert-Schmidt (l2) norm.
double	getElement(int i, int j) Returns an element of the matrix.
double	infNorm() Returns the l-norm.
AbstractDoubleSquareMatrix	inverse() Returns the inverse of this matrix.
AbstractDoubleSquareMatrix[]	luDecompose() Returns the LU decomposition of this matrix.
AbstractDoubleSquareMatrix[]	luDecompose(int[] pivot) Returns the LU decomposition of this matrix.
AbstractDoubleMatrix	mapElements(Mapping f) Applies a function on all the matrix elements.
AbstractDoubleSquareMatrix	multiply(AbstractDoubleSquareMatrix m) Returns the multiplication of this matrix and another.
AbstractDoubleVector	multiply(AbstractDoubleVector v) Returns the multiplication of a vector by this matrix.
DoubleSquareMatrix	multiply(DoubleSquareMatrix m)
AbelianGroup.Member	negate() Returns the negative of this matrix.
AbstractDoubleSquareMatrix[]	polarDecompose() Returns the polar decomposition of this matrix.
AbstractDoubleSquareMatrix[]	qrDecompose() Returns the QR decomposition of this matrix.
AbstractDoubleMatrix	scalarDivide(double x) Returns the division of this matrix by a scalar.
AbstractDoubleMatrix	scalarMultiply(double x) Returns the multiplication of this matrix by a scalar.
double	scalarProduct(AbstractDoubleSquareMatrix m) Returns the scalar product of this matrix and another.
double	scalarProduct(DoubleSquareMatrix m)
void	setElement(int i, int j, double x) Sets the value of an element of the matrix.
AbstractDoubleSquareMatrix[]	singularValueDecompose() Returns the singular value decomposition of this matrix.
AbstractDoubleSquareMatrix	subtract(AbstractDoubleSquareMatrix m) Returns the subtraction of this matrix by another.
DoubleSquareMatrix	subtract(DoubleSquareMatrix m)
AbstractDoubleSquareMatrix	tensor(AbstractDoubleSquareMatrix m) Returns the tensor product of this matrix and another.
AbstractComplexMatrix	toComplexMatrix() Converts this matrix to a complex matrix.
AbstractIntegerMatrix	toIntegerMatrix() Converts this matrix to an integer matrix.
java.lang.String	toString() Returns a string representing this matrix.
double	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.matrices.AbstractDoubleSquareMatrix

add, isSymmetric, isUnitary, luDecompose_cache, operatorNorm, scalarProduct, subtract

Methods inherited from class JSci.maths.matrices.AbstractDoubleMatrix

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

Field Detail

matrix

protected final double[][] matrix

Array containing the elements of the matrix.

Constructor Detail

DoubleSquareMatrix

public DoubleSquareMatrix(double[][] array)

Constructs a matrix by wrapping an array.

Parameters:

array - an assigned value

DoubleSquareMatrix

public DoubleSquareMatrix(int size)

Constructs an empty matrix.

DoubleSquareMatrix

public DoubleSquareMatrix(AbstractDoubleVector[] array)

Constructs a matrix from an array of vectors (columns).

Parameters:

array - an assigned value

Method Detail

equals

public boolean equals(AbstractDoubleMatrix m,
                      double tol)

Compares two ${nativeTyp} matrices for equality.

Overrides:

equals in class AbstractDoubleMatrix

Parameters:

m - a double matrix

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class AbstractDoubleMatrix

toIntegerMatrix

public AbstractIntegerMatrix toIntegerMatrix()

Converts this matrix to an integer matrix.

Overrides:

toIntegerMatrix in class AbstractDoubleSquareMatrix

Returns:

an integer matrix

toComplexMatrix

public AbstractComplexMatrix toComplexMatrix()

Converts this matrix to a complex matrix.

Overrides:

toComplexMatrix in class AbstractDoubleSquareMatrix

Returns:

a complex matrix

getElement

public double getElement(int i,
                         int j)

Returns an element of the matrix.

Specified by:

getElement in class AbstractDoubleMatrix

Parameters:

i - row index of the element

j - column index of the element

Throws:

MatrixDimensionException - If attempting to access an invalid element.

setElement

public void setElement(int i,
                       int j,
                       double x)

Sets the value of an element of the matrix. Should only be used to initialise this matrix.

Specified by:

setElement in class AbstractDoubleMatrix

Parameters:

i - row index of the element

j - column index of the element

x - a number

Throws:

MatrixDimensionException - If attempting to access an invalid element.

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractDoubleMatrix

frobeniusNorm

public double frobeniusNorm()

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

Overrides:

frobeniusNorm in class AbstractDoubleMatrix

PlanetMath references:

FrobeniusMatrixNorm

det

public double det()

Returns the determinant.

Overrides:

det in class AbstractDoubleSquareMatrix

trace

public double trace()

Returns the trace.

Overrides:

trace in class AbstractDoubleSquareMatrix

negate

public AbelianGroup.Member negate()

Returns the negative of this matrix.

Specified by:

negate in interface AbelianGroup.Member

Overrides:

negate in class AbstractDoubleSquareMatrix

add

public AbstractDoubleSquareMatrix add(AbstractDoubleSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class AbstractDoubleSquareMatrix

Parameters:

m - a double matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public DoubleSquareMatrix add(DoubleSquareMatrix m)

subtract

public AbstractDoubleSquareMatrix subtract(AbstractDoubleSquareMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class AbstractDoubleSquareMatrix

Parameters:

m - a double matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public DoubleSquareMatrix subtract(DoubleSquareMatrix m)

scalarMultiply

public AbstractDoubleMatrix scalarMultiply(double x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class AbstractDoubleSquareMatrix

Parameters:

x - a double.

Returns:

a double square matrix.

scalarDivide

public AbstractDoubleMatrix scalarDivide(double x)

Returns the division of this matrix by a scalar.

Overrides:

scalarDivide in class AbstractDoubleSquareMatrix

Parameters:

x - a double.

Returns:

a double square matrix.

scalarProduct

public double scalarProduct(AbstractDoubleSquareMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class AbstractDoubleSquareMatrix

Parameters:

m - a double matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarProduct

public double scalarProduct(DoubleSquareMatrix m)

multiply

public AbstractDoubleVector multiply(AbstractDoubleVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class AbstractDoubleMatrix

Parameters:

v - a double vector.

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public AbstractDoubleSquareMatrix multiply(AbstractDoubleSquareMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class AbstractDoubleSquareMatrix

Parameters:

m - a double matrix

Returns:

a AbstractDoubleMatrix or a AbstractDoubleSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are incompatible.

multiply

public DoubleSquareMatrix multiply(DoubleSquareMatrix m)

directSum

public AbstractDoubleSquareMatrix directSum(AbstractDoubleSquareMatrix m)

Returns the direct sum of this matrix and another.

Overrides:

directSum in class AbstractDoubleSquareMatrix

tensor

public AbstractDoubleSquareMatrix tensor(AbstractDoubleSquareMatrix m)

Returns the tensor product of this matrix and another.

Overrides:

tensor in class AbstractDoubleSquareMatrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractDoubleSquareMatrix

Returns:

a double matrix

inverse

public AbstractDoubleSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class AbstractDoubleSquareMatrix

Returns:

a double square matrix.

luDecompose

public final AbstractDoubleSquareMatrix[] luDecompose(int[] pivot)

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class AbstractDoubleSquareMatrix

Parameters:

pivot - an empty array of length rows()+1 to hold the pivot information (null if not interested). The last array element will contain the parity.

Returns:

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

PlanetMath references:

LUDecomposition

luDecompose

public final AbstractDoubleSquareMatrix[] luDecompose()

Returns the LU decomposition of this matrix. Warning: no pivoting.

Overrides:

luDecompose in class AbstractDoubleSquareMatrix

Returns:

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

PlanetMath references:

LUDecomposition

choleskyDecompose

public AbstractDoubleSquareMatrix[] choleskyDecompose()

Returns the Cholesky decomposition of this matrix. Matrix must be symmetric and positive definite.

Overrides:

choleskyDecompose in class AbstractDoubleSquareMatrix

Returns:

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

PlanetMath references:

CholeskyDecomposition

qrDecompose

public AbstractDoubleSquareMatrix[] qrDecompose()

Returns the QR decomposition of this matrix. Based on the code from JAMA (public domain).

Overrides:

qrDecompose in class AbstractDoubleSquareMatrix

Returns:

an array with [0] containing the Q-matrix and [1] containing the R-matrix.

PlanetMath references:

QRDecomposition

singularValueDecompose

public AbstractDoubleSquareMatrix[] singularValueDecompose()

Returns the singular value decomposition of this matrix. Based on the code from JAMA (public domain).

Overrides:

singularValueDecompose in class AbstractDoubleSquareMatrix

Returns:

an array with [0] containing the U-matrix, [1] containing the S-matrix and [2] containing the V-matrix.

PlanetMath references:

SingularValueDecomposition

polarDecompose

public AbstractDoubleSquareMatrix[] polarDecompose()

Returns the polar decomposition of this matrix.

Overrides:

polarDecompose in class AbstractDoubleSquareMatrix

mapElements

public AbstractDoubleMatrix mapElements(Mapping f)

Applies a function on all the matrix elements.

Overrides:

mapElements in class AbstractDoubleSquareMatrix

Parameters:

f - a user-defined function

Returns:

a double matrix