JSci.maths.matrices
Class IntegerSquareMatrix

java.lang.Object
  JSci.maths.matrices.Matrix
      JSci.maths.matrices.AbstractIntegerMatrix
          JSci.maths.matrices.AbstractIntegerSquareMatrix
              JSci.maths.matrices.IntegerSquareMatrix

All Implemented Interfaces:

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

public class IntegerSquareMatrix
extends AbstractIntegerSquareMatrix

The IntegerSquareMatrix class provides an object for encapsulating integer square matrices.

See Also:

Serialized Form

Field Summary

protected int[][]

matrix Array containing the elements of the matrix.

Fields inherited from class JSci.maths.matrices.AbstractIntegerSquareMatrix

luCache

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

IntegerSquareMatrix(AbstractIntegerVector[] array)
Constructs a matrix from an array of vectors (columns).

IntegerSquareMatrix(int size)
Constructs an empty matrix.

IntegerSquareMatrix(int[][] array)
Constructs a matrix by wrapping an array.

Method Summary

AbstractIntegerSquareMatrix	add(AbstractIntegerSquareMatrix m) Returns the addition of this matrix and another.
IntegerSquareMatrix	add(IntegerSquareMatrix m)
AbstractDoubleSquareMatrix[]	choleskyDecompose() Returns the Cholesky decomposition of this matrix.
int	det() Returns the determinant.
AbstractIntegerSquareMatrix	directSum(AbstractIntegerSquareMatrix m) Returns the direct sum of this matrix and another.
boolean	equals(AbstractIntegerMatrix m, double tol) Compares two ${nativeTyp} matrices for equality.
double	frobeniusNorm() Returns the Frobenius or Hilbert-Schmidt (l2) norm.
int	getElement(int i, int j) Returns an element of the matrix.
int	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.
AbstractIntegerSquareMatrix	multiply(AbstractIntegerSquareMatrix m) Returns the multiplication of this matrix and another.
AbstractIntegerVector	multiply(AbstractIntegerVector v) Returns the multiplication of a vector by this matrix.
IntegerSquareMatrix	multiply(IntegerSquareMatrix m)
AbelianGroup.Member	negate() Returns the negative of this matrix.
AbstractDoubleSquareMatrix[]	qrDecompose() Returns the QR decomposition of this matrix.
AbstractIntegerMatrix	scalarMultiply(int x) Returns the multiplication of this matrix by a scalar.
int	scalarProduct(AbstractIntegerSquareMatrix m) Returns the scalar product of this matrix and another.
int	scalarProduct(IntegerSquareMatrix m)
void	setElement(int i, int j, int x) Sets the value of an element of the matrix.
AbstractDoubleSquareMatrix[]	singularValueDecompose() Returns the singular value decomposition of this matrix.
AbstractIntegerSquareMatrix	subtract(AbstractIntegerSquareMatrix m) Returns the subtraction of this matrix by another.
IntegerSquareMatrix	subtract(IntegerSquareMatrix m)
AbstractIntegerSquareMatrix	tensor(AbstractIntegerSquareMatrix m) Returns the tensor product of this matrix and another.
AbstractComplexMatrix	toComplexMatrix() Converts this matrix to a complex matrix.
AbstractDoubleMatrix	toDoubleMatrix() Converts this matrix to a double matrix.
java.lang.String	toString() Returns a string representing this matrix.
int	trace() Returns the trace.
Matrix	transpose() Returns the transpose of this matrix.

Methods inherited from class JSci.maths.matrices.AbstractIntegerSquareMatrix

add, isSymmetric, isUnitary, luDecompose_cache, scalarProduct, subtract

Methods inherited from class JSci.maths.matrices.AbstractIntegerMatrix

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 int[][] matrix

Array containing the elements of the matrix.

Constructor Detail

IntegerSquareMatrix

public IntegerSquareMatrix(int[][] array)

Constructs a matrix by wrapping an array.

Parameters:

array - an assigned value

IntegerSquareMatrix

public IntegerSquareMatrix(int size)

Constructs an empty matrix.

IntegerSquareMatrix

public IntegerSquareMatrix(AbstractIntegerVector[] array)

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

Parameters:

array - an assigned value

Method Detail

equals

public boolean equals(AbstractIntegerMatrix m,
                      double tol)

Compares two ${nativeTyp} matrices for equality.

Overrides:

equals in class AbstractIntegerMatrix

Parameters:

m - a int matrix

toString

public java.lang.String toString()

Returns a string representing this matrix.

Overrides:

toString in class AbstractIntegerMatrix

toDoubleMatrix

public AbstractDoubleMatrix toDoubleMatrix()

Converts this matrix to a double matrix.

Overrides:

toDoubleMatrix in class AbstractIntegerSquareMatrix

Returns:

a double matrix

toComplexMatrix

public AbstractComplexMatrix toComplexMatrix()

Converts this matrix to a complex matrix.

Overrides:

toComplexMatrix in class AbstractIntegerSquareMatrix

Returns:

a complex matrix

getElement

public int getElement(int i,
                      int j)

Returns an element of the matrix.

Specified by:

getElement in class AbstractIntegerMatrix

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,
                       int x)

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

Specified by:

setElement in class AbstractIntegerMatrix

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 int infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractIntegerMatrix

frobeniusNorm

public double frobeniusNorm()

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

Overrides:

frobeniusNorm in class AbstractIntegerMatrix

PlanetMath references:

FrobeniusMatrixNorm

det

public int det()

Returns the determinant.

Overrides:

det in class AbstractIntegerSquareMatrix

trace

public int trace()

Returns the trace.

Overrides:

trace in class AbstractIntegerSquareMatrix

negate

public AbelianGroup.Member negate()

Returns the negative of this matrix.

Specified by:

negate in interface AbelianGroup.Member

Overrides:

negate in class AbstractIntegerSquareMatrix

add

public AbstractIntegerSquareMatrix add(AbstractIntegerSquareMatrix m)

Returns the addition of this matrix and another.

Overrides:

add in class AbstractIntegerSquareMatrix

Parameters:

m - a int matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

add

public IntegerSquareMatrix add(IntegerSquareMatrix m)

subtract

public AbstractIntegerSquareMatrix subtract(AbstractIntegerSquareMatrix m)

Returns the subtraction of this matrix by another.

Overrides:

subtract in class AbstractIntegerSquareMatrix

Parameters:

m - a int matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

subtract

public IntegerSquareMatrix subtract(IntegerSquareMatrix m)

scalarMultiply

public AbstractIntegerMatrix scalarMultiply(int x)

Returns the multiplication of this matrix by a scalar.

Overrides:

scalarMultiply in class AbstractIntegerSquareMatrix

Parameters:

x - a int.

Returns:

a int square matrix.

scalarProduct

public int scalarProduct(AbstractIntegerSquareMatrix m)

Returns the scalar product of this matrix and another.

Overrides:

scalarProduct in class AbstractIntegerSquareMatrix

Parameters:

m - a int matrix.

Throws:

MatrixDimensionException - If the matrices are different sizes.

scalarProduct

public int scalarProduct(IntegerSquareMatrix m)

multiply

public AbstractIntegerVector multiply(AbstractIntegerVector v)

Returns the multiplication of a vector by this matrix.

Overrides:

multiply in class AbstractIntegerMatrix

Parameters:

v - a int vector.

Throws:

DimensionException - If the matrix and vector are incompatible.

multiply

public AbstractIntegerSquareMatrix multiply(AbstractIntegerSquareMatrix m)

Returns the multiplication of this matrix and another.

Overrides:

multiply in class AbstractIntegerSquareMatrix

Parameters:

m - a int matrix

Returns:

a AbstractIntegerMatrix or a AbstractIntegerSquareMatrix as appropriate

Throws:

MatrixDimensionException - If the matrices are incompatible.

multiply

public IntegerSquareMatrix multiply(IntegerSquareMatrix m)

directSum

public AbstractIntegerSquareMatrix directSum(AbstractIntegerSquareMatrix m)

Returns the direct sum of this matrix and another.

Overrides:

directSum in class AbstractIntegerSquareMatrix

tensor

public AbstractIntegerSquareMatrix tensor(AbstractIntegerSquareMatrix m)

Returns the tensor product of this matrix and another.

Overrides:

tensor in class AbstractIntegerSquareMatrix

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractIntegerSquareMatrix

Returns:

a int matrix

inverse

public AbstractDoubleSquareMatrix inverse()

Returns the inverse of this matrix.

Overrides:

inverse in class AbstractIntegerSquareMatrix

Returns:

a double square matrix.

luDecompose

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

Returns the LU decomposition of this matrix.

Overrides:

luDecompose in class AbstractIntegerSquareMatrix

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 AbstractIntegerSquareMatrix

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 AbstractIntegerSquareMatrix

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 AbstractIntegerSquareMatrix

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 AbstractIntegerSquareMatrix

Returns:

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

PlanetMath references:

SingularValueDecomposition