JSci.maths.matrices
Class IntegerTridiagonalMatrix

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

All Implemented Interfaces:

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

public class IntegerTridiagonalMatrix
extends AbstractIntegerSquareMatrix
implements TridiagonalMatrix

The IntegerTridiagonalMatrix class provides an object for encapsulating integer tridiagonal matrices.

See Also:

Serialized Form

Field Summary

protected int[]	diag
protected int[]	ldiag Tridiagonal data.
protected int[]	udiag

Fields inherited from class JSci.maths.matrices.AbstractIntegerSquareMatrix

luCache

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

IntegerTridiagonalMatrix(int size)
Constructs an empty matrix.

IntegerTridiagonalMatrix(int[][] array)
Constructs a matrix from an array.

Method Summary

AbstractIntegerSquareMatrix	add(AbstractIntegerSquareMatrix m) Returns the addition of this matrix and another.
IntegerSquareMatrix	add(IntegerSquareMatrix m)
IntegerTridiagonalMatrix	add(IntegerTridiagonalMatrix m) Returns the addition of this matrix and another.
AbstractDoubleSquareMatrix[]	choleskyDecompose() Returns the Cholesky decomposition of this matrix.
boolean	equals(AbstractIntegerMatrix m, double tol) Compares two ${nativeTyp} matrices for equality.
double	frobeniusNorm() Returns the Frobenius (l2) norm.
int	getElement(int i, int j) Returns an element of the matrix.
int	infNorm() Returns the l-norm.
boolean	isSymmetric() Returns true if this matrix is symmetric.
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)
IntegerSquareMatrix	multiply(IntegerTridiagonalMatrix m)
double	operatorNorm() Returns the operator norm.
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)
int	scalarProduct(IntegerTridiagonalMatrix 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)
IntegerTridiagonalMatrix	subtract(IntegerTridiagonalMatrix m) Returns the subtraction 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, det, directSum, inverse, isUnitary, luDecompose_cache, luDecompose, luDecompose, negate, scalarProduct, subtract, tensor

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

ldiag

protected final int[] ldiag

Tridiagonal data.

diag

protected final int[] diag

udiag

protected final int[] udiag

Constructor Detail

IntegerTridiagonalMatrix

public IntegerTridiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

IntegerTridiagonalMatrix

public IntegerTridiagonalMatrix(int[][] array)

Constructs a matrix from an array. Any non-tridiagonal elements in the array are ignored.

Parameters:

array - an assigned value

Throws:

MatrixDimensionException - If the array is not square.

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.

isSymmetric

public boolean isSymmetric()

Returns true if this matrix is symmetric.

Overrides:

isSymmetric in class AbstractIntegerSquareMatrix

trace

public int trace()

Returns the trace.

Overrides:

trace in class AbstractIntegerSquareMatrix

infNorm

public int infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractIntegerMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class AbstractIntegerMatrix

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

Throws:

MaximumIterationsExceededException - If it takes more than 50 iterations to determine an eigenvalue.

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)

add

public IntegerTridiagonalMatrix add(IntegerTridiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a int tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

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)

subtract

public IntegerTridiagonalMatrix subtract(IntegerTridiagonalMatrix m)

Returns the subtraction of this matrix and another.

Parameters:

m - a int tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

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)

scalarProduct

public int scalarProduct(IntegerTridiagonalMatrix 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)

multiply

public IntegerSquareMatrix multiply(IntegerTridiagonalMatrix m)

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractIntegerSquareMatrix

Returns:

a int matrix

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.

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.