JSci.maths.matrices
Class DoubleTridiagonalMatrix

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

All Implemented Interfaces:

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

public class DoubleTridiagonalMatrix
extends AbstractDoubleSquareMatrix
implements TridiagonalMatrix

The DoubleTridiagonalMatrix class provides an object for encapsulating double tridiagonal matrices.

See Also:

Serialized Form

Field Summary

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

Fields inherited from class JSci.maths.matrices.AbstractDoubleSquareMatrix

luCache

Fields inherited from class JSci.maths.matrices.Matrix

numCols, numRows

Constructor Summary

DoubleTridiagonalMatrix(double[][] array)
Constructs a matrix from an array.

DoubleTridiagonalMatrix(int size)
Constructs an empty matrix.

Method Summary

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

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

ldiag

protected final double[] ldiag

Tridiagonal data.

diag

protected final double[] diag

udiag

protected final double[] udiag

Constructor Detail

DoubleTridiagonalMatrix

public DoubleTridiagonalMatrix(int size)

Constructs an empty matrix.

Parameters:

size - the number of rows/columns

DoubleTridiagonalMatrix

public DoubleTridiagonalMatrix(double[][] 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(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.

isSymmetric

public boolean isSymmetric()

Returns true if this matrix is symmetric.

Overrides:

isSymmetric in class AbstractDoubleSquareMatrix

trace

public double trace()

Returns the trace.

Overrides:

trace in class AbstractDoubleSquareMatrix

infNorm

public double infNorm()

Returns the l-norm.

Overrides:

infNorm in class AbstractDoubleMatrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius (l²) norm.

Overrides:

frobeniusNorm in class AbstractDoubleMatrix

operatorNorm

public double operatorNorm()
                    throws MaximumIterationsExceededException

Returns the operator norm.

Overrides:

operatorNorm in class AbstractDoubleSquareMatrix

Throws:

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

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)

add

public DoubleTridiagonalMatrix add(DoubleTridiagonalMatrix m)

Returns the addition of this matrix and another.

Parameters:

m - a double tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

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)

subtract

public DoubleTridiagonalMatrix subtract(DoubleTridiagonalMatrix m)

Returns the subtraction of this matrix and another.

Parameters:

m - a double tridiagonal matrix

Throws:

MatrixDimensionException - If the matrices are different sizes.

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)

scalarProduct

public double scalarProduct(DoubleTridiagonalMatrix 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)

multiply

public DoubleSquareMatrix multiply(DoubleTridiagonalMatrix m)

transpose

public Matrix transpose()

Returns the transpose of this matrix.

Overrides:

transpose in class AbstractDoubleSquareMatrix

Returns:

a double matrix

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.

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.

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