no.uib.cipr.matrix
Class BandMatrix

java.lang.Object
  no.uib.cipr.matrix.AbstractMatrix
      no.uib.cipr.matrix.BandMatrix

All Implemented Interfaces:

java.lang.Iterable<MatrixEntry>, Matrix

public class BandMatrix
extends AbstractMatrix

Banded matrix. The banded matrix is a useful sparse structure for many kinds of direct computations, however it should only be used if the band is sufficiently narrow as wide bands actually wastes both memory and compute time. The matrix

a11	a12
a21	a22	a23
a31	a32	a33	a34
	a42	a43	a44	a45
		a53	a54	a55

has two lower diagonals and one upper diagonal. It will be stored in the array

a11

a21

a31

a21

a22

a32

a42

a23

a33

a43

a53

a34

a44

a54

a45

a55

Empty cells are allocated, but never referenced.

Nested Class Summary

Nested classes/interfaces inherited from interface no.uib.cipr.matrix.Matrix

Matrix.Norm

Field Summary

Fields inherited from class no.uib.cipr.matrix.AbstractMatrix

numColumns, numRows

Constructor Summary

BandMatrix(int n, int kl, int ku)
Constructor for BandMatrix

BandMatrix(Matrix A, int kl, int ku)
Constructor for BandMatrix

BandMatrix(Matrix A, int kl, int ku, boolean deep)
Constructor for BandMatrix

Method Summary

void	add(int row, int column, double value) A(row,column) += value
BandMatrix	copy() Creates a deep copy of the matrix
double	get(int row, int column) Returns A(row,column)
double[]	getData() Returns the matrix contents
java.util.Iterator<MatrixEntry>	iterator()
Vector	multAdd(double alpha, Vector x, Vector y) y = alpha*A*x + y
int	numSubDiagonals() Returns the number of lower diagonals
int	numSuperDiagonals() Returns the number of upper diagonals
void	set(int row, int column, double value) A(row,column) = value
Matrix	set(Matrix B) A=B.
Matrix	solve(Matrix B, Matrix X) X = A\B.
Vector	solve(Vector b, Vector x) x = A\b.
Vector	transMultAdd(double alpha, Vector x, Vector y) y = alpha*AT*x + y
Matrix	transpose() Transposes the matrix in-place.
Matrix	zero() Zeros all the entries in the matrix, while preserving any underlying structure.

Methods inherited from class no.uib.cipr.matrix.AbstractMatrix

add, add, check, checkMultAdd, checkMultAdd, checkRank1, checkRank1, checkRank2, checkRank2, checkSize, checkSolve, checkSolve, checkTransABmultAdd, checkTransAmultAdd, checkTransBmultAdd, checkTransMultAdd, checkTranspose, checkTranspose, checkTransRank1, checkTransRank2, isSquare, max, max, mult, mult, mult, mult, multAdd, multAdd, multAdd, norm, norm1, normF, normInf, numColumns, numRows, rank1, rank1, rank1, rank1, rank1, rank1, rank2, rank2, rank2, rank2, scale, set, toString, transABmult, transABmult, transABmultAdd, transABmultAdd, transAmult, transAmult, transAmultAdd, transAmultAdd, transBmult, transBmult, transBmultAdd, transBmultAdd, transMult, transMult, transMultAdd, transpose, transRank1, transRank1, transRank2, transRank2, transSolve, transSolve

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

BandMatrix

public BandMatrix(int n,
                  int kl,
                  int ku)

Constructor for BandMatrix

Parameters:

n - Size of the matrix. Since the matrix must be square, this equals both the number of rows and columns

kl - Number of bands above the main diagonal (superdiagonals)

ku - Number of bands below the main diagonal (subdiagonals)

BandMatrix

public BandMatrix(Matrix A,
                  int kl,
                  int ku)

Constructor for BandMatrix

Parameters:

A - Matrix to copy contents from. Only the parts of A that lie within the allocated band are copied over, the rest is ignored

kl - Number of bands above the main diagonal (superdiagonals)

ku - Number of bands below the main diagonal (subdiagonals)

BandMatrix

public BandMatrix(Matrix A,
                  int kl,
                  int ku,
                  boolean deep)

Constructor for BandMatrix

Parameters:

A - Matrix to copy contents from. Only the parts of A that lie within the allocated band are copied over, the rest is ignored

kl - Number of bands above the main diagonal (superdiagonals)

ku - Number of bands below the main diagonal (subdiagonals)

deep - True for a deep copy. For shallow copies, A must be a banded matrix

Method Detail

copy

public BandMatrix copy()

Description copied from interface: Matrix

Creates a deep copy of the matrix

Specified by:

copy in interface Matrix

Overrides:

copy in class AbstractMatrix

Returns:

A

zero

public Matrix zero()

Description copied from interface: Matrix

Zeros all the entries in the matrix, while preserving any underlying structure. Useful for general, unstructured matrices.

Specified by:

zero in interface Matrix

Returns:

A

multAdd

public Vector multAdd(double alpha,
                      Vector x,
                      Vector y)

Description copied from interface: Matrix

y = alpha*A*x + y

Specified by:

multAdd in interface Matrix

Overrides:

multAdd in class AbstractMatrix

x - Vector of size A.numColumns()

y - Vector of size A.numRows()

Returns:

y

transMultAdd

public Vector transMultAdd(double alpha,
                           Vector x,
                           Vector y)

Description copied from interface: Matrix

y = alpha*AT*x + y

Specified by:

transMultAdd in interface Matrix

Overrides:

transMultAdd in class AbstractMatrix

x - Vector of size A.numRows()

y - Vector of size A.numColumns()

Returns:

y

solve

public Matrix solve(Matrix B,
                    Matrix X)

Description copied from interface: Matrix

X = A\B. Not all matrices support this operation, those that do not throw UnsupportedOperationException. Note that it is often more efficient to use a matrix decomposition and its associated solver

Specified by:

solve in interface Matrix

Overrides:

solve in class AbstractMatrix

Parameters:

B - Matrix with the same number of rows as A, and the same number of columns as X

X - Matrix with a number of rows equal A.numColumns(), and the same number of columns as B

Returns:

X

solve

public Vector solve(Vector b,
                    Vector x)

Description copied from interface: Matrix

x = A\b. Not all matrices support this operation, those that do not throw UnsupportedOperationException. Note that it is often more efficient to use a matrix decomposition and its associated solver

Specified by:

solve in interface Matrix

Overrides:

solve in class AbstractMatrix

Parameters:

b - Vector of size A.numRows()

x - Vector of size A.numColumns()

Returns:

x

transpose

public Matrix transpose()

Description copied from interface: Matrix

Transposes the matrix in-place. In most cases, the matrix must be square for this to work.

Specified by:

transpose in interface Matrix

Overrides:

transpose in class AbstractMatrix

Returns:

This matrix

getData

public double[] getData()

Returns the matrix contents

add

public void add(int row,
                int column,
                double value)

Description copied from interface: Matrix

A(row,column) += value

Specified by:

add in interface Matrix

Overrides:

add in class AbstractMatrix

set

public void set(int row,
                int column,
                double value)

Description copied from interface: Matrix

A(row,column) = value

Specified by:

set in interface Matrix

Overrides:

set in class AbstractMatrix

get

public double get(int row,
                  int column)

Description copied from interface: Matrix

Returns A(row,column)

Specified by:

get in interface Matrix

Overrides:

get in class AbstractMatrix

numSubDiagonals

public int numSubDiagonals()

Returns the number of lower diagonals

numSuperDiagonals

public int numSuperDiagonals()

Returns the number of upper diagonals

set

public Matrix set(Matrix B)

Description copied from interface: Matrix

A=B. The matrices must be of the same size

Specified by:

set in interface Matrix

Overrides:

set in class AbstractMatrix

Returns:

A

iterator

public java.util.Iterator<MatrixEntry> iterator()

Specified by:

iterator in interface java.lang.Iterable<MatrixEntry>

Overrides:

iterator in class AbstractMatrix