no.uib.cipr.matrix
Class BandMatrix

java.lang.Object
  extended by no.uib.cipr.matrix.AbstractMatrix
      extended by 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