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A comprehensive collection of matrix data structures, linear solvers, least squares methods,
eigenvalue, and singular value decompositions.
/*
* Copyright (C) 2003-2006 Bjørn-Ove Heimsund
*
* This file is part of MTJ.
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Lesser General Public License as published by the
* Free Software Foundation; either version 2.1 of the License, or (at your
* option) any later version.
*
* This library is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License
* for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
package no.uib.cipr.matrix;
import java.util.Arrays;
import java.util.Iterator;
import com.github.fommil.netlib.LAPACK;
import org.netlib.util.intW;
/**
* Tridiagonal matrix. Stored in three arrays, one of length n for
* the diagonal, two of length n-1 for the superdiagonal and
* subdiagonal entries.
*/
public class TridiagMatrix extends AbstractMatrix {
/**
* Diagonal, super-diagonal and sub-diagonal
*/
double[] diag, superDiag, subDiag;
/**
* Size of the matrix
*/
private int n;
/**
* Constructor for TridiagMatrix
*
* @param n
* Size of the matrix. Since the matrix must be square, this
* equals both the number of rows and columns
*/
public TridiagMatrix(int n) {
super(n, n);
if (n < 1)
throw new IllegalArgumentException("n must be >= 1");
this.n = n;
diag = new double[n];
superDiag = new double[n - 1];
subDiag = new double[n - 1];
}
/**
* Constructor for TridiagMatrix
*
* @param A
* Matrix to copy from. Only the tridiagonal part is copied
*/
public TridiagMatrix(Matrix A) {
this(A, true);
}
/**
* Constructor for TridiagMatrix
*
* @param A
* Matrix to copy from. Only the tridiagonal part is copied
* @param deep
* True for a deep copy, else it's shallow. For shallow copies,
* A must be a TridiagMatrix
*/
public TridiagMatrix(Matrix A, boolean deep) {
super(A);
if (!isSquare())
throw new IllegalArgumentException(
"Tridiagonal matrix must be square");
if (A.numRows() < 1)
throw new IllegalArgumentException("numRows must be >= 1");
n = numRows;
if (deep) {
diag = new double[n];
superDiag = new double[n - 1];
subDiag = new double[n - 1];
for (MatrixEntry e : A)
if (e.row() == e.column() || e.row() == e.column() - 1
|| e.row() == e.column() + 1)
set(e.row(), e.column(), e.get());
} else {
TridiagMatrix B = (TridiagMatrix) A;
this.diag = B.getDiagonal();
this.subDiag = B.getSubDiagonal();
this.superDiag = B.getSuperDiagonal();
}
}
/**
* Returns the diagonal entries. Length equal n
*/
public double[] getDiagonal() {
return diag;
}
/**
* Returns the sub diagonal entries. Length equal n-1
*/
public double[] getSubDiagonal() {
return subDiag;
}
/**
* Returns the super diagonal entries. Length equal n-1
*/
public double[] getSuperDiagonal() {
return superDiag;
}
@Override
public void add(int row, int column, double value) {
check(row, column);
if (row == column)
diag[row] += value;
else if (row == column + 1)
subDiag[column] += value;
else if (row == column - 1)
superDiag[row] += value;
else
throw new IndexOutOfBoundsException(
"Insertion index outside of band");
}
@Override
public double get(int row, int column) {
check(row, column);
if (row == column)
return diag[row];
else if (row == column + 1)
return subDiag[column];
else if (row == column - 1)
return superDiag[row];
else
return 0;
}
@Override
public void set(int row, int column, double value) {
check(row, column);
if (row == column)
diag[row] = value;
else if (row == column + 1)
subDiag[column] = value;
else if (row == column - 1)
superDiag[row] = value;
else
throw new IndexOutOfBoundsException(
"Insertion index outside of band");
}
@Override
public TridiagMatrix copy() {
return new TridiagMatrix(this);
}
@Override
public TridiagMatrix zero() {
Arrays.fill(diag, 0);
Arrays.fill(subDiag, 0);
Arrays.fill(superDiag, 0);
return this;
}
@Override
public Matrix solve(Matrix B, Matrix X) {
if (!(X instanceof DenseMatrix))
throw new UnsupportedOperationException("X must be a DenseMatrix");
checkSolve(B, X);
double[] Xd = ((DenseMatrix) X).getData();
X.set(B);
intW info = new intW(0);
LAPACK.getInstance()
.dgtsv(numRows, X.numColumns(), subDiag.clone(), diag.clone(),
superDiag.clone(), Xd, Matrices.ld(numRows), info);
if (info.val > 0)
throw new MatrixSingularException();
else if (info.val < 0)
throw new IllegalArgumentException();
return X;
}
@Override
public Vector solve(Vector b, Vector x) {
DenseMatrix B = new DenseMatrix(b, false), X = new DenseMatrix(x, false);
solve(B, X);
return x;
}
@Override
public Matrix transpose() {
double[] otherDiag = subDiag;
subDiag = superDiag;
superDiag = otherDiag;
return this;
}
@Override
public Iterator iterator() {
return new TridiagMatrixIterator();
}
/**
* Iterator over a tridiagonal matrix
*/
private class TridiagMatrixIterator extends RefMatrixIterator {
/**
* Current band, starting with the main diagonal
*/
private double[] band = diag;
/**
* Band index
*/
private int bandIndex;
/**
* Which band in use (0 for main, 1 for sub, 2 for super)
*/
private int whichBand;
@Override
public boolean hasNext() {
return whichBand < 3;
}
@Override
public MatrixEntry next() {
entry.update(row, column);
// Move in the band
if (bandIndex < band.length - 1)
bandIndex++;
else {
// Move to the next band
bandIndex = 0;
whichBand++;
if (whichBand == 1)
band = subDiag;
else if (whichBand == 2)
band = superDiag;
// If the off-diagonals are zero-sized, we are done
// This happens if the matrix is 1*1
if (band.length == 0)
whichBand = 3;
}
// Set row index
if (whichBand == 1)
row = bandIndex + 1;
else
row = bandIndex;
// Set column index
if (whichBand == 2)
column = bandIndex + 1;
else
column = bandIndex;
return entry;
}
}
}