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Matrix data structures, linear solvers, least squares methods, eigenvalue,
and singular value decompositions. For larger random dense matrices (above ~ 350 x 350)
matrix-matrix multiplication C = A.B is about 50% faster than MTJ.
/*
* 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;
/**
* Symmetrical tridiagonal matrix. Storage as for
* {@link no.uib.cipr.matrix.TridiagMatrix TridiagMatrix}, but only one
* off-diagonal array is stored.
*/
public class SymmTridiagMatrix extends AbstractMatrix {
/**
* Diagonal and off-diagonal
*/
double[] diag, offDiag;
/**
* Size of the matrix
*/
int n;
/**
* Constructor for SymmTridiagMatrix
*
* @param diag
* Main diagonal
* @param offDiag
* Offdiagonals, both upper and lower
* @param n
* Size of the matrix. The main diagonal must be at least as long
* as n, and the off diagonal part must be at least as long as
* n-1
*/
public SymmTridiagMatrix(double[] diag, double[] offDiag, int n) {
super(n, n);
this.n = n;
if (n < 1)
throw new IllegalArgumentException("n must be >= 1");
if (diag.length < n)
throw new IllegalArgumentException("diag.length < n");
if (offDiag.length < n - 1)
throw new IllegalArgumentException("offDiag.length < n - 1");
this.diag = diag;
this.offDiag = offDiag;
}
/**
* Constructor for SymmTridiagMatrix
*
* @param diag
* Main diagonal
* @param offDiag
* Offdiagonals. Must be one shorter than diag
*/
public SymmTridiagMatrix(double[] diag, double[] offDiag) {
this(diag, offDiag, diag.length);
}
/**
* Constructor for SymmTridiagMatrix
*
* @param n
* Size of the matrix. Since the matrix must be square, this
* equals both the number of rows and columns. n
* cannot be zero
*/
public SymmTridiagMatrix(int n) {
super(n, n);
if (n < 1)
throw new IllegalArgumentException("n must be >= 1");
this.n = numRows;
diag = new double[n];
offDiag = new double[n - 1];
}
/**
* Constructor for SymmTridiagMatrix
*
* @param A
* Matrix to copy contents from. Only main and the superdiagonal
* is copied over
*/
public SymmTridiagMatrix(Matrix A) {
this(A, true);
}
/**
* Constructor for SymmTridiagMatrix
*
* @param A
* Matrix to copy contents from. Only main and the superdiagonal
* is copied over. It must be square and cannot have any zero
* dimension lengths
* @param deep
* True for a deep copy. For shallow copies A must
* be a SymmTridiagMatrix
*/
public SymmTridiagMatrix(Matrix A, boolean deep) {
super(A);
if (!isSquare())
throw new IllegalArgumentException(
"Symmetric matrix must be square");
if (A.numRows() < 1)
throw new IllegalArgumentException("numRows must be >= 1");
n = numRows;
if (deep) {
diag = new double[n];
offDiag = new double[Math.max(n - 1, 0)];
for (MatrixEntry e : A)
if (e.row() == e.column() || e.row() == e.column() + 1)
set(e.row(), e.column(), e.get());
} else {
SymmTridiagMatrix B = (SymmTridiagMatrix) A;
this.diag = B.getDiagonal();
this.offDiag = B.getOffDiagonal();
}
}
/**
* Returns the diagonal entries. Length equal n
*/
public double[] getDiagonal() {
return diag;
}
/**
* Returns the off diagonal entries. Length equal n-1
*/
public double[] getOffDiagonal() {
return offDiag;
}
@Override
public void add(int row, int column, double value) {
check(row, column);
if (row == column)
diag[row] += value;
else if (row == column + 1)
offDiag[column] += value;
else if (row != column - 1)
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 offDiag[column];
else if (row == column - 1)
return offDiag[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)
offDiag[column] = value;
else if (row != column - 1)
throw new IndexOutOfBoundsException(
"Insertion index outside of band");
}
@Override
public SymmTridiagMatrix copy() {
return new SymmTridiagMatrix(this);
}
@Override
public SymmTridiagMatrix zero() {
Arrays.fill(diag, 0);
Arrays.fill(offDiag, 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(), offDiag.clone(),
diag.clone(), offDiag.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 transSolve(Matrix B, Matrix X) {
return solve(B, X);
}
@Override
public Vector transSolve(Vector b, Vector x) {
return solve(b, x);
}
@Override
public Matrix transpose() {
return this;
}
@Override
public Iterator iterator() {
return new SymmTridiagMatrixIterator();
}
/**
* Iterator over a symmetrical, tridiagonal matrix
*/
private class SymmTridiagMatrixIterator 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 off)
*/
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 off-diagonal (twice)
bandIndex = 0;
whichBand++;
band = offDiag;
// 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;
}
}
}
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