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A comprehensive collection of matrix data structures, linear solvers, least squares methods,
eigenvalue, and singular value decompositions.
Forked from: https://github.com/fommil/matrix-toolkits-java
and added support for eigenvalue computation of general matrices
The newest version!
/*
* 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 com.github.fommil.netlib.BLAS;
import com.github.fommil.netlib.LAPACK;
import org.netlib.util.intW;
/**
* 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.
*
*/
public class BandMatrix extends AbstractBandMatrix {
/**
* Constructor for BandMatrix
*
* @param n
* Size of the matrix. Since the matrix must be square, this
* equals both the number of rows and columns
* @param kl
* Number of bands above the main diagonal (superdiagonals)
* @param ku
* Number of bands below the main diagonal (subdiagonals)
*/
public BandMatrix(int n, int kl, int ku) {
super(n, kl, ku);
}
/**
* Constructor for BandMatrix
*
* @param A
* Matrix to copy contents from. Only the parts of A
* that lie within the allocated band are copied over, the rest
* is ignored
* @param kl
* Number of bands above the main diagonal (superdiagonals)
* @param ku
* Number of bands below the main diagonal (subdiagonals)
*/
public BandMatrix(Matrix A, int kl, int ku) {
super(A, kl, ku);
}
/**
* Constructor for BandMatrix
*
* @param A
* Matrix to copy contents from. Only the parts of A
* that lie within the allocated band are copied over, the rest
* is ignored
* @param kl
* Number of bands above the main diagonal (superdiagonals)
* @param ku
* Number of bands below the main diagonal (subdiagonals)
* @param deep
* True for a deep copy. For shallow copies, A must
* be a banded matrix
*/
public BandMatrix(Matrix A, int kl, int ku, boolean deep) {
super(A, kl, ku, deep);
}
@Override
public BandMatrix copy() {
return new BandMatrix(this, kl, ku);
}
@Override
public Matrix zero() {
Arrays.fill(data, 0);
return this;
}
@Override
public Vector multAdd(double alpha, Vector x, Vector y) {
if (!(x instanceof DenseVector) || !(y instanceof DenseVector))
return super.multAdd(alpha, x, y);
checkMultAdd(x, y);
double[] xd = ((DenseVector) x).getData(), yd = ((DenseVector) y)
.getData();
BLAS.getInstance().dgbmv(Transpose.NoTranspose.netlib(), numRows,
numColumns, kl, ku, alpha, data, kl + ku + 1, xd, 1, 1, yd, 1);
return y;
}
@Override
public Vector transMultAdd(double alpha, Vector x, Vector y) {
if (!(x instanceof DenseVector) || !(y instanceof DenseVector))
return super.transMultAdd(alpha, x, y);
checkTransMultAdd(x, y);
double[] xd = ((DenseVector) x).getData(), yd = ((DenseVector) y)
.getData();
BLAS.getInstance().dgbmv(Transpose.Transpose.netlib(), numRows,
numColumns, kl, ku, alpha, data, kl + ku + 1, xd, 1, 1, yd, 1);
return y;
}
@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);
// Allocate factorization matrix. The factorization matrix will be
// large enough to accomodate any pivots
BandMatrix Af = new BandMatrix(this, kl, ku + kl);
int[] ipiv = new int[numRows];
intW info = new intW(0);
LAPACK.getInstance().dgbsv(numRows, kl, ku, X.numColumns(),
Af.getData(), Matrices.ld(2 * kl + ku + 1), ipiv, 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() {
checkTranspose();
if (kl != ku)
throw new IllegalArgumentException("kl != ku");
for (int j = 0; j < numColumns; ++j)
for (int i = j + 1; i < Math.min(j + kl + 1, numRows); ++i) {
double value = get(i, j);
set(i, j, get(j, i));
set(j, i, value);
}
return this;
}
}