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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 no.uib.cipr.matrix.Matrix.Norm;
import com.github.fommil.netlib.LAPACK;
import org.netlib.util.doubleW;
import org.netlib.util.intW;
/**
* Banded LU decomposition.
*/
public class BandLU {
/**
* Matrix dimension
*/
private final int n;
/**
* Number of bands in the matrix A
*/
private final int kl, ku;
/**
* Holds the LU factors
*/
private final BandMatrix LU;
/**
* Row pivotations
*/
private final int[] ipiv;
/**
* True if the matrix was singular
*/
private boolean singular;
/**
* Constructor for BandLU.
*
* @param n
* Matrix size
* @param kl
* Number of lower matrix bands
* @param ku
* Number of upper matrix bands
*/
public BandLU(int n, int kl, int ku) {
this.n = n;
this.kl = kl;
this.ku = ku;
LU = new BandMatrix(n, kl, ku + kl);
ipiv = new int[n];
}
/**
* Creates an LU decomposition of the given matrix.
*
* @param A
* Matrix to decompose. Not modified
* @return A LU decomposition of the matrix
*/
public static BandLU factorize(BandMatrix A) {
return new BandLU(A.numRows(), A.kl, A.ku).factor(A, false);
}
/**
* Creates an LU decomposition of the given matrix.
*
* @param A
* Matrix to decompose. If the decomposition is in-place, its
* number of superdiagonals must equal kl+ku
* @param inplace
* Whether or not the decomposition should overwrite the passed
* matrix
* @return The current decomposition
*/
public BandLU factor(BandMatrix A, boolean inplace) {
if (inplace)
return factor(A);
else
return factor(new BandMatrix(A, kl, kl + ku));
}
/**
* Creates an LU decomposition of the given matrix.
*
* @param A
* Matrix to decompose. It will be overwritten with the
* decomposition. Its number of superdiagonals must equal
* kl+ku
* @return The current decomposition
*/
public BandLU factor(BandMatrix A) {
if (!(A.isSquare()))
throw new IllegalArgumentException("!A.isSquare()");
if (n != A.numRows())
throw new IllegalArgumentException("n != A.numRows()");
if (A.ku != ku + kl)
throw new IllegalArgumentException("A.ku != ku + kl");
singular = false;
intW info = new intW(0);
LAPACK.getInstance().dgbtrf(n, n, kl, ku, A.getData(), 2 * kl + ku + 1,
ipiv, info);
if (info.val > 0)
singular = true;
else if (info.val < 0)
throw new IllegalArgumentException();
LU.set(A);
return this;
}
/**
* Returns the lower triangular factor.
*/
public UnitLowerTriangBandMatrix getL() {
return new UnitLowerTriangBandMatrix(LU, LU.numSubDiagonals(), false);
}
/**
* Returns the upper triangular factor.
*/
public UpperTriangBandMatrix getU() {
return new UpperTriangBandMatrix(LU, LU.numSuperDiagonals(), false);
}
/**
* Returns the decomposition matrix.
*/
public BandMatrix getLU() {
return LU;
}
/**
* Returns the row pivots.
*/
public int[] getPivots() {
return ipiv;
}
/**
* Checks for singularity.
*/
public boolean isSingular() {
return singular;
}
/**
* Computes the reciprocal condition number, using either the infinity norm
* of the 1 norm.
*
* @param A
* The matrix this is a decomposition of
* @param norm
* Either Norm.One or Norm.Infinity
* @return The reciprocal condition number. Values close to unity indicate a
* well-conditioned system, while numbers close to zero do not.
*/
public double rcond(Matrix A, Norm norm) {
if (norm != Norm.One && norm != Norm.Infinity)
throw new IllegalArgumentException(
"Only the 1 or the Infinity norms are supported");
if (A.numRows() != n)
throw new IllegalArgumentException("A.numRows() != n");
if (!A.isSquare())
throw new IllegalArgumentException("!A.isSquare()");
double anorm = A.norm(norm);
double[] work = new double[3 * n];
int[] lwork = new int[n];
intW info = new intW(0);
doubleW rcond = new doubleW(0);
LAPACK.getInstance().dgbcon(norm.netlib(), n, kl, ku, LU.getData(),
Matrices.ld(2 * kl + ku + 1), ipiv, anorm, rcond, work, lwork,
info);
if (info.val < 0)
throw new IllegalArgumentException();
return rcond.val;
}
/**
* Computes A\B, overwriting B
*/
public DenseMatrix solve(DenseMatrix B) throws MatrixSingularException {
return solve(B, Transpose.NoTranspose);
}
/**
* Computes AT\B, overwriting B
*/
public DenseMatrix transSolve(DenseMatrix B) throws MatrixSingularException {
return solve(B, Transpose.Transpose);
}
private DenseMatrix solve(DenseMatrix B, Transpose trans)
throws MatrixSingularException {
if (singular)
throw new MatrixSingularException();
if (B.numRows() != n)
throw new IllegalArgumentException("B.numRows() != n");
intW info = new intW(0);
LAPACK.getInstance().dgbtrs(trans.netlib(), n, kl, ku, B.numColumns(),
LU.getData(), 2 * kl + ku + 1, ipiv, B.getData(),
Matrices.ld(n), info);
if (info.val < 0)
throw new IllegalArgumentException();
return B;
}
}
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