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A comprehensive collection of matrix data structures, linear solvers, least squares methods,
eigenvalue, and singular value decompositions.
/*
* Copyright (C) 2006 Rafael de Pelegrini Soares
*
* MTJ additions.
*
* 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 com.github.fommil.netlib.LAPACK;
import org.netlib.util.intW;
/**
* Computes QR decompositions with column pivoting:
*
* {@code A*P = Q*R} where
*
* {@code A(m,n)}, {@code Q(m,m)}, and {@code R(m,n)}, more generally:
*
* {@code A*P = [Q1 Q2] * [R11, R12; 0 R22]} and {@code R22} elements are
* negligible.
*
*/
public class QRP {
/** Pivoting vector */
int jpvt[];
/**
* Scales for the reflectors
*/
final double[] tau;
/**
* Factorisation sizes
*/
final int m, n, k;
/** The factored matrix rank */
int rank;
/**
* Work array
*/
double[] work;
/**
* The factored matrix
*/
final DenseMatrix Afact;
/**
* The orthogonal matrix
*/
final DenseMatrix Q;
/**
* The general upper triangular matrix.
*/
final DenseMatrix R;
/**
* Constructs an empty QR decomposition
*
* @param m the number of rows.
* @param n the number of columns.
*/
public QRP(int m, int n) {
this.m = m;
this.n = n;
this.k = Math.min(m, n);
this.rank = 0;
jpvt = new int[n];
tau = new double[k];
Q = new DenseMatrix(m, m);
R = new DenseMatrix(m, n);
Afact = new DenseMatrix(m, Math.max(m, n));
int lwork1, lwork2;
intW info = new intW(0);
double dummy[] = new double[1];
double ret[] = new double[1];
LAPACK lapack = LAPACK.getInstance();
// Query optimal workspace. First for computing the factorization
lapack.dgeqrf(m, n, dummy, Matrices.ld(m), dummy, ret, -1, info);
lwork1 = (info.val != 0) ? n : (int) ret[0];
// Workspace needed for generating an explicit orthogonal matrix
lapack.dorgqr(m, m, k, dummy, Matrices.ld(m), dummy, ret, -1, info);
lwork2 = (info.val != 0) ? n : (int) ret[0];
work = new double[Math.max(lwork1, lwork2)];
}
/**
* Convenience method to compute a QR decomposition
*
* @param A the matrix to decompose (not modified)
* @return Newly allocated decomposition
*/
public static QRP factorize(Matrix A) {
return new QRP(A.numRows(), A.numColumns()).factor(A);
}
/**
* Executes a QR factorization for the given matrix.
*
* @param A the matrix to be factored (not modified)
* @return the factorization object
*/
public QRP factor(Matrix A) {
if (Q.numRows() != A.numRows())
throw new IllegalArgumentException("Q.numRows() != A.numRows()");
else if (R.numColumns() != A.numColumns())
throw new IllegalArgumentException("R.numColumns() != A.numColumns()");
// copy A values in Afact
Afact.zero();
for (MatrixEntry e : A) {
Afact.set(e.row(), e.column(), e.get());
}
intW info = new intW(0);
LAPACK lapack = LAPACK.getInstance();
/*
* Calculate factorisation
*/
lapack.dgeqp3(m, n, Afact.getData(), Matrices.ld(m), jpvt, tau, work,
work.length, info);
if (info.val < 0)
throw new IllegalArgumentException();
/*
* Get R from Afact
*/
R.zero();
for (MatrixEntry e : Afact) {
if (e.row() <= e.column() && e.column() < R.numColumns()) {
R.set(e.row(), e.column(), e.get());
}
}
/*
* Calculate the rank based on a precision EPS
*/
final double EPS = 1e-12;
for (rank = 0; rank < k; rank++) {
if (Math.abs(R.get(rank, rank)) < EPS)
break;
}
/*
* Explicit the orthogonal matrix
*/
lapack.dorgqr(m, m, k, Afact.getData(), Matrices.ld(m), tau, work,
work.length, info);
for (MatrixEntry e : Afact) {
if (e.column() < Q.numColumns())
Q.set(e.row(), e.column(), e.get());
}
if (info.val < 0)
throw new IllegalArgumentException();
// Adjust the permutation to zero offset
for (int i = 0; i < jpvt.length; i++) {
--jpvt[i];
}
return this;
}
/**
* Returns the upper triangular factor
*/
public DenseMatrix getR() {
return R;
}
/**
* Returns the orthogonal matrix
*/
public DenseMatrix getQ() {
return Q;
}
/**
* Returns the column pivoting vector.
* This function is cheaper than {@link #getP()}.
*/
public int[] getPVector() {
return jpvt;
}
/**
* Returns the column pivoting matrix.
* This function allocates a new Matrix to be returned,
* a more cheap option is tu use {@link #getPVector()}.
*/
public Matrix getP() {
Matrix P = new DenseMatrix(jpvt.length, jpvt.length);
for (int i = 0; i < jpvt.length; i++) {
P.set(jpvt[i], i, 1);
}
return P;
}
/**
* Returns the rank of the factored matrix
*/
public int getRank() {
return rank;
}
}