/*
* Copyright (c) 2009-2012, Peter Abeles. All Rights Reserved.
*
* This file is part of Efficient Java Matrix Library (EJML).
*
* EJML 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 3
* of the License, or (at your option) any later version.
*
* EJML 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 EJML. If not, see <http://www.gnu.org/licenses/>.
*/
package org.ejml.alg.dense.linsol.qr;
import org.ejml.alg.dense.decomposition.TriangularSolver;
import org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder;
import org.ejml.alg.dense.linsol.LinearSolverAbstract;
import org.ejml.data.DenseMatrix64F;
import org.ejml.ops.SpecializedOps;
/**
* <p>
* QR decomposition can be used to solve for systems. However, this is not as computationally efficient
* as LU decomposition and costs about 3n<sup>2</sup> flops.
* </p>
* <p>
* It solve for x by first multiplying b by the transpose of Q then solving for the result.
* <br>
* QRx=b<br>
* Rx=Q^T b<br>
* </p>
*
* @author Peter Abeles
*/
public class LinearSolverQrHouse extends LinearSolverAbstract {
private QRDecompositionHouseholder decomposer;
private double []a,u;
private int maxRows = -1;
private DenseMatrix64F QR;
private double gammas[];
/**
* Creates a linear solver that uses QR decomposition.
*/
public LinearSolverQrHouse() {
decomposer = new QRDecompositionHouseholder();
}
public void setMaxSize( int maxRows ) {
this.maxRows = maxRows;
a = new double[ maxRows ];
u = new double[ maxRows ];
}
/**
* Performs QR decomposition on A
*
* @param A not modified.
*/
@Override
public boolean setA(DenseMatrix64F A) {
if( A.numRows > maxRows ) {
setMaxSize(A.numRows);
}
_setA(A);
if( !decomposer.decompose(A) )
return false;
gammas = decomposer.getGammas();
QR = decomposer.getQR();
return true;
}
@Override
public double quality() {
return SpecializedOps.qualityTriangular(true, QR);
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is writen to. Modified.
*/
@Override
public void solve(DenseMatrix64F B, DenseMatrix64F X) {
if( X.numRows != numCols )
throw new IllegalArgumentException("Unexpected dimensions for X");
else if( B.numRows != numRows || B.numCols != X.numCols )
throw new IllegalArgumentException("Unexpected dimensions for B");
int BnumCols = B.numCols;
// solve each column one by one
for( int colB = 0; colB < BnumCols; colB++ ) {
// make a copy of this column in the vector
for( int i = 0; i < numRows; i++ ) {
a[i] = B.data[i*BnumCols + colB];
}
// Solve Qa=b
// a = Q'b
// a = Q_{n-1}...Q_2*Q_1*b
//
// Q_n*b = (I-gamma*u*u^T)*b = b - u*(gamma*U^T*b)
for( int n = 0; n < numCols; n++ ) {
u[n] = 1;
double ub = a[n];
// U^T*b
for( int i = n+1; i < numRows; i++ ) {
ub += (u[i] = QR.unsafe_get(i,n))*a[i];
}
// gamma*U^T*b
ub *= gammas[n];
for( int i = n; i < numRows; i++ ) {
a[i] -= u[i]*ub;
}
}
// solve for Rx = b using the standard upper triangular solver
TriangularSolver.solveU(QR.data,a,numCols);
// save the results
for( int i = 0; i < numCols; i++ ) {
X.data[i*X.numCols+colB] = a[i];
}
}
}
@Override
public boolean modifiesA() {
return false;
}
@Override
public boolean modifiesB() {
return false;
}
}