org.ejml.dense.row.linsol.qr.LinearSolverQrHouseTran_DDRM Maven / Gradle / Ivy

/*
 * Copyright (c) 2009-2018, Peter Abeles. All Rights Reserved.
 *
 * This file is part of Efficient Java Matrix Library (EJML).
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.ejml.dense.row.linsol.qr;

import org.ejml.data.DMatrixRMaj;
import org.ejml.dense.row.SpecializedOps_DDRM;
import org.ejml.dense.row.decomposition.TriangularSolver_DDRM;
import org.ejml.dense.row.decomposition.qr.QRDecompositionHouseholderTran_DDRM;
import org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM;
import org.ejml.interfaces.decomposition.QRDecomposition;


/**
 * 
 * QR decomposition can be used to solve for systems.  However, this is not as computationally efficient
 * as LU decomposition and costs about 3n² flops.
 * 
 * 
 * It solve for x by first multiplying b by the transpose of Q then solving for the result.
 * 

 * QRx=b

 * Rx=Q^T b

 * 
 *
 * 
 * A column major decomposition is used in this solver.
 * 
 *
 * @author Peter Abeles
 */
public class LinearSolverQrHouseTran_DDRM extends LinearSolverAbstract_DDRM {

    private QRDecompositionHouseholderTran_DDRM decomposer;

    private double []a;

    protected int maxRows = -1;
    protected int maxCols = -1;

    private DMatrixRMaj QR; // a column major QR matrix
    private DMatrixRMaj U;

    /**
     * Creates a linear solver that uses QR decomposition.
     */
    public LinearSolverQrHouseTran_DDRM() {
        decomposer = new QRDecompositionHouseholderTran_DDRM();
    }

    public void setMaxSize( int maxRows , int maxCols )
    {
        this.maxRows = maxRows; this.maxCols = maxCols;

        a = new double[ maxRows ];
    }

    /**
     * Performs QR decomposition on A
     *
     * @param A not modified.
     */
    @Override
    public boolean setA(DMatrixRMaj A) {
        if( A.numRows > maxRows || A.numCols > maxCols )
            setMaxSize(A.numRows,A.numCols);

        _setA(A);
        if( !decomposer.decompose(A) )
            return false;

        QR = decomposer.getQR();
        return true;
    }

    @Override
    public /**/double quality() {
        // even those it is transposed the diagonal elements are at the same
        // elements
        return SpecializedOps_DDRM.qualityTriangular(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 written to.  Modified.
     */
    @Override
    public void solve(DMatrixRMaj B, DMatrixRMaj X) {
        if( B.numRows != numRows )
            throw new IllegalArgumentException("Unexpected dimensions for X: X rows = "+X.numRows+" expected = "+numCols);
        X.reshape(numCols,B.numCols);

        U = decomposer.getR(U,true);
        final double gammas[] = decomposer.getGammas();
        final double dataQR[] = QR.data;

        final 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++ ) {
                int indexU = n*numRows + n + 1;

                double ub = a[n];
                // U^T*b
                for( int i = n+1; i < numRows; i++ , indexU++ ) {
                    ub += dataQR[indexU]*a[i];
                }

                // gamma*U^T*b
                ub *= gammas[n];

                a[n] -= ub;
                indexU = n*numRows + n + 1;
                for( int i = n+1; i < numRows; i++ , indexU++) {
                    a[i] -= dataQR[indexU]*ub;
                }
            }

            // solve for Rx = b using the standard upper triangular solver
            TriangularSolver_DDRM.solveU(U.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 decomposer.inputModified();
    }

    @Override
    public boolean modifiesB() {
        return false;
    }

    @Override
    public QRDecomposition getDecomposition() {
        return decomposer;
    }
}