QRPTest.java

/*
 * 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 org.junit.Test;

import static org.junit.Assert.assertEquals;

/**
 * QRP test
 */
public class QRPTest {

    @Test
    public void testIdentity() {
        Matrix A = Matrices.identity(5);

        QRP qrp = QRP.factorize(A);

        assertMatrixEquals(A,
                mult(qrp.getQ(), qrp.getPVector(), qrp.getR(), A.copy().zero()));
    }

    @Test
    public void testRectangularIdentity1() {
        Matrix A = new DenseMatrix(5, 6);
        for (MatrixEntry i : A) {
            if (i.row() == i.column())
                i.set(1);
        }

        QRP qrp = QRP.factorize(A);

        assertMatrixEquals(A,
                mult(qrp.getQ(), qrp.getPVector(), qrp.getR(), A.copy().zero()));
    }

    @Test
    public void testRectangularIdentity2() {
        Matrix A = new DenseMatrix(6, 5);
        for (MatrixEntry i : A) {
            if (i.row() == i.column())
                i.set(1);
        }

        QRP qrp = QRP.factorize(A);

        assertMatrixEquals(A,
                mult(qrp.getQ(), qrp.getPVector(), qrp.getR(), A.copy().zero()));
    }

    @Test
    public void testOrthogonality() {
        Matrix A = Matrices.random(6, 4);

        QRP qrp = QRP.factorize(A);

        Matrix QP = qrp.getQ();

        assertMatrixEquals(Matrices.identity(QP.numRows()),
                QP.transAmult(QP, QP.copy().zero()));
    }

    @Test
    public void testOrthogonality2() {
        Matrix A = Matrices.random(4, 6);

        QRP qrp = QRP.factorize(A);

        Matrix QP = qrp.getQ();

        assertMatrixEquals(Matrices.identity(QP.numRows()),
                QP.transAmult(QP, QP.copy().zero()));
    }

    @Test
    public void testRandSquare() {
        Matrix A = Matrices.random(5, 5);

        QRP qrp = QRP.factorize(A);
        Matrix Q = qrp.getQ();
        Matrix R = qrp.getR();
        int P[] = qrp.getPVector();

        assertMatrixEquals(A, mult(Q, P, R, A.copy().zero()));
    }

    @Test
    public void testRandRectangular1() {
        Matrix A = Matrices.random(4, 6);

        QRP qrp = QRP.factorize(A);

        assertMatrixEquals(A,
                mult(qrp.getQ(), qrp.getPVector(), qrp.getR(), A.copy().zero()));
    }

    @Test
    public void testRandRectangular2() {
        Matrix A = Matrices.random(6, 4);

        QRP qrp = QRP.factorize(A);

        assertMatrixEquals(A,
                mult(qrp.getQ(), qrp.getPVector(), qrp.getR(), A.copy().zero()));
    }

    @Test
    public void testPivotingMatrix() {
        Matrix A = Matrices.random(6, 4);

        QRP qrp = QRP.factorize(A);
        Matrix Q = qrp.getQ();
        Matrix R = qrp.getR();
        Matrix P = qrp.getP();

        Matrix C = A.copy().zero();
        Matrix D = A.copy().zero();

        Q.mult(R, C);
        C.transBmult(P, D);

        assertMatrixEquals(A, D);
    }

    @Test
    public void testRank1() {
        Matrix rand = Matrices.random(6, 4);

        Matrix A = new DenseMatrix(rand.numRows(), rand.numRows());
        rand.transBmult(rand, A);

        QRP qrp = QRP.factorize(A);

        assertEquals(Math.min(rand.numRows(), rand.numColumns()), qrp.getRank());
    }

    @Test
    public void testRank2() {
        Matrix rand = Matrices.random(4, 6);

        Matrix A = new DenseMatrix(rand.numRows(), rand.numRows());
        rand.transBmult(rand, A);

        QRP qrp = QRP.factorize(A);

        assertEquals(Math.min(rand.numRows(), rand.numColumns()), qrp.getRank());
    }

    /**
     * Executes the multiplication C = Q*P*R
     * 
     * @param Q
     *            matrix Q
     * @param P
     *            column permutation of R
     * @param R
     *            matrix R
     * @param C
     *            matrix tu put the results
     * @return the matrix C
     */
    protected Matrix mult(Matrix Q, int[] P, Matrix R, Matrix C) {
        for (int i = 0; i < Q.numRows(); ++i) {
            for (int j = 0; j < C.numColumns(); ++j) {
                double dot = 0;
                for (int k = 0; k < Q.numColumns(); ++k) {
                    dot += Q.get(i, k) * R.get(k, j);
                }
                C.add(i, P[j], dot);
            }
        }
        return C;
    }
    private static final double DELTA = 1e-12;

    /**
     * Assert that the given matrices are identical
     */
    protected void assertMatrixEquals(Matrix A, Matrix B) {
        assertEquals(A.numRows(), B.numRows());
        assertEquals(A.numColumns(), B.numColumns());
        for (int i = 0; i < A.numRows(); ++i) {
            for (int j = 0; j < A.numColumns(); ++j) {
                assertEquals(A.get(i, j), B.get(i, j), DELTA);
            }
        }
    }
}