Examples of HouseholderQR

mikera.matrixx.decompose.impl.qr.HouseholderQR

This variation of QR decomposition uses reflections to compute the Q matrix. Each reflection uses a householder operations, hence its name. To provide a meaningful solution the original matrix must have full rank. This is intended for processing of small to medium matrices.

Both Q and R are stored in the same m by n matrix. Q is not stored directly, instead the u from Q_k=(I-γ*u*u^T) is stored. Decomposition requires about 2n*m²-2m²/3 flops.

See the QR reflections algorithm described in:
David S. Watkins, "Fundamentals of Matrix Computations" 2nd Edition, 2002

For the most part this is a straight forward implementation. To improve performance on large matrices a column is written to an array and the order of some of the loops has been changed. This will degrade performance noticeably on small matrices. Since it is unlikely that the QR decomposition would be a bottle neck when small matrices are involved only one implementation is provided.
@author Peter Abeles

Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR

    Random rand = new Random(0xff);




    @Override
    protected QRDecomposition createQRDecomposition(boolean compact) {
        return new HouseholderQR(compact);
    }

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Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR


  @Test
  public void testDecompose() {
    double[][] dataA = { { 0, 3, 1 }, { 0, 4, -2 }, { 2, 1, 1 } };
    Matrix A = Matrix.create(dataA);
    HouseholderQR alg = new HouseholderQR(false);
    IQRResult result = alg.decompose(A);
    
    AMatrix Q = result.getQ();
    AMatrix R = result.getR();


    Matrix expectQ = Matrix.create(new double[][] { { 0, -0.6, 0.8 },
        { 0, -0.8, -0.6 }, { -1, 0, 0 } });
    Matrix expectR = Matrix.create(new double[][] { { -2, -1, -1 },
        { 0, -5, 1 }, { 0, 0, 2 } });
    assertEquals(Q, expectQ);
    assertEquals(R, expectR);


    A = Matrix.create(dataA);
    alg = new HouseholderQR(true);
    result = alg.decompose(A);
    Q = result.getQ();
    R = result.getR();


    assertEquals(Q, expectQ);
    assertEquals(R, expectR);

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Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR

  }


  @Test
  public void testZeroDecompose() {
    AMatrix a = ZeroMatrix.create(4, 3);
    HouseholderQR alg = new HouseholderQR(false);
    IQRResult result = alg.decompose(a);
    AMatrix q = result.getQ();
    AMatrix r = result.getR();


    assertEquals(IdentityMatrix.create(3), q.subMatrix(0, 3, 0, 3));
    assertTrue(r.isZero());

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Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR

  }


  @Test
  public void testZeroDecomposeSquare() {
    AMatrix a = ZeroMatrix.create(3, 3);
    HouseholderQR alg = new HouseholderQR(false);
    IQRResult result = alg.decompose(a);
    AMatrix q = result.getQ();
    AMatrix r = result.getR();


    assertEquals(IdentityMatrix.create(3), q);

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Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR

     * 
     * @param matrix
     * @return
     */
    public static IQRResult decompose(AMatrix matrix) {
        HouseholderQR alg = new HouseholderQR(false);
        return alg.decompose(matrix);  
    }

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Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR

     * 
     * @param matrix
     * @return
     */
    public static IQRResult decompose(AMatrix matrix, boolean compact) {
        HouseholderQR alg = new HouseholderQR(compact);
        return alg.decompose(matrix);  
    }

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Examples of mikera.matrixx.decompose.impl.qr.HouseholderQR

   * 
   * @param matrix
   * @return
   */
  public static IQRResult decomposeCompact(AMatrix matrix) {
    HouseholderQR alg = new HouseholderQR(true);
    return alg.decompose(matrix);  
  }

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