RRQRDecomposition.java

  1. /*
  2.  * Licensed to the Apache Software Foundation (ASF) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * The ASF licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *      http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */

  18. package org.apache.commons.math4.legacy.linear;

  20. import org.apache.commons.math4.core.jdkmath.JdkMath;


  23. /**
  24.  * Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting.
  25.  * <p>The rank-revealing QR-decomposition of a matrix A consists of three matrices Q,
  26.  * R and P such that AP=QR.  Q is orthogonal (Q<sup>T</sup>Q = I), and R is upper triangular.
  27.  * If A is m&times;n, Q is m&times;m and R is m&times;n and P is n&times;n.</p>
  28.  * <p>QR decomposition with column pivoting produces a rank-revealing QR
  29.  * decomposition and the {@link #getRank(double)} method may be used to return the rank of the
  30.  * input matrix A.</p>
  31.  * <p>This class compute the decomposition using Householder reflectors.</p>
  32.  * <p>For efficiency purposes, the decomposition in packed form is transposed.
  33.  * This allows inner loop to iterate inside rows, which is much more cache-efficient
  34.  * in Java.</p>
  35.  * <p>This class is based on the class with similar name from the
  36.  * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
  37.  * following changes:</p>
  38.  * <ul>
  39.  *   <li>a {@link #getQT() getQT} method has been added,</li>
  40.  *   <li>the {@code solve} and {@code isFullRank} methods have been replaced
  41.  *   by a {@link #getSolver() getSolver} method and the equivalent methods
  42.  *   provided by the returned {@link DecompositionSolver}.</li>
  43.  * </ul>
  44.  *
  45.  * @see <a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>
  46.  * @see <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a>
  47.  *
  48.  * @since 3.2
  49.  */
  50. public class RRQRDecomposition extends QRDecomposition {

  52.     /** An array to record the column pivoting for later creation of P. */
  53.     private int[] p;

  55.     /** Cached value of P. */
  56.     private RealMatrix cachedP;


  59.     /**
  60.      * Calculates the QR-decomposition of the given matrix.
  61.      * The singularity threshold defaults to zero.
  62.      *
  63.      * @param matrix The matrix to decompose.
  64.      *
  65.      * @see #RRQRDecomposition(RealMatrix, double)
  66.      */
  67.     public RRQRDecomposition(RealMatrix matrix) {
  68.         this(matrix, 0d);
  69.     }

  71.     /**
  72.      * Calculates the QR-decomposition of the given matrix.
  73.      *
  74.      * @param matrix The matrix to decompose.
  75.      * @param threshold Singularity threshold.
  76.      * @see #RRQRDecomposition(RealMatrix)
  77.      */
  78.     public RRQRDecomposition(RealMatrix matrix,  double threshold) {
  79.         super(matrix, threshold);
  80.     }

  82.     /** Decompose matrix.
  83.      * @param qrt transposed matrix
  84.      */
  85.     @Override
  86.     protected void decompose(double[][] qrt) {
  87.         p = new int[qrt.length];
  88.         for (int i = 0; i < p.length; i++) {
  89.             p[i] = i;
  90.         }
  91.         super.decompose(qrt);
  92.     }

  94.     /** Perform Householder reflection for a minor A(minor, minor) of A.
  95.      *
  96.      * @param minor minor index
  97.      * @param qrt transposed matrix
  98.      */
  99.     @Override
  100.     protected void performHouseholderReflection(int minor, double[][] qrt) {
  101.         double l2NormSquaredMax = 0;
  102.         // Find the unreduced column with the greatest L2-Norm
  103.         int l2NormSquaredMaxIndex = minor;
  104.         for (int i = minor; i < qrt.length; i++) {
  105.             double l2NormSquared = 0;
  106.             for (int j = minor; j < qrt[i].length; j++) {
  107.                 l2NormSquared += qrt[i][j] * qrt[i][j];
  108.             }
  109.             if (l2NormSquared > l2NormSquaredMax) {
  110.                 l2NormSquaredMax = l2NormSquared;
  111.                 l2NormSquaredMaxIndex = i;
  112.             }
  113.         }
  114.         // swap the current column with that with the greated L2-Norm and record in p
  115.         if (l2NormSquaredMaxIndex != minor) {
  116.             double[] tmp1 = qrt[minor];
  117.             qrt[minor] = qrt[l2NormSquaredMaxIndex];
  118.             qrt[l2NormSquaredMaxIndex] = tmp1;
  119.             int tmp2 = p[minor];
  120.             p[minor] = p[l2NormSquaredMaxIndex];
  121.             p[l2NormSquaredMaxIndex] = tmp2;
  122.         }

  124.         super.performHouseholderReflection(minor, qrt);
  125.     }


  128.     /**
  129.      * Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.
  130.      *
  131.      * If no pivoting is used in this decomposition then P is equal to the identity matrix.
  132.      *
  133.      * @return a permutation matrix.
  134.      */
  135.     public RealMatrix getP() {
  136.         if (cachedP == null) {
  137.             int n = p.length;
  138.             cachedP = MatrixUtils.createRealMatrix(n,n);
  139.             for (int i = 0; i < n; i++) {
  140.                 cachedP.setEntry(p[i], i, 1);
  141.             }
  142.         }
  143.         return cachedP ;
  144.     }

  146.     /**
  147.      * Return the effective numerical matrix rank.
  148.      * <p>The effective numerical rank is the number of non-negligible
  149.      * singular values.</p>
  150.      * <p>This implementation looks at Frobenius norms of the sequence of
  151.      * bottom right submatrices.  When a large fall in norm is seen,
  152.      * the rank is returned. The drop is computed as:</p>
  153.      * <pre>
  154.      *   (thisNorm/lastNorm) * rNorm &lt; dropThreshold
  155.      * </pre>
  156.      * <p>
  157.      * where thisNorm is the Frobenius norm of the current submatrix,
  158.      * lastNorm is the Frobenius norm of the previous submatrix,
  159.      * rNorm is is the Frobenius norm of the complete matrix
  160.      * </p>
  161.      *
  162.      * @param dropThreshold threshold triggering rank computation
  163.      * @return effective numerical matrix rank
  164.      */
  165.     public int getRank(final double dropThreshold) {
  166.         RealMatrix r    = getR();
  167.         int rows        = r.getRowDimension();
  168.         int columns     = r.getColumnDimension();
  169.         int rank        = 1;
  170.         double lastNorm = r.getFrobeniusNorm();
  171.         double rNorm    = lastNorm;
  172.         while (rank < JdkMath.min(rows, columns)) {
  173.             double thisNorm = r.getSubMatrix(rank, rows - 1, rank, columns - 1).getFrobeniusNorm();
  174.             if (thisNorm == 0 || (thisNorm / lastNorm) * rNorm < dropThreshold) {
  175.                 break;
  176.             }
  177.             lastNorm = thisNorm;
  178.             rank++;
  179.         }
  180.         return rank;
  181.     }

  183.     /**
  184.      * Get a solver for finding the A &times; X = B solution in least square sense.
  185.      * <p>
  186.      * Least Square sense means a solver can be computed for an overdetermined system,
  187.      * (i.e. a system with more equations than unknowns, which corresponds to a tall A
  188.      * matrix with more rows than columns). In any case, if the matrix is singular
  189.      * within the tolerance set at {@link RRQRDecomposition#RRQRDecomposition(RealMatrix,
  190.      * double) construction}, an error will be triggered when
  191.      * the {@link DecompositionSolver#solve(RealVector) solve} method will be called.
  192.      * </p>
  193.      * @return a solver
  194.      */
  195.     @Override
  196.     public DecompositionSolver getSolver() {
  197.         return new Solver(super.getSolver(), this.getP());
  198.     }

  200.     /** Specialized solver. */
  201.     private static final class Solver implements DecompositionSolver {

  203.         /** Upper level solver. */
  204.         private final DecompositionSolver upper;

  206.         /** A permutation matrix for the pivots used in the QR decomposition. */
  207.         private RealMatrix p;

  209.         /**
  210.          * Build a solver from decomposed matrix.
  211.          *
  212.          * @param upper upper level solver.
  213.          * @param p permutation matrix
  214.          */
  215.         private Solver(final DecompositionSolver upper, final RealMatrix p) {
  216.             this.upper = upper;
  217.             this.p     = p;
  218.         }

  220.         /** {@inheritDoc} */
  221.         @Override
  222.         public boolean isNonSingular() {
  223.             return upper.isNonSingular();
  224.         }

  226.         /** {@inheritDoc} */
  227.         @Override
  228.         public RealVector solve(RealVector b) {
  229.             return p.operate(upper.solve(b));
  230.         }

  232.         /** {@inheritDoc} */
  233.         @Override
  234.         public RealMatrix solve(RealMatrix b) {
  235.             return p.multiply(upper.solve(b));
  236.         }

  238.         /**
  239.          * {@inheritDoc}
  240.          * @throws SingularMatrixException if the decomposed matrix is singular.
  241.          */
  242.         @Override
  243.         public RealMatrix getInverse() {
  244.             return solve(MatrixUtils.createRealIdentityMatrix(p.getRowDimension()));
  245.         }
  246.     }
  247. }
Created with JaCoCo 0.8.10.202304240956Code Coverage Report for Apache Commons Math 4.0-SNAPSHOT