Examples of org.apache.commons.math3.linear.RRQRDecomposition

org.apache.commons.math3.linear.RealMatrix
nist.gov/javanumerics/jama/">JAMA library, with the following changes:
- a {@link #getQT() getQT} method has been added,
- the {@code solve} and {@code isFullRank} methods have been replacedby a {@link #getSolver() getSolver} method and the equivalent methodsprovided by the returned {@link DecompositionSolver}.
@see MathWorld @see Wikipedia @since 3.2

  @Override
  public Solver getSolver(RealMatrix M) {
    if (M == null) {
      return null;
    }
    RRQRDecomposition decomposition = new RRQRDecomposition(M, SINGULARITY_THRESHOLD);
    DecompositionSolver solver = decomposition.getSolver();
    if (solver.isNonSingular()) {
      return new CommonsMathSolver(solver);
    }
    // Otherwise try to report apparent rank
    int apparentRank = decomposition.getRank(0.01); // Better value?
    log.warn("{} x {} matrix is near-singular (threshold {}). Add more data or decrease the value of model.features, " +
             "to <= about {}",
             M.getRowDimension(), 
             M.getColumnDimension(), 
             SINGULARITY_THRESHOLD,

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    throw new SingularMatrixSolverException(apparentRank, "Apparent rank: " + apparentRank);
  }  


  @Override
  public boolean isNonSingular(RealMatrix M) {
    QRDecomposition decomposition = new RRQRDecomposition(M, SINGULARITY_THRESHOLD);
    DecompositionSolver solver = decomposition.getSolver();
    return solver.isNonSingular();
  }

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  public Solver getSolver(RealMatrix M) {
    if (M == null) {
      return null;
    }
    RRQRDecomposition decomposition = new RRQRDecomposition(M, SINGULARITY_THRESHOLD);
    DecompositionSolver solver = decomposition.getSolver();
    if (solver.isNonSingular()) {
      return new Solver(solver);
    }
    // Otherwise try to report apparent rank
    int apparentRank = decomposition.getRank(0.01); // Better value?
    log.warn("{} x {} matrix is near-singular (threshold {}). Add more data or decrease the " +
             "value of als.hyperparams.features, to <= about {}",
             M.getRowDimension(), 
             M.getColumnDimension(), 
             SINGULARITY_THRESHOLD,

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             apparentRank);
    throw new SingularMatrixSolverException(apparentRank, "Apparent rank: " + apparentRank);
  }  


  public boolean isNonSingular(RealMatrix M) {
    QRDecomposition decomposition = new RRQRDecomposition(M, SINGULARITY_THRESHOLD);
    DecompositionSolver solver = decomposition.getSolver();
    return solver.isNonSingular();
  }

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     * if the covariance matrix cannot be computed (singular problem).
     */
    public double[][] computeCovariances(double[] params,
                                         double threshold) {
        // Set up the Jacobian.
        final RealMatrix j = computeWeightedJacobian(params);


        // Compute transpose(J)J.
        final RealMatrix jTj = j.transpose().multiply(j);


        // Compute the covariances matrix.
        final DecompositionSolver solver
            = new QRDecomposition(jTj, threshold).getSolver();
        return solver.getInverse().getData();

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     * @return the square-root of the weight matrix.
     */
    private RealMatrix squareRoot(RealMatrix m) {
        if (m instanceof DiagonalMatrix) {
            final int dim = m.getRowDimension();
            final RealMatrix sqrtM = new DiagonalMatrix(dim);
            for (int i = 0; i < dim; i++) {
                sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();

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      List<SiteWithPolynomial> nearestSites =
          nearestSiteMap.get(site);
      
      RealVector vector = new ArrayRealVector(SITES_FOR_APPROX);
      RealMatrix matrix = new Array2DRowRealMatrix(
          SITES_FOR_APPROX, DefaultPolynomial.NUM_COEFFS);
      
      for (int row = 0; row < SITES_FOR_APPROX; row++) {
        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);

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     * @param matrix matrix with columns representing variables to correlate
     * @return correlation matrix
     */
    public RealMatrix computeCorrelationMatrix(final RealMatrix matrix) {
        int nVars = matrix.getColumnDimension();
        RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
        for (int i = 0; i < nVars; i++) {
            for (int j = 0; j < i; j++) {
                double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));
                outMatrix.setEntry(i, j, corr);
                outMatrix.setEntry(j, i, corr);
            }
            outMatrix.setEntry(i, i, 1d);
        }
        return outMatrix;
    }

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        // solve the rectangular system in the least square sense
        // to get the best estimate of the Nordsieck vector [s2 ... sk]
        QRDecomposition decomposition;
        decomposition = new QRDecomposition(new Array2DRowRealMatrix(a, false));
        RealMatrix x = decomposition.getSolver().solve(new Array2DRowRealMatrix(b, false));
        return new Array2DRowRealMatrix(x.getData(), false);
    }

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        double[] qtf     = new double[nR];
        double[] work1   = new double[nC];
        double[] work2   = new double[nC];
        double[] work3   = new double[nC];


        final RealMatrix weightMatrixSqrt = getWeightSquareRoot();


        // Evaluate the function at the starting point and calculate its norm.
        double[] currentObjective = computeObjectiveValue(currentPoint);
        double[] currentResiduals = computeResiduals(currentObjective);
        PointVectorValuePair current = new PointVectorValuePair(currentPoint, currentObjective);
        double currentCost = computeCost(currentResiduals);


        // Outer loop.
        lmPar = 0;
        boolean firstIteration = true;
        final ConvergenceChecker<PointVectorValuePair> checker = getConvergenceChecker();
        while (true) {
            incrementIterationCount();


            final PointVectorValuePair previous = current;


            // QR decomposition of the jacobian matrix
            qrDecomposition(computeWeightedJacobian(currentPoint));


            weightedResidual = weightMatrixSqrt.operate(currentResiduals);
            for (int i = 0; i < nR; i++) {
                qtf[i] = weightedResidual[i];
            }


            // compute Qt.res

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