Examples of QRDecomposition

Jama.QRDecomposition
QR Decomposition.
For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.
The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.
org.apache.commons.math.linear.QRDecomposition
nist.gov/javanumerics/jama/">JAMA library, with the following changes:
- a {@link #getQT() getQT} method has been added,
- the solve and isFullRank methods have been replaced by a {@link #getSolver() getSolver} method and the equivalent methods provided bythe returned {@link DecompositionSolver}.
@see MathWorld @see Wikipedia @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $ @since 1.2
org.apache.commons.math3.linear.QRDecomposition
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 1.2 (changed to concrete class in 3.0)
org.apache.mahout.math.QRDecomposition
partially deprecated until unit tests are in place. Until this time, this class/interface is unsupported.
org.ejml.factory.QRDecomposition
QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'. Where A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix, and R ∈ ℜ ^{n × m} is an upper triangular matrix. Some implementations of QR decomposition require that A has full rank.

Some features of QR decompositions:
- Can decompose rectangular matrices.
- Numerically stable solutions to least-squares problem, but not as stable as SVD
- Can incrementally add and remove columns from the decomposed matrix. See {@link org.ejml.alg.dense.linsol.qr.AdjLinearSolverQr}
Orthogonal matrices have the following properties:
- QQ^T=I
- Q^T=Q^-1
@see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholder @see org.ejml.alg.dense.decomposition.qr.QRDecompositionHouseholderColumn @author Peter Abeles
org.encog.mathutil.matrices.decomposition.QRDecomposition
nist.gov/javanumerics/jama/
org.jquantlib.math.matrixutilities.QRDecomposition
fpl.fs.fed.us/optimization.html">MINPACK/J
This subroutine uses householder transformations with optional column pivoting to compute a QR factorization of the {@latex$ m} by {@latex$ n} matrix {@latex$ A}.
That is, Minpack_f77#qrfac determines an orthogonal matrix {@latex$ Q}, a permutation matrix {@latex$ P}, and an upper trapezoidal matrix {@latex$ R} with diagonal elements of nonincreasing magnitude, such that {@latex$ A*P = Q*R}.
Return value ipvt is an integer array of length {@latex$ n}, which defines the permutation matrix {@latex$ P}such that {@latex$ A*P = Q*R}.
Column {@latex$ j} of {@latex$ P} is column ipvt[j] of the identity matrix.
See lmdiff.cpp for further details. @see MathWorld @see Wikipedia @see MINPACK/J @see MINPACK @author Richard Gomes

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

     * once it is successfully loaded.</p>
     */
    @Override
    protected void newXSampleData(double[][] x) {
        super.newXSampleData(x);
        qr = new QRDecomposition(getX());
    }

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

            }
        }


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

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


        }


        // 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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Examples of org.apache.commons.math3.linear.QRDecomposition

        // 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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Examples of org.apache.commons.math3.linear.QRDecomposition

            try {
                // solve the linearized least squares problem
                RealMatrix mA = new BlockRealMatrix(a);
                DecompositionSolver solver = useLU ?
                        new LUDecomposition(mA).getSolver() :
                        new QRDecomposition(mA).getSolver();
                final double[] dX = solver.solve(new ArrayRealVector(b, false)).toArray();
                // update the estimated parameters
                for (int i = 0; i < nC; ++i) {
                    currentPoint[i] += dX[i];
                }

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

        // 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();
    }

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

        // 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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Examples of org.apache.commons.math3.linear.QRDecomposition

     * <p>This implementation computes and caches the QR decomposition of the X matrix.</p>
     */
    @Override
    public void newSampleData(double[] data, int nobs, int nvars) {
        super.newSampleData(data, nobs, nvars);
        qr = new QRDecomposition(getX(), threshold);
    }

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

     * once it is successfully loaded.</p>
     */
    @Override
    protected void newXSampleData(double[][] x) {
        super.newXSampleData(x);
        qr = new QRDecomposition(getX());
    }

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

        // 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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