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- the solve and isFullRank methods have been replaced by a {@link #getSolver() getSolver} method and the equivalent methods provided bythe returned {@link DecompositionSolver}.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 Jama.QRDecomposition

     * inversion/qr decomposition until the preferable
     * Apache commons class catches up. Matrix is the Jama version
     * RealMatrixImpl is the commons version.
     */
    Matrix v = new Matrix(new VandermondeMatrix(x,order+1).getMatrix().getData());
    QRDecomposition qr = new QRDecomposition(v);
    rMatrix = new RealMatrixImpl(qr.getR().getArray());
    qMatrix = new RealMatrixImpl(qr.getQ().getArray());
    RealMatrix qMatrixTransposed = qMatrix.transpose();
    RealMatrix qByY = qMatrixTransposed.multiply(yMatrix);
    RealMatrix  rMatrixInverse = new RealMatrixImpl(new Matrix(rMatrix.getData()).inverse().getArray());
    RealMatrix resultMatrix = rMatrixInverse.multiply(qByY);
    coefficiants= resultMatrix.getColumn(0);

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Examples of Jama.QRDecomposition

            errorCount = try_failure(errorCount, "times(double)...",
                    "incorrect Matrix-scalar product calculation");
        }


        A = new Matrix(columnwise, 4);
        QRDecomposition QR = A.qr();


        R = QR.getR();
        try {
            check(A, QR.getQ().times(R));
            try_success("QRDecomposition...", "");
        } catch (java.lang.RuntimeException e) {
            errorCount = try_failure(errorCount, "QRDecomposition...",
                    "incorrect QR decomposition calculation");
        }

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Examples of Jama.QRDecomposition

            Matrix R = L.times(U).minus(M.getMatrix(p, 0, n - 1));
            double res = R.norm1() / (n * eps);


            print(fixedWidthDoubletoString(res, 12, 3));


            QRDecomposition QR = new QRDecomposition(M);
            Matrix Q = QR.getQ();


            R = QR.getR();
            R = Q.times(R).minus(M);
            res = R.norm1() / (n * eps);
            print(fixedWidthDoubletoString(res, 12, 3));


            print("\n");

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

        }
    }


    /** test solve */
    public void testSolve() {
        QRDecomposition decomposition =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular));
        DecompositionSolver solver = decomposition.getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { -102, 12250 }, { 544, 24500 }, { 167, -36750 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 2515 }, { 2, 422 }, { -3, 898 }

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

    }


    private void checkDimension(RealMatrix m) {
        int rows = m.getRowDimension();
        int columns = m.getColumnDimension();
        QRDecomposition qr = new QRDecompositionImpl(m);
        assertEquals(rows,    qr.getQ().getRowDimension());
        assertEquals(rows,    qr.getQ().getColumnDimension());
        assertEquals(rows,    qr.getR().getRowDimension());
        assertEquals(columns, qr.getR().getColumnDimension());        
    }

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

        checkAEqualQR(createTestMatrix(r, q, p));


    }


    private void checkAEqualQR(RealMatrix m) {
        QRDecomposition qr = new QRDecompositionImpl(m);
        double norm = qr.getQ().multiply(qr.getR()).subtract(m).getNorm();
        assertEquals(0, norm, normTolerance);
    }

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

        checkQOrthogonal(createTestMatrix(r, q, p));


    }


    private void checkQOrthogonal(RealMatrix m) {
        QRDecomposition qr = new QRDecompositionImpl(m);
        RealMatrix eye = MatrixUtils.createRealIdentityMatrix(m.getRowDimension());
        double norm = qr.getQT().multiply(qr.getQ()).subtract(eye).getNorm();
        assertEquals(0, norm, normTolerance);
    }

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

            }
        });
    }
    /** test matrices values */
    public void testMatricesValues() {
        QRDecomposition qr =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular));
        RealMatrix qRef = MatrixUtils.createRealMatrix(new double[][] {
                { -12.0 / 14.0,   69.0 / 175.0,  -58.0 / 175.0 },
                {  -6.0 / 14.0, -158.0 / 175.0,    6.0 / 175.0 },
                {   4.0 / 14.0,  -30.0 / 175.0, -165.0 / 175.0 }
        });
        RealMatrix rRef = MatrixUtils.createRealMatrix(new double[][] {
                { -14.0,  -21.0, 14.0 },
                {   0.0, -175.0, 70.0 },
                {   0.0,    0.0, 35.0 }
        });
        RealMatrix hRef = MatrixUtils.createRealMatrix(new double[][] {
                { 26.0 / 14.0, 0.0, 0.0 },
                {  6.0 / 14.0, 648.0 / 325.0, 0.0 },
                { -4.0 / 14.0,  36.0 / 325.0, 2.0 }
        });


        // check values against known references
        RealMatrix q = qr.getQ();
        assertEquals(0, q.subtract(qRef).getNorm(), 1.0e-13);
        RealMatrix qT = qr.getQT();
        assertEquals(0, qT.subtract(qRef.transpose()).getNorm(), 1.0e-13);
        RealMatrix r = qr.getR();
        assertEquals(0, r.subtract(rRef).getNorm(), 1.0e-13);
        RealMatrix h = qr.getH();
        assertEquals(0, h.subtract(hRef).getNorm(), 1.0e-13);


        // check the same cached instance is returned the second time
        assertTrue(q == qr.getQ());
        assertTrue(r == qr.getR());
        assertTrue(h == qr.getH());
        
    }

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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

        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);
        vector.setEntry(row, nearSite.pos.y);
      }
      
      QRDecomposition qr = new QRDecomposition(matrix);
      RealVector solution = qr.getSolver().solve(vector);
        
      double[] coeffs = solution.toArray();
      
      for (double coeff : coeffs) {
        if (coeff > 10e3) {

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