Examples of org.apache.commons.math.linear.Array2DRowRealMatrix

org.apache.commons.math.linear.Array2DRowRealMatrix
ath.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf"> LU decomposition to support linear system solution and inverse.
The LU decomposition is performed as needed, to support the following operations:
- solve
- isSingular
- getDeterminant
- inverse
Usage notes:
- The LU decomposition is cached and reused on subsequent calls. If data are modified via references to the underlying array obtained using getDataRef(), then the stored LU decomposition will not be discarded. In this case, you need to explicitly invoke LUDecompose() to recompute the decomposition before using any of the methods above.
- As specified in the {@link RealMatrix} interface, matrix element indexingis 0-based -- e.g., getEntry(0, 0) returns the element in the first row, first column of the matrix.
@version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $

            new Covariance().covariance(one, two, false);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected
        }
        RealMatrix matrix = new Array2DRowRealMatrix(new double[][] {{0},{1}});
        try {
            new Covariance(matrix);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected

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        assertEquals(covarianceMatrix.getEntry(2, 3), 
                new Covariance().covariance(matrix.getColumn(2), matrix.getColumn(3), true), 10E-14);
        assertEquals(covarianceMatrix.getEntry(2, 3), covarianceMatrix.getEntry(3, 2), Double.MIN_VALUE);
        
        // All columns same -> all entries = column variance
        RealMatrix repeatedColumns = new Array2DRowRealMatrix(47, 3);
        for (int i = 0; i < 3; i++) {
            repeatedColumns.setColumnMatrix(i, matrix.getColumnMatrix(0));
        }
        RealMatrix repeatedCovarianceMatrix = new Covariance(repeatedColumns).getCovarianceMatrix();
        double columnVariance = variance.evaluate(matrix.getColumn(0));
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {

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        int ptr = 0;
        for (int i = 0; i < nRows; i++) {
            System.arraycopy(data, ptr, matrixData[i], 0, nCols);
            ptr += nCols;
        }
        return new Array2DRowRealMatrix(matrixData); 
    }

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                               1e-14);
        double[] residuals = regression.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{0d,0d,0d,0d,0d,0d},
                               1e-14);
        RealMatrix errors =
            new Array2DRowRealMatrix(regression.estimateRegressionParametersVariance(), false);
        final double[] s = { 1.0, -1.0 /  2.0, -1.0 /  3.0, -1.0 /  4.0, -1.0 /  5.0, -1.0 /  6.0 };
        RealMatrix referenceVariance = new Array2DRowRealMatrix(s.length, s.length);
        referenceVariance.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
            @Override
            public double visit(int row, int column, double value)
                throws MatrixVisitorException {
                if (row == 0) {
                    return s[column];
                }
                double x = s[row] * s[column];
                return (row == column) ? 2 * x : x;
            }
        });
       assertEquals(0.0,
                     errors.subtract(referenceVariance).getNorm(),
                     5.0e-16 * referenceVariance.getNorm());
    }

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    public RealMatrix calculateHat() {
        // Create augmented identity matrix
        RealMatrix Q = qr.getQ();
        final int p = qr.getR().getColumnDimension();
        final int n = Q.getColumnDimension();
        Array2DRowRealMatrix augI = new Array2DRowRealMatrix(n, n);
        double[][] augIData = augI.getDataRef();
        for (int i = 0; i < n; i++) {
            for (int j =0; j < n; j++) {
                if (i == j && i < p) {
                    augIData[i][j] = 1d;
                } else {

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     * 
     * @param x the [n,k] array representing the x sample
     */
    @Override
    protected void newXSampleData(double[][] x) {
        this.X = new Array2DRowRealMatrix(x);
        qr = new QRDecompositionImpl(X);
    }

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     * Add the covariance data.
     * 
     * @param omega the [n,n] array representing the covariance
     */
    protected void newCovarianceData(double[][] omega){
        this.Omega = new Array2DRowRealMatrix(omega);
        this.OmegaInverse = null;
    }

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        this.numDecisionVariables   = getNumVariables() + (restrictToNonNegative ? 0 : 1);
        this.numSlackVariables      = getConstraintTypeCounts(Relationship.LEQ) +
                                      getConstraintTypeCounts(Relationship.GEQ);
        this.numArtificialVariables = getConstraintTypeCounts(Relationship.EQ) +
                                      getConstraintTypeCounts(Relationship.GEQ);
        this.tableau = new Array2DRowRealMatrix(createTableau(goalType == GoalType.MAXIMIZE));
        initialize();
    }

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            for (int j = 0; j < width - 1; j++) {
                matrix[i][j] = getEntry(i + 1, j + 1);
            }
            matrix[i][width - 1] = getEntry(i + 1, getRhsOffset());
        }
        this.tableau = new Array2DRowRealMatrix(matrix);
        this.numArtificialVariables = 0;
    }

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        referenceTime = interpolator.referenceTime;
        if (interpolator.scaled != null) {
            scaled = interpolator.scaled.clone();
        }
        if (interpolator.nordsieck != null) {
            nordsieck = new Array2DRowRealMatrix(interpolator.nordsieck.getDataRef(), true);
        }
        if (interpolator.stateVariation != null) {
            stateVariation = interpolator.stateVariation.clone();
        }
    }

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