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) $

            x[i][0] = 1.0d;
            for (int j = 1; j < nvars + 1; j++) {
                x[i][j] = data[pointer++];
            }
        }
        this.X = new Array2DRowRealMatrix(x);
        this.Y = new ArrayRealVector(y);
    }

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     * Loads new x sample data, overriding any previous sample
     *
     * @param x the [n,k] array representing the x sample
     */
    protected void newXSampleData(double[][] x) {
        this.X = new Array2DRowRealMatrix(x);
    }

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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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    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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        // create a matrix of the correct size
        int width = numDecisionVariables + numSlackVariables +
        numArtificialVariables + getNumObjectiveFunctions() + 1; // + 1 is for RHS
        int height = constraints.size() + getNumObjectiveFunctions();
        Array2DRowRealMatrix matrix = new Array2DRowRealMatrix(height, width);


        // initialize the objective function rows
        if (getNumObjectiveFunctions() == 2) {
            matrix.setEntry(0, 0, -1);
        }
        int zIndex = (getNumObjectiveFunctions() == 1) ? 0 : 1;
        matrix.setEntry(zIndex, zIndex, maximize ? 1 : -1);
        RealVector objectiveCoefficients =
            maximize ? f.getCoefficients().mapMultiply(-1) : f.getCoefficients();
        copyArray(objectiveCoefficients.getData(), matrix.getDataRef()[zIndex]);
        matrix.setEntry(zIndex, width - 1,
            maximize ? f.getConstantTerm() : -1 * f.getConstantTerm());


        if (!restrictToNonNegative) {
            matrix.setEntry(zIndex, getSlackVariableOffset() - 1,
                getInvertedCoeffiecientSum(objectiveCoefficients));
        }


        // initialize the constraint rows
        int slackVar = 0;
        int artificialVar = 0;
        for (int i = 0; i < constraints.size(); i++) {
            LinearConstraint constraint = constraints.get(i);
            int row = getNumObjectiveFunctions() + i;


            // decision variable coefficients
            copyArray(constraint.getCoefficients().getData(), matrix.getDataRef()[row]);


            // x-
            if (!restrictToNonNegative) {
                matrix.setEntry(row, getSlackVariableOffset() - 1,
                    getInvertedCoeffiecientSum(constraint.getCoefficients()));
            }


            // RHS
            matrix.setEntry(row, width - 1, constraint.getValue());


            // slack variables
            if (constraint.getRelationship() == Relationship.LEQ) {
                matrix.setEntry(row, getSlackVariableOffset() + slackVar++, 1);  // slack
            } else if (constraint.getRelationship() == Relationship.GEQ) {
                matrix.setEntry(row, getSlackVariableOffset() + slackVar++, -1); // excess
            }


            // artificial variables
            if ((constraint.getRelationship() == Relationship.EQ) ||
                    (constraint.getRelationship() == Relationship.GEQ)) {
                matrix.setEntry(0, getArtificialVariableOffset() + artificialVar, 1);
                matrix.setEntry(row, getArtificialVariableOffset() + artificialVar++, 1);
                matrix.setRowVector(0, matrix.getRowVector(0).subtract(matrix.getRowVector(row)));
            }
        }


        return matrix;
    }

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        for (int i = columnsToDrop.size() - 1; i >= 0; i--) {
          columnLabels.remove((int) columnsToDrop.get(i));
        }


        this.tableau = new Array2DRowRealMatrix(matrix);
        this.numArtificialVariables = 0;
    }

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                    // update Nordsieck vector
                    final double[] predictedScaled = new double[y0.length];
                    for (int j = 0; j < y0.length; ++j) {
                        predictedScaled[j] = stepSize * yDot[j];
                    }
                    final Array2DRowRealMatrix nordsieckTmp = updateHighOrderDerivativesPhase1(nordsieck);
                    updateHighOrderDerivativesPhase2(scaled, predictedScaled, nordsieckTmp);


                    // discrete events handling
                    interpolatorTmp.reinitialize(stepEnd, stepSize, predictedScaled, nordsieckTmp);
                    interpolatorTmp.storeTime(stepStart);

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                // update Nordsieck vector
                final double[] predictedScaled = new double[y0.length];
                for (int j = 0; j < y0.length; ++j) {
                    predictedScaled[j] = stepSize * yDot[j];
                }
                final Array2DRowRealMatrix nordsieckTmp = updateHighOrderDerivativesPhase1(nordsieck);
                updateHighOrderDerivativesPhase2(scaled, predictedScaled, nordsieckTmp);


                // apply correction (C in the PECE sequence)
                error = nordsieckTmp.walkInOptimizedOrder(new Corrector(y, predictedScaled, yTmp));


                if (error <= 1.0) {


                    // evaluate a final estimate of the derivative (second E in the PECE sequence)
                    computeDerivatives(stepEnd, yTmp, yDot);

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