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) $

     * 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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        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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            // 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);
            interpolator.reinitialize(stepEnd, stepSize, predictedScaled, nordsieckTmp);


            // discrete events handling
            interpolator.storeTime(stepEnd);

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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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                               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) {
                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());
       assertEquals(1, ((OLSMultipleLinearRegression) regression).calculateRSquared(), 1E-12);
    }

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            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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  @Test
  public void testLeastSquares1()
  throws FunctionEvaluationException, ConvergenceException {


      final RealMatrix factors =
          new Array2DRowRealMatrix(new double[][] {
              { 1.0, 0.0 },
              { 0.0, 1.0 }
          }, false);
      LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
          public double[] value(double[] variables) {
              return factors.operate(variables);
          }
      }, new double[] { 2.0, -3.0 });
      NelderMead optimizer = new NelderMead();
      optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
      optimizer.setMaxIterations(200);

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