Package org.apache.commons.math3.linear

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

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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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     * @param residuals Residuals.
     * @return the cost.
     * @see #computeResiduals(double[])
     */
    protected double computeCost(double[] residuals) {
        final ArrayRealVector r = new ArrayRealVector(residuals);
        return FastMath.sqrt(r.dotProduct(getWeight().operate(r)));
    }
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    for (SiteWithPolynomial site : sites) {
     
      List<SiteWithPolynomial> nearestSites =
          nearestSiteMap.get(site);
     
      RealVector vector = new ArrayRealVector(SITES_FOR_APPROX);
      RealMatrix matrix = new Array2DRowRealMatrix(
          SITES_FOR_APPROX, DefaultPolynomial.NUM_COEFFS);
     
      for (int row = 0; row < SITES_FOR_APPROX; row++) {
        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);
       
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    /**
     * @return a comparator for sorting the optima.
     */
    private Comparator<PointVectorValuePair> getPairComparator() {
        return new Comparator<PointVectorValuePair>() {
            private final RealVector target = new ArrayRealVector(optimizer.getTarget(), false);
            private final RealMatrix weight = optimizer.getWeight();

            public int compare(final PointVectorValuePair o1,
                               final PointVectorValuePair o2) {
                if (o1 == null) {
                    return (o2 == null) ? 0 : 1;
                } else if (o2 == null) {
                    return -1;
                }
                return Double.compare(weightedResidual(o1),
                                      weightedResidual(o2));
            }

            private double weightedResidual(final PointVectorValuePair pv) {
                final RealVector v = new ArrayRealVector(pv.getValueRef(), false);
                final RealVector r = target.subtract(v);
                return r.dotProduct(weight.operate(r));
            }
        };
    }
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    }

    private void checkdimensions(RealMatrix matrix) {
        final int m = matrix.getRowDimension();
        final int n = matrix.getColumnDimension();
        BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix);
        Assert.assertEquals(m, transformer.getU().getRowDimension());
        Assert.assertEquals(m, transformer.getU().getColumnDimension());
        Assert.assertEquals(m, transformer.getB().getRowDimension());
        Assert.assertEquals(n, transformer.getB().getColumnDimension());
        Assert.assertEquals(n, transformer.getV().getRowDimension());
        Assert.assertEquals(n, transformer.getV().getColumnDimension());

    }
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        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare).transpose());
    }

    private void checkAEqualUSVt(RealMatrix matrix) {
        BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix);
        RealMatrix u = transformer.getU();
        RealMatrix b = transformer.getB();
        RealMatrix v = transformer.getV();
        double norm = u.multiply(b).multiply(v.transpose()).subtract(matrix).getNorm();
        Assert.assertEquals(0, norm, 1.0e-14);
    }
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        Assert.assertEquals(0, norm, 1.0e-14);
    }

    @Test
    public void testUOrthogonal() {
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getU());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getU());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getU());
    }
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        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getU());
    }

    @Test
    public void testVOrthogonal() {
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getV());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getV());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getV());
    }
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        Assert.assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-14);
    }

    @Test
    public void testBBiDiagonal() {
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getB());
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getB());
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getB());
    }
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        }
    }

    @Test
    public void testSingularMatrix() {
       BiDiagonalTransformer transformer =
            new BiDiagonalTransformer(MatrixUtils.createRealMatrix(new double[][] {
                { 1.0, 2.0, 3.0 },
                { 2.0, 3.0, 4.0 },
                { 3.0, 5.0, 7.0 }
            }));
       final double s3  = FastMath.sqrt(3.0);
       final double s14 = FastMath.sqrt(14.0);
       final double s1553 = FastMath.sqrt(1553.0);
       RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
           {  -1.0 / s14,  5.0 / (s3 * s14),  1.0 / s3 },
           {  -2.0 / s14, -4.0 / (s3 * s14),  1.0 / s3 },
           {  -3.0 / s14,  1.0 / (s3 * s14), -1.0 / s3 }
       });
       RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] {
           { -s14, s1553 / s14,   0.0 },
           {  0.0, -87 * s3 / (s14 * s1553), -s3 * s14 / s1553 },
           {  0.0, 0.0, 0.0 }
       });
       RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
           { 1.0,   0.0,         0.0        },
           { 0.0,  -23 / s1553,  32 / s1553 },
           { 0.0,  -32 / s1553, -23 / s1553 }
       });

       // check values against known references
       RealMatrix u = transformer.getU();
       Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14);
       RealMatrix b = transformer.getB();
       Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14);
       RealMatrix v = transformer.getV();
       Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14);

       // check the same cached instance is returned the second time
       Assert.assertTrue(u == transformer.getU());
       Assert.assertTrue(b == transformer.getB());
       Assert.assertTrue(v == transformer.getV());

    }
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Related Classes of org.apache.commons.math3.linear.BiDiagonalTransformer

  • org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • org.apache.commons.math3.analysis.function.HarmonicOscillator
  • org.apache.commons.math3.analysis.function.Sin
  • org.apache.commons.math3.analysis.function.Sinc
  • org.apache.commons.math3.analysis.MultivariateFunction
  • org.apache.commons.math3.analysis.QuinticFunction
  • org.apache.commons.math3.analysis.solvers.BrentSolver
  • org.apache.commons.math3.analysis.UnivariateFunction
  • org.apache.commons.math3.complex.Complex
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