Examples of org.apache.commons.math3.analysis.differentiation.DerivativeStructure

Package org.apache.commons.math3.analysis.differentiation

Examples of org.apache.commons.math3.analysis.differentiation.DerivativeStructure

org.apache.commons.math3.analysis.differentiation.DerivativeStructure
american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf">Doubly Recursive Multivariate Automatic Differentiation, Mathematics Magazine, vol. 75, no. 3, June 2002.
. Rall's numbers are an extension to the real numbers used throughout mathematical expressions; they hold the derivative together with the value of a function. Dan Kalman's derivative structures hold all partial derivatives up to any specified order, with respect to any number of free parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free parameter, and real numbers can be seen as derivative structures with zero order derivative and no free parameters.

{@link DerivativeStructure} instances can be used directly thanks tothe arithmetic operators to the mathematical functions provided as methods by this class (+, -, *, /, %, sin, cos ...).

Implementing complex expressions by hand using these classes is a tedious and error-prone task but has the advantage of having no limitation on the derivation order despite no requiring users to compute the derivatives by themselves. Implementing complex expression can also be done by developing computation code using standard primitive double values and to use {@link UnivariateFunctionDifferentiator differentiators} to create the {@link DerivativeStructure}-based instances. This method is simpler but may be limited in the accuracy and derivation orders and may be computationally intensive (this is typically the case for {@link FiniteDifferencesDifferentiator finite differencesdifferentiator}.

Instances of this class are guaranteed to be immutable.
@see DSCompiler @since 3.1

                new PolynomialFunctionNewtonForm(new double[] { 0, 1, 3, 1 },
                                                 new double[] { 0, 1, 2 });


        double eps = 2.0e-14;
        for (double t = 0.0; t < 10.0; t += 0.1) {
            DerivativeStructure x = new DerivativeStructure(1, 4, 0, t);
            DerivativeStructure y = p.value(x);
            Assert.assertEquals(t * t * t,   y.getValue(),              eps * t * t * t);
            Assert.assertEquals(3.0 * t * t, y.getPartialDerivative(1), eps * 3.0 * t * t);
            Assert.assertEquals(6.0 * t,     y.getPartialDerivative(2), eps * 6.0 * t);
            Assert.assertEquals(6.0,         y.getPartialDerivative(3), eps * 6.0);
            Assert.assertEquals(0.0,         y.getPartialDerivative(4), eps);
        }


    }

View Full Code Here

                                        FunctionUtils.multiply(new Constant(1e6), inv),
                                        FunctionUtils.multiply(new Constant(1e4),
                                                               FunctionUtils.compose(inv, sqrt)));


                public double value(double x) {
                    return func.value(new DerivativeStructure(1, 1, 0, x)).getPartialDerivative(1);
                }


            };


        BrentSolver solver = new BrentSolver();

View Full Code Here

        public double getMax() {
            return max;
        }


        public double value(final double x) {
            return value(new DerivativeStructure(0, 0, x)).getValue();
        }

View Full Code Here

            }


            public UnivariateFunction derivative() {
                return new UnivariateFunction() {
                    public double value(double x) {
                        return q.value(new DerivativeStructure(1, 1, 0, x)).getPartialDerivative(1);
                    }
                };
            }


        };

View Full Code Here


        return w;
    }


    public double[] value(double[] params) {
        final Model line = new Model(new DerivativeStructure(0, 0, params[0]),
                                     new DerivativeStructure(0, 0, params[1]));


        final double[] model = new double[points.size()];
        for (int i = 0; i < points.size(); i++) {
            final double[] p = points.get(i);
            model[i] = line.value(p[0]);

View Full Code Here

    public DerivativeStructure[] value(DerivativeStructure[] params) {
        final Model line = new Model(params[0], params[1]);


        final DerivativeStructure[] model = new DerivativeStructure[points.size()];
        for (int i = 0; i < points.size(); i++) {
            final DerivativeStructure p0 = params[0].getField().getZero().add(points.get(i)[0]);
            model[i] = line.value(p0);
        }


        return model;
    }

View Full Code Here

        this.problem = new MultivariateDifferentiableVectorFunction() {


            public double[] value(final double[] a) {
                DerivativeStructure[] dsA = new DerivativeStructure[a.length];
                for (int i = 0; i < a.length; ++i) {
                    dsA[i] = new DerivativeStructure(a.length, 0, a[i]);
                }
                final int n = getNumObservations();
                final double[] yhat = new double[n];
                for (int i = 0; i < n; i++) {
                    yhat[i] = getModelValue(getX(i), dsA).getValue();

View Full Code Here

      }


      public double[] value(double[] variables) {
          DerivativeStructure[] dsV = new DerivativeStructure[variables.length];
          for (int i = 0; i < variables.length; ++i) {
              dsV[i] = new DerivativeStructure(0, 0, variables[i]);
          }
          DerivativeStructure[] dsY = value(dsV);
          double[] y = new double[dsY.length];
          for (int i = 0; i < dsY.length; ++i) {
              y[i] = dsY[i].getValue();

View Full Code Here

            buildArray(n, -1.0));
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
      DerivativeStructure sum = variables[0].getField().getZero();
      for (int i = 0; i < n; ++i) {
        sum = sum.add(variables[i]);
      }
      DerivativeStructure t  = sum.multiply(2.0 / m).add(1);
      DerivativeStructure[] f = new DerivativeStructure[m];
      for (int i = 0; i < n; ++i) {
        f[i] = variables[i].subtract(t);
      }
      Arrays.fill(f, n, m, t.negate());
      return f;
    }

View Full Code Here

                for (int j = 0; j < factors.getColumnDimension(); ++j) {
                    y[i] = y[i].add(variables[j].multiply(factors.getEntry(i, j)));
                }
            }


            DerivativeStructure sum = variables[0].getField().getZero();
            for (int i = 0; i < y.length; ++i) {
                DerivativeStructure ri = y[i].subtract(target[i]);
                sum = sum.add(ri.multiply(ri));
            }
            return sum;
        }

View Full Code Here

0 1 2 3 4 5 6 7 8 9

TOP

Related Classes of org.apache.commons.math3.analysis.differentiation.DerivativeStructure

org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction

org.apache.commons.math3.analysis.function.Constant

org.apache.commons.math3.analysis.function.GaussianTest

org.apache.commons.math3.analysis.function.LogitTest

org.apache.commons.math3.analysis.function.SigmoidTest

org.apache.commons.math3.analysis.function.Sin

org.apache.commons.math3.analysis.function.Sinc

org.apache.commons.math3.analysis.function.SincTest

org.apache.commons.math3.analysis.function.SqrtTest

org.apache.commons.math3.analysis.FunctionUtils

All source code are property of their respective owners. Java is a trademark of Sun Microsystems, Inc and owned by ORACLE Inc. Contact coftware#gmail.com.