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

      super(3, startParams, 0.0, new double[] { 1.0, 0.0, 0.0 });
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure tmp1 = variables[0].getField().getZero();
        if (x1.getValue() == 0) {
            tmp1 = tmp1.add((x2.getValue() >= 0) ? 0.25 : -0.25);
        } else {
            tmp1 = x2.divide(x1).atan().divide(twoPi);
            if (x1.getValue() < 0) {
                tmp1 = tmp1.add(0.5);
            }
        }
        DerivativeStructure tmp2 = x1.multiply(x1).add(x2.multiply(x2)).sqrt();
        return new DerivativeStructure[] {
            x3.subtract(tmp1.multiply(10)).multiply(10),
            tmp2.subtract(1).multiply(10),
            x3
        };
    }

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      super(4, startParams, 0.0, buildArray(4, 0.0));
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure x4 = variables[3];
      return new DerivativeStructure[] {
        x1.add(x2.multiply(10)),
        x3.subtract(x4).multiply(sqrt5),
        x2.subtract(x3.multiply(2)).multiply(x2.subtract(x3.multiply(2))),
        x1.subtract(x4).multiply(x1.subtract(x4)).multiply(sqrt10)

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            theoreticalMinParams);
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        return new DerivativeStructure[] {
            x1.subtract(13.0).add(x2.negate().add(5.0).multiply(x2).subtract(2).multiply(x2)),
            x1.subtract(29.0).add(x2.add(1).multiply(x2).subtract(14).multiply(x2))
        };
    }

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            theoreticalMinParams);
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure   x1 = variables[0];
        DerivativeStructure   x2 = variables[1];
        DerivativeStructure   x3 = variables[2];
        DerivativeStructure[] f = new DerivativeStructure[m];
      for (int i = 0; i < m; ++i) {
        double tmp1 = i + 1;
        double tmp2 = 15 - i;
        double tmp3 = (i <= 7) ? tmp1 : tmp2;
        f[i] = x1.add(x2.multiply(tmp2).add(x3.multiply(tmp3)).reciprocal().multiply(tmp1)).negate().add(y[i]);
      }
      return f;
    }

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      }
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure x4 = variables[3];
        DerivativeStructure[] f = new DerivativeStructure[m];
        for (int i = 0; i < m; ++i) {
            f[i] = x1.multiply(x2.add(v[i]).multiply(v[i])).divide(x4.add(x3.add(v[i]).multiply(v[i]))).negate().add(y[i]);
        }
        return f;
    }

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      }
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure[] f = new DerivativeStructure[m];
      for (int i = 0; i < m; ++i) {
        f[i] = x1.multiply(x2.divide(x3.add(5.0 * (i + 1) + 45.0)).exp()).subtract(y[i]);
      }
     return f;
    }

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    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure[] f = new DerivativeStructure[m];
        for (int i = 0; i < (m - 2); ++i) {
            double div = (i + 1) / 29.0;
            DerivativeStructure s1 = variables[0].getField().getZero();
            DerivativeStructure dx = variables[0].getField().getOne();
            for (int j = 1; j < n; ++j) {
                s1 = s1.add(dx.multiply(j).multiply(variables[j]));
                dx = dx.multiply(div);
            }
            DerivativeStructure s2 = variables[0].getField().getZero();
            dx = variables[0].getField().getOne();
            for (int j = 0; j < n; ++j) {
                s2 = s2.add(dx.multiply(variables[j]));
                dx = dx.multiply(div);
            }
            f[i] = s1.subtract(s2.multiply(s2)).subtract(1);
        }


        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        f[m - 2] = x1;
        f[m - 1] = x2.subtract(x1.multiply(x1)).subtract(1);


        return f;


    }

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            new double[] { 1.0, 10.0, 1.0 });
   }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure[] f = new DerivativeStructure[m];
      for (int i = 0; i < m; ++i) {
        double tmp = (i + 1) / 10.0;
        f[i] = x1.multiply(-tmp).exp().subtract(x2.multiply(-tmp).exp()).add(
                  x3.multiply(FastMath.exp(-i - 1) - FastMath.exp(-tmp)));
      }
      return f;
    }

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            theoreticalMinParams);
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure[] f = new DerivativeStructure[m];
        for (int i = 0; i < m; ++i) {
            double temp = i + 1;
            f[i] = x1.multiply(temp).exp().add(x2.multiply(temp).exp()).subtract(2 + 2 * temp).negate();
        }
        return f;
    }

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      setCostAccuracy(2.5e-8);
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure x4 = variables[3];
        DerivativeStructure[] f = new DerivativeStructure[m];
        for (int i = 0; i < m; ++i) {
            double temp = (i + 1) / 5.0;
            DerivativeStructure tmp1 = x1.add(x2.multiply(temp)).subtract(FastMath.exp(temp));
            DerivativeStructure tmp2 = x3.add(x4.multiply(FastMath.sin(temp))).subtract(FastMath.cos(temp));
            f[i] = tmp1.multiply(tmp1).add(tmp2.multiply(tmp2));
        }
        return f;
    }

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

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

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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

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