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


        DerivativeStructure[] f = new DerivativeStructure[m];
        Arrays.fill(f, variables[0].getField().getZero());


        for (int j = 0; j < n; ++j) {
            DerivativeStructure tmp1 = variables[0].getField().getOne();
            DerivativeStructure tmp2 = variables[j].multiply(2).subtract(1);
            DerivativeStructure temp = tmp2.multiply(2);
            for (int i = 0; i < m; ++i) {
                f[i] = f[i].add(tmp2);
                DerivativeStructure ti = temp.multiply(tmp2).subtract(tmp1);
                tmp1 = tmp2;
                tmp2 = ti;
            }
        }

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    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure[] f = new DerivativeStructure[m];
        DerivativeStructure sum  = variables[0].getField().getZero().subtract(n + 1);
        DerivativeStructure prod = variables[0].getField().getOne();
      for (int j = 0; j < n; ++j) {
        sum  = sum.add(variables[j]);
        prod = prod.multiply(variables[j]);
      }
      for (int i = 0; i < n; ++i) {
        f[i] = variables[i].add(sum);
      }
      f[n - 1] = prod.subtract(1);
      return f;
    }

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            theoreticalMinParams);
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x1 = variables[0];
        DerivativeStructure x2 = variables[1];
        DerivativeStructure x3 = variables[2];
        DerivativeStructure x4 = variables[3];
        DerivativeStructure x5 = variables[4];
        DerivativeStructure[] f = new DerivativeStructure[m];
      for (int i = 0; i < m; ++i) {
        double temp = 10.0 * i;
        DerivativeStructure tmp1 = x4.multiply(-temp).exp();
        DerivativeStructure tmp2 = x5.multiply(-temp).exp();
        f[i] = x1.add(x2.multiply(tmp1)).add(x3.multiply(tmp2)).negate().add(y[i]);
      }
      return f;
    }

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            theoreticalMinParams);
    }


    @Override
    public DerivativeStructure[] value(DerivativeStructure[] variables) {
        DerivativeStructure x01 = variables[0];
        DerivativeStructure x02 = variables[1];
        DerivativeStructure x03 = variables[2];
        DerivativeStructure x04 = variables[3];
        DerivativeStructure x05 = variables[4];
        DerivativeStructure x06 = variables[5];
        DerivativeStructure x07 = variables[6];
        DerivativeStructure x08 = variables[7];
        DerivativeStructure x09 = variables[8];
        DerivativeStructure x10 = variables[9];
        DerivativeStructure x11 = variables[10];
        DerivativeStructure[] f = new DerivativeStructure[m];
        for (int i = 0; i < m; ++i) {
            double temp = i / 10.0;
            DerivativeStructure tmp1 = x05.multiply(-temp).exp();
            DerivativeStructure tmp2 = x06.negate().multiply(x09.subtract(temp).multiply(x09.subtract(temp))).exp();
            DerivativeStructure tmp3 = x07.negate().multiply(x10.subtract(temp).multiply(x10.subtract(temp))).exp();
            DerivativeStructure tmp4 = x08.negate().multiply(x11.subtract(temp).multiply(x11.subtract(temp))).exp();
            f[i] = x01.multiply(tmp1).add(x02.multiply(tmp2)).add(x03.multiply(tmp3)).add(x04.multiply(tmp4)).negate().add(y[i]);
        }
        return f;
    }

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        return model;
    }


    public DerivativeStructure[] value(DerivativeStructure[] params) {
        final DerivativeStructure cx = params[0];
        final DerivativeStructure cy = params[1];
        final DerivativeStructure r = params[2];


        final DerivativeStructure[] model = new DerivativeStructure[points.size() * 2];


        for (int i = 0; i < points.size(); i++) {
            final Vector2D p = points.get(i);


            // Find the circle point closest to the observed point
            // (observed points are points add through the addPoint method above)
            final DerivativeStructure dX = cx.subtract(p.getX());
            final DerivativeStructure dY = cy.subtract(p.getY());
            final DerivativeStructure scaling = r.divide(dX.multiply(dX).add(dY.multiply(dY)).sqrt());
            final int index  = i * 2;
            model[index]     = cx.subtract(scaling.multiply(dX));
            model[index + 1] = cy.subtract(scaling.multiply(dY));


        }


        return model;

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        try {
            dataset = new StatisticalReferenceDataset(in) {


                @Override
                public DerivativeStructure getModelValue(final double x, final DerivativeStructure[] a) {
                    final DerivativeStructure p = a[0].add(a[1].add(a[2].multiply(x)).multiply(x));
                    final DerivativeStructure q = a[3].add(a[4].multiply(x)).multiply(x).add(1.0);
                    return p.divide(q);
                }


            };
        } finally {

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        try {
            dataset = new StatisticalReferenceDataset(in) {


                @Override
                public DerivativeStructure getModelValue(final double x, final DerivativeStructure[] a) {
                    final DerivativeStructure p = a[0].add(a[1].add(a[2].add(a[3].multiply(x)).multiply(x)).multiply(x));
                    final DerivativeStructure q = a[4].add(a[5].add(a[6].multiply(x)).multiply(x)).multiply(x).add(1.0);
                    return p.divide(q);
                }


            };
        } finally {

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        return r / points.size();
    }


    private DerivativeStructure distance(Vector2D point,
                                         DerivativeStructure cx, DerivativeStructure cy) {
        DerivativeStructure dx = cx.subtract(point.getX());
        DerivativeStructure dy = cy.subtract(point.getY());
        return dx.multiply(dx).add(dy.multiply(dy)).sqrt();
    }

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        DerivativeStructure dy = cy.subtract(point.getY());
        return dx.multiply(dx).add(dy.multiply(dy)).sqrt();
    }


    public DerivativeStructure getRadius(DerivativeStructure cx, DerivativeStructure cy) {
        DerivativeStructure r = cx.getField().getZero();
        for (Vector2D point : points) {
            r = r.add(distance(point, cx, cy));
        }
        return r.divide(points.size());
    }

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        return sum;
    }


    public DerivativeStructure value(DerivativeStructure[] variables)  {
        DerivativeStructure radius = getRadius(variables[0], variables[1]);


        DerivativeStructure sum = variables[0].getField().getZero();
        for (Vector2D point : points) {
            DerivativeStructure di = distance(point, variables[0], variables[1]).subtract(radius);
            sum = sum.add(di.multiply(di));
        }


        return sum;
    }

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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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