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 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.analysis.differentiation;

import java.io.Serializable;

import org.apache.commons.math3.Field;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;

Class representing both the value and the differentials of a function.
This class is the workhorse of the differentiation package.
This class is an implementation of the extension to Rall's
numbers described in Dan Kalman's paper 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.
DerivativeStructure instances can be used directly thanks to the 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 differentiators to create the 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 finite differences
differentiator.
Instances of this class are guaranteed to be immutable.
See Also:
DSCompiler
Since:
3.1/** Class representing both the value and the differentials of a function.
 * <p>This class is the workhorse of the differentiation package.</p>
 * <p>This class is an implementation of the extension to Rall's
 * numbers described in Dan Kalman's paper <a
 * href="http://www1.american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf">Doubly
 * Recursive Multivariate Automatic Differentiation</a>, 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.</p>
 * <p>{@link DerivativeStructure} instances can be used directly thanks to
 * the arithmetic operators to the mathematical functions provided as
 * methods by this class (+, -, *, /, %, sin, cos ...).</p>
 * <p>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 differences
 * differentiator}.</p>
 * <p>Instances of this class are guaranteed to be immutable.</p>
 * @see DSCompiler
 * @since 3.1
 */
public class DerivativeStructure implements RealFieldElement<DerivativeStructure>, Serializable {

    
Serializable UID. /** Serializable UID. */
    private static final long serialVersionUID = 20120730L;

    
Compiler for the current dimensions. /** Compiler for the current dimensions. */
    private transient DSCompiler compiler;

    
Combined array holding all values. /** Combined array holding all values. */
    private final double[] data;

    
Build an instance with all values and derivatives set to 0.
Params:
compiler – compiler to use for computation/** Build an instance with all values and derivatives set to 0.
     * @param compiler compiler to use for computation
     */
    private DerivativeStructure(final DSCompiler compiler) {
        this.compiler = compiler;
        this.data     = new double[compiler.getSize()];
    }

    
Build an instance with all values and derivatives set to 0.
Params:
parameters – number of free parameters
order – derivation order
Throws:
NumberIsTooLargeException – if order is too large/** Build an instance with all values and derivatives set to 0.
     * @param parameters number of free parameters
     * @param order derivation order
     * @throws NumberIsTooLargeException if order is too large
     */
    public DerivativeStructure(final int parameters, final int order)
        throws NumberIsTooLargeException {
        this(DSCompiler.getCompiler(parameters, order));
    }

    
Build an instance representing a constant value.
Params:
parameters – number of free parameters
order – derivation order
value – value of the constant
Throws:
NumberIsTooLargeException – if order is too large
See Also:
DerivativeStructure(int, int, int, double)/** Build an instance representing a constant value.
     * @param parameters number of free parameters
     * @param order derivation order
     * @param value value of the constant
     * @throws NumberIsTooLargeException if order is too large
     * @see #DerivativeStructure(int, int, int, double)
     */
    public DerivativeStructure(final int parameters, final int order, final double value)
        throws NumberIsTooLargeException {
        this(parameters, order);
        this.data[0] = value;
    }

    
Build an instance representing a variable.
Instances built using this constructor are considered
to be the free variables with respect to which differentials
are computed. As such, their differential with respect to
themselves is +1.
Params:
parameters – number of free parameters
order – derivation order
index – index of the variable (from 0 to parameters - 1)
value – value of the variable
Throws:
NumberIsTooLargeException – if index >= parameters.
See Also:
DerivativeStructure(int, int, double)/** Build an instance representing a variable.
     * <p>Instances built using this constructor are considered
     * to be the free variables with respect to which differentials
     * are computed. As such, their differential with respect to
     * themselves is +1.</p>
     * @param parameters number of free parameters
     * @param order derivation order
     * @param index index of the variable (from 0 to {@code parameters - 1})
     * @param value value of the variable
     * @exception NumberIsTooLargeException if {@code index >= parameters}.
     * @see #DerivativeStructure(int, int, double)
     */
    public DerivativeStructure(final int parameters, final int order,
                               final int index, final double value)
        throws NumberIsTooLargeException {
        this(parameters, order, value);

        if (index >= parameters) {
            throw new NumberIsTooLargeException(index, parameters, false);
        }

        if (order > 0) {
            // the derivative of the variable with respect to itself is 1.
            data[DSCompiler.getCompiler(index, order).getSize()] = 1.0;
        }

    }

    
Linear combination constructor.
The derivative structure built will be a1 * ds1 + a2 * ds2
Params:
a1 – first scale factor
ds1 – first base (unscaled) derivative structure
a2 – second scale factor
ds2 – second base (unscaled) derivative structure
Throws:
DimensionMismatchException – if number of free parameters or orders are inconsistent/** Linear combination constructor.
     * The derivative structure built will be a1 * ds1 + a2 * ds2
     * @param a1 first scale factor
     * @param ds1 first base (unscaled) derivative structure
     * @param a2 second scale factor
     * @param ds2 second base (unscaled) derivative structure
     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
     */
    public DerivativeStructure(final double a1, final DerivativeStructure ds1,
                               final double a2, final DerivativeStructure ds2)
        throws DimensionMismatchException {
        this(ds1.compiler);
        compiler.checkCompatibility(ds2.compiler);
        compiler.linearCombination(a1, ds1.data, 0, a2, ds2.data, 0, data, 0);
    }

    
Linear combination constructor.
The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3
Params:
a1 – first scale factor
ds1 – first base (unscaled) derivative structure
a2 – second scale factor
ds2 – second base (unscaled) derivative structure
a3 – third scale factor
ds3 – third base (unscaled) derivative structure
Throws:
DimensionMismatchException – if number of free parameters or orders are inconsistent/** Linear combination constructor.
     * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3
     * @param a1 first scale factor
     * @param ds1 first base (unscaled) derivative structure
     * @param a2 second scale factor
     * @param ds2 second base (unscaled) derivative structure
     * @param a3 third scale factor
     * @param ds3 third base (unscaled) derivative structure
     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
     */
    public DerivativeStructure(final double a1, final DerivativeStructure ds1,
                               final double a2, final DerivativeStructure ds2,
                               final double a3, final DerivativeStructure ds3)
        throws DimensionMismatchException {
        this(ds1.compiler);
        compiler.checkCompatibility(ds2.compiler);
        compiler.checkCompatibility(ds3.compiler);
        compiler.linearCombination(a1, ds1.data, 0, a2, ds2.data, 0, a3, ds3.data, 0, data, 0);
    }

    
Linear combination constructor.
The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
Params:
a1 – first scale factor
ds1 – first base (unscaled) derivative structure
a2 – second scale factor
ds2 – second base (unscaled) derivative structure
a3 – third scale factor
ds3 – third base (unscaled) derivative structure
a4 – fourth scale factor
ds4 – fourth base (unscaled) derivative structure
Throws:
DimensionMismatchException – if number of free parameters or orders are inconsistent/** Linear combination constructor.
     * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
     * @param a1 first scale factor
     * @param ds1 first base (unscaled) derivative structure
     * @param a2 second scale factor
     * @param ds2 second base (unscaled) derivative structure
     * @param a3 third scale factor
     * @param ds3 third base (unscaled) derivative structure
     * @param a4 fourth scale factor
     * @param ds4 fourth base (unscaled) derivative structure
     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
     */
    public DerivativeStructure(final double a1, final DerivativeStructure ds1,
                               final double a2, final DerivativeStructure ds2,
                               final double a3, final DerivativeStructure ds3,
                               final double a4, final DerivativeStructure ds4)
        throws DimensionMismatchException {
        this(ds1.compiler);
        compiler.checkCompatibility(ds2.compiler);
        compiler.checkCompatibility(ds3.compiler);
        compiler.checkCompatibility(ds4.compiler);
        compiler.linearCombination(a1, ds1.data, 0, a2, ds2.data, 0,
                                   a3, ds3.data, 0, a4, ds4.data, 0,
                                   data, 0);
    }

    
Build an instance from all its derivatives.
Params:
parameters – number of free parameters
order – derivation order
derivatives – derivatives sorted according to DSCompiler.getPartialDerivativeIndex(int...)
Throws:
DimensionMismatchException – if derivatives array does not match the size expected by the compiler
NumberIsTooLargeException – if order is too large
See Also:
getAllDerivatives()/** Build an instance from all its derivatives.
     * @param parameters number of free parameters
     * @param order derivation order
     * @param derivatives derivatives sorted according to
     * {@link DSCompiler#getPartialDerivativeIndex(int...)}
     * @exception DimensionMismatchException if derivatives array does not match the
     * {@link DSCompiler#getSize() size} expected by the compiler
     * @throws NumberIsTooLargeException if order is too large
     * @see #getAllDerivatives()
     */
    public DerivativeStructure(final int parameters, final int order, final double ... derivatives)
        throws DimensionMismatchException, NumberIsTooLargeException {
        this(parameters, order);
        if (derivatives.length != data.length) {
            throw new DimensionMismatchException(derivatives.length, data.length);
        }
        System.arraycopy(derivatives, 0, data, 0, data.length);
    }

    
Copy constructor.
Params:
ds – instance to copy/** Copy constructor.
     * @param ds instance to copy
     */
    private DerivativeStructure(final DerivativeStructure ds) {
        this.compiler = ds.compiler;
        this.data     = ds.data.clone();
    }

    
Get the number of free parameters.
Returns:
number of free parameters/** Get the number of free parameters.
     * @return number of free parameters
     */
    public int getFreeParameters() {
        return compiler.getFreeParameters();
    }

    
Get the derivation order.
Returns:
derivation order/** Get the derivation order.
     * @return derivation order
     */
    public int getOrder() {
        return compiler.getOrder();
    }

    
Create a constant compatible with instance order and number of parameters.
 This method is a convenience factory method, it simply calls new DerivativeStructure(getFreeParameters(), getOrder(), c) 
Params:
c – value of the constant
See Also:
DerivativeStructure(int, int, double)
Returns:
a constant compatible with instance order and number of parameters
Since:
3.3/** Create a constant compatible with instance order and number of parameters.
     * <p>
     * This method is a convenience factory method, it simply calls
     * {@code new DerivativeStructure(getFreeParameters(), getOrder(), c)}
     * </p>
     * @param c value of the constant
     * @return a constant compatible with instance order and number of parameters
     * @see #DerivativeStructure(int, int, double)
     * @since 3.3
     */
    public DerivativeStructure createConstant(final double c) {
        return new DerivativeStructure(getFreeParameters(), getOrder(), c);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public double getReal() {
        return data[0];
    }

    
Get the value part of the derivative structure.
See Also:
getPartialDerivative(int...)
Returns:
value part of the derivative structure/** Get the value part of the derivative structure.
     * @return value part of the derivative structure
     * @see #getPartialDerivative(int...)
     */
    public double getValue() {
        return data[0];
    }

    
Get a partial derivative.
Params:
orders – derivation orders with respect to each variable (if all orders are 0,
the value is returned)
Throws:
DimensionMismatchException – if the numbers of variables does not
match the instance
NumberIsTooLargeException – if sum of derivation orders is larger
than the instance limits
See Also:
getValue()
Returns:
partial derivative/** Get a partial derivative.
     * @param orders derivation orders with respect to each variable (if all orders are 0,
     * the value is returned)
     * @return partial derivative
     * @see #getValue()
     * @exception DimensionMismatchException if the numbers of variables does not
     * match the instance
     * @exception NumberIsTooLargeException if sum of derivation orders is larger
     * than the instance limits
     */
    public double getPartialDerivative(final int ... orders)
        throws DimensionMismatchException, NumberIsTooLargeException {
        return data[compiler.getPartialDerivativeIndex(orders)];
    }

    
Get all partial derivatives.
Returns:
a fresh copy of partial derivatives, in an array sorted according to DSCompiler.getPartialDerivativeIndex(int...)/** Get all partial derivatives.
     * @return a fresh copy of partial derivatives, in an array sorted according to
     * {@link DSCompiler#getPartialDerivativeIndex(int...)}
     */
    public double[] getAllDerivatives() {
        return data.clone();
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure add(final double a) {
        final DerivativeStructure ds = new DerivativeStructure(this);
        ds.data[0] += a;
        return ds;
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     */
    public DerivativeStructure add(final DerivativeStructure a)
        throws DimensionMismatchException {
        compiler.checkCompatibility(a.compiler);
        final DerivativeStructure ds = new DerivativeStructure(this);
        compiler.add(data, 0, a.data, 0, ds.data, 0);
        return ds;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure subtract(final double a) {
        return add(-a);
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     */
    public DerivativeStructure subtract(final DerivativeStructure a)
        throws DimensionMismatchException {
        compiler.checkCompatibility(a.compiler);
        final DerivativeStructure ds = new DerivativeStructure(this);
        compiler.subtract(data, 0, a.data, 0, ds.data, 0);
        return ds;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public DerivativeStructure multiply(final int n) {
        return multiply((double) n);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure multiply(final double a) {
        final DerivativeStructure ds = new DerivativeStructure(this);
        for (int i = 0; i < ds.data.length; ++i) {
            ds.data[i] *= a;
        }
        return ds;
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     */
    public DerivativeStructure multiply(final DerivativeStructure a)
        throws DimensionMismatchException {
        compiler.checkCompatibility(a.compiler);
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.multiply(data, 0, a.data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure divide(final double a) {
        final DerivativeStructure ds = new DerivativeStructure(this);
        for (int i = 0; i < ds.data.length; ++i) {
            ds.data[i] /= a;
        }
        return ds;
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     */
    public DerivativeStructure divide(final DerivativeStructure a)
        throws DimensionMismatchException {
        compiler.checkCompatibility(a.compiler);
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.divide(data, 0, a.data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public DerivativeStructure remainder(final double a) {
        final DerivativeStructure ds = new DerivativeStructure(this);
        ds.data[0] = FastMath.IEEEremainder(ds.data[0], a);
        return ds;
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure remainder(final DerivativeStructure a)
        throws DimensionMismatchException {
        compiler.checkCompatibility(a.compiler);
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.remainder(data, 0, a.data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public DerivativeStructure negate() {
        final DerivativeStructure ds = new DerivativeStructure(compiler);
        for (int i = 0; i < ds.data.length; ++i) {
            ds.data[i] = -data[i];
        }
        return ds;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure abs() {
        if (Double.doubleToLongBits(data[0]) < 0) {
            // we use the bits representation to also handle -0.0
            return negate();
        } else {
            return this;
        }
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure ceil() {
        return new DerivativeStructure(compiler.getFreeParameters(),
                                       compiler.getOrder(),
                                       FastMath.ceil(data[0]));
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure floor() {
        return new DerivativeStructure(compiler.getFreeParameters(),
                                       compiler.getOrder(),
                                       FastMath.floor(data[0]));
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure rint() {
        return new DerivativeStructure(compiler.getFreeParameters(),
                                       compiler.getOrder(),
                                       FastMath.rint(data[0]));
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public long round() {
        return FastMath.round(data[0]);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure signum() {
        return new DerivativeStructure(compiler.getFreeParameters(),
                                       compiler.getOrder(),
                                       FastMath.signum(data[0]));
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure copySign(final DerivativeStructure sign){
        long m = Double.doubleToLongBits(data[0]);
        long s = Double.doubleToLongBits(sign.data[0]);
        if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
            return this;
        }
        return negate(); // flip sign
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure copySign(final double sign) {
        long m = Double.doubleToLongBits(data[0]);
        long s = Double.doubleToLongBits(sign);
        if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
            return this;
        }
        return negate(); // flip sign
    }

    
Return the exponent of the instance value, removing the bias.

For double numbers of the form 2x, the unbiased
exponent is exactly x.

Returns:
exponent for instance in IEEE754 representation, without bias/**
     * Return the exponent of the instance value, removing the bias.
     * <p>
     * For double numbers of the form 2<sup>x</sup>, the unbiased
     * exponent is exactly x.
     * </p>
     * @return exponent for instance in IEEE754 representation, without bias
     */
    public int getExponent() {
        return FastMath.getExponent(data[0]);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure scalb(final int n) {
        final DerivativeStructure ds = new DerivativeStructure(compiler);
        for (int i = 0; i < ds.data.length; ++i) {
            ds.data[i] = FastMath.scalb(data[i], n);
        }
        return ds;
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure hypot(final DerivativeStructure y)
        throws DimensionMismatchException {

        compiler.checkCompatibility(y.compiler);

        if (Double.isInfinite(data[0]) || Double.isInfinite(y.data[0])) {
            return new DerivativeStructure(compiler.getFreeParameters(),
                                           compiler.getFreeParameters(),
                                           Double.POSITIVE_INFINITY);
        } else if (Double.isNaN(data[0]) || Double.isNaN(y.data[0])) {
            return new DerivativeStructure(compiler.getFreeParameters(),
                                           compiler.getFreeParameters(),
                                           Double.NaN);
        } else {

            final int expX = getExponent();
            final int expY = y.getExponent();
            if (expX > expY + 27) {
                // y is neglectible with respect to x
                return abs();
            } else if (expY > expX + 27) {
                // x is neglectible with respect to y
                return y.abs();
            } else {

                // find an intermediate scale to avoid both overflow and underflow
                final int middleExp = (expX + expY) / 2;

                // scale parameters without losing precision
                final DerivativeStructure scaledX = scalb(-middleExp);
                final DerivativeStructure scaledY = y.scalb(-middleExp);

                // compute scaled hypotenuse
                final DerivativeStructure scaledH =
                        scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();

                // remove scaling
                return scaledH.scalb(middleExp);

            }

        }
    }

    
Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2)
avoiding intermediate overflow or underflow.

 If either argument is infinite, then the result is positive infinity.
 else, if either argument is NaN then the result is NaN.

Params:
x – a value
y – a value
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Returns:
sqrt(x2 +y2)
Since:
3.2/**
     * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
     * - sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
     * avoiding intermediate overflow or underflow.
     *
     * <ul>
     * <li> If either argument is infinite, then the result is positive infinity.</li>
     * <li> else, if either argument is NaN then the result is NaN.</li>
     * </ul>
     *
     * @param x a value
     * @param y a value
     * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public static DerivativeStructure hypot(final DerivativeStructure x, final DerivativeStructure y)
        throws DimensionMismatchException {
        return x.hypot(y);
    }

    
Compute composition of the instance by a univariate function.
Params:
f – array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).
Throws:
DimensionMismatchException – if the number of derivatives in the array is not equal to order + 1
Returns:
f(this)/** Compute composition of the instance by a univariate function.
     * @param f array of value and derivatives of the function at
     * the current point (i.e. [f({@link #getValue()}),
     * f'({@link #getValue()}), f''({@link #getValue()})...]).
     * @return f(this)
     * @exception DimensionMismatchException if the number of derivatives
     * in the array is not equal to {@link #getOrder() order} + 1
     */
    public DerivativeStructure compose(final double ... f)
        throws DimensionMismatchException {
        if (f.length != getOrder() + 1) {
            throw new DimensionMismatchException(f.length, getOrder() + 1);
        }
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.compose(data, 0, f, result.data, 0);
        return result;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public DerivativeStructure reciprocal() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.pow(data, 0, -1, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure sqrt() {
        return rootN(2);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure cbrt() {
        return rootN(3);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure rootN(final int n) {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.rootN(data, 0, n, result.data, 0);
        return result;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public Field<DerivativeStructure> getField() {
        return new Field<DerivativeStructure>() {

            
{@inheritDoc} /** {@inheritDoc} */
            public DerivativeStructure getZero() {
                return new DerivativeStructure(compiler.getFreeParameters(), compiler.getOrder(), 0.0);
            }

            
{@inheritDoc} /** {@inheritDoc} */
            public DerivativeStructure getOne() {
                return new DerivativeStructure(compiler.getFreeParameters(), compiler.getOrder(), 1.0);
            }

            
{@inheritDoc} /** {@inheritDoc} */
            public Class<? extends FieldElement<DerivativeStructure>> getRuntimeClass() {
                return DerivativeStructure.class;
            }

        };
    }

    
Compute ax where a is a double and x a DerivativeStructure 
Params:
a – number to exponentiate
x – power to apply
Returns:
ax
Since:
3.3/** Compute a<sup>x</sup> where a is a double and x a {@link DerivativeStructure}
     * @param a number to exponentiate
     * @param x power to apply
     * @return a<sup>x</sup>
     * @since 3.3
     */
    public static DerivativeStructure pow(final double a, final DerivativeStructure x) {
        final DerivativeStructure result = new DerivativeStructure(x.compiler);
        x.compiler.pow(a, x.data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure pow(final double p) {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.pow(data, 0, p, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure pow(final int n) {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.pow(data, 0, n, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure pow(final DerivativeStructure e)
        throws DimensionMismatchException {
        compiler.checkCompatibility(e.compiler);
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.pow(data, 0, e.data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure exp() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.exp(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure expm1() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.expm1(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure log() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.log(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure log1p() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.log1p(data, 0, result.data, 0);
        return result;
    }

    
Base 10 logarithm.
Returns:
base 10 logarithm of the instance/** Base 10 logarithm.
     * @return base 10 logarithm of the instance
     */
    public DerivativeStructure log10() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.log10(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure cos() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.cos(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure sin() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.sin(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure tan() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.tan(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure acos() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.acos(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure asin() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.asin(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure atan() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.atan(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure atan2(final DerivativeStructure x)
        throws DimensionMismatchException {
        compiler.checkCompatibility(x.compiler);
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.atan2(data, 0, x.data, 0, result.data, 0);
        return result;
    }

    
Two arguments arc tangent operation.
Params:
y – first argument of the arc tangent
x – second argument of the arc tangent
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Returns:
atan2(y, x)
Since:
3.2/** Two arguments arc tangent operation.
     * @param y first argument of the arc tangent
     * @param x second argument of the arc tangent
     * @return atan2(y, x)
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public static DerivativeStructure atan2(final DerivativeStructure y, final DerivativeStructure x)
        throws DimensionMismatchException {
        return y.atan2(x);
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure cosh() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.cosh(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure sinh() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.sinh(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure tanh() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.tanh(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure acosh() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.acosh(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure asinh() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.asinh(data, 0, result.data, 0);
        return result;
    }

    
{@inheritDoc}
Since:
3.2/** {@inheritDoc}
     * @since 3.2
     */
    public DerivativeStructure atanh() {
        final DerivativeStructure result = new DerivativeStructure(compiler);
        compiler.atanh(data, 0, result.data, 0);
        return result;
    }

    
Convert radians to degrees, with error of less than 0.5 ULP
 @return instance converted into degrees
/** Convert radians to degrees, with error of less than 0.5 ULP
     *  @return instance converted into degrees
     */
    public DerivativeStructure toDegrees() {
        final DerivativeStructure ds = new DerivativeStructure(compiler);
        for (int i = 0; i < ds.data.length; ++i) {
            ds.data[i] = FastMath.toDegrees(data[i]);
        }
        return ds;
    }

    
Convert degrees to radians, with error of less than 0.5 ULP
 @return instance converted into radians
/** Convert degrees to radians, with error of less than 0.5 ULP
     *  @return instance converted into radians
     */
    public DerivativeStructure toRadians() {
        final DerivativeStructure ds = new DerivativeStructure(compiler);
        for (int i = 0; i < ds.data.length; ++i) {
            ds.data[i] = FastMath.toRadians(data[i]);
        }
        return ds;
    }

    
Evaluate Taylor expansion a derivative structure.
Params:
delta – parameters offsets (Δx, Δy, ...)
Throws:
MathArithmeticException – if factorials becomes too large
Returns:
value of the Taylor expansion at x + Δx, y + Δy, .../** Evaluate Taylor expansion a derivative structure.
     * @param delta parameters offsets (&Delta;x, &Delta;y, ...)
     * @return value of the Taylor expansion at x + &Delta;x, y + &Delta;y, ...
     * @throws MathArithmeticException if factorials becomes too large
     */
    public double taylor(final double ... delta) throws MathArithmeticException {
        return compiler.taylor(data, 0, delta);
    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final DerivativeStructure[] a, final DerivativeStructure[] b)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double[] aDouble = new double[a.length];
        for (int i = 0; i < a.length; ++i) {
            aDouble[i] = a[i].getValue();
        }
        final double[] bDouble = new double[b.length];
        for (int i = 0; i < b.length; ++i) {
            bDouble[i] = b[i].getValue();
        }
        final double accurateValue = MathArrays.linearCombination(aDouble, bDouble);

        // compute a simple value, with all partial derivatives
        DerivativeStructure simpleValue = a[0].getField().getZero();
        for (int i = 0; i < a.length; ++i) {
            simpleValue = simpleValue.add(a[i].multiply(b[i]));
        }

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(simpleValue.getFreeParameters(), simpleValue.getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final double[] a, final DerivativeStructure[] b)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double[] bDouble = new double[b.length];
        for (int i = 0; i < b.length; ++i) {
            bDouble[i] = b[i].getValue();
        }
        final double accurateValue = MathArrays.linearCombination(a, bDouble);

        // compute a simple value, with all partial derivatives
        DerivativeStructure simpleValue = b[0].getField().getZero();
        for (int i = 0; i < a.length; ++i) {
            simpleValue = simpleValue.add(b[i].multiply(a[i]));
        }

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(simpleValue.getFreeParameters(), simpleValue.getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final DerivativeStructure a1, final DerivativeStructure b1,
                                                 final DerivativeStructure a2, final DerivativeStructure b2)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double accurateValue = MathArrays.linearCombination(a1.getValue(), b1.getValue(),
                                                                  a2.getValue(), b2.getValue());

        // compute a simple value, with all partial derivatives
        final DerivativeStructure simpleValue = a1.multiply(b1).add(a2.multiply(b2));

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(getFreeParameters(), getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final double a1, final DerivativeStructure b1,
                                                 final double a2, final DerivativeStructure b2)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double accurateValue = MathArrays.linearCombination(a1, b1.getValue(),
                                                                  a2, b2.getValue());

        // compute a simple value, with all partial derivatives
        final DerivativeStructure simpleValue = b1.multiply(a1).add(b2.multiply(a2));

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(getFreeParameters(), getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final DerivativeStructure a1, final DerivativeStructure b1,
                                                 final DerivativeStructure a2, final DerivativeStructure b2,
                                                 final DerivativeStructure a3, final DerivativeStructure b3)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double accurateValue = MathArrays.linearCombination(a1.getValue(), b1.getValue(),
                                                                  a2.getValue(), b2.getValue(),
                                                                  a3.getValue(), b3.getValue());

        // compute a simple value, with all partial derivatives
        final DerivativeStructure simpleValue = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(getFreeParameters(), getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final double a1, final DerivativeStructure b1,
                                                 final double a2, final DerivativeStructure b2,
                                                 final double a3, final DerivativeStructure b3)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double accurateValue = MathArrays.linearCombination(a1, b1.getValue(),
                                                                  a2, b2.getValue(),
                                                                  a3, b3.getValue());

        // compute a simple value, with all partial derivatives
        final DerivativeStructure simpleValue = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3));

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(getFreeParameters(), getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final DerivativeStructure a1, final DerivativeStructure b1,
                                                 final DerivativeStructure a2, final DerivativeStructure b2,
                                                 final DerivativeStructure a3, final DerivativeStructure b3,
                                                 final DerivativeStructure a4, final DerivativeStructure b4)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double accurateValue = MathArrays.linearCombination(a1.getValue(), b1.getValue(),
                                                                  a2.getValue(), b2.getValue(),
                                                                  a3.getValue(), b3.getValue(),
                                                                  a4.getValue(), b4.getValue());

        // compute a simple value, with all partial derivatives
        final DerivativeStructure simpleValue = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(getFreeParameters(), getOrder(), all);

    }

    
{@inheritDoc}
Throws:
DimensionMismatchException – if number of free parameters
or orders do not match
Since:
3.2/** {@inheritDoc}
     * @exception DimensionMismatchException if number of free parameters
     * or orders do not match
     * @since 3.2
     */
    public DerivativeStructure linearCombination(final double a1, final DerivativeStructure b1,
                                                 final double a2, final DerivativeStructure b2,
                                                 final double a3, final DerivativeStructure b3,
                                                 final double a4, final DerivativeStructure b4)
        throws DimensionMismatchException {

        // compute an accurate value, taking care of cancellations
        final double accurateValue = MathArrays.linearCombination(a1, b1.getValue(),
                                                                  a2, b2.getValue(),
                                                                  a3, b3.getValue(),
                                                                  a4, b4.getValue());

        // compute a simple value, with all partial derivatives
        final DerivativeStructure simpleValue = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3)).add(b4.multiply(a4));

        // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
        final double[] all = simpleValue.getAllDerivatives();
        all[0] = accurateValue;
        return new DerivativeStructure(getFreeParameters(), getOrder(), all);

    }

    
Test for the equality of two derivative structures.

Derivative structures are considered equal if they have the same number
of free parameters, the same derivation order, and the same derivatives.

Params:
other – Object to test for equality to this
Returns:
true if two derivative structures are equal
Since:
3.2/**
     * Test for the equality of two derivative structures.
     * <p>
     * Derivative structures are considered equal if they have the same number
     * of free parameters, the same derivation order, and the same derivatives.
     * </p>
     * @param other Object to test for equality to this
     * @return true if two derivative structures are equal
     * @since 3.2
     */
    @Override
    public boolean equals(Object other) {

        if (this == other) {
            return true;
        }

        if (other instanceof DerivativeStructure) {
            final DerivativeStructure rhs = (DerivativeStructure)other;
            return (getFreeParameters() == rhs.getFreeParameters()) &&
                   (getOrder() == rhs.getOrder()) &&
                   MathArrays.equals(data, rhs.data);
        }

        return false;

    }

    
Get a hashCode for the derivative structure.
Returns:
a hash code value for this object
Since:
3.2/**
     * Get a hashCode for the derivative structure.
     * @return a hash code value for this object
     * @since 3.2
     */
    @Override
    public int hashCode() {
        return 227 + 229 * getFreeParameters() + 233 * getOrder() + 239 * MathUtils.hash(data);
    }

    
Replace the instance with a data transfer object for serialization.
Returns:
data transfer object that will be serialized/**
     * Replace the instance with a data transfer object for serialization.
     * @return data transfer object that will be serialized
     */
    private Object writeReplace() {
        return new DataTransferObject(compiler.getFreeParameters(), compiler.getOrder(), data);
    }

    
Internal class used only for serialization. /** Internal class used only for serialization. */
    private static class DataTransferObject implements Serializable {

        
Serializable UID. /** Serializable UID. */
        private static final long serialVersionUID = 20120730L;

        
Number of variables.
@serial
/** Number of variables.
         * @serial
         */
        private final int variables;

        
Derivation order.
@serial
/** Derivation order.
         * @serial
         */
        private final int order;

        
Partial derivatives.
@serial
/** Partial derivatives.
         * @serial
         */
        private final double[] data;

        
Simple constructor.
Params:
variables – number of variables
order – derivation order
data – partial derivatives/** Simple constructor.
         * @param variables number of variables
         * @param order derivation order
         * @param data partial derivatives
         */
        DataTransferObject(final int variables, final int order, final double[] data) {
            this.variables = variables;
            this.order     = order;
            this.data      = data;
        }

        
Replace the deserialized data transfer object with a DerivativeStructure. 
Returns:
replacement DerivativeStructure/** Replace the deserialized data transfer object with a {@link DerivativeStructure}.
         * @return replacement {@link DerivativeStructure}
         */
        private Object readResolve() {
            return new DerivativeStructure(variables, order, data);
        }

    }

}