/*
    * Licensed to the Hipparchus project under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The Hipparchus project 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
    *
    *      https://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.hipparchus.analysis.differentiation;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.Field;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.FieldSinhCosh;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.MathUtils;
  
  import java.util.Arrays;
  
  /** Class representing both the value and the differentials of a function.
   * <p>This class is similar to {@link DerivativeStructure} except function
   * parameters and value can be any {@link CalculusFieldElement}.</p>
   * <p>Instances of this class are guaranteed to be immutable.</p>
   * @see DerivativeStructure
   * @see FDSFactory
   * @see DSCompiler
   * @param <T> the type of the field elements
   */
  public class FieldDerivativeStructure<T extends CalculusFieldElement<T>>
      implements FieldDerivative<T, FieldDerivativeStructure<T>> {
  
      /** Factory that built the instance. */
      private final FDSFactory<T> factory;
  
      /** Combined array holding all values. */
      private final T[] data;
  
      /** Build an instance with all values and derivatives set to 0.
       * @param factory factory that built the instance
       * @param data combined array holding all values
       */
      FieldDerivativeStructure(final FDSFactory<T> factory, final T[] data) {
          this.factory = factory;
          this.data    = data.clone();
      }
  
      /** Build an instance with all values and derivatives set to 0.
       * @param factory factory that built the instance
       * @since 1.4
       */
      FieldDerivativeStructure(final FDSFactory<T> factory) {
          this.factory = factory;
          this.data    = MathArrays.buildArray(factory.getValueField(), factory.getCompiler().getSize());
      }
  
      /** {@inheritDoc} */
      @Override
      public FieldDerivativeStructure<T> newInstance(final double value) {
          return factory.constant(value);
      }
  
      /** {@inheritDoc} */
      @Override
      public FieldDerivativeStructure<T> newInstance(final T value) {
          return factory.constant(value);
      }
  
      /** {@inheritDoc} */
      @Override
      public FieldDerivativeStructure<T> withValue(final T value) {
          final FieldDerivativeStructure<T> ds = factory.build();
          System.arraycopy(data, 1, ds.data, 1, data.length - 1);
          ds.data[0] = value;
          return ds;
      }
  
      /** Get the factory that built the instance.
       * @return factory that built the instance
       */
      public FDSFactory<T> getFactory() {
          return factory;
      }
  
      /** {@inheritDoc} */
      @Override
      public int getFreeParameters() {
          return getFactory().getCompiler().getFreeParameters();
      }
  
     /** {@inheritDoc} */
     @Override
     public int getOrder() {
         return getFactory().getCompiler().getOrder();
     }
 
     /** Set a derivative component.
      * <p>
      * This method is package-private (no modifier specified), as it is intended
      * to be used only by Hipparchus classes since it relied on the ordering of
      * derivatives within the class. This allows avoiding checks on the index,
      * for performance reasons.
      * </p>
      * @param index index of the derivative
      * @param value of the derivative to set
      * @since 1.4
      */
     void setDerivativeComponent(final int index, final T value) {
         data[index] = value;
     }
 
     /** Get a derivative component.
      * <p>
      * This method is package-private (no modifier specified), as it is intended
      * to be used only by Hipparchus classes since it relied on the ordering of
      * derivatives within the class. This allows avoiding checks on the index,
      * for performance reasons.
      * </p>
      * @param index index of the derivative
      * @return value of the derivative
      * @since 2.2
      */
     T getDerivativeComponent(final int index) {
         return data[index];
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> getAddendum() {
         final T[] addendum = data.clone();
         addendum[0] = addendum[0].getField().getZero();
         return new FieldDerivativeStructure<>(factory, addendum);
     }
 
     /** Get the value part of the derivative structure.
      * @return value part of the derivative structure
      * @see #getPartialDerivative(int...)
      */
     @Override
     public T getValue() {
         return data[0];
     }
 
     /** {@inheritDoc} */
     @Override
     public T getPartialDerivative(final int ... orders)
         throws MathIllegalArgumentException {
         return data[factory.getCompiler().getPartialDerivativeIndex(orders)];
     }
 
     /** Get all partial derivatives.
      * @return a fresh copy of partial derivatives, in an array sorted according to
      * {@link DSCompiler#getPartialDerivativeIndex(int...)}
      */
     public T[] getAllDerivatives() {
         return data.clone();
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> add(final double a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         System.arraycopy(data, 0, ds.data, 0, data.length);
         ds.data[0] = ds.data[0].add(a);
         return ds;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> add(final FieldDerivativeStructure<T> a)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(a.factory);
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().add(data, 0, a.data, 0, ds.data, 0);
         return ds;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> subtract(final double a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         System.arraycopy(data, 0, ds.data, 0, data.length);
         ds.data[0] = ds.data[0].subtract(a);
         return ds;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> subtract(final FieldDerivativeStructure<T> a)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(a.factory);
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().subtract(data, 0, a.data, 0, ds.data, 0);
         return ds;
     }
 
     /** '&times;' operator.
      * @param a right hand side parameter of the operator
      * @return this&times;a
      */
     public FieldDerivativeStructure<T> multiply(final T a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].multiply(a);
         }
         return ds;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> multiply(final double a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].multiply(a);
         }
         return ds;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> multiply(final FieldDerivativeStructure<T> a)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(a.factory);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().multiply(data, 0, a.data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> square() {
         return multiply(this);
     }
 
     /** '&divide;' operator.
      * @param a right hand side parameter of the operator
      * @return this&divide;a
      */
     public FieldDerivativeStructure<T> divide(final T a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].divide(a);
         }
         return ds;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> divide(final double a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].divide(a);
         }
         return ds;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> divide(final FieldDerivativeStructure<T> a)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(a.factory);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().divide(data, 0, a.data, 0, result.data, 0);
         return result;
     }
 
     /** IEEE remainder operator.
      * @param a right hand side parameter of the operator
      * @return this - n &times; a where n is the closest integer to this/a
      * (the even integer is chosen for n if this/a is halfway between two integers)
      */
     public FieldDerivativeStructure<T> remainder(final T a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         System.arraycopy(data, 0, ds.data, 0, data.length);
         ds.data[0] = data[0].remainder(a);
         return ds;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> remainder(final double a) {
         final FieldDerivativeStructure<T> ds = factory.build();
         System.arraycopy(data, 0, ds.data, 0, data.length);
         ds.data[0] = data[0].remainder(a);
         return ds;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> remainder(final FieldDerivativeStructure<T> a)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(a.factory);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().remainder(data, 0, a.data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> negate() {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].negate();
         }
         return ds;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> abs() {
         if (Double.doubleToLongBits(data[0].getReal()) < 0) {
             // we use the bits representation to also handle -0.0
             return negate();
         } else {
             return this;
         }
     }
 
     /**
      * Returns the instance with the sign of the argument.
      * A NaN {@code sign} argument is treated as positive.
      *
      * @param sign the sign for the returned value
      * @return the instance with the same sign as the {@code sign} argument
      */
     public FieldDerivativeStructure<T> copySign(final T sign) {
         long m = Double.doubleToLongBits(data[0].getReal());
         long s = Double.doubleToLongBits(sign.getReal());
         if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
             return this;
         }
         return negate(); // flip sign
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> copySign(final double sign) {
         long m = Double.doubleToLongBits(data[0].getReal());
         long s = Double.doubleToLongBits(sign);
         if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
             return this;
         }
         return negate(); // flip sign
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> copySign(final FieldDerivativeStructure<T> sign) {
         long m = Double.doubleToLongBits(data[0].getReal());
         long s = Double.doubleToLongBits(sign.data[0].getReal());
         if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
             return this;
         }
         return negate(); // flip sign
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> scalb(final int n) {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].scalb(n);
         }
         return ds;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> hypot(final FieldDerivativeStructure<T> y)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(y.factory);
 
         if (data[0].isInfinite() || y.data[0].isInfinite()) {
             return factory.constant(Double.POSITIVE_INFINITY);
         } else if (data[0].isNaN() || y.data[0].isNaN()) {
             return factory.constant(Double.NaN);
         } else {
 
             final int expX = getExponent();
             final int expY = y.getExponent();
             if (expX > expY + 27) {
                 // y is negligible with respect to x
                 return abs();
             } else if (expY > expX + 27) {
                 // x is negligible 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 FieldDerivativeStructure<T> scaledX = scalb(-middleExp);
                 final FieldDerivativeStructure<T> scaledY = y.scalb(-middleExp);
 
                 // compute scaled hypotenuse
                 final FieldDerivativeStructure<T> scaledH =
                         scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
 
                 // remove scaling
                 return scaledH.scalb(middleExp);
 
             }
 
         }
     }
 
     /**
      * 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 MathIllegalArgumentException if number of free parameters
      * or orders do not match
      * @param <T> the type of the field elements
      */
     public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>
         hypot(final FieldDerivativeStructure<T> x, final FieldDerivativeStructure<T> y)
         throws MathIllegalArgumentException {
         return x.hypot(y);
     }
 
     /** 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 MathIllegalArgumentException if the number of derivatives
      * in the array is not equal to {@link #getOrder() order} + 1
      */
     @SafeVarargs
     public final FieldDerivativeStructure<T> compose(final T ... f)
         throws MathIllegalArgumentException {
 
         MathUtils.checkDimension(f.length, getOrder() + 1);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().compose(data, 0, f, result.data, 0);
         return result;
     }
 
     /** 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 MathIllegalArgumentException if the number of derivatives
      * in the array is not equal to {@link #getOrder() order} + 1
      */
     public FieldDerivativeStructure<T> compose(final double ... f)
         throws MathIllegalArgumentException {
 
         MathUtils.checkDimension(f.length, getOrder() + 1);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().compose(data, 0, f, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> reciprocal() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().reciprocal(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> sqrt() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().sqrt(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> rootN(final int n) {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().rootN(data, 0, n, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public Field<FieldDerivativeStructure<T>> getField() {
         return factory.getDerivativeField();
     }
 
     /** Compute a<sup>x</sup> where a is a double and x a {@link FieldDerivativeStructure}
      * @param a number to exponentiate
      * @param x power to apply
      * @param <T> the type of the field elements
      * @return a<sup>x</sup>
      */
     public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> pow(final double a, final FieldDerivativeStructure<T> x) {
         final FieldDerivativeStructure<T> result = x.factory.build();
         x.factory.getCompiler().pow(a, x.data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> pow(final double p) {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().pow(data, 0, p, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> pow(final int n) {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().pow(data, 0, n, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> pow(final FieldDerivativeStructure<T> e)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(e.factory);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().pow(data, 0, e.data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> exp() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().exp(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> expm1() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().expm1(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> log() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().log(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> log1p() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().log1p(data, 0, result.data, 0);
         return result;
     }
 
     /** Base 10 logarithm.
      * @return base 10 logarithm of the instance
      */
     @Override
     public FieldDerivativeStructure<T> log10() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().log10(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> cos() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().cos(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> sin() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().sin(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldSinCos<FieldDerivativeStructure<T>> sinCos() {
         final FieldDerivativeStructure<T> sin = factory.build();
         final FieldDerivativeStructure<T> cos = factory.build();
         factory.getCompiler().sinCos(data, 0, sin.data, 0, cos.data, 0);
         return new FieldSinCos<>(sin, cos);
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> tan() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().tan(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> acos() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().acos(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> asin() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().asin(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> atan() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().atan(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> atan2(final FieldDerivativeStructure<T> x)
         throws MathIllegalArgumentException {
         factory.checkCompatibility(x.factory);
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().atan2(data, 0, x.data, 0, result.data, 0);
         return result;
     }
 
     /** Two arguments arc tangent operation.
      * @param y first argument of the arc tangent
      * @param x second argument of the arc tangent
      * @param <T> the type of the field elements
      * @return atan2(y, x)
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     public static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T> atan2(final FieldDerivativeStructure<T> y,
                                                                                         final FieldDerivativeStructure<T> x)
         throws MathIllegalArgumentException {
         return y.atan2(x);
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> cosh() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().cosh(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> sinh() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().sinh(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldSinhCosh<FieldDerivativeStructure<T>> sinhCosh() {
         final FieldDerivativeStructure<T> sinh = factory.build();
         final FieldDerivativeStructure<T> cosh = factory.build();
         factory.getCompiler().sinhCosh(data, 0, sinh.data, 0, cosh.data, 0);
         return new FieldSinhCosh<>(sinh, cosh);
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> tanh() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().tanh(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> acosh() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().acosh(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> asinh() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().asinh(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> atanh() {
         final FieldDerivativeStructure<T> result = factory.build();
         factory.getCompiler().atanh(data, 0, result.data, 0);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> toDegrees() {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].toDegrees();
         }
         return ds;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldDerivativeStructure<T> toRadians() {
         final FieldDerivativeStructure<T> ds = factory.build();
         for (int i = 0; i < ds.data.length; ++i) {
             ds.data[i] = data[i].toRadians();
         }
         return ds;
     }
 
     /** Integrate w.r.t. one independent variable.
      * <p>
      * Rigorously, if the derivatives of a function are known up to
      * order N, the ones of its M-th integral w.r.t. a given variable
      * (seen as a function itself) are actually known up to order N+M.
      * However, this method still casts the output as a DerivativeStructure
      * of order N. The integration constants are systematically set to zero.
      * </p>
      * @param varIndex Index of independent variable w.r.t. which integration is done.
      * @param integrationOrder Number of times the integration operator must be applied. If non-positive, call the
      *                         differentiation operator.
      * @return DerivativeStructure on which integration operator has been applied a certain number of times.
      * @since 2.2
      */
     public FieldDerivativeStructure<T> integrate(final int varIndex, final int integrationOrder) {
 
         // Deal first with trivial case
         if (integrationOrder > getOrder()) {
             return factory.constant(0.);
         } else if (integrationOrder == 0) {
             return factory.build(data);
         }
 
         // Call 'inverse' (not rigorously) operation if necessary
         if (integrationOrder < 0) {
             return differentiate(varIndex, -integrationOrder);
         }
 
         final T[] newData = MathArrays.buildArray(factory.getValueField(), data.length);
         final DSCompiler dsCompiler = factory.getCompiler();
         for (int i = 0; i < newData.length; i++) {
             if (!data[i].isZero()) {
                 final int[] orders = dsCompiler.getPartialDerivativeOrders(i);
                 int sum = 0;
                 for (int order : orders) {
                     sum += order;
                 }
                 if (sum + integrationOrder <= getOrder()) {
                     final int saved = orders[varIndex];
                     orders[varIndex] += integrationOrder;
                     final int index = dsCompiler.getPartialDerivativeIndex(orders);
                     orders[varIndex] = saved;
                     newData[index] = data[i];
                 }
             }
         }
 
         return factory.build(newData);
     }
 
     /** Differentiate w.r.t. one independent variable.
      * <p>
      * Rigorously, if the derivatives of a function are known up to
      * order N, the ones of its M-th derivative w.r.t. a given variable
      * (seen as a function itself) are only known up to order N-M.
      * However, this method still casts the output as a DerivativeStructure
      * of order N with zeroes for the higher order terms.
      * </p>
      * @param varIndex Index of independent variable w.r.t. which differentiation is done.
      * @param differentiationOrder Number of times the differentiation operator must be applied. If non-positive, call
      *                             the integration operator instead.
      * @return DerivativeStructure on which differentiation operator has been applied a certain number of times
      * @since 2.2
      */
     public FieldDerivativeStructure<T> differentiate(final int varIndex, final int differentiationOrder) {
 
         // Deal first with trivial case
         if (differentiationOrder > getOrder()) {
             return factory.constant(0.);
         } else if (differentiationOrder == 0) {
             return factory.build(data);
         }
 
         // Call 'inverse' (not rigorously) operation if necessary
         if (differentiationOrder < 0) {
             return integrate(varIndex, -differentiationOrder);
         }
 
         final T[] newData = MathArrays.buildArray(factory.getValueField(), data.length);
         final DSCompiler dsCompiler = factory.getCompiler();
         for (int i = 0; i < newData.length; i++) {
             if (!data[i].isZero()) {
                 final int[] orders = dsCompiler.getPartialDerivativeOrders(i);
                 if (orders[varIndex] - differentiationOrder >= 0) {
                     final int saved = orders[varIndex];
                     orders[varIndex] -= differentiationOrder;
                     final int index = dsCompiler.getPartialDerivativeIndex(orders);
                     orders[varIndex] = saved;
                     newData[index] = data[i];
                 }
             }
         }
 
         return factory.build(newData);
     }
 
     /** Evaluate Taylor expansion of 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 MathRuntimeException if factorials becomes too large
      */
     @SafeVarargs
     public final T taylor(final T ... delta) throws MathRuntimeException {
         return factory.getCompiler().taylor(data, 0, delta);
     }
 
     /** Evaluate Taylor expansion of 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 MathRuntimeException if factorials becomes too large
      */
     public T taylor(final double ... delta) throws MathRuntimeException {
         return factory.getCompiler().taylor(data, 0, delta);
     }
 
     /** Rebase instance with respect to low level parameter functions.
      * <p>
      * The instance is considered to be a function of {@link #getFreeParameters()
      * n free parameters} up to order {@link #getOrder() o} \(f(p_0, p_1, \ldots p_{n-1})\).
      * Its {@link #getPartialDerivative(int...) partial derivatives} are therefore
      * \(f, \frac{\partial f}{\partial p_0}, \frac{\partial f}{\partial p_1}, \ldots
      * \frac{\partial^2 f}{\partial p_0^2}, \frac{\partial^2 f}{\partial p_0 p_1},
      * \ldots \frac{\partial^o f}{\partial p_{n-1}^o}\). The free parameters
      * \(p_0, p_1, \ldots p_{n-1}\) are considered to be functions of \(m\) lower
      * level other parameters \(q_0, q_1, \ldots q_{m-1}\).
      * </p>
      * \( \begin{align}
      * p_0 &amp; = p_0(q_0, q_1, \ldots q_{m-1})\\
      * p_1 &amp; = p_1(q_0, q_1, \ldots q_{m-1})\\
      * p_{n-1} &amp; = p_{n-1}(q_0, q_1, \ldots q_{m-1})
      * \end{align}\)
      * <p>
      * This method compute the composition of the partial derivatives of \(f\)
      * and the partial derivatives of \(p_0, p_1, \ldots p_{n-1}\), i.e. the
      * {@link #getPartialDerivative(int...) partial derivatives} of the value
      * returned will be
      * \(f, \frac{\partial f}{\partial q_0}, \frac{\partial f}{\partial q_1}, \ldots
      * \frac{\partial^2 f}{\partial q_0^2}, \frac{\partial^2 f}{\partial q_0 q_1},
      * \ldots \frac{\partial^o f}{\partial q_{m-1}^o}\).
      * </p>
      * <p>
      * The number of parameters must match {@link #getFreeParameters()} and the
      * derivation orders of the instance and parameters must also match.
      * </p>
      * @param p base parameters with respect to which partial derivatives
      * were computed in the instance
      * @return derivative structure with partial derivatives computed
      * with respect to the lower level parameters used in the \(p_i\)
      * @since 2.2
      */
     public FieldDerivativeStructure<T> rebase(@SuppressWarnings("unchecked") final FieldDerivativeStructure<T>... p) {
 
         MathUtils.checkDimension(getFreeParameters(), p.length);
 
         // handle special case of no variables at all
         if (p.length == 0) {
             return this;
         }
 
         final int pSize = p[0].getFactory().getCompiler().getSize();
         final T[] pData = MathArrays.buildArray(p[0].getFactory().getValueField(), p.length * pSize);
         for (int i = 0; i < p.length; ++i) {
             MathUtils.checkDimension(getOrder(), p[i].getOrder());
             MathUtils.checkDimension(p[0].getFreeParameters(), p[i].getFreeParameters());
             System.arraycopy(p[i].data, 0, pData, i * pSize, pSize);
         }
 
         final FieldDerivativeStructure<T> result = p[0].factory.build();
         factory.getCompiler().rebase(data, 0, p[0].factory.getCompiler(), pData, result.data, 0);
         return result;
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T>[] a,
                                                          final FieldDerivativeStructure<T>[] b)
         throws MathIllegalArgumentException {
 
         // compute an accurate value, taking care of cancellations
         final T[] aT = MathArrays.buildArray(factory.getValueField(), a.length);
         for (int i = 0; i < a.length; ++i) {
             aT[i] = a[i].getValue();
         }
         final T[] bT = MathArrays.buildArray(factory.getValueField(), b.length);
         for (int i = 0; i < b.length; ++i) {
             bT[i] = b[i].getValue();
         }
         final T accurateValue = aT[0].linearCombination(aT, bT);
 
         // compute a simple value, with all partial derivatives
         FieldDerivativeStructure<T> 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 T[] all = simpleValue.getAllDerivatives();
         all[0] = accurateValue;
         return factory.build(all);
 
     }
 
     /**
      * Compute a linear combination.
      * @param a Factors.
      * @param b Factors.
      * @return <code>&Sigma;<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
      * @throws MathIllegalArgumentException if arrays dimensions don't match
      */
     public FieldDerivativeStructure<T> linearCombination(final T[] a, final FieldDerivativeStructure<T>[] b)
                     throws MathIllegalArgumentException {
 
         // compute an accurate value, taking care of cancellations
         final T[] bT = MathArrays.buildArray(factory.getValueField(), b.length);
         for (int i = 0; i < b.length; ++i) {
             bT[i] = b[i].getValue();
         }
         final T accurateValue = bT[0].linearCombination(a, bT);
 
         // compute a simple value, with all partial derivatives
         FieldDerivativeStructure<T> 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 T[] all = simpleValue.getAllDerivatives();
         all[0] = accurateValue;
         return factory.build(all);
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final double[] a, final FieldDerivativeStructure<T>[] b)
         throws MathIllegalArgumentException {
 
         // compute an accurate value, taking care of cancellations
         final T[] bT = MathArrays.buildArray(factory.getValueField(), b.length);
         for (int i = 0; i < b.length; ++i) {
             bT[i] = b[i].getValue();
         }
         final T accurateValue = bT[0].linearCombination(a, bT);
 
         // compute a simple value, with all partial derivatives
         FieldDerivativeStructure<T> 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 T[] all = simpleValue.getAllDerivatives();
         all[0] = accurateValue;
         return factory.build(all);
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T> a1, final FieldDerivativeStructure<T> b1,
                                                          final FieldDerivativeStructure<T> a2, final FieldDerivativeStructure<T> b2)
         throws MathIllegalArgumentException {
 
         // compute an accurate value, taking care of cancellations
         final T accurateValue = a1.getValue().linearCombination(a1.getValue(), b1.getValue(),
                                                                 a2.getValue(), b2.getValue());
 
         // compute a simple value, with all partial derivatives
         final FieldDerivativeStructure<T> 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 T[] all = simpleValue.getAllDerivatives();
         all[0] = accurateValue;
         return factory.build(all);
 
     }
 
     /**
      * Compute a linear combination.
      * @param a1 first factor of the first term
      * @param b1 second factor of the first term
      * @param a2 first factor of the second term
      * @param b2 second factor of the second term
      * @return a<sub>1</sub>&times;b<sub>1</sub> +
      * a<sub>2</sub>&times;b<sub>2</sub>
      * @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
      * @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
      * @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
      */
     public FieldDerivativeStructure<T> linearCombination(final T a1, final FieldDerivativeStructure<T> b1,
                                                          final T a2, final FieldDerivativeStructure<T> b2)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(b1.factory);
         factory.checkCompatibility(b2.factory);
 
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().linearCombination(a1, b1.data, 0,
                                                 a2, b2.data, 0,
                                                 ds.data, 0);
 
         return ds;
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final double a1, final FieldDerivativeStructure<T> b1,
                                                          final double a2, final FieldDerivativeStructure<T> b2)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(b1.factory);
         factory.checkCompatibility(b2.factory);
 
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().linearCombination(a1, b1.data, 0,
                                                 a2, b2.data, 0,
                                                 ds.data, 0);
 
         return ds;
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T> a1, final FieldDerivativeStructure<T> b1,
                                                          final FieldDerivativeStructure<T> a2, final FieldDerivativeStructure<T> b2,
                                                          final FieldDerivativeStructure<T> a3, final FieldDerivativeStructure<T> b3)
         throws MathIllegalArgumentException {
 
         // compute an accurate value, taking care of cancellations
         final T accurateValue = a1.getValue().linearCombination(a1.getValue(), b1.getValue(),
                                                                 a2.getValue(), b2.getValue(),
                                                                 a3.getValue(), b3.getValue());
 
         // compute a simple value, with all partial derivatives
         final FieldDerivativeStructure<T> 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 T[] all = simpleValue.getAllDerivatives();
         all[0] = accurateValue;
         return factory.build(all);
 
     }
 
     /**
      * Compute a linear combination.
      * @param a1 first factor of the first term
      * @param b1 second factor of the first term
      * @param a2 first factor of the second term
      * @param b2 second factor of the second term
      * @param a3 first factor of the third term
      * @param b3 second factor of the third term
      * @return a<sub>1</sub>&times;b<sub>1</sub> +
      * a<sub>2</sub>&times;b<sub>2</sub> + a<sub>3</sub>&times;b<sub>3</sub>
      * @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
      * @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
      * @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
      */
     public FieldDerivativeStructure<T> linearCombination(final T a1, final FieldDerivativeStructure<T> b1,
                                                          final T a2, final FieldDerivativeStructure<T> b2,
                                                          final T a3, final FieldDerivativeStructure<T> b3)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(b1.factory);
         factory.checkCompatibility(b2.factory);
         factory.checkCompatibility(b3.factory);
 
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().linearCombination(a1, b1.data, 0,
                                                 a2, b2.data, 0,
                                                 a3, b3.data, 0,
                                                 ds.data, 0);
 
         return ds;
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final double a1, final FieldDerivativeStructure<T> b1,
                                                          final double a2, final FieldDerivativeStructure<T> b2,
                                                          final double a3, final FieldDerivativeStructure<T> b3)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(b1.factory);
         factory.checkCompatibility(b2.factory);
         factory.checkCompatibility(b3.factory);
 
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().linearCombination(a1, b1.data, 0,
                                                 a2, b2.data, 0,
                                                 a3, b3.data, 0,
                                                 ds.data, 0);
 
         return ds;
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final FieldDerivativeStructure<T> a1, final FieldDerivativeStructure<T> b1,
                                                          final FieldDerivativeStructure<T> a2, final FieldDerivativeStructure<T> b2,
                                                          final FieldDerivativeStructure<T> a3, final FieldDerivativeStructure<T> b3,
                                                          final FieldDerivativeStructure<T> a4, final FieldDerivativeStructure<T> b4)
         throws MathIllegalArgumentException {
 
         // compute an accurate value, taking care of cancellations
         final T accurateValue = a1.getValue().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 FieldDerivativeStructure<T> 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 T[] all = simpleValue.getAllDerivatives();
         all[0] = accurateValue;
         return factory.build(all);
 
     }
 
     /**
      * Compute a linear combination.
      * @param a1 first factor of the first term
      * @param b1 second factor of the first term
      * @param a2 first factor of the second term
      * @param b2 second factor of the second term
      * @param a3 first factor of the third term
      * @param b3 second factor of the third term
      * @param a4 first factor of the third term
      * @param b4 second factor of the third term
      * @return a<sub>1</sub>&times;b<sub>1</sub> +
      * a<sub>2</sub>&times;b<sub>2</sub> + a<sub>3</sub>&times;b<sub>3</sub> +
      * a<sub>4</sub>&times;b<sub>4</sub>
      * @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
      * @see #linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)
      * @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
      */
     public FieldDerivativeStructure<T> linearCombination(final T a1, final FieldDerivativeStructure<T> b1,
                                                          final T a2, final FieldDerivativeStructure<T> b2,
                                                          final T a3, final FieldDerivativeStructure<T> b3,
                                                          final T a4, final FieldDerivativeStructure<T> b4)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(b1.factory);
         factory.checkCompatibility(b2.factory);
         factory.checkCompatibility(b3.factory);
         factory.checkCompatibility(b4.factory);
 
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().linearCombination(a1, b1.data, 0,
                                                 a2, b2.data, 0,
                                                 a3, b3.data, 0,
                                                 a4, b4.data, 0,
                                                 ds.data, 0);
 
         return ds;
 
     }
 
     /** {@inheritDoc}
      * @exception MathIllegalArgumentException if number of free parameters
      * or orders do not match
      */
     @Override
     public FieldDerivativeStructure<T> linearCombination(final double a1, final FieldDerivativeStructure<T> b1,
                                                          final double a2, final FieldDerivativeStructure<T> b2,
                                                          final double a3, final FieldDerivativeStructure<T> b3,
                                                          final double a4, final FieldDerivativeStructure<T> b4)
         throws MathIllegalArgumentException {
 
         factory.checkCompatibility(b1.factory);
         factory.checkCompatibility(b2.factory);
         factory.checkCompatibility(b3.factory);
         factory.checkCompatibility(b4.factory);
 
         final FieldDerivativeStructure<T> ds = factory.build();
         factory.getCompiler().linearCombination(a1, b1.data, 0,
                                                 a2, b2.data, 0,
                                                 a3, b3.data, 0,
                                                 a4, b4.data, 0,
                                                 ds.data, 0);
 
         return ds;
 
     }
 
     /** {@inheritDoc}
      */
     @Override
     public FieldDerivativeStructure<T> getPi() {
         return factory.getDerivativeField().getPi();
     }
 
     /**
      * 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
      */
     @Override
     public boolean equals(Object other) {
 
         if (this == other) {
             return true;
         }
 
         if (other instanceof FieldDerivativeStructure &&
             ((FieldDerivativeStructure<?>) other).getField().equals(getField())) {
             final FieldDerivativeStructure<T> rhs = (FieldDerivativeStructure<T>) other;
             return (getFreeParameters() == rhs.getFreeParameters()) &&
                    (getOrder() == rhs.getOrder()) &&
                    MathArrays.equals(data, rhs.data);
         }
 
         return false;
 
     }
 
     /**
      * Get a hashCode for the derivative structure.
      * @return a hash code value for this object
      */
     @Override
     public int hashCode() {
         return 227 + 229 * getFreeParameters() + 233 * getOrder() + 239 * Arrays.hashCode(data);
     }
 
 }