java.lang.Object
- org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure

All Implemented Interfaces:

FieldElement<DerivativeStructure>, RealFieldElement<DerivativeStructure>
```
public class DerivativeStructure
extends Object
implements RealFieldElement<DerivativeStructure>
```
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 not 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.

Since:

3.1

See Also:

DSCompiler

Constructor Summary

Constructors
Constructor	Description
`DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2)`	Linear combination constructor.
`DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2, double a3, DerivativeStructure ds3)`	Linear combination constructor.
`DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2, double a3, DerivativeStructure ds3, double a4, DerivativeStructure ds4)`	Linear combination constructor.
`DerivativeStructure(int parameters, int order)`	Build an instance with all values and derivatives set to 0.
`DerivativeStructure(int parameters, int order, double value)`	Build an instance representing a constant value.
`DerivativeStructure(int parameters, int order, double... derivatives)`	Build an instance from all its derivatives.
`DerivativeStructure(int parameters, int order, int index, double value)`	Build an instance representing a variable.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`DerivativeStructure`	`abs()`
`DerivativeStructure`	`acos()`
`DerivativeStructure`	`acosh()`
`DerivativeStructure`	`add(double a)`
`DerivativeStructure`	`add(DerivativeStructure a)`
`DerivativeStructure`	`asin()`
`DerivativeStructure`	`asinh()`
`DerivativeStructure`	`atan()`
`DerivativeStructure`	`atan2(DerivativeStructure x)`
`static DerivativeStructure`	`atan2(DerivativeStructure y, DerivativeStructure x)`	Two arguments arc tangent operation.
`DerivativeStructure`	`atanh()`
`DerivativeStructure`	`cbrt()`
`DerivativeStructure`	`ceil()`
`DerivativeStructure`	`compose(double... f)`	Compute composition of the instance by a univariate function.
`DerivativeStructure`	`copySign(double sign)`
`DerivativeStructure`	`copySign(DerivativeStructure sign)`
`DerivativeStructure`	`cos()`
`DerivativeStructure`	`cosh()`
`DerivativeStructure`	`createConstant(double c)`	Create a constant compatible with instance order and number of parameters.
`DerivativeStructure`	`divide(double a)`
`DerivativeStructure`	`divide(DerivativeStructure a)`
`boolean`	`equals(Object other)`	Test for the equality of two derivative structures.
`DerivativeStructure`	`exp()`
`DerivativeStructure`	`expm1()`
`DerivativeStructure`	`floor()`
`double[]`	`getAllDerivatives()`	Get all partial derivatives.
`int`	`getExponent()`	Return the exponent of the instance value, removing the bias.
`Field<DerivativeStructure>`	`getField()`
`int`	`getFreeParameters()`	Get the number of free parameters.
`int`	`getOrder()`	Get the derivation order.
`double`	`getPartialDerivative(int... orders)`	Get a partial derivative.
`double`	`getReal()`
`double`	`getValue()`	Get the value part of the derivative structure.
`int`	`hashCode()`	Get a hashCode for the derivative structure.
`DerivativeStructure`	`hypot(DerivativeStructure y)`
`static DerivativeStructure`	`hypot(DerivativeStructure x, DerivativeStructure y)`	Returns the hypotenuse of a triangle with sides `x` and `y` - sqrt(x² +y²) avoiding intermediate overflow or underflow.
`DerivativeStructure`	`linearCombination(double[] a, DerivativeStructure[] b)`
`DerivativeStructure`	`linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2)`
`DerivativeStructure`	`linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2, double a3, DerivativeStructure b3)`
`DerivativeStructure`	`linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2, double a3, DerivativeStructure b3, double a4, DerivativeStructure b4)`
`DerivativeStructure`	`linearCombination(DerivativeStructure[] a, DerivativeStructure[] b)`
`DerivativeStructure`	`linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2)`
`DerivativeStructure`	`linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2, DerivativeStructure a3, DerivativeStructure b3)`
`DerivativeStructure`	`linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2, DerivativeStructure a3, DerivativeStructure b3, DerivativeStructure a4, DerivativeStructure b4)`
`DerivativeStructure`	`log()`
`DerivativeStructure`	`log10()`	Base 10 logarithm.
`DerivativeStructure`	`log1p()`
`DerivativeStructure`	`multiply(double a)`
`DerivativeStructure`	`multiply(int n)`
`DerivativeStructure`	`multiply(DerivativeStructure a)`
`DerivativeStructure`	`negate()`
`DerivativeStructure`	`pow(double p)`
`static DerivativeStructure`	`pow(double a, DerivativeStructure x)`	Compute a^x where a is a double and x a `DerivativeStructure`.
`DerivativeStructure`	`pow(int n)`
`DerivativeStructure`	`pow(DerivativeStructure e)`
`DerivativeStructure`	`reciprocal()`
`DerivativeStructure`	`remainder(double a)`
`DerivativeStructure`	`remainder(DerivativeStructure a)`
`DerivativeStructure`	`rint()`
`DerivativeStructure`	`rootN(int n)`
`long`	`round()`
`DerivativeStructure`	`scalb(int n)`
`DerivativeStructure`	`signum()`
`DerivativeStructure`	`sin()`
`DerivativeStructure`	`sinh()`
`DerivativeStructure`	`sqrt()`
`DerivativeStructure`	`subtract(double a)`
`DerivativeStructure`	`subtract(DerivativeStructure a)`
`DerivativeStructure`	`tan()`
`DerivativeStructure`	`tanh()`
`double`	`taylor(double... delta)`	Evaluate Taylor expansion a derivative structure.
`DerivativeStructure`	`toDegrees()`	Convert radians to degrees, with error of less than 0.5 ULP.
`DerivativeStructure`	`toRadians()`	Convert degrees to radians, with error of less than 0.5 ULP.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - DerivativeStructure
```
public DerivativeStructure(int parameters,
                           int order)
```
    Build an instance with all values and derivatives set to 0.
    
    Parameters:
    
    parameters - number of free parameters
    
    order - derivation order
    
    Throws:
    
    NumberIsTooLargeException - if order is too large.
  - DerivativeStructure
```
public DerivativeStructure(int parameters,
                           int order,
                           double value)
```
    Build an instance representing a constant value.
    
    Parameters:
    
    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)
  - DerivativeStructure
```
public DerivativeStructure(int parameters,
                           int order,
                           int index,
                           double 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.
    
    Parameters:
    
    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)
  - DerivativeStructure
```
public DerivativeStructure(double a1,
                           DerivativeStructure ds1,
                           double a2,
                           DerivativeStructure ds2)
```
    Linear combination constructor. The derivative structure built will be a1 * ds1 + a2 * ds2
    
    Parameters:
    
    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
  - DerivativeStructure
```
public DerivativeStructure(double a1,
                           DerivativeStructure ds1,
                           double a2,
                           DerivativeStructure ds2,
                           double a3,
                           DerivativeStructure ds3)
```
    Linear combination constructor. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3
    
    Parameters:
    
    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.
  - DerivativeStructure
```
public DerivativeStructure(double a1,
                           DerivativeStructure ds1,
                           double a2,
                           DerivativeStructure ds2,
                           double a3,
                           DerivativeStructure ds3,
                           double a4,
                           DerivativeStructure ds4)
```
    Linear combination constructor. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Parameters:
    
    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.
  - DerivativeStructure
```
public DerivativeStructure(int parameters,
                           int order,
                           double... derivatives)
```
    Build an instance from all its derivatives.
    
    Parameters:
    
    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()
- Method Detail
  - getFreeParameters
```
public int getFreeParameters()
```
    Get the number of free parameters.
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Get the derivation order.
    
    Returns:
    
    derivation order
  - createConstant
```
public DerivativeStructure createConstant(double c)
```
    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)
    
    Parameters:
    
    c - value of the constant
    
    Returns:
    
    a constant compatible with instance order and number of parameters
    
    Since:
    
    3.3
    
    See Also:
    
    DerivativeStructure(int, int, double)
  - getReal
```
public double getReal()
```
    Specified by:
    
    getReal in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - getValue
```
public double getValue()
```
    Get the value part of the derivative structure.
    
    Returns:
    
    value part of the derivative structure
    
    See Also:
    
    getPartialDerivative(int...)
  - getPartialDerivative
```
public double getPartialDerivative(int... orders)
```
    Get a partial derivative.
    
    Parameters:
    
    orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)
    
    Returns:
    
    partial derivative
    
    Throws:
    
    DimensionMismatchException - if the numbers of variables does not match the instance.
    
    NumberIsTooLargeException - if the sum of derivation orders is larger than the instance limits.
    
    See Also:
    
    getValue()
  - getAllDerivatives
```
public double[] getAllDerivatives()
```
    Get all partial derivatives.
    
    Returns:
    
    a fresh copy of partial derivatives, in an array sorted according to DSCompiler.getPartialDerivativeIndex(int...)
  - add
```
public DerivativeStructure add(double a)
```
    Specified by:
    
    add in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - add
```
public DerivativeStructure add(DerivativeStructure a)
```
    Specified by:
    
    add in interface FieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match.
  - subtract
```
public DerivativeStructure subtract(double a)
```
    Specified by:
    
    subtract in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - subtract
```
public DerivativeStructure subtract(DerivativeStructure a)
```
    Specified by:
    
    subtract in interface FieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
  - multiply
```
public DerivativeStructure multiply(int n)
```
    Specified by:
    
    multiply in interface FieldElement<DerivativeStructure>
  - multiply
```
public DerivativeStructure multiply(double a)
```
    Specified by:
    
    multiply in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - multiply
```
public DerivativeStructure multiply(DerivativeStructure a)
```
    Specified by:
    
    multiply in interface FieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
  - divide
```
public DerivativeStructure divide(double a)
```
    Specified by:
    
    divide in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - divide
```
public DerivativeStructure divide(DerivativeStructure a)
```
    Specified by:
    
    divide in interface FieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
  - remainder
```
public DerivativeStructure remainder(double a)
```
    Specified by:
    
    remainder in interface RealFieldElement<DerivativeStructure>
  - remainder
```
public DerivativeStructure remainder(DerivativeStructure a)
```
    Specified by:
    
    remainder in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - negate
```
public DerivativeStructure negate()
```
    Specified by:
    
    negate in interface FieldElement<DerivativeStructure>
  - abs
```
public DerivativeStructure abs()
```
    Specified by:
    
    abs in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - ceil
```
public DerivativeStructure ceil()
```
    Specified by:
    
    ceil in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - floor
```
public DerivativeStructure floor()
```
    Specified by:
    
    floor in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - rint
```
public DerivativeStructure rint()
```
    Specified by:
    
    rint in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - round
```
public long round()
```
    Specified by:
    
    round in interface RealFieldElement<DerivativeStructure>
  - signum
```
public DerivativeStructure signum()
```
    Specified by:
    
    signum in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - copySign
```
public DerivativeStructure copySign(DerivativeStructure sign)
```
    Specified by:
    
    copySign in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - copySign
```
public DerivativeStructure copySign(double sign)
```
    Specified by:
    
    copySign in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - getExponent
```
public int getExponent()
```
    Return the exponent of the instance value, removing the bias.
    For double numbers of the form 2^x, the unbiased exponent is exactly x.
    
    Returns:
    
    exponent for instance in IEEE754 representation, without bias
  - scalb
```
public DerivativeStructure scalb(int n)
```
    Specified by:
    
    scalb in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - hypot
```
public DerivativeStructure hypot(DerivativeStructure y)
```
    Specified by:
    
    hypot in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - hypot
```
public static DerivativeStructure hypot(DerivativeStructure x,
                                        DerivativeStructure y)
```
    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.
    Parameters:
    
    x - a value
    
    y - a value
    
    Returns:
    
    sqrt(x² +y²)
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - compose
```
public DerivativeStructure compose(double... f)
```
    Compute composition of the instance by a univariate function.
    
    Parameters:
    
    f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).
    
    Returns:
    
    f(this)
    
    Throws:
    
    DimensionMismatchException - if the number of derivatives in the array is not equal to order + 1
  - reciprocal
```
public DerivativeStructure reciprocal()
```
    Specified by:
    
    reciprocal in interface FieldElement<DerivativeStructure>
    
    Specified by:
    
    reciprocal in interface RealFieldElement<DerivativeStructure>
  - sqrt
```
public DerivativeStructure sqrt()
```
    Specified by:
    
    sqrt in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - cbrt
```
public DerivativeStructure cbrt()
```
    Specified by:
    
    cbrt in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - rootN
```
public DerivativeStructure rootN(int n)
```
    Specified by:
    
    rootN in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - getField
```
public Field<DerivativeStructure> getField()
```
    Specified by:
    
    getField in interface FieldElement<DerivativeStructure>
  - pow
```
public static DerivativeStructure pow(double a,
                                      DerivativeStructure x)
```
    Compute a^x where a is a double and x a DerivativeStructure.
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
    
    Since:
    
    3.3
  - pow
```
public DerivativeStructure pow(double p)
```
    Specified by:
    
    pow in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - pow
```
public DerivativeStructure pow(int n)
```
    Specified by:
    
    pow in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - pow
```
public DerivativeStructure pow(DerivativeStructure e)
```
    Specified by:
    
    pow in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - exp
```
public DerivativeStructure exp()
```
    Specified by:
    
    exp in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - expm1
```
public DerivativeStructure expm1()
```
    Specified by:
    
    expm1 in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - log
```
public DerivativeStructure log()
```
    Specified by:
    
    log in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - log1p
```
public DerivativeStructure log1p()
```
    Specified by:
    
    log1p in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - log10
```
public DerivativeStructure log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public DerivativeStructure cos()
```
    Specified by:
    
    cos in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - sin
```
public DerivativeStructure sin()
```
    Specified by:
    
    sin in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - tan
```
public DerivativeStructure tan()
```
    Specified by:
    
    tan in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - acos
```
public DerivativeStructure acos()
```
    Specified by:
    
    acos in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - asin
```
public DerivativeStructure asin()
```
    Specified by:
    
    asin in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - atan
```
public DerivativeStructure atan()
```
    Specified by:
    
    atan in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - atan2
```
public DerivativeStructure atan2(DerivativeStructure x)
```
    Specified by:
    
    atan2 in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - atan2
```
public static DerivativeStructure atan2(DerivativeStructure y,
                                        DerivativeStructure x)
```
    Two arguments arc tangent operation.
    
    Parameters:
    
    y - first argument of the arc tangent
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(y, x)
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - cosh
```
public DerivativeStructure cosh()
```
    Specified by:
    
    cosh in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - sinh
```
public DerivativeStructure sinh()
```
    Specified by:
    
    sinh in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - tanh
```
public DerivativeStructure tanh()
```
    Specified by:
    
    tanh in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - acosh
```
public DerivativeStructure acosh()
```
    Specified by:
    
    acosh in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - asinh
```
public DerivativeStructure asinh()
```
    Specified by:
    
    asinh in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - atanh
```
public DerivativeStructure atanh()
```
    Specified by:
    
    atanh in interface RealFieldElement<DerivativeStructure>
    
    Since:
    
    3.2
  - toDegrees
```
public DerivativeStructure toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP.
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public DerivativeStructure toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP.
    
    Returns:
    
    instance converted into radians
  - taylor
```
public double taylor(double... delta)
```
    Evaluate Taylor expansion a derivative structure.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathArithmeticException - if factorials becomes too large
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure[] a,
                                             DerivativeStructure[] b)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(double[] a,
                                             DerivativeStructure[] b)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                             DerivativeStructure b1,
                                             DerivativeStructure a2,
                                             DerivativeStructure b2)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                             DerivativeStructure b1,
                                             double a2,
                                             DerivativeStructure b2)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                             DerivativeStructure b1,
                                             DerivativeStructure a2,
                                             DerivativeStructure b2,
                                             DerivativeStructure a3,
                                             DerivativeStructure b3)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                             DerivativeStructure b1,
                                             double a2,
                                             DerivativeStructure b2,
                                             double a3,
                                             DerivativeStructure b3)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                             DerivativeStructure b1,
                                             DerivativeStructure a2,
                                             DerivativeStructure b2,
                                             DerivativeStructure a3,
                                             DerivativeStructure b3,
                                             DerivativeStructure a4,
                                             DerivativeStructure b4)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                             DerivativeStructure b1,
                                             double a2,
                                             DerivativeStructure b2,
                                             double a3,
                                             DerivativeStructure b3,
                                             double a4,
                                             DerivativeStructure b4)
```
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    
    Since:
    
    3.2
  - equals
```
public boolean equals(Object other)
```
    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.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    
    other - Object to test for equality to this
    
    Returns:
    
    true if two derivative structures are equal
    
    Since:
    
    3.2
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the derivative structure.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    a hash code value for this object
    
    Since:
    
    3.2

Class DerivativeStructure

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

Method Detail

getFreeParameters

getOrder

createConstant

getReal

getValue

getPartialDerivative

getAllDerivatives

add

add

subtract

subtract

multiply

multiply

multiply

divide

divide

remainder

remainder

negate

abs

ceil

floor

rint

round

signum

copySign

copySign

getExponent

scalb

hypot

hypot

compose

reciprocal

sqrt

cbrt

rootN

getField

pow

pow

pow

pow

exp

expm1

log

log1p

log10

cos

sin

tan

acos

asin

atan

atan2

atan2

cosh

sinh

tanh

acosh

asinh

atanh

toDegrees

toRadians

taylor

linearCombination

linearCombination

linearCombination

linearCombination