DerivativeStructure (patrius 4.0 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.analysis.differentiation.DerivativeStructure

All Implemented Interfaces:

FieldElement<DerivativeStructure>, RealFieldElement<DerivativeStructure>, Serializable
```
public class DerivativeStructure
extends Object
implements RealFieldElement<DerivativeStructure>, Serializable
```
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 static 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.

Since:

3.1

Version:

$Id: DerivativeStructure.java 18108 2017-10-04 06:45:27Z bignon $

See Also:
DSCompiler, Serialized Form

Constructor Summary

Constructors
Constructor and 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... derivatives)` Build an instance from all its derivatives.
`DerivativeStructure(int parameters, int order, double value)` Build an instance representing a constant value.
`DerivativeStructure(int parameters, int order, int index, double value)` Build an instance representing a variable.

Method Summary

Methods
Modifier and Type	Method and Description
`DerivativeStructure`	`abs()` absolute value.
`DerivativeStructure`	`acos()` Arc cosine operation.
`DerivativeStructure`	`acosh()` Inverse hyperbolic cosine operation.
`DerivativeStructure`	`add(DerivativeStructure a)` '+' operator.
`DerivativeStructure`	`add(double a)` '+' operator.
`DerivativeStructure`	`asin()` Arc sine operation.
`DerivativeStructure`	`asinh()` Inverse hyperbolic sine operation.
`DerivativeStructure`	`atan()` Arc tangent operation.
`DerivativeStructure`	`atan2(DerivativeStructure x)` Two arguments arc tangent operation.
`static DerivativeStructure`	`atan2(DerivativeStructure y, DerivativeStructure x)` Two arguments arc tangent operation.
`DerivativeStructure`	`atanh()` Inverse hyperbolic tangent operation.
`DerivativeStructure`	`cbrt()` Cubic root.
`DerivativeStructure`	`ceil()` Get the smallest whole number larger than instance.
`DerivativeStructure`	`compose(double... f)` Compute composition of the instance by a univariate function.
`DerivativeStructure`	`copySign(DerivativeStructure sign)` Returns the instance with the sign of the argument.
`DerivativeStructure`	`copySign(double sign)` Returns the instance with the sign of the argument.
`DerivativeStructure`	`cos()` Cosine operation.
`DerivativeStructure`	`cosh()` Hyperbolic cosine operation.
`DerivativeStructure`	`createConstant(double c)` Create a constant compatible with instance order and number of parameters.
`DerivativeStructure`	`divide(DerivativeStructure a)` '÷s;' operator.
`DerivativeStructure`	`divide(double a)` '÷s;' operator.
`boolean`	`equals(Object other)` Test for the equality of two derivative structures.
`DerivativeStructure`	`exp()` Exponential.
`DerivativeStructure`	`expm1()` Exponential minus 1.
`DerivativeStructure`	`floor()` Get the largest whole number smaller than instance.
`double[]`	`getAllDerivatives()` Get all partial derivatives.
`int`	`getExponent()` Return the exponent of the instance value, removing the bias.
`Field<DerivativeStructure>`	`getField()` Get the `Field` to which the instance belongs.
`int`	`getFreeParameters()` Get the number of free parameters.
`int`	`getOrder()` Get the derivation order.
`double`	`getPartialDerivative(int... orders)` Get a partial derivative.
`double`	`getReal()` Get the real value of the number.
`double`	`getValue()` Get the value part of the derivative structure.
`int`	`hashCode()` Get a hashCode for the derivative structure.
`DerivativeStructure`	`hypot(DerivativeStructure y)` Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`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(DerivativeStructure[] a, DerivativeStructure[] b)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2, DerivativeStructure a3, DerivativeStructure b3)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2, DerivativeStructure a3, DerivativeStructure b3, DerivativeStructure a4, DerivativeStructure b4)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(double[] a, DerivativeStructure[] b)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2, double a3, DerivativeStructure b3)` Compute a linear combination.
`DerivativeStructure`	`linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2, double a3, DerivativeStructure b3, double a4, DerivativeStructure b4)` Compute a linear combination.
`DerivativeStructure`	`log()` Natural logarithm.
`DerivativeStructure`	`log10()` Base 10 logarithm.
`DerivativeStructure`	`log1p()` Shifted natural logarithm.
`DerivativeStructure`	`multiply(DerivativeStructure a)` '×' operator.
`DerivativeStructure`	`multiply(double a)` '×' operator.
`DerivativeStructure`	`multiply(int n)` Compute n × this.
`DerivativeStructure`	`negate()` unary '-' operator.
`DerivativeStructure`	`pow(DerivativeStructure e)` Power operation.
`DerivativeStructure`	`pow(double p)` Power operation.
`static DerivativeStructure`	`pow(double a, DerivativeStructure x)` Compute a^x where a is a double and x a `DerivativeStructure`
`DerivativeStructure`	`pow(int n)` Integer power operation.
`DerivativeStructure`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`DerivativeStructure`	`remainder(DerivativeStructure a)` '%' operator.
`DerivativeStructure`	`remainder(double a)` '%' operator.
`DerivativeStructure`	`rint()` Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
`DerivativeStructure`	`rootN(int n)` N^th root.
`long`	`round()` Get the closest long to instance value.
`DerivativeStructure`	`scalb(int n)` Multiply the instance by a power of 2.
`DerivativeStructure`	`signum()` Compute the signum of the instance.
`DerivativeStructure`	`sin()` Sine operation.
`DerivativeStructure`	`sinh()` Hyperbolic sine operation.
`DerivativeStructure`	`sqrt()` Square root.
`DerivativeStructure`	`subtract(DerivativeStructure a)` '-' operator.
`DerivativeStructure`	`subtract(double a)` '-' operator.
`DerivativeStructure`	`tan()` Tangent operation.
`DerivativeStructure`	`tanh()` Hyperbolic tangent operation.
`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
  - 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
    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
    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:
    
    3.1
    
    See Also:
    DerivativeStructure(int, int, double)
  - getReal
```
public double getReal()
```
    Get the real value of the number.
    
    Specified by:
    
    getReal in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    real value
    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 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)
```
    '+' operator.
    
    Specified by:
    
    add in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this+a
  - add
```
public DerivativeStructure add(DerivativeStructure a)
```
    '+' operator.
    
    Specified by:
    
    add in interface FieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this+a
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders are inconsistent
  - subtract
```
public DerivativeStructure subtract(double a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this-a
  - subtract
```
public DerivativeStructure subtract(DerivativeStructure a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface FieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this-a
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders are inconsistent
  - multiply
```
public DerivativeStructure multiply(int n)
```
    Compute n × this. Multiplication by an integer number is defined as the following sum n × this = ∑_i=1ⁿ this.
    
    Specified by:
    
    multiply in interface FieldElement<DerivativeStructure>
    
    Parameters:
    n - Number of times this must be added to itself.
    
    Returns:
    A new element representing n × this.
  - multiply
```
public DerivativeStructure multiply(double a)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this×a
  - multiply
```
public DerivativeStructure multiply(DerivativeStructure a)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface FieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this×a
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders are inconsistent
  - divide
```
public DerivativeStructure divide(double a)
```
    '÷s;' operator.
    
    Specified by:
    
    divide in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this÷s;a
  - divide
```
public DerivativeStructure divide(DerivativeStructure a)
```
    '÷s;' operator.
    
    Specified by:
    
    divide in interface FieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this÷s;a
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders are inconsistent
  - remainder
```
public DerivativeStructure remainder(double a)
```
    '%' operator.
    
    Specified by:
    
    remainder in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this%a
  - remainder
```
public DerivativeStructure remainder(DerivativeStructure a)
```
    '%' operator.
    
    Specified by:
    
    remainder in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - right hand side parameter of the operator
    
    Returns:
    this%a
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders are inconsistent
  - negate
```
public DerivativeStructure negate()
```
    unary '-' operator.
    
    Specified by:
    
    negate in interface FieldElement<DerivativeStructure>
    
    Returns:
    -this
  - abs
```
public DerivativeStructure abs()
```
    absolute value.
    
    Specified by:
    
    abs in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    abs(this)
  - ceil
```
public DerivativeStructure ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    ceil(this)
  - floor
```
public DerivativeStructure floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    floor(this)
  - rint
```
public DerivativeStructure rint()
```
    Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
    
    Specified by:
    
    rint in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    a double number r such that r is an integer r - 0.5 <= this <= r + 0.5
  - round
```
public long round()
```
    Get the closest long to instance value.
    
    Specified by:
    
    round in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    closest long to getValue()
  - signum
```
public DerivativeStructure signum()
```
    Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
    
    Specified by:
    
    signum in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  - copySign
```
public DerivativeStructure copySign(DerivativeStructure sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    sign - the sign for the returned value
    
    Returns:
    the instance with the same sign as the sign argument
    Since:
    
    3.1
  - copySign
```
public DerivativeStructure copySign(double sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    sign - the sign for the returned value
    
    Returns:
    the instance with the same sign as the sign argument
  - 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)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    n - power of 2
    
    Returns:
    this × 2ⁿ
  - hypot
```
public DerivativeStructure hypot(DerivativeStructure y)
```
    Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +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.
    Specified by:
    
    hypot in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    y - a value
    
    Returns:
    sqrt(this² +y²)
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
  - 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 are inconsistent
  - 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()
```
    Returns the multiplicative inverse of this element.
    
    Specified by:
    
    reciprocal in interface FieldElement<DerivativeStructure>
    
    Specified by:
    
    reciprocal in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    the inverse of this.
  - sqrt
```
public DerivativeStructure sqrt()
```
    Square root.
    
    Specified by:
    
    sqrt in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    square root of the instance
  - cbrt
```
public DerivativeStructure cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    cubic root of the instance
  - rootN
```
public DerivativeStructure rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    n - order of the root
    
    Returns:
    n^th root of the instance
  - getField
```
public Field<DerivativeStructure> getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<DerivativeStructure>
    
    Returns:
    Field to which the instance belongs
  - 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:
    
    3.1
  - pow
```
public DerivativeStructure pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    p - power to apply
    
    Returns:
    this^p
  - pow
```
public DerivativeStructure pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    n - power to apply
    
    Returns:
    thisⁿ
  - pow
```
public DerivativeStructure pow(DerivativeStructure e)
```
    Power operation.
    
    Specified by:
    
    pow in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    e - exponent
    
    Returns:
    this^e
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders are inconsistent
  - exp
```
public DerivativeStructure exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    exponential of the instance
  - expm1
```
public DerivativeStructure expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    exponential minus one of the instance
  - log
```
public DerivativeStructure log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    logarithm of the instance
  - log1p
```
public DerivativeStructure log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    logarithm of one plus the instance
  - log10
```
public DerivativeStructure log10()
```
    Base 10 logarithm.
    
    Returns:
    base 10 logarithm of the instance
  - cos
```
public DerivativeStructure cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    cos(this)
  - sin
```
public DerivativeStructure sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    sin(this)
  - tan
```
public DerivativeStructure tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    tan(this)
  - acos
```
public DerivativeStructure acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    acos(this)
  - asin
```
public DerivativeStructure asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    asin(this)
  - atan
```
public DerivativeStructure atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    atan(this)
  - atan2
```
public DerivativeStructure atan2(DerivativeStructure x)
```
    Two arguments arc tangent operation.
    
    Specified by:
    
    atan2 in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    x - second argument of the arc tangent
    
    Returns:
    atan2(this, x)
    Since:
    
    3.1
  - 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 are inconsistent
  - cosh
```
public DerivativeStructure cosh()
```
    Hyperbolic cosine operation.
    
    Specified by:
    
    cosh in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    cosh(this)
  - sinh
```
public DerivativeStructure sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    sinh(this)
  - tanh
```
public DerivativeStructure tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    tanh(this)
  - acosh
```
public DerivativeStructure acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    acosh(this)
  - asinh
```
public DerivativeStructure asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    asin(this)
  - atanh
```
public DerivativeStructure atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface RealFieldElement<DerivativeStructure>
    
    Returns:
    atanh(this)
  - 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, ...
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure[] a,
                                    DerivativeStructure[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - Factors.
    b - Factors.
    
    Returns:
    Σ_i a_i b_i.
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
  - linearCombination
```
public DerivativeStructure linearCombination(double[] a,
                                    DerivativeStructure[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a - Factors.
    b - Factors.
    
    Returns:
    Σ_i a_i b_i.
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                    DerivativeStructure b1,
                                    DerivativeStructure a2,
                                    DerivativeStructure b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a1 - first factor of the first term
    b1 - second factor of the first term
    a2 - first factor of the second term
    b2 - second factor of the second term
    
    Returns:
    a₁×b₁ + a₂×b₂
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
    
    See Also:
    RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object), RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                    DerivativeStructure b1,
                                    double a2,
                                    DerivativeStructure b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a1 - first factor of the first term
    b1 - second factor of the first term
    a2 - first factor of the second term
    b2 - second factor of the second term
    
    Returns:
    a₁×b₁ + a₂×b₂
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
    
    See Also:
    RealFieldElement.linearCombination(double, Object, double, Object, double, Object), RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                    DerivativeStructure b1,
                                    DerivativeStructure a2,
                                    DerivativeStructure b2,
                                    DerivativeStructure a3,
                                    DerivativeStructure b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a1 - first factor of the first term
    b1 - second factor of the first term
    a2 - first factor of the second term
    b2 - second factor of the second term
    a3 - first factor of the third term
    b3 - second factor of the third term
    
    Returns:
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
    
    See Also:
    RealFieldElement.linearCombination(Object, Object, Object, Object), RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                    DerivativeStructure b1,
                                    double a2,
                                    DerivativeStructure b2,
                                    double a3,
                                    DerivativeStructure b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a1 - first factor of the first term
    b1 - second factor of the first term
    a2 - first factor of the second term
    b2 - second factor of the second term
    a3 - first factor of the third term
    b3 - second factor of the third term
    
    Returns:
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
    
    See Also:
    RealFieldElement.linearCombination(double, Object, double, Object), RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                    DerivativeStructure b1,
                                    DerivativeStructure a2,
                                    DerivativeStructure b2,
                                    DerivativeStructure a3,
                                    DerivativeStructure b3,
                                    DerivativeStructure a4,
                                    DerivativeStructure b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a1 - first factor of the first term
    b1 - second factor of the first term
    a2 - first factor of the second term
    b2 - second factor of the second term
    a3 - first factor of the third term
    b3 - second factor of the third term
    a4 - first factor of the third term
    b4 - second factor of the third term
    
    Returns:
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
    
    See Also:
    RealFieldElement.linearCombination(Object, Object, Object, Object), RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                    DerivativeStructure b1,
                                    double a2,
                                    DerivativeStructure b2,
                                    double a3,
                                    DerivativeStructure b3,
                                    double a4,
                                    DerivativeStructure b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface RealFieldElement<DerivativeStructure>
    
    Parameters:
    a1 - first factor of the first term
    b1 - second factor of the first term
    a2 - first factor of the second term
    b2 - second factor of the second term
    a3 - first factor of the third term
    b3 - second factor of the third term
    a4 - first factor of the third term
    b4 - second factor of the third term
    
    Returns:
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    DimensionMismatchException - if number of free parameters or orders do not match
    Since:
    
    3.1
    
    See Also:
    RealFieldElement.linearCombination(double, Object, double, Object), RealFieldElement.linearCombination(double, Object, double, Object, double, Object)
  - 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:
    
    3.1
  - 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:
    
    3.1

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