java.lang.Object
- org.hipparchus.analysis.differentiation.FieldUnivariateDerivative<T,FieldUnivariateDerivative2<T>>
- - org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2<T>

Type Parameters:

T - the type of the function parameters and value

All Implemented Interfaces:

FieldDerivative<T,FieldUnivariateDerivative2<T>>, CalculusFieldElement<FieldUnivariateDerivative2<T>>, FieldElement<FieldUnivariateDerivative2<T>>
```
public class FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>
extends FieldUnivariateDerivative<T,FieldUnivariateDerivative2<T>>
```
Class representing both the value and the differentials of a function.
This class is a stripped-down version of FieldDerivativeStructure with only one free parameter and derivation order limited to two. It should have less overhead than FieldDerivativeStructure in its domain.

This class is an implementation of Rall's numbers. 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.

FieldUnivariateDerivative2 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.

Instances of this class are guaranteed to be immutable.

Since:

1.7

See Also:

DerivativeStructure, UnivariateDerivative1, UnivariateDerivative2, Gradient, FieldDerivativeStructure, FieldUnivariateDerivative1, FieldGradient

Constructor Summary

Constructors
Constructor	Description
`FieldUnivariateDerivative2(FieldDerivativeStructure<T> ds)`	Build an instance from a `DerivativeStructure`.
`FieldUnivariateDerivative2(T f0, T f1, T f2)`	Build an instance with values and derivative.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`FieldUnivariateDerivative2<T>`	`abs()`	absolute value.
`FieldUnivariateDerivative2<T>`	`acos()`	Arc cosine operation.
`FieldUnivariateDerivative2<T>`	`acosh()`	Inverse hyperbolic cosine operation.
`FieldUnivariateDerivative2<T>`	`add(double a)`	'+' operator.
`FieldUnivariateDerivative2<T>`	`add(FieldUnivariateDerivative2<T> a)`	Compute this + a.
`FieldUnivariateDerivative2<T>`	`add(T a)`	'+' operator.
`FieldUnivariateDerivative2<T>`	`asin()`	Arc sine operation.
`FieldUnivariateDerivative2<T>`	`asinh()`	Inverse hyperbolic sine operation.
`FieldUnivariateDerivative2<T>`	`atan()`	Arc tangent operation.
`FieldUnivariateDerivative2<T>`	`atan2(FieldUnivariateDerivative2<T> x)`	Two arguments arc tangent operation.
`FieldUnivariateDerivative2<T>`	`atanh()`	Inverse hyperbolic tangent operation.
`FieldUnivariateDerivative2<T>`	`cbrt()`	Cubic root.
`FieldUnivariateDerivative2<T>`	`ceil()`	Get the smallest whole number larger than instance.
`FieldUnivariateDerivative2<T>`	`compose(T g0, T g1, T g2)`	Compute composition of the instance by a function.
`FieldUnivariateDerivative2<T>`	`copySign(double sign)`	Returns the instance with the sign of the argument.
`FieldUnivariateDerivative2<T>`	`copySign(FieldUnivariateDerivative2<T> sign)`	Returns the instance with the sign of the argument.
`FieldUnivariateDerivative2<T>`	`copySign(T sign)`	Returns the instance with the sign of the argument.
`FieldUnivariateDerivative2<T>`	`cos()`	Cosine operation.
`FieldUnivariateDerivative2<T>`	`cosh()`	Hyperbolic cosine operation.
`FieldUnivariateDerivative2<T>`	`divide(double a)`	'÷' operator.
`FieldUnivariateDerivative2<T>`	`divide(FieldUnivariateDerivative2<T> a)`	Compute this ÷ a.
`FieldUnivariateDerivative2<T>`	`divide(T a)`	'÷' operator.
`boolean`	`equals(Object other)`	Test for the equality of two univariate derivatives.
`FieldUnivariateDerivative2<T>`	`exp()`	Exponential.
`FieldUnivariateDerivative2<T>`	`expm1()`	Exponential minus 1.
`FieldUnivariateDerivative2<T>`	`floor()`	Get the largest whole number smaller than instance.
`T`	`getDerivative(int n)`	Get a derivative from the univariate derivative.
`int`	`getExponent()`	Return the exponent of the instance, removing the bias.
`FieldUnivariateDerivative2Field<T>`	`getField()`	Get the `Field` to which the instance belongs.
`T`	`getFirstDerivative()`	Get the first derivative.
`int`	`getOrder()`	Get the derivation order.
`FieldUnivariateDerivative2<T>`	`getPi()`	Get the Archimedes constant π.
`double`	`getReal()`	Get the real value of the number.
`T`	`getSecondDerivative()`	Get the second derivative.
`T`	`getValue()`	Get the value part of the univariate derivative.
`Field<T>`	`getValueField()`	Get the `Field` the value and parameters of the function belongs to.
`int`	`hashCode()`	Get a hashCode for the univariate derivative.
`FieldUnivariateDerivative2<T>`	`hypot(FieldUnivariateDerivative2<T> y)`	Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`FieldUnivariateDerivative2<T>`	`linearCombination(double[] a, FieldUnivariateDerivative2<T>[] b)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2, double a3, FieldUnivariateDerivative2<T> b3)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2, double a3, FieldUnivariateDerivative2<T> b3, double a4, FieldUnivariateDerivative2<T> b4)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(FieldUnivariateDerivative2<T>[] a, FieldUnivariateDerivative2<T>[] b)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2, FieldUnivariateDerivative2<T> a3, FieldUnivariateDerivative2<T> b3)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2, FieldUnivariateDerivative2<T> a3, FieldUnivariateDerivative2<T> b3, FieldUnivariateDerivative2<T> a4, FieldUnivariateDerivative2<T> b4)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(T[] a, FieldUnivariateDerivative2<T>[] b)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`linearCombination(T a1, FieldUnivariateDerivative2<T> b1, T a2, FieldUnivariateDerivative2<T> b2, T a3, FieldUnivariateDerivative2<T> b3)`	Compute a linear combination.
`FieldUnivariateDerivative2<T>`	`log()`	Natural logarithm.
`FieldUnivariateDerivative2<T>`	`log10()`	Base 10 logarithm.
`FieldUnivariateDerivative2<T>`	`log1p()`	Shifted natural logarithm.
`FieldUnivariateDerivative2<T>`	`multiply(double a)`	'×' operator.
`FieldUnivariateDerivative2<T>`	`multiply(int n)`	Compute n × this.
`FieldUnivariateDerivative2<T>`	`multiply(FieldUnivariateDerivative2<T> a)`	Compute this × a.
`FieldUnivariateDerivative2<T>`	`multiply(T a)`	'×' operator.
`FieldUnivariateDerivative2<T>`	`negate()`	Returns the additive inverse of `this` element.
`FieldUnivariateDerivative2<T>`	`newInstance(double value)`	Create an instance corresponding to a constant real value.
`FieldUnivariateDerivative2<T>`	`pow(double p)`	Power operation.
`static <T extends CalculusFieldElement<T>> FieldUnivariateDerivative2<T>`	`pow(double a, FieldUnivariateDerivative2<T> x)`	Compute a^x where a is a double and x a `FieldUnivariateDerivative2`
`FieldUnivariateDerivative2<T>`	`pow(int n)`	Integer power operation.
`FieldUnivariateDerivative2<T>`	`pow(FieldUnivariateDerivative2<T> e)`	Power operation.
`FieldUnivariateDerivative2<T>`	`reciprocal()`	Returns the multiplicative inverse of `this` element.
`FieldUnivariateDerivative2<T>`	`remainder(double a)`	IEEE remainder operator.
`FieldUnivariateDerivative2<T>`	`remainder(FieldUnivariateDerivative2<T> a)`	IEEE remainder operator.
`FieldUnivariateDerivative2<T>`	`remainder(T a)`	IEEE remainder operator.
`FieldUnivariateDerivative2<T>`	`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.
`FieldUnivariateDerivative2<T>`	`rootN(int n)`	N^th root.
`FieldUnivariateDerivative2<T>`	`scalb(int n)`	Multiply the instance by a power of 2.
`FieldUnivariateDerivative2<T>`	`sign()`	Compute the sign of the instance.
`FieldUnivariateDerivative2<T>`	`sin()`	Sine operation.
`FieldSinCos<FieldUnivariateDerivative2<T>>`	`sinCos()`	Combined Sine and Cosine operation.
`FieldUnivariateDerivative2<T>`	`sinh()`	Hyperbolic sine operation.
`FieldSinhCosh<FieldUnivariateDerivative2<T>>`	`sinhCosh()`	Combined hyperbolic sine and sosine operation.
`FieldUnivariateDerivative2<T>`	`sqrt()`	Square root.
`FieldUnivariateDerivative2<T>`	`subtract(double a)`	'-' operator.
`FieldUnivariateDerivative2<T>`	`subtract(FieldUnivariateDerivative2<T> a)`	Compute this - a.
`FieldUnivariateDerivative2<T>`	`subtract(T a)`	'-' operator.
`FieldUnivariateDerivative2<T>`	`tan()`	Tangent operation.
`FieldUnivariateDerivative2<T>`	`tanh()`	Hyperbolic tangent operation.
`T`	`taylor(double delta)`	Evaluate Taylor expansion a univariate derivative.
`T`	`taylor(T delta)`	Evaluate Taylor expansion a univariate derivative.
`FieldUnivariateDerivative2<T>`	`toDegrees()`	Convert radians to degrees, with error of less than 0.5 ULP
`FieldDerivativeStructure<T>`	`toDerivativeStructure()`	Convert the instance to a `FieldDerivativeStructure`.
`FieldUnivariateDerivative2<T>`	`toRadians()`	Convert degrees to radians, with error of less than 0.5 ULP
`FieldUnivariateDerivative2<T>`	`ulp()`	Compute least significant bit (Unit in Last Position) for a number.

Methods inherited from class org.hipparchus.analysis.differentiation.FieldUnivariateDerivative
getFreeParameters, getPartialDerivative

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

Methods inherited from interface org.hipparchus.CalculusFieldElement
isFinite, isInfinite, isNaN, norm, round

Methods inherited from interface org.hipparchus.FieldElement
isZero

- Constructor Detail
  - FieldUnivariateDerivative2
```
public FieldUnivariateDerivative2(T f0,
                                  T f1,
                                  T f2)
```
    Build an instance with values and derivative.
    
    Parameters:
    
    f0 - value of the function
    
    f1 - first derivative of the function
    
    f2 - second derivative of the function
  - FieldUnivariateDerivative2
```
public FieldUnivariateDerivative2(FieldDerivativeStructure<T> ds)
                           throws MathIllegalArgumentException
```
    Build an instance from a DerivativeStructure.
    
    Parameters:
    
    ds - derivative structure
    
    Throws:
    
    MathIllegalArgumentException - if either ds parameters is not 1 or ds order is not 2
- Method Detail
  - newInstance
```
public FieldUnivariateDerivative2<T> newInstance(double value)
```
    Create an instance corresponding to a constant real value.
    
    Parameters:
    
    value - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - getReal
```
public double getReal()
```
    Get the real value of the number.
    
    Returns:
    
    real value
  - getValue
```
public T getValue()
```
    Get the value part of the univariate derivative.
    
    Returns:
    
    value part of the univariate derivative
  - getDerivative
```
public T getDerivative(int n)
```
    Get a derivative from the univariate derivative.
    
    Specified by:
    
    getDerivative in class FieldUnivariateDerivative<T extends CalculusFieldElement<T>,FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    n - derivation order (must be between 0 and getOrder(), both inclusive)
    
    Returns:
    
    n^th derivative, or NaN if n is either negative or strictly larger than getOrder()
  - getOrder
```
public int getOrder()
```
    Get the derivation order.
    
    Returns:
    
    derivation order
  - getFirstDerivative
```
public T getFirstDerivative()
```
    Get the first derivative.
    
    Returns:
    
    first derivative
    
    See Also:
    
    getValue()
  - getSecondDerivative
```
public T getSecondDerivative()
```
    Get the second derivative.
    
    Returns:
    
    second derivative
    
    See Also:
    
    getValue(), getFirstDerivative()
  - getValueField
```
public Field<T> getValueField()
```
    Get the Field the value and parameters of the function belongs to.
    
    Returns:
    
    Field the value and parameters of the function belongs to
  - toDerivativeStructure
```
public FieldDerivativeStructure<T> toDerivativeStructure()
```
    Convert the instance to a FieldDerivativeStructure.
    
    Specified by:
    
    toDerivativeStructure in class FieldUnivariateDerivative<T extends CalculusFieldElement<T>,FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    derivative structure with same value and derivative as the instance
  - add
```
public FieldUnivariateDerivative2<T> add(T a)
```
    '+' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public FieldUnivariateDerivative2<T> add(double a)
```
    '+' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public FieldUnivariateDerivative2<T> add(FieldUnivariateDerivative2<T> a)
```
    Compute this + a.
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - subtract
```
public FieldUnivariateDerivative2<T> subtract(T a)
```
    '-' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public FieldUnivariateDerivative2<T> subtract(double a)
```
    '-' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public FieldUnivariateDerivative2<T> subtract(FieldUnivariateDerivative2<T> a)
```
    Compute this - a.
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
  - multiply
```
public FieldUnivariateDerivative2<T> multiply(T a)
```
    '×' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public FieldUnivariateDerivative2<T> multiply(int n)
```
    Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]
    
    Parameters:
    
    n - Number of times this must be added to itself.
    
    Returns:
    
    A new element representing n × this.
  - multiply
```
public FieldUnivariateDerivative2<T> multiply(double a)
```
    '×' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public FieldUnivariateDerivative2<T> multiply(FieldUnivariateDerivative2<T> a)
```
    Compute this × a.
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
  - divide
```
public FieldUnivariateDerivative2<T> divide(T a)
```
    '÷' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public FieldUnivariateDerivative2<T> divide(double a)
```
    '÷' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public FieldUnivariateDerivative2<T> divide(FieldUnivariateDerivative2<T> a)
```
    Compute this ÷ a.
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
  - remainder
```
public FieldUnivariateDerivative2<T> remainder(T a)
```
    IEEE remainder operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × 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)
  - remainder
```
public FieldUnivariateDerivative2<T> remainder(double a)
```
    IEEE remainder operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - remainder
```
public FieldUnivariateDerivative2<T> remainder(FieldUnivariateDerivative2<T> a)
```
    IEEE remainder operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - negate
```
public FieldUnivariateDerivative2<T> negate()
```
    Returns the additive inverse of this element.
    
    Returns:
    
    the opposite of this.
  - abs
```
public FieldUnivariateDerivative2<T> abs()
```
    absolute value.
    Just another name for CalculusFieldElement.norm()
    
    Returns:
    
    abs(this)
  - ceil
```
public FieldUnivariateDerivative2<T> ceil()
```
    Get the smallest whole number larger than instance.
    
    Returns:
    
    ceil(this)
  - floor
```
public FieldUnivariateDerivative2<T> floor()
```
    Get the largest whole number smaller than instance.
    
    Returns:
    
    floor(this)
  - rint
```
public FieldUnivariateDerivative2<T> 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.
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - sign
```
public FieldUnivariateDerivative2<T> sign()
```
    Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)
    
    Returns:
    
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  - copySign
```
public FieldUnivariateDerivative2<T> copySign(T sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public FieldUnivariateDerivative2<T> copySign(FieldUnivariateDerivative2<T> sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public FieldUnivariateDerivative2<T> copySign(double sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    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, removing the bias.
    For double numbers of the form 2^x, the unbiased exponent is exactly x.
    
    Returns:
    
    exponent for the instance, without bias
  - scalb
```
public FieldUnivariateDerivative2<T> scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - ulp
```
public FieldUnivariateDerivative2<T> ulp()
```
    Compute least significant bit (Unit in Last Position) for a number.
    The ulp function is a step function, hence all its derivatives are 0.
    
    Returns:
    
    ulp(this)
    
    Since:
    
    2.0
  - hypot
```
public FieldUnivariateDerivative2<T> hypot(FieldUnivariateDerivative2<T> 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.
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
  - reciprocal
```
public FieldUnivariateDerivative2<T> reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Returns:
    
    the inverse of this.
  - compose
```
public FieldUnivariateDerivative2<T> compose(T g0,
                                             T g1,
                                             T g2)
```
    Compute composition of the instance by a function.
    
    Parameters:
    
    g0 - value of the function at the current point (i.e. at g(getValue()))
    
    g1 - first derivative of the function at the current point (i.e. at g'(getValue()))
    
    g2 - second derivative of the function at the current point (i.e. at g''(getValue()))
    
    Returns:
    
    g(this)
  - sqrt
```
public FieldUnivariateDerivative2<T> sqrt()
```
    Square root.
    
    Returns:
    
    square root of the instance
  - cbrt
```
public FieldUnivariateDerivative2<T> cbrt()
```
    Cubic root.
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public FieldUnivariateDerivative2<T> rootN(int n)
```
    N^th root.
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
  - getField
```
public FieldUnivariateDerivative2Field<T> getField()
```
    Get the Field to which the instance belongs.
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static <T extends CalculusFieldElement<T>> FieldUnivariateDerivative2<T> pow(double a,
                                                                                    FieldUnivariateDerivative2<T> x)
```
    Compute a^x where a is a double and x a FieldUnivariateDerivative2
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - pow
```
public FieldUnivariateDerivative2<T> pow(double p)
```
    Power operation.
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public FieldUnivariateDerivative2<T> pow(int n)
```
    Integer power operation.
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - pow
```
public FieldUnivariateDerivative2<T> pow(FieldUnivariateDerivative2<T> e)
```
    Power operation.
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
  - exp
```
public FieldUnivariateDerivative2<T> exp()
```
    Exponential.
    
    Returns:
    
    exponential of the instance
  - expm1
```
public FieldUnivariateDerivative2<T> expm1()
```
    Exponential minus 1.
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public FieldUnivariateDerivative2<T> log()
```
    Natural logarithm.
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public FieldUnivariateDerivative2<T> log1p()
```
    Shifted natural logarithm.
    
    Returns:
    
    logarithm of one plus the instance
  - log10
```
public FieldUnivariateDerivative2<T> log10()
```
    Base 10 logarithm.
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public FieldUnivariateDerivative2<T> cos()
```
    Cosine operation.
    
    Returns:
    
    cos(this)
  - sin
```
public FieldUnivariateDerivative2<T> sin()
```
    Sine operation.
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<FieldUnivariateDerivative2<T>> sinCos()
```
    Combined Sine and Cosine operation.
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public FieldUnivariateDerivative2<T> tan()
```
    Tangent operation.
    
    Returns:
    
    tan(this)
  - acos
```
public FieldUnivariateDerivative2<T> acos()
```
    Arc cosine operation.
    
    Returns:
    
    acos(this)
  - asin
```
public FieldUnivariateDerivative2<T> asin()
```
    Arc sine operation.
    
    Returns:
    
    asin(this)
  - atan
```
public FieldUnivariateDerivative2<T> atan()
```
    Arc tangent operation.
    
    Returns:
    
    atan(this)
  - atan2
```
public FieldUnivariateDerivative2<T> atan2(FieldUnivariateDerivative2<T> x)
```
    Two arguments arc tangent operation.
    Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
  - cosh
```
public FieldUnivariateDerivative2<T> cosh()
```
    Hyperbolic cosine operation.
    
    Returns:
    
    cosh(this)
  - sinh
```
public FieldUnivariateDerivative2<T> sinh()
```
    Hyperbolic sine operation.
    
    Returns:
    
    sinh(this)
  - sinhCosh
```
public FieldSinhCosh<FieldUnivariateDerivative2<T>> sinhCosh()
```
    Combined hyperbolic sine and sosine operation.
    
    Returns:
    
    [sinh(this), cosh(this)]
  - tanh
```
public FieldUnivariateDerivative2<T> tanh()
```
    Hyperbolic tangent operation.
    
    Returns:
    
    tanh(this)
  - acosh
```
public FieldUnivariateDerivative2<T> acosh()
```
    Inverse hyperbolic cosine operation.
    
    Returns:
    
    acosh(this)
  - asinh
```
public FieldUnivariateDerivative2<T> asinh()
```
    Inverse hyperbolic sine operation.
    
    Returns:
    
    asin(this)
  - atanh
```
public FieldUnivariateDerivative2<T> atanh()
```
    Inverse hyperbolic tangent operation.
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public FieldUnivariateDerivative2<T> toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public FieldUnivariateDerivative2<T> toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Returns:
    
    instance converted into radians
  - taylor
```
public T taylor(double delta)
```
    Evaluate Taylor expansion a univariate derivative.
    
    Parameters:
    
    delta - parameter offset Δx
    
    Returns:
    
    value of the Taylor expansion at x + Δx
  - taylor
```
public T taylor(T delta)
```
    Evaluate Taylor expansion a univariate derivative.
    
    Parameters:
    
    delta - parameter offset Δx
    
    Returns:
    
    value of the Taylor expansion at x + Δx
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(T[] a,
                                                       FieldUnivariateDerivative2<T>[] b)
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if arrays dimensions don't match
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T>[] a,
                                                       FieldUnivariateDerivative2<T>[] b)
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(double[] a,
                                                       FieldUnivariateDerivative2<T>[] b)
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       FieldUnivariateDerivative2<T> a2,
                                                       FieldUnivariateDerivative2<T> b2)
```
    Compute a linear combination.
    
    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
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(double a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       double a2,
                                                       FieldUnivariateDerivative2<T> b2)
```
    Compute a linear combination.
    
    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
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       FieldUnivariateDerivative2<T> a2,
                                                       FieldUnivariateDerivative2<T> b2,
                                                       FieldUnivariateDerivative2<T> a3,
                                                       FieldUnivariateDerivative2<T> b3)
```
    Compute a linear combination.
    
    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
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(T a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       T a2,
                                                       FieldUnivariateDerivative2<T> b2,
                                                       T a3,
                                                       FieldUnivariateDerivative2<T> b3)
```
    Compute a linear combination.
    
    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:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
    
    See Also:
    
    linearCombination(double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2), linearCombination(double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2)
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(double a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       double a2,
                                                       FieldUnivariateDerivative2<T> b2,
                                                       double a3,
                                                       FieldUnivariateDerivative2<T> b3)
```
    Compute a linear combination.
    
    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
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       FieldUnivariateDerivative2<T> a2,
                                                       FieldUnivariateDerivative2<T> b2,
                                                       FieldUnivariateDerivative2<T> a3,
                                                       FieldUnivariateDerivative2<T> b3,
                                                       FieldUnivariateDerivative2<T> a4,
                                                       FieldUnivariateDerivative2<T> b4)
```
    Compute a linear combination.
    
    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 fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public FieldUnivariateDerivative2<T> linearCombination(double a1,
                                                       FieldUnivariateDerivative2<T> b1,
                                                       double a2,
                                                       FieldUnivariateDerivative2<T> b2,
                                                       double a3,
                                                       FieldUnivariateDerivative2<T> b3,
                                                       double a4,
                                                       FieldUnivariateDerivative2<T> b4)
```
    Compute a linear combination.
    
    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 fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
  - getPi
```
public FieldUnivariateDerivative2<T> getPi()
```
    Get the Archimedes constant π.
    Archimedes constant is the ratio of a circle's circumference to its diameter.
    
    Returns:
    
    Archimedes constant π
  - equals
```
public boolean equals(Object other)
```
    Test for the equality of two univariate derivatives.
    univariate derivatives are considered equal if they have the same derivatives.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    
    other - Object to test for equality to this
    
    Returns:
    
    true if two univariate derivatives are equal
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the univariate derivative.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    a hash code value for this object

Class FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>

Constructor Summary

Method Summary

Methods inherited from class org.hipparchus.analysis.differentiation.FieldUnivariateDerivative

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Methods inherited from interface org.hipparchus.FieldElement

Constructor Detail

FieldUnivariateDerivative2

FieldUnivariateDerivative2

Method Detail

newInstance

getReal

getValue

getDerivative

getOrder

getFirstDerivative

getSecondDerivative

getValueField

toDerivativeStructure

add

add

add

subtract

subtract

subtract

multiply

multiply

multiply

multiply

divide

divide

divide

remainder

remainder

remainder

negate

abs

ceil

floor

rint

sign

copySign

copySign

copySign

getExponent

scalb

ulp

hypot

reciprocal

compose

sqrt

cbrt

rootN

getField

pow

pow

pow

pow

exp

expm1

log

log1p

log10

cos

sin

sinCos

tan

acos

asin

atan

atan2

cosh

sinh

sinhCosh

tanh

acosh

asinh

atanh

toDegrees