java.lang.Object
- org.hipparchus.analysis.differentiation.UnivariateDerivative<UnivariateDerivative2>
- - org.hipparchus.analysis.differentiation.UnivariateDerivative2

All Implemented Interfaces:

Serializable, Comparable<UnivariateDerivative2>, Derivative<UnivariateDerivative2>, DifferentialAlgebra, CalculusFieldElement<UnivariateDerivative2>, FieldElement<UnivariateDerivative2>
```
public class UnivariateDerivative2
extends UnivariateDerivative<UnivariateDerivative2>
```
Class representing both the value and the differentials of a function.
This class is a stripped-down version of DerivativeStructure with only one free parameter and derivation order also limited to two. It should have less overhead than DerivativeStructure 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.

UnivariateDerivative2 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 Derivative-based classes (or in fact any CalculusFieldElement class) is a tedious and error-prone task but has the advantage of not requiring users to compute the derivatives by themselves and allowing to switch for one derivative implementation to another as they all share the same filed API.

Instances of this class are guaranteed to be immutable.

Since:

1.7

See Also:

DerivativeStructure, UnivariateDerivative2, Gradient, FieldDerivativeStructure, FieldUnivariateDerivative2, FieldUnivariateDerivative2, FieldGradient, Serialized Form

Field Summary

Fields
Modifier and Type Field Description

static UnivariateDerivative2 PI
The constant value of π as a UnivariateDerivative2.

Constructor Summary

Constructors
Constructor	Description
`UnivariateDerivative2(double f0, double f1, double f2)`	Build an instance with values and derivative.
`UnivariateDerivative2(DerivativeStructure ds)`	Build an instance from a `DerivativeStructure`.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`UnivariateDerivative2`	`abs()`	absolute value.
`UnivariateDerivative2`	`acos()`	Arc cosine operation.
`UnivariateDerivative2`	`acosh()`	Inverse hyperbolic cosine operation.
`UnivariateDerivative2`	`add(UnivariateDerivative2 a)`	Compute this + a.
`UnivariateDerivative2`	`asin()`	Arc sine operation.
`UnivariateDerivative2`	`asinh()`	Inverse hyperbolic sine operation.
`UnivariateDerivative2`	`atan()`	Arc tangent operation.
`UnivariateDerivative2`	`atan2(UnivariateDerivative2 x)`	Two arguments arc tangent operation.
`UnivariateDerivative2`	`atanh()`	Inverse hyperbolic tangent operation.
`UnivariateDerivative2`	`cbrt()`	Cubic root.
`int`	`compareTo(UnivariateDerivative2 o)`
`UnivariateDerivative2`	`compose(double... f)`	Compute composition of the instance by a univariate function.
`UnivariateDerivative2`	`copySign(double sign)`	Returns the instance with the sign of the argument.
`UnivariateDerivative2`	`copySign(UnivariateDerivative2 sign)`	Returns the instance with the sign of the argument.
`UnivariateDerivative2`	`cos()`	Cosine operation.
`UnivariateDerivative2`	`cosh()`	Hyperbolic cosine operation.
`UnivariateDerivative2`	`divide(double a)`	'÷' operator.
`UnivariateDerivative2`	`divide(UnivariateDerivative2 a)`	Compute this ÷ a.
`boolean`	`equals(Object other)`	Test for the equality of two univariate derivatives.
`UnivariateDerivative2`	`exp()`	Exponential.
`UnivariateDerivative2`	`expm1()`	Exponential minus 1.
`UnivariateDerivative2`	`getAddendum()`	Get the addendum to the real value of the number.
`double`	`getDerivative(int n)`	Get a derivative from the univariate derivative.
`UnivariateDerivative2Field`	`getField()`	Get the `Field` to which the instance belongs.
`double`	`getFirstDerivative()`	Get the first derivative.
`int`	`getOrder()`	Get the maximum derivation order.
`UnivariateDerivative2`	`getPi()`	Get the Archimedes constant π.
`double`	`getSecondDerivative()`	Get the second derivative.
`double`	`getValue()`	Get the value part of the function.
`int`	`hashCode()`	Get a hashCode for the univariate derivative.
`UnivariateDerivative2`	`hypot(UnivariateDerivative2 y)`	Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`UnivariateDerivative2`	`linearCombination(double[] a, UnivariateDerivative2[] b)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(double a1, UnivariateDerivative2 b1, double a2, UnivariateDerivative2 b2)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(double a1, UnivariateDerivative2 b1, double a2, UnivariateDerivative2 b2, double a3, UnivariateDerivative2 b3)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(double a1, UnivariateDerivative2 b1, double a2, UnivariateDerivative2 b2, double a3, UnivariateDerivative2 b3, double a4, UnivariateDerivative2 b4)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(UnivariateDerivative2[] a, UnivariateDerivative2[] b)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(UnivariateDerivative2 a1, UnivariateDerivative2 b1, UnivariateDerivative2 a2, UnivariateDerivative2 b2)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(UnivariateDerivative2 a1, UnivariateDerivative2 b1, UnivariateDerivative2 a2, UnivariateDerivative2 b2, UnivariateDerivative2 a3, UnivariateDerivative2 b3)`	Compute a linear combination.
`UnivariateDerivative2`	`linearCombination(UnivariateDerivative2 a1, UnivariateDerivative2 b1, UnivariateDerivative2 a2, UnivariateDerivative2 b2, UnivariateDerivative2 a3, UnivariateDerivative2 b3, UnivariateDerivative2 a4, UnivariateDerivative2 b4)`	Compute a linear combination.
`UnivariateDerivative2`	`log()`	Natural logarithm.
`UnivariateDerivative2`	`log10()`	Base 10 logarithm.
`UnivariateDerivative2`	`log1p()`	Shifted natural logarithm.
`UnivariateDerivative2`	`multiply(double a)`	'×' operator.
`UnivariateDerivative2`	`multiply(int n)`	Compute n × this.
`UnivariateDerivative2`	`multiply(UnivariateDerivative2 a)`	Compute this × a.
`UnivariateDerivative2`	`negate()`	Returns the additive inverse of `this` element.
`UnivariateDerivative2`	`newInstance(double value)`	Create an instance corresponding to a constant real value.
`UnivariateDerivative2`	`pow(double p)`	Power operation.
`static UnivariateDerivative2`	`pow(double a, UnivariateDerivative2 x)`	Compute a^x where a is a double and x a `UnivariateDerivative2`
`UnivariateDerivative2`	`pow(int n)`	Integer power operation.
`UnivariateDerivative2`	`reciprocal()`	Returns the multiplicative inverse of `this` element.
`UnivariateDerivative2`	`remainder(UnivariateDerivative2 a)`	IEEE remainder operator.
`UnivariateDerivative2`	`rootN(int n)`	N^th root.
`UnivariateDerivative2`	`scalb(int n)`	Multiply the instance by a power of 2.
`UnivariateDerivative2`	`sin()`	Sine operation.
`FieldSinCos<UnivariateDerivative2>`	`sinCos()`	Combined Sine and Cosine operation.
`UnivariateDerivative2`	`sinh()`	Hyperbolic sine operation.
`FieldSinhCosh<UnivariateDerivative2>`	`sinhCosh()`	Combined hyperbolic sine and cosine operation.
`UnivariateDerivative2`	`sqrt()`	Square root.
`UnivariateDerivative2`	`square()`	Compute this × this.
`UnivariateDerivative2`	`subtract(UnivariateDerivative2 a)`	Compute this - a.
`UnivariateDerivative2`	`tan()`	Tangent operation.
`UnivariateDerivative2`	`tanh()`	Hyperbolic tangent operation.
`double`	`taylor(double delta)`	Evaluate Taylor expansion a univariate derivative.
`UnivariateDerivative2`	`toDegrees()`	Convert radians to degrees, with error of less than 0.5 ULP
`DerivativeStructure`	`toDerivativeStructure()`	Convert the instance to a `DerivativeStructure`.
`UnivariateDerivative2`	`toRadians()`	Convert degrees to radians, with error of less than 0.5 ULP
`UnivariateDerivative2`	`withValue(double value)`	Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.

Methods inherited from class org.hipparchus.analysis.differentiation.UnivariateDerivative
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
ceil, floor, isFinite, isInfinite, isNaN, norm, rint, round, sign, ulp

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative
add, getExponent, getReal, pow, remainder, subtract

Methods inherited from interface org.hipparchus.FieldElement
isZero

- Field Detail
  - PI
```
public static final UnivariateDerivative2 PI
```
    The constant value of π as a UnivariateDerivative2.
    
    Since:
    
    2.0
- Constructor Detail
  - UnivariateDerivative2
```
public UnivariateDerivative2(double f0,
                             double f1,
                             double 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
  - UnivariateDerivative2
```
public UnivariateDerivative2(DerivativeStructure 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 UnivariateDerivative2 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
  - withValue
```
public UnivariateDerivative2 withValue(double value)
```
    Description copied from interface: Derivative
    
    Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.
    This default implementation is there so that no API gets broken by the next release, which is not a major one. Custom inheritors should probably overwrite it.
    
    Parameters:
    
    value - zeroth-order derivative of new represented function
    
    Returns:
    
    new object with changed value
  - getAddendum
```
public UnivariateDerivative2 getAddendum()
```
    Get the addendum to the real value of the number.
    The addendum is considered to be the part that when added back to the real part recovers the instance. This means that when e.getReal() is finite (i.e. neither infinite nor NaN), then e.getAddendum().add(e.getReal()) is e and e.subtract(e.getReal()) is e.getAddendum(). Beware that for non-finite numbers, these two equalities may not hold. The first equality (with the addition), always holds even for infinity and NaNs if the real part is independent of the addendum (this is the case for all derivatives types, as well as for complex and Dfp, but it is not the case for Tuple and FieldTuple). The second equality (with the subtraction), generally doesn't hold for non-finite numbers, because the subtraction generates NaNs.
    
    Returns:
    
    real value
  - getValue
```
public double getValue()
```
    Get the value part of the function.
    
    Returns:
    
    value part of the value of the function
  - getDerivative
```
public double getDerivative(int n)
```
    Get a derivative from the univariate derivative.
    
    Specified by:
    
    getDerivative in class UnivariateDerivative<UnivariateDerivative2>
    
    Parameters:
    
    n - derivation order (must be between 0 and DifferentialAlgebra.getOrder(), both inclusive)
    
    Returns:
    
    n^th derivative
  - getOrder
```
public int getOrder()
```
    Get the maximum derivation order.
    
    Returns:
    
    maximum derivation order
  - getFirstDerivative
```
public double getFirstDerivative()
```
    Get the first derivative.
    
    Returns:
    
    first derivative
    
    See Also:
    
    getValue(), getSecondDerivative()
  - getSecondDerivative
```
public double getSecondDerivative()
```
    Get the second derivative.
    
    Returns:
    
    second derivative
    
    See Also:
    
    getValue(), getFirstDerivative()
  - toDerivativeStructure
```
public DerivativeStructure toDerivativeStructure()
```
    Convert the instance to a DerivativeStructure.
    
    Specified by:
    
    toDerivativeStructure in class UnivariateDerivative<UnivariateDerivative2>
    
    Returns:
    
    derivative structure with same value and derivative as the instance
  - add
```
public UnivariateDerivative2 add(UnivariateDerivative2 a)
```
    Compute this + a.
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - subtract
```
public UnivariateDerivative2 subtract(UnivariateDerivative2 a)
```
    Compute this - a.
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
  - multiply
```
public UnivariateDerivative2 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 UnivariateDerivative2 multiply(double a)
```
    '×' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public UnivariateDerivative2 multiply(UnivariateDerivative2 a)
```
    Compute this × a.
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
  - square
```
public UnivariateDerivative2 square()
```
    Compute this × this.
    
    Returns:
    
    a new element representing this × this
  - divide
```
public UnivariateDerivative2 divide(double a)
```
    '÷' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public UnivariateDerivative2 divide(UnivariateDerivative2 a)
```
    Compute this ÷ a.
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
  - remainder
```
public UnivariateDerivative2 remainder(UnivariateDerivative2 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 UnivariateDerivative2 negate()
```
    Returns the additive inverse of this element.
    
    Returns:
    
    the opposite of this.
  - abs
```
public UnivariateDerivative2 abs()
```
    absolute value.
    
    Returns:
    
    abs(this)
  - copySign
```
public UnivariateDerivative2 copySign(UnivariateDerivative2 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 UnivariateDerivative2 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
  - scalb
```
public UnivariateDerivative2 scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - hypot
```
public UnivariateDerivative2 hypot(UnivariateDerivative2 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 UnivariateDerivative2 reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Returns:
    
    the inverse of this.
  - compose
```
public UnivariateDerivative2 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(Derivative.getValue()), f'(Derivative.getValue()), f''(Derivative.getValue())...]).
    
    Returns:
    
    f(this)
  - sqrt
```
public UnivariateDerivative2 sqrt()
```
    Square root.
    
    Returns:
    
    square root of the instance
  - cbrt
```
public UnivariateDerivative2 cbrt()
```
    Cubic root.
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public UnivariateDerivative2 rootN(int n)
```
    N^th root.
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
  - getField
```
public UnivariateDerivative2Field getField()
```
    Get the Field to which the instance belongs.
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static UnivariateDerivative2 pow(double a,
                                        UnivariateDerivative2 x)
```
    Compute a^x where a is a double and x a UnivariateDerivative2
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - pow
```
public UnivariateDerivative2 pow(double p)
```
    Power operation.
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public UnivariateDerivative2 pow(int n)
```
    Integer power operation.
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - exp
```
public UnivariateDerivative2 exp()
```
    Exponential.
    
    Returns:
    
    exponential of the instance
  - expm1
```
public UnivariateDerivative2 expm1()
```
    Exponential minus 1.
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public UnivariateDerivative2 log()
```
    Natural logarithm.
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public UnivariateDerivative2 log1p()
```
    Shifted natural logarithm.
    
    Returns:
    
    logarithm of one plus the instance
  - log10
```
public UnivariateDerivative2 log10()
```
    Base 10 logarithm.
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public UnivariateDerivative2 cos()
```
    Cosine operation.
    
    Returns:
    
    cos(this)
  - sin
```
public UnivariateDerivative2 sin()
```
    Sine operation.
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<UnivariateDerivative2> sinCos()
```
    Combined Sine and Cosine operation.
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public UnivariateDerivative2 tan()
```
    Tangent operation.
    
    Returns:
    
    tan(this)
  - acos
```
public UnivariateDerivative2 acos()
```
    Arc cosine operation.
    
    Returns:
    
    acos(this)
  - asin
```
public UnivariateDerivative2 asin()
```
    Arc sine operation.
    
    Returns:
    
    asin(this)
  - atan
```
public UnivariateDerivative2 atan()
```
    Arc tangent operation.
    
    Returns:
    
    atan(this)
  - atan2
```
public UnivariateDerivative2 atan2(UnivariateDerivative2 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 UnivariateDerivative2 cosh()
```
    Hyperbolic cosine operation.
    
    Returns:
    
    cosh(this)
  - sinh
```
public UnivariateDerivative2 sinh()
```
    Hyperbolic sine operation.
    
    Returns:
    
    sinh(this)
  - sinhCosh
```
public FieldSinhCosh<UnivariateDerivative2> sinhCosh()
```
    Combined hyperbolic sine and cosine operation.
    
    Returns:
    
    [sinh(this), cosh(this)]
  - tanh
```
public UnivariateDerivative2 tanh()
```
    Hyperbolic tangent operation.
    
    Returns:
    
    tanh(this)
  - acosh
```
public UnivariateDerivative2 acosh()
```
    Inverse hyperbolic cosine operation.
    
    Returns:
    
    acosh(this)
  - asinh
```
public UnivariateDerivative2 asinh()
```
    Inverse hyperbolic sine operation.
    
    Returns:
    
    asin(this)
  - atanh
```
public UnivariateDerivative2 atanh()
```
    Inverse hyperbolic tangent operation.
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public UnivariateDerivative2 toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public UnivariateDerivative2 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 univariate derivative.
    
    Parameters:
    
    delta - parameter offset Δx
    
    Returns:
    
    value of the Taylor expansion at x + Δx
  - linearCombination
```
public UnivariateDerivative2 linearCombination(UnivariateDerivative2[] a,
                                               UnivariateDerivative2[] b)
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public UnivariateDerivative2 linearCombination(double[] a,
                                               UnivariateDerivative2[] b)
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public UnivariateDerivative2 linearCombination(UnivariateDerivative2 a1,
                                               UnivariateDerivative2 b1,
                                               UnivariateDerivative2 a2,
                                               UnivariateDerivative2 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 UnivariateDerivative2 linearCombination(double a1,
                                               UnivariateDerivative2 b1,
                                               double a2,
                                               UnivariateDerivative2 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 UnivariateDerivative2 linearCombination(UnivariateDerivative2 a1,
                                               UnivariateDerivative2 b1,
                                               UnivariateDerivative2 a2,
                                               UnivariateDerivative2 b2,
                                               UnivariateDerivative2 a3,
                                               UnivariateDerivative2 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 UnivariateDerivative2 linearCombination(double a1,
                                               UnivariateDerivative2 b1,
                                               double a2,
                                               UnivariateDerivative2 b2,
                                               double a3,
                                               UnivariateDerivative2 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 UnivariateDerivative2 linearCombination(UnivariateDerivative2 a1,
                                               UnivariateDerivative2 b1,
                                               UnivariateDerivative2 a2,
                                               UnivariateDerivative2 b2,
                                               UnivariateDerivative2 a3,
                                               UnivariateDerivative2 b3,
                                               UnivariateDerivative2 a4,
                                               UnivariateDerivative2 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 UnivariateDerivative2 linearCombination(double a1,
                                               UnivariateDerivative2 b1,
                                               double a2,
                                               UnivariateDerivative2 b2,
                                               double a3,
                                               UnivariateDerivative2 b3,
                                               double a4,
                                               UnivariateDerivative2 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 UnivariateDerivative2 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
  - compareTo
```
public int compareTo(UnivariateDerivative2 o)
```
    Comparison performed considering that derivatives are intrinsically linked to monomials in the corresponding Taylor expansion and that the higher the degree, the smaller the term.
    
    Since:
    
    3.0

Class UnivariateDerivative2

Field Summary

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative

Methods inherited from interface org.hipparchus.FieldElement

Field Detail

PI

Constructor Detail

UnivariateDerivative2

UnivariateDerivative2

Method Detail

newInstance

withValue

getAddendum

getValue

getDerivative

getOrder

getFirstDerivative

getSecondDerivative

toDerivativeStructure

add

subtract

multiply

multiply

multiply

square

divide

divide

remainder

negate

abs

copySign

copySign

scalb

hypot

reciprocal

compose

sqrt

cbrt

rootN

getField

pow

pow

pow

exp

expm1

log

log1p

log10

cos

sin

sinCos

tan

acos

asin

atan

atan2

cosh

sinh

sinhCosh

tanh

acosh

asinh

atanh

toDegrees

toRadians

taylor

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

getPi