DerivativeStructure (Hipparchus 2.3 API)

java.lang.Object
- org.hipparchus.analysis.differentiation.DerivativeStructure

All Implemented Interfaces:

Serializable, Derivative<DerivativeStructure>, CalculusFieldElement<DerivativeStructure>, FieldElement<DerivativeStructure>
```
public class DerivativeStructure
extends Object
implements Derivative<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 methods by this class (+, -, *, /, %, sin, cos ...).

Implementing complex expressions by hand using these classes is a tedious and error-prone task but has the advantage of having no limitation on the derivation order despite not requiring users to compute the derivatives by themselves. Implementing complex expression can also be done by developing computation code using standard primitive double values and to use differentiators to create the DerivativeStructure-based instances. This method is simpler but may be limited in the accuracy and derivation orders and may be computationally intensive (this is typically the case for finite differences differentiator.

Instances of this class are guaranteed to be immutable.

See Also:

DSCompiler, FieldDerivativeStructure, Serialized Form

Method Summary

All Methods Static Methods Instance Methods Concrete 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)` Compute this + a.
`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`	`differentiate(int varIndex, int differentiationOrder)` Differentiate w.r.t.
`DerivativeStructure`	`divide(DerivativeStructure a)` Compute this ÷ a.
`DerivativeStructure`	`divide(double a)` '÷' 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.
`DSFactory`	`getFactory()` Get the factory that built the instance.
`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.
`DerivativeStructure`	`getPi()` Get the Archimedes constant π.
`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`	`integrate(int varIndex, int integrationOrder)` Integrate w.r.t.
`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)` Compute this × a.
`DerivativeStructure`	`multiply(double a)` '×' operator.
`DerivativeStructure`	`multiply(int n)` Compute n × this.
`DerivativeStructure`	`negate()` Returns the additive inverse of `this` element.
`DerivativeStructure`	`newInstance(double value)` Create an instance corresponding to a constant real value.
`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`	`rebase(DerivativeStructure... p)` Rebase instance with respect to low level parameter functions.
`DerivativeStructure`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`DerivativeStructure`	`remainder(DerivativeStructure a)` IEEE remainder operator.
`DerivativeStructure`	`remainder(double a)` IEEE remainder 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.
`DerivativeStructure`	`scalb(int n)` Multiply the instance by a power of 2.
`DerivativeStructure`	`sign()` Compute the sign of the instance.
`DerivativeStructure`	`sin()` Sine operation.
`FieldSinCos<DerivativeStructure>`	`sinCos()` Combined Sine and Cosine operation.
`DerivativeStructure`	`sinh()` Hyperbolic sine operation.
`FieldSinhCosh<DerivativeStructure>`	`sinhCosh()` Combined hyperbolic sine and sosine operation.
`DerivativeStructure`	`sqrt()` Square root.
`DerivativeStructure`	`subtract(DerivativeStructure a)` Compute this - a.
`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
`DerivativeStructure`	`ulp()` Compute least significant bit (Unit in Last Position) for a number.

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

- Method Detail
  - newInstance
```
public DerivativeStructure newInstance(double value)
```
    Create an instance corresponding to a constant real value.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    value - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - getFactory
```
public DSFactory getFactory()
```
    Get the factory that built the instance.
    
    Returns:
    
    factory that built the instance
  - getFreeParameters
```
public int getFreeParameters()
```
    Description copied from interface: Derivative
    
    Get the number of free parameters.
    
    Specified by:
    
    getFreeParameters in interface Derivative<DerivativeStructure>
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Description copied from interface: Derivative
    
    Get the derivation order.
    
    Specified by:
    
    getOrder in interface Derivative<DerivativeStructure>
    
    Returns:
    
    derivation order
  - getReal
```
public double getReal()
```
    Get the real value of the number.
    
    Specified by:
    
    getReal in interface FieldElement<DerivativeStructure>
    
    Returns:
    
    real value
  - getValue
```
public double getValue()
```
    Get the value part of the derivative structure.
    
    Specified by:
    
    getValue in interface Derivative<DerivativeStructure>
    
    Returns:
    
    value part of the derivative structure
    
    See Also:
    
    getPartialDerivative(int...)
  - getPartialDerivative
```
public double getPartialDerivative(int... orders)
                            throws MathIllegalArgumentException
```
    Get a partial derivative.
    
    Specified by:
    
    getPartialDerivative in interface Derivative<DerivativeStructure>
    
    Parameters:
    
    orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)
    
    Returns:
    
    partial derivative
    
    Throws:
    
    MathIllegalArgumentException - if the numbers of variables does not match the instance
    
    See Also:
    
    Derivative.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 CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public DerivativeStructure add(DerivativeStructure a)
                        throws MathIllegalArgumentException
```
    Compute this + a.
    
    Specified by:
    
    add in interface FieldElement<DerivativeStructure>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - subtract
```
public DerivativeStructure subtract(double a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public DerivativeStructure subtract(DerivativeStructure a)
                             throws MathIllegalArgumentException
```
    Compute this - a.
    
    Specified by:
    
    subtract in interface FieldElement<DerivativeStructure>
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - 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 CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public DerivativeStructure multiply(DerivativeStructure a)
                             throws MathIllegalArgumentException
```
    Compute this × a.
    
    Specified by:
    
    multiply in interface FieldElement<DerivativeStructure>
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - divide
```
public DerivativeStructure divide(double a)
```
    '÷' operator.
    
    Specified by:
    
    divide in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public DerivativeStructure divide(DerivativeStructure a)
                           throws MathIllegalArgumentException
```
    Compute this ÷ a.
    
    Specified by:
    
    divide in interface FieldElement<DerivativeStructure>
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - remainder
```
public DerivativeStructure remainder(double a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - remainder
```
public DerivativeStructure remainder(DerivativeStructure a)
                              throws MathIllegalArgumentException
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - negate
```
public DerivativeStructure negate()
```
    Returns the additive inverse of this element.
    
    Specified by:
    
    negate in interface FieldElement<DerivativeStructure>
    
    Returns:
    
    the opposite of this.
  - abs
```
public DerivativeStructure abs()
```
    absolute value.
    Just another name for CalculusFieldElement.norm()
    
    Specified by:
    
    abs in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    abs(this)
  - ceil
```
public DerivativeStructure ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    ceil(this)
  - floor
```
public DerivativeStructure floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface CalculusFieldElement<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 CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - sign
```
public DerivativeStructure 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)
    
    Specified by:
    
    sign in interface CalculusFieldElement<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 CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - 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 CalculusFieldElement<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.
    
    Specified by:
    
    getExponent in interface CalculusFieldElement<DerivativeStructure>
    
    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 CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - ulp
```
public DerivativeStructure 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.
    
    Specified by:
    
    ulp in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    ulp(this)
    
    Since:
    
    2.0
  - hypot
```
public DerivativeStructure hypot(DerivativeStructure y)
                          throws MathIllegalArgumentException
```
    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 CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - hypot
```
public static DerivativeStructure hypot(DerivativeStructure x,
                                        DerivativeStructure y)
                                 throws MathIllegalArgumentException
```
    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:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - compose
```
public DerivativeStructure compose(double... f)
                            throws MathIllegalArgumentException
```
    Compute composition of the instance by a univariate function.
    
    Specified by:
    
    compose in interface Derivative<DerivativeStructure>
    
    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:
    
    MathIllegalArgumentException - 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 CalculusFieldElement<DerivativeStructure>
    
    Specified by:
    
    reciprocal in interface FieldElement<DerivativeStructure>
    
    Returns:
    
    the inverse of this.
  - sqrt
```
public DerivativeStructure sqrt()
```
    Square root.
    
    Specified by:
    
    sqrt in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    square root of the instance
  - cbrt
```
public DerivativeStructure cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public DerivativeStructure rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<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
  - pow
```
public DerivativeStructure pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public DerivativeStructure pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - pow
```
public DerivativeStructure pow(DerivativeStructure e)
                        throws MathIllegalArgumentException
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - exp
```
public DerivativeStructure exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    exponential of the instance
  - expm1
```
public DerivativeStructure expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public DerivativeStructure log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public DerivativeStructure log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    logarithm of one plus the instance
  - log10
```
public DerivativeStructure log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public DerivativeStructure cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    cos(this)
  - sin
```
public DerivativeStructure sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<DerivativeStructure> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public DerivativeStructure tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    tan(this)
  - acos
```
public DerivativeStructure acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    acos(this)
  - asin
```
public DerivativeStructure asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    asin(this)
  - atan
```
public DerivativeStructure atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    atan(this)
  - atan2
```
public DerivativeStructure atan2(DerivativeStructure x)
                          throws MathIllegalArgumentException
```
    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.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
  - atan2
```
public static DerivativeStructure atan2(DerivativeStructure y,
                                        DerivativeStructure x)
                                 throws MathIllegalArgumentException
```
    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:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - cosh
```
public DerivativeStructure cosh()
```
    Hyperbolic cosine operation.
    
    Specified by:
    
    cosh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    cosh(this)
  - sinh
```
public DerivativeStructure sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    sinh(this)
  - sinhCosh
```
public FieldSinhCosh<DerivativeStructure> sinhCosh()
```
    Combined hyperbolic sine and sosine operation.
    
    Specified by:
    
    sinhCosh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    [sinh(this), cosh(this)]
  - tanh
```
public DerivativeStructure tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    tanh(this)
  - acosh
```
public DerivativeStructure acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    acosh(this)
  - asinh
```
public DerivativeStructure asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    asin(this)
  - atanh
```
public DerivativeStructure atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public DerivativeStructure toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public DerivativeStructure toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Specified by:
    
    toRadians in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    instance converted into radians
  - integrate
```
public DerivativeStructure integrate(int varIndex,
                                     int integrationOrder)
```
    Integrate w.r.t. one independent variable.
    Rigorously, if the derivatives of a function are known up to order N, the ones of its M-th integral w.r.t. a given variable (seen as a function itself) are actually known up to order N+M. However, this method still casts the output as a DerivativeStructure of order N. The integration constants are systematically set to zero.
    
    Parameters:
    
    varIndex - Index of independent variable w.r.t. which integration is done.
    
    integrationOrder - Number of times the integration operator must be applied. If non-positive, call the differentiation operator.
    
    Returns:
    
    DerivativeStructure on which integration operator has been applied a certain number of times.
    
    Since:
    
    2.2
  - differentiate
```
public DerivativeStructure differentiate(int varIndex,
                                         int differentiationOrder)
```
    Differentiate w.r.t. one independent variable.
    Rigorously, if the derivatives of a function are known up to order N, the ones of its M-th derivative w.r.t. a given variable (seen as a function itself) are only known up to order N-M. However, this method still casts the output as a DerivativeStructure of order N with zeroes for the higher order terms.
    
    Parameters:
    
    varIndex - Index of independent variable w.r.t. which differentiation is done.
    
    differentiationOrder - Number of times the differentiation operator must be applied. If non-positive, call the integration operator instead.
    
    Returns:
    
    DerivativeStructure on which differentiation operator has been applied a certain number of times
    
    Since:
    
    2.2
  - taylor
```
public double taylor(double... delta)
              throws MathRuntimeException
```
    Evaluate Taylor expansion a derivative structure.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathRuntimeException - if factorials becomes too large
  - rebase
```
public DerivativeStructure rebase(DerivativeStructure... p)
```
    Rebase instance with respect to low level parameter functions.
    The instance is considered to be a function of n free parameters up to order o \(f(p_0, p_1, \ldots p_{n-1})\). Its partial derivatives are therefore \(f, \frac{\partial f}{\partial p_0}, \frac{\partial f}{\partial p_1}, \ldots \frac{\partial^2 f}{\partial p_0^2}, \frac{\partial^2 f}{\partial p_0 p_1}, \ldots \frac{\partial^o f}{\partial p_{n-1}^o}\). The free parameters \(p_0, p_1, \ldots p_{n-1}\) are considered to be functions of \(m\) lower level other parameters \(q_0, q_1, \ldots q_{m-1}\).
    \( \begin{align} p_0 & = p_0(q_0, q_1, \ldots q_{m-1})\\ p_1 & = p_1(q_0, q_1, \ldots q_{m-1})\\ p_{n-1} & = p_{n-1}(q_0, q_1, \ldots q_{m-1}) \end{align}\)
    This method compute the composition of the partial derivatives of \(f\) and the partial derivatives of \(p_0, p_1, \ldots p_{n-1}\), i.e. the partial derivatives of the value returned will be \(f, \frac{\partial f}{\partial q_0}, \frac{\partial f}{\partial q_1}, \ldots \frac{\partial^2 f}{\partial q_0^2}, \frac{\partial^2 f}{\partial q_0 q_1}, \ldots \frac{\partial^o f}{\partial q_{m-1}^o}\).
    
    The number of parameters must match getFreeParameters() and the derivation orders of the instance and parameters must also match.
    
    Parameters:
    
    p - base parameters with respect to which partial derivatives were computed in the instance
    
    Returns:
    
    derivative structure with partial derivatives computed with respect to the lower level parameters used in the \(p_i\)
    
    Since:
    
    2.2
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure[] a,
                                             DerivativeStructure[] b)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - linearCombination
```
public DerivativeStructure linearCombination(double[] a,
                                             DerivativeStructure[] b)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<DerivativeStructure>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                             DerivativeStructure b1,
                                             DerivativeStructure a2,
                                             DerivativeStructure b2)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<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:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                             DerivativeStructure b1,
                                             double a2,
                                             DerivativeStructure b2)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<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:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                             DerivativeStructure b1,
                                             DerivativeStructure a2,
                                             DerivativeStructure b2,
                                             DerivativeStructure a3,
                                             DerivativeStructure b3)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<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:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                             DerivativeStructure b1,
                                             double a2,
                                             DerivativeStructure b2,
                                             double a3,
                                             DerivativeStructure b3)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<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:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public DerivativeStructure linearCombination(DerivativeStructure a1,
                                             DerivativeStructure b1,
                                             DerivativeStructure a2,
                                             DerivativeStructure b2,
                                             DerivativeStructure a3,
                                             DerivativeStructure b3,
                                             DerivativeStructure a4,
                                             DerivativeStructure b4)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<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 fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public DerivativeStructure linearCombination(double a1,
                                             DerivativeStructure b1,
                                             double a2,
                                             DerivativeStructure b2,
                                             double a3,
                                             DerivativeStructure b3,
                                             double a4,
                                             DerivativeStructure b4)
                                      throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<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 fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders do not match
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
  - getPi
```
public DerivativeStructure getPi()
```
    Get the Archimedes constant π.
    Archimedes constant is the ratio of a circle's circumference to its diameter.
    
    Specified by:
    
    getPi in interface CalculusFieldElement<DerivativeStructure>
    
    Returns:
    
    Archimedes constant π
  - 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
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the derivative structure.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    a hash code value for this object

Class DerivativeStructure

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Methods inherited from interface org.hipparchus.FieldElement

Method Detail

newInstance

getFactory

getFreeParameters

getOrder

getReal

getValue

getPartialDerivative

getAllDerivatives

add

add

subtract

subtract

multiply

multiply

multiply

divide

divide

remainder

remainder

negate

abs

ceil

floor

rint

sign

copySign

copySign

getExponent

scalb

ulp

hypot

hypot

compose

reciprocal

sqrt

cbrt

rootN

getField

pow

pow

pow

pow

exp

expm1

log

log1p

log10

cos

sin

sinCos

tan

acos

asin

atan

atan2

atan2

cosh

sinh

sinhCosh

tanh

acosh

asinh

atanh

toDegrees

toRadians

integrate

differentiate

taylor

rebase

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination