Gradient (Hipparchus 2.0 API)

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

All Implemented Interfaces:

Serializable, Derivative<Gradient>, CalculusFieldElement<Gradient>, FieldElement<Gradient>
```
public class Gradient
extends Object
implements Derivative<Gradient>, CalculusFieldElement<Gradient>, Serializable
```
Class representing both the value and the differentials of a function.
This class is a stripped-down version of DerivativeStructure with derivation order limited to one. 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.

Gradient 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, FieldDerivativeStructure, FieldUnivariateDerivative1, FieldUnivariateDerivative2, FieldGradient, Serialized Form

Constructor Summary

Constructors
Constructor and Description
`Gradient(DerivativeStructure ds)` Build an instance from a `DerivativeStructure`.
`Gradient(double value, double... gradient)` Build an instance with values and derivative.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Gradient`	`abs()` absolute value.
`Gradient`	`acos()` Arc cosine operation.
`Gradient`	`acosh()` Inverse hyperbolic cosine operation.
`Gradient`	`add(double a)` '+' operator.
`Gradient`	`add(Gradient a)` Compute this + a.
`Gradient`	`asin()` Arc sine operation.
`Gradient`	`asinh()` Inverse hyperbolic sine operation.
`Gradient`	`atan()` Arc tangent operation.
`Gradient`	`atan2(Gradient x)` Two arguments arc tangent operation.
`Gradient`	`atanh()` Inverse hyperbolic tangent operation.
`Gradient`	`cbrt()` Cubic root.
`Gradient`	`ceil()` Get the smallest whole number larger than instance.
`Gradient`	`compose(double... f)` Compute composition of the instance by a univariate function.
`static Gradient`	`constant(int freeParameters, double value)` Build an instance corresponding to a constant value.
`Gradient`	`copySign(double sign)` Returns the instance with the sign of the argument.
`Gradient`	`copySign(Gradient sign)` Returns the instance with the sign of the argument.
`Gradient`	`cos()` Cosine operation.
`Gradient`	`cosh()` Hyperbolic cosine operation.
`Gradient`	`divide(double a)` '÷' operator.
`Gradient`	`divide(Gradient a)` Compute this ÷ a.
`boolean`	`equals(Object other)` Test for the equality of two univariate derivatives.
`Gradient`	`exp()` Exponential.
`Gradient`	`expm1()` Exponential minus 1.
`Gradient`	`floor()` Get the largest whole number smaller than instance.
`int`	`getExponent()` Return the exponent of the instance, removing the bias.
`GradientField`	`getField()` Get the `Field` to which the instance belongs.
`int`	`getFreeParameters()` Get the number of free parameters.
`double[]`	`getGradient()` Get the gradient part of the function.
`int`	`getOrder()` Get the derivation order.
`double`	`getPartialDerivative(int... orders)` Get a partial derivative.
`double`	`getPartialDerivative(int n)` Get the partial derivative with respect to one parameter.
`Gradient`	`getPi()` Get the Archimedes constant π.
`double`	`getReal()` Get the real value of the number.
`double`	`getValue()` Get the value part of the function.
`int`	`hashCode()` Get a hashCode for the univariate derivative.
`Gradient`	`hypot(Gradient y)` Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`Gradient`	`linearCombination(double[] a, Gradient[] b)` Compute a linear combination.
`Gradient`	`linearCombination(double a1, Gradient b1, double a2, Gradient b2)` Compute a linear combination.
`Gradient`	`linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3)` Compute a linear combination.
`Gradient`	`linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3, double a4, Gradient b4)` Compute a linear combination.
`Gradient`	`linearCombination(Gradient[] a, Gradient[] b)` Compute a linear combination.
`Gradient`	`linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2)` Compute a linear combination.
`Gradient`	`linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3)` Compute a linear combination.
`Gradient`	`linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3, Gradient a4, Gradient b4)` Compute a linear combination.
`Gradient`	`log()` Natural logarithm.
`Gradient`	`log10()` Base 10 logarithm.
`Gradient`	`log1p()` Shifted natural logarithm.
`Gradient`	`multiply(double a)` '×' operator.
`Gradient`	`multiply(Gradient a)` Compute this × a.
`Gradient`	`multiply(int n)` Compute n × this.
`Gradient`	`negate()` Returns the additive inverse of `this` element.
`Gradient`	`newInstance(double c)` Create an instance corresponding to a constant real value.
`Gradient`	`pow(double p)` Power operation.
`static Gradient`	`pow(double a, Gradient x)` Compute a^x where a is a double and x a `Gradient`
`Gradient`	`pow(Gradient e)` Power operation.
`Gradient`	`pow(int n)` Integer power operation.
`Gradient`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`Gradient`	`remainder(double a)` IEEE remainder operator.
`Gradient`	`remainder(Gradient a)` IEEE remainder operator.
`Gradient`	`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.
`Gradient`	`rootN(int n)` N^th root.
`Gradient`	`scalb(int n)` Multiply the instance by a power of 2.
`Gradient`	`sign()` Compute the sign of the instance.
`Gradient`	`sin()` Sine operation.
`FieldSinCos<Gradient>`	`sinCos()` Combined Sine and Cosine operation.
`Gradient`	`sinh()` Hyperbolic sine operation.
`FieldSinhCosh<Gradient>`	`sinhCosh()` Combined hyperbolic sine and sosine operation.
`Gradient`	`sqrt()` Square root.
`Gradient`	`subtract(double a)` '-' operator.
`Gradient`	`subtract(Gradient a)` Compute this - a.
`Gradient`	`tan()` Tangent operation.
`Gradient`	`tanh()` Hyperbolic tangent operation.
`double`	`taylor(double... delta)` Evaluate Taylor expansion a derivative structure.
`Gradient`	`toDegrees()` Convert radians to degrees, with error of less than 0.5 ULP
`DerivativeStructure`	`toDerivativeStructure()` Convert the instance to a `DerivativeStructure`.
`Gradient`	`toRadians()` Convert degrees to radians, with error of less than 0.5 ULP
`Gradient`	`ulp()` Compute least significant bit (Unit in Last Position) for a number.
`static Gradient`	`variable(int freeParameters, int index, double value)` Build a `Gradient` representing a variable.

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
  - Gradient
```
public Gradient(double value,
                double... gradient)
```
    Build an instance with values and derivative.
    
    Parameters:
    
    value - value of the function
    
    gradient - gradient of the function
  - Gradient
```
public Gradient(DerivativeStructure ds)
         throws MathIllegalArgumentException
```
    Build an instance from a DerivativeStructure.
    
    Parameters:
    
    ds - derivative structure
    
    Throws:
    
    MathIllegalArgumentException - if ds order is not 1
- Method Detail
  - constant
```
public static Gradient constant(int freeParameters,
                                double value)
```
    Build an instance corresponding to a constant value.
    
    Parameters:
    
    freeParameters - number of free parameters (i.e. dimension of the gradient)
    
    value - constant value of the function
    
    Returns:
    
    a Gradient with a constant value and all derivatives set to 0.0
  - variable
```
public static Gradient variable(int freeParameters,
                                int index,
                                double value)
```
    Build a Gradient representing a variable.
    Instances built using this method are considered to be the free variables with respect to which differentials are computed. As such, their differential with respect to themselves is +1.
    
    Parameters:
    
    freeParameters - number of free parameters (i.e. dimension of the gradient)
    
    index - index of the variable (from 0 to getFreeParameters() - 1)
    
    value - value of the variable
    
    Returns:
    
    a Gradient with a constant value and all derivatives set to 0.0 except the one at index which will be set to 1.0
  - newInstance
```
public Gradient newInstance(double c)
```
    Create an instance corresponding to a constant real value.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    c - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - getReal
```
public double getReal()
```
    Get the real value of the number.
    
    Specified by:
    
    getReal in interface FieldElement<Gradient>
    
    Returns:
    
    real value
  - getValue
```
public double getValue()
```
    Get the value part of the function.
    
    Specified by:
    
    getValue in interface Derivative<Gradient>
    
    Returns:
    
    value part of the value of the function
  - getGradient
```
public double[] getGradient()
```
    Get the gradient part of the function.
    
    Returns:
    
    gradient part of the value of the function
    
    See Also:
    
    getPartialDerivative(int)
  - getFreeParameters
```
public int getFreeParameters()
```
    Get the number of free parameters.
    
    Specified by:
    
    getFreeParameters in interface Derivative<Gradient>
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Get the derivation order.
    
    Specified by:
    
    getOrder in interface Derivative<Gradient>
    
    Returns:
    
    derivation order
  - getPartialDerivative
```
public double getPartialDerivative(int... orders)
                            throws MathIllegalArgumentException
```
    Get a partial derivative.
    
    Specified by:
    
    getPartialDerivative in interface Derivative<Gradient>
    
    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()
  - getPartialDerivative
```
public double getPartialDerivative(int n)
                            throws MathIllegalArgumentException
```
    Get the partial derivative with respect to one parameter.
    
    Parameters:
    
    n - index of the parameter (counting from 0)
    
    Returns:
    
    partial derivative with respect to the n^th parameter
    
    Throws:
    
    MathIllegalArgumentException - if n is either negative or larger or equal to getFreeParameters()
  - toDerivativeStructure
```
public DerivativeStructure toDerivativeStructure()
```
    Convert the instance to a DerivativeStructure.
    
    Returns:
    
    derivative structure with same value and derivative as the instance
  - add
```
public Gradient add(double a)
```
    '+' operator.
    
    Specified by:
    
    add in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public Gradient add(Gradient a)
```
    Compute this + a.
    
    Specified by:
    
    add in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - subtract
```
public Gradient subtract(double a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public Gradient subtract(Gradient a)
```
    Compute this - a.
    
    Specified by:
    
    subtract in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
  - multiply
```
public Gradient 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<Gradient>
    
    Parameters:
    
    n - Number of times this must be added to itself.
    
    Returns:
    
    A new element representing n × this.
  - multiply
```
public Gradient multiply(double a)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public Gradient multiply(Gradient a)
```
    Compute this × a.
    
    Specified by:
    
    multiply in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
  - divide
```
public Gradient divide(double a)
```
    '÷' operator.
    
    Specified by:
    
    divide in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public Gradient divide(Gradient a)
```
    Compute this ÷ a.
    
    Specified by:
    
    divide in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
  - remainder
```
public Gradient remainder(double a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - remainder
```
public Gradient remainder(Gradient a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - negate
```
public Gradient negate()
```
    Returns the additive inverse of this element.
    
    Specified by:
    
    negate in interface FieldElement<Gradient>
    
    Returns:
    
    the opposite of this.
  - abs
```
public Gradient abs()
```
    absolute value.
    Just another name for CalculusFieldElement.norm()
    
    Specified by:
    
    abs in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    abs(this)
  - ceil
```
public Gradient ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    ceil(this)
  - floor
```
public Gradient floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    floor(this)
  - rint
```
public Gradient 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<Gradient>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - sign
```
public Gradient 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<Gradient>
    
    Returns:
    
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  - copySign
```
public Gradient copySign(Gradient sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public Gradient 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<Gradient>
    
    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.
    
    Specified by:
    
    getExponent in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    exponent for the instance, without bias
  - scalb
```
public Gradient scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - ulp
```
public Gradient 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<Gradient>
    
    Returns:
    
    ulp(this)
    
    Since:
    
    2.0
  - hypot
```
public Gradient hypot(Gradient y)
```
    Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
    - If either argument is infinite, then the result is positive infinity.
    - else, if either argument is NaN then the result is NaN.
    Specified by:
    
    hypot in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
  - reciprocal
```
public Gradient reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Specified by:
    
    reciprocal in interface CalculusFieldElement<Gradient>
    
    Specified by:
    
    reciprocal in interface FieldElement<Gradient>
    
    Returns:
    
    the inverse of this.
  - compose
```
public Gradient compose(double... f)
```
    Compute composition of the instance by a univariate function.
    
    Specified by:
    
    compose in interface Derivative<Gradient>
    
    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 Gradient sqrt()
```
    Square root.
    
    Specified by:
    
    sqrt in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    square root of the instance
  - cbrt
```
public Gradient cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public Gradient rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
  - getField
```
public GradientField getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<Gradient>
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static Gradient pow(double a,
                           Gradient x)
```
    Compute a^x where a is a double and x a Gradient
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - pow
```
public Gradient pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public Gradient pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - pow
```
public Gradient pow(Gradient e)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
  - exp
```
public Gradient exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    exponential of the instance
  - expm1
```
public Gradient expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public Gradient log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public Gradient log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    logarithm of one plus the instance
  - log10
```
public Gradient log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public Gradient cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    cos(this)
  - sin
```
public Gradient sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<Gradient> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public Gradient tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    tan(this)
  - acos
```
public Gradient acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    acos(this)
  - asin
```
public Gradient asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    asin(this)
  - atan
```
public Gradient atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    atan(this)
  - atan2
```
public Gradient atan2(Gradient 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.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
  - cosh
```
public Gradient cosh()
```
    Hyperbolic cosine operation.
    
    Specified by:
    
    cosh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    cosh(this)
  - sinh
```
public Gradient sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    sinh(this)
  - sinhCosh
```
public FieldSinhCosh<Gradient> sinhCosh()
```
    Combined hyperbolic sine and sosine operation.
    
    Specified by:
    
    sinhCosh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    [sinh(this), cosh(this)]
  - tanh
```
public Gradient tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    tanh(this)
  - acosh
```
public Gradient acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    acosh(this)
  - asinh
```
public Gradient asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    asin(this)
  - atanh
```
public Gradient atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public Gradient toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public Gradient toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Specified by:
    
    toRadians in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    instance converted into radians
  - taylor
```
public double taylor(double... delta)
```
    Evaluate Taylor expansion a derivative structure.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
  - linearCombination
```
public Gradient linearCombination(Gradient[] a,
                                  Gradient[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public Gradient linearCombination(double[] a,
                                  Gradient[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public Gradient linearCombination(Gradient a1,
                                  Gradient b1,
                                  Gradient a2,
                                  Gradient b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    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 Gradient linearCombination(double a1,
                                  Gradient b1,
                                  double a2,
                                  Gradient b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    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 Gradient linearCombination(Gradient a1,
                                  Gradient b1,
                                  Gradient a2,
                                  Gradient b2,
                                  Gradient a3,
                                  Gradient b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    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 Gradient linearCombination(double a1,
                                  Gradient b1,
                                  double a2,
                                  Gradient b2,
                                  double a3,
                                  Gradient b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    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 Gradient linearCombination(Gradient a1,
                                  Gradient b1,
                                  Gradient a2,
                                  Gradient b2,
                                  Gradient a3,
                                  Gradient b3,
                                  Gradient a4,
                                  Gradient b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    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 Gradient linearCombination(double a1,
                                  Gradient b1,
                                  double a2,
                                  Gradient b2,
                                  double a3,
                                  Gradient b3,
                                  double a4,
                                  Gradient b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    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 Gradient 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<Gradient>
    
    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 Gradient

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Methods inherited from interface org.hipparchus.FieldElement

Constructor Detail

Gradient

Gradient

Method Detail

constant

variable

newInstance

getReal

getValue

getGradient

getFreeParameters

getOrder

getPartialDerivative

getPartialDerivative

toDerivativeStructure

add

add

subtract

subtract

multiply

multiply

multiply

divide

divide

remainder

remainder

negate

abs

ceil

floor

rint

sign

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

toRadians

taylor

linearCombination

linearCombination

linearCombination