java.lang.Object
- org.hipparchus.analysis.differentiation.FieldGradient<T>

Type Parameters:

T - the type of the function parameters and value

All Implemented Interfaces:

DifferentialAlgebra, FieldDerivative<T,FieldGradient<T>>, FieldDerivative1<T,FieldGradient<T>>, CalculusFieldElement<FieldGradient<T>>, FieldElement<FieldGradient<T>>
```
public class FieldGradient<T extends CalculusFieldElement<T>>
extends Object
implements FieldDerivative1<T,FieldGradient<T>>
```
Class representing both the value and the differentials of a function.
This class is a stripped-down version of FieldDerivativeStructure with derivation order limited to one. It should have less overhead than FieldDerivativeStructure in its domain.

This class is an implementation of Rall's numbers. Rall's numbers are an extension to the real numbers used throughout mathematical expressions; they hold the derivative together with the value of a function.

FieldGradient 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, UnivariateDerivative1, UnivariateDerivative2, Gradient, FieldDerivativeStructure, FieldUnivariateDerivative1, FieldUnivariateDerivative2

Constructor Summary

Constructors
Constructor	Description
`FieldGradient(FieldDerivativeStructure<T> ds)`	Build an instance from a `FieldDerivativeStructure`.
`FieldGradient(T value, T... gradient)`	Build an instance with values and derivative.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`FieldGradient<T>`	`abs()`	absolute value.
`FieldGradient<T>`	`add(double a)`	'+' operator.
`FieldGradient<T>`	`add(FieldGradient<T> a)`	Compute this + a.
`FieldGradient<T>`	`atan2(FieldGradient<T> x)`	Two arguments arc tangent operation.
`FieldGradient<T>`	`compose(T g0, T g1)`	Compute composition of the instance by a function.
`static <T extends CalculusFieldElement<T>> FieldGradient<T>`	`constant(int freeParameters, T value)`	Build an instance corresponding to a constant value.
`FieldGradient<T>`	`copySign(double sign)`	Returns the instance with the sign of the argument.
`FieldGradient<T>`	`copySign(FieldGradient<T> sign)`	Returns the instance with the sign of the argument.
`FieldGradient<T>`	`copySign(T sign)`	Returns the instance with the sign of the argument.
`FieldGradient<T>`	`divide(double a)`	'÷' operator.
`FieldGradient<T>`	`divide(FieldGradient<T> a)`	Compute this ÷ a.
`FieldGradient<T>`	`divide(T a)`	'÷' operator.
`boolean`	`equals(Object other)`	Test for the equality of two univariate derivatives.
`FieldGradient<T>`	`getAddendum()`	Get the addendum to the real value of the number.
`FieldGradientField<T>`	`getField()`	Get the `Field` to which the instance belongs.
`int`	`getFreeParameters()`	Get the number of free parameters.
`T[]`	`getGradient()`	Get the gradient part of the function.
`T`	`getPartialDerivative(int n)`	Get the partial derivative with respect to one parameter.
`T`	`getPartialDerivative(int... orders)`	Get a partial derivative.
`FieldGradient<T>`	`getPi()`	Get the Archimedes constant π.
`T`	`getValue()`	Get the value part of the function.
`Field<T>`	`getValueField()`	Get the `Field` the value and parameters of the function belongs to.
`int`	`hashCode()`	Get a hashCode for the univariate derivative.
`FieldGradient<T>`	`hypot(FieldGradient<T> y)`	Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`FieldGradient<T>`	`linearCombination(double[] a, FieldGradient<T>[] b)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2, double a3, FieldGradient<T> b3)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2, double a3, FieldGradient<T> b3, double a4, FieldGradient<T> b4)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(FieldGradient<T>[] a, FieldGradient<T>[] b)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2, FieldGradient<T> a3, FieldGradient<T> b3)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2, FieldGradient<T> a3, FieldGradient<T> b3, FieldGradient<T> a4, FieldGradient<T> b4)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(T[] a, FieldGradient<T>[] b)`	Compute a linear combination.
`FieldGradient<T>`	`linearCombination(T a1, FieldGradient<T> b1, T a2, FieldGradient<T> b2, T a3, FieldGradient<T> b3)`	Compute a linear combination.
`FieldGradient<T>`	`multiply(double a)`	'×' operator.
`FieldGradient<T>`	`multiply(int n)`	Compute n × this.
`FieldGradient<T>`	`multiply(FieldGradient<T> a)`	Compute this × a.
`FieldGradient<T>`	`multiply(T n)`	'×' operator.
`FieldGradient<T>`	`negate()`	Returns the additive inverse of `this` element.
`FieldGradient<T>`	`newInstance(double c)`	Create an instance corresponding to a constant real value.
`FieldGradient<T>`	`newInstance(T c)`	Create an instance corresponding to a constant Field value.
`FieldGradient<T>`	`pow(double p)`	Power operation.
`static <T extends CalculusFieldElement<T>> FieldGradient<T>`	`pow(double a, FieldGradient<T> x)`	Compute a^x where a is a double and x a `FieldGradient`
`FieldGradient<T>`	`pow(int n)`	Integer power operation.
`FieldGradient<T>`	`remainder(double a)`	IEEE remainder operator.
`FieldGradient<T>`	`remainder(FieldGradient<T> a)`	IEEE remainder operator.
`FieldGradient<T>`	`remainder(T a)`	IEEE remainder operator.
`FieldGradient<T>`	`rootN(int n)`	N^th root.
`FieldGradient<T>`	`scalb(int n)`	Multiply the instance by a power of 2.
`FieldSinCos<FieldGradient<T>>`	`sinCos()`	Combined Sine and Cosine operation.
`FieldSinhCosh<FieldGradient<T>>`	`sinhCosh()`	Combined hyperbolic sine and cosine operation.
`FieldGradient<T>`	`stackVariable()`	Add an independent variable to the Taylor expansion.
`FieldGradient<T>`	`subtract(double a)`	'-' operator.
`FieldGradient<T>`	`subtract(FieldGradient<T> a)`	Compute this - a.
`T`	`taylor(double... delta)`	Evaluate Taylor expansion of a gradient.
`T`	`taylor(T... delta)`	Evaluate Taylor expansion of a gradient.
`FieldGradient<T>`	`toDegrees()`	Convert radians to degrees, with error of less than 0.5 ULP
`FieldDerivativeStructure<T>`	`toDerivativeStructure()`	Convert the instance to a `FieldDerivativeStructure`.
`FieldGradient<T>`	`toRadians()`	Convert degrees to radians, with error of less than 0.5 ULP
`static <T extends CalculusFieldElement<T>> FieldGradient<T>`	`variable(int freeParameters, int index, T value)`	Build a `Gradient` representing a variable.
`FieldGradient<T>`	`withValue(T v)`	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 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.analysis.differentiation.FieldDerivative
add, ceil, floor, getExponent, getReal, pow, rint, sign, subtract, ulp

Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative1
acos, acosh, asin, asinh, atan, atanh, cbrt, cos, cosh, exp, expm1, getOrder, log, log10, log1p, reciprocal, sin, sinh, sqrt, square, tan, tanh

Methods inherited from interface org.hipparchus.FieldElement
isZero

- Constructor Detail
  - FieldGradient
```
@SafeVarargs
public FieldGradient(T value,
                     T... gradient)
```
    Build an instance with values and derivative.
    
    Parameters:
    
    value - value of the function
    
    gradient - gradient of the function
  - FieldGradient
```
public FieldGradient(FieldDerivativeStructure<T> ds)
              throws MathIllegalArgumentException
```
    Build an instance from a FieldDerivativeStructure.
    
    Parameters:
    
    ds - derivative structure
    
    Throws:
    
    MathIllegalArgumentException - if ds order is not 1
- Method Detail
  - constant
```
public static <T extends CalculusFieldElement<T>> FieldGradient<T> constant(int freeParameters,
                                                                            T value)
```
    Build an instance corresponding to a constant value.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    freeParameters - number of free parameters (i.e. dimension of the gradient)
    
    value - constant value of the function
    
    Returns:
    
    a FieldGradient with a constant value and all derivatives set to 0.0
  - variable
```
public static <T extends CalculusFieldElement<T>> FieldGradient<T> variable(int freeParameters,
                                                                            int index,
                                                                            T 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.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    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 FieldGradient with a constant value and all derivatives set to 0.0 except the one at index which will be set to 1.0
  - getValueField
```
public Field<T> getValueField()
```
    Get the Field the value and parameters of the function belongs to.
    
    Returns:
    
    Field the value and parameters of the function belongs to
  - newInstance
```
public FieldGradient<T> newInstance(double c)
```
    Create an instance corresponding to a constant real value.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    c - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - newInstance
```
public FieldGradient<T> newInstance(T c)
```
    Create an instance corresponding to a constant Field value.
    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.
    
    Specified by:
    
    newInstance in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    c - constant value
    
    Returns:
    
    instance corresponding to a constant Field value
  - withValue
```
public FieldGradient<T> withValue(T v)
```
    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.
    
    Specified by:
    
    withValue in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    v - zeroth-order derivative of new represented function
    
    Returns:
    
    new object with changed value
  - getAddendum
```
public FieldGradient<T> 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.
    
    Specified by:
    
    getAddendum in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Returns:
    
    real value
  - getValue
```
public T getValue()
```
    Get the value part of the function.
    
    Specified by:
    
    getValue in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    value part of the value of the function
  - getGradient
```
public T[] getGradient()
```
    Get the gradient part of the function.
    
    Returns:
    
    gradient part of the value of the function
  - getFreeParameters
```
public int getFreeParameters()
```
    Get the number of free parameters.
    
    Specified by:
    
    getFreeParameters in interface DifferentialAlgebra
    
    Returns:
    
    number of free parameters
  - getPartialDerivative
```
public T getPartialDerivative(int... orders)
                       throws MathIllegalArgumentException
```
    Get a partial derivative.
    
    Specified by:
    
    getPartialDerivative in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    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:
    
    FieldDerivative.getValue()
  - getPartialDerivative
```
public T 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 FieldDerivativeStructure<T> toDerivativeStructure()
```
    Convert the instance to a FieldDerivativeStructure.
    
    Returns:
    
    derivative structure with same value and derivative as the instance
  - add
```
public FieldGradient<T> add(double a)
```
    '+' operator.
    
    Specified by:
    
    add in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public FieldGradient<T> add(FieldGradient<T> a)
```
    Compute this + a.
    
    Specified by:
    
    add in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - subtract
```
public FieldGradient<T> subtract(double a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public FieldGradient<T> subtract(FieldGradient<T> a)
```
    Compute this - a.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Specified by:
    
    subtract in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
  - multiply
```
public FieldGradient<T> multiply(T n)
```
    '×' operator.
    
    Parameters:
    
    n - right hand side parameter of the operator
    
    Returns:
    
    this×n
  - multiply
```
public FieldGradient<T> multiply(int n)
```
    Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]
    
    Specified by:
    
    multiply in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Specified by:
    
    multiply in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    n - Number of times this must be added to itself.
    
    Returns:
    
    A new element representing n × this.
  - multiply
```
public FieldGradient<T> multiply(double a)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public FieldGradient<T> multiply(FieldGradient<T> a)
```
    Compute this × a.
    
    Specified by:
    
    multiply in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
  - divide
```
public FieldGradient<T> divide(T a)
```
    '÷' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public FieldGradient<T> divide(double a)
```
    '÷' operator.
    
    Specified by:
    
    divide in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public FieldGradient<T> divide(FieldGradient<T> a)
```
    Compute this ÷ a.
    
    Specified by:
    
    divide in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Specified by:
    
    divide in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
  - remainder
```
public FieldGradient<T> remainder(T a)
```
    IEEE remainder operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)
  - remainder
```
public FieldGradient<T> remainder(double a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - remainder
```
public FieldGradient<T> remainder(FieldGradient<T> a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - negate
```
public FieldGradient<T> negate()
```
    Returns the additive inverse of this element.
    
    Specified by:
    
    negate in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Returns:
    
    the opposite of this.
  - abs
```
public FieldGradient<T> abs()
```
    absolute value.
    
    Specified by:
    
    abs in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Returns:
    
    abs(this)
  - copySign
```
public FieldGradient<T> copySign(T sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public FieldGradient<T> copySign(FieldGradient<T> sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public FieldGradient<T> 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<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - scalb
```
public FieldGradient<T> scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - hypot
```
public FieldGradient<T> hypot(FieldGradient<T> y)
```
    Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
    
    If either argument is infinite, then the result is positive infinity.
    
    else, if either argument is NaN then the result is NaN.
    Specified by:
    
    hypot in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
  - compose
```
public FieldGradient<T> compose(T g0,
                                T g1)
```
    Compute composition of the instance by a function.
    
    Specified by:
    
    compose in interface FieldDerivative1<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Parameters:
    
    g0 - value of the function at the current point (i.e. at g(getValue()))
    
    g1 - first derivative of the function at the current point (i.e. at g'(getValue()))
    
    Returns:
    
    g(this)
  - rootN
```
public FieldGradient<T> rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
  - getField
```
public FieldGradientField<T> getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<T extends CalculusFieldElement<T>>
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static <T extends CalculusFieldElement<T>> FieldGradient<T> pow(double a,
                                                                       FieldGradient<T> x)
```
    Compute a^x where a is a double and x a FieldGradient
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - pow
```
public FieldGradient<T> pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public FieldGradient<T> pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - sinCos
```
public FieldSinCos<FieldGradient<T>> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Specified by:
    
    sinCos in interface FieldDerivative1<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    [sin(this), cos(this)]
  - atan2
```
public FieldGradient<T> atan2(FieldGradient<T> x)
```
    Two arguments arc tangent operation.
    Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
  - sinhCosh
```
public FieldSinhCosh<FieldGradient<T>> sinhCosh()
```
    Combined hyperbolic sine and cosine operation.
    
    Specified by:
    
    sinhCosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Specified by:
    
    sinhCosh in interface FieldDerivative1<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    [sinh(this), cosh(this)]
  - toDegrees
```
public FieldGradient<T> toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public FieldGradient<T> toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Specified by:
    
    toRadians in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Returns:
    
    instance converted into radians
  - taylor
```
public T taylor(double... delta)
```
    Evaluate Taylor expansion of a gradient.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
  - taylor
```
public T taylor(T... delta)
```
    Evaluate Taylor expansion of a gradient.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
  - linearCombination
```
public FieldGradient<T> linearCombination(FieldGradient<T>[] a,
                                          FieldGradient<T>[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public FieldGradient<T> linearCombination(T[] a,
                                          FieldGradient<T>[] b)
```
    Compute a linear combination.
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if arrays dimensions don't match
  - linearCombination
```
public FieldGradient<T> linearCombination(double[] a,
                                          FieldGradient<T>[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public FieldGradient<T> linearCombination(FieldGradient<T> a1,
                                          FieldGradient<T> b1,
                                          FieldGradient<T> a2,
                                          FieldGradient<T> b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    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 FieldGradient<T> linearCombination(double a1,
                                          FieldGradient<T> b1,
                                          double a2,
                                          FieldGradient<T> b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    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 FieldGradient<T> linearCombination(FieldGradient<T> a1,
                                          FieldGradient<T> b1,
                                          FieldGradient<T> a2,
                                          FieldGradient<T> b2,
                                          FieldGradient<T> a3,
                                          FieldGradient<T> b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    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 FieldGradient<T> linearCombination(T a1,
                                          FieldGradient<T> b1,
                                          T a2,
                                          FieldGradient<T> b2,
                                          T a3,
                                          FieldGradient<T> b3)
```
    Compute a linear combination.
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent
    
    See Also:
    
    linearCombination(double, FieldGradient, double, FieldGradient), linearCombination(double, FieldGradient, double, FieldGradient, double, FieldGradient, double, FieldGradient)
  - linearCombination
```
public FieldGradient<T> linearCombination(double a1,
                                          FieldGradient<T> b1,
                                          double a2,
                                          FieldGradient<T> b2,
                                          double a3,
                                          FieldGradient<T> b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    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 FieldGradient<T> linearCombination(FieldGradient<T> a1,
                                          FieldGradient<T> b1,
                                          FieldGradient<T> a2,
                                          FieldGradient<T> b2,
                                          FieldGradient<T> a3,
                                          FieldGradient<T> b3,
                                          FieldGradient<T> a4,
                                          FieldGradient<T> b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    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 FieldGradient<T> linearCombination(double a1,
                                          FieldGradient<T> b1,
                                          double a2,
                                          FieldGradient<T> b2,
                                          double a3,
                                          FieldGradient<T> b3,
                                          double a4,
                                          FieldGradient<T> b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>
    
    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)
  - stackVariable
```
public FieldGradient<T> stackVariable()
```
    Add an independent variable to the Taylor expansion.
    
    Returns:
    
    object with one more variable
    
    Since:
    
    4.0
  - getPi
```
public FieldGradient<T> 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<T extends CalculusFieldElement<T>>
    
    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 FieldGradient<T extends CalculusFieldElement<T>>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

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

Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative1

Methods inherited from interface org.hipparchus.FieldElement

Constructor Detail

FieldGradient

FieldGradient

Method Detail

constant

variable

getValueField

newInstance

newInstance

withValue

getAddendum

getValue

getGradient

getFreeParameters

getPartialDerivative

getPartialDerivative

toDerivativeStructure

add

add

subtract

subtract

multiply

multiply

multiply

multiply

divide

divide

divide

remainder

remainder

remainder

negate

abs

copySign

copySign

copySign

scalb

hypot

compose

rootN

getField

pow

pow

pow

sinCos

atan2

sinhCosh

toDegrees

toRadians

taylor

taylor

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

stackVariable

getPi

equals

hashCode