FieldGradient (Hipparchus 1.7 API)

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

Type Parameters:

T - the type of the function parameters and value

All Implemented Interfaces:

FieldDerivative<T,FieldGradient<T>>, CalculusFieldElement<FieldGradient<T>>, FieldElement<FieldGradient<T>>, RealFieldElement<FieldGradient<T>>
```
public class FieldGradient<T extends RealFieldElement<T>>
extends Object
implements FieldDerivative<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 these classes is a tedious and error-prone task but has the advantage of having no limitation on the derivation order despite not requiring users to compute the derivatives by themselves.

Instances of this class are guaranteed to be immutable.

Since:

1.7

See Also:

DerivativeStructure, UnivariateDerivative1, UnivariateDerivative2, Gradient, FieldDerivativeStructure, FieldUnivariateDerivative1, FieldUnivariateDerivative2

Field Summary
- Fields inherited from interface org.hipparchus.CalculusFieldElement
  DEG_TO_RAD, RAD_TO_DEG

Constructor Summary

Constructors
Constructor and Description
`FieldGradient(FieldDerivativeStructure<T> ds)` Build an instance from a `DerivativeStructure`.
`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 and Description
`FieldGradient<T>`	`abs()` absolute value.
`FieldGradient<T>`	`acos()` Arc cosine operation.
`FieldGradient<T>`	`acosh()` Inverse hyperbolic cosine operation.
`FieldGradient<T>`	`add(double a)` '+' operator.
`FieldGradient<T>`	`add(FieldGradient<T> a)` Compute this + a.
`FieldGradient<T>`	`add(T a)` '+' operator.
`FieldGradient<T>`	`asin()` Arc sine operation.
`FieldGradient<T>`	`asinh()` Inverse hyperbolic sine operation.
`FieldGradient<T>`	`atan()` Arc tangent operation.
`FieldGradient<T>`	`atan2(FieldGradient<T> x)` Two arguments arc tangent operation.
`FieldGradient<T>`	`atanh()` Inverse hyperbolic tangent operation.
`FieldGradient<T>`	`cbrt()` Cubic root.
`FieldGradient<T>`	`ceil()` Get the smallest whole number larger than instance.
`FieldGradient<T>`	`compose(T g0, T g1)` Compute composition of the instance by a function.
`static <T extends RealFieldElement<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>`	`cos()` Cosine operation.
`FieldGradient<T>`	`cosh()` Hyperbolic cosine operation.
`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>`	`exp()` Exponential.
`FieldGradient<T>`	`expm1()` Exponential minus 1.
`FieldGradient<T>`	`floor()` Get the largest whole number smaller than instance.
`int`	`getExponent()` Return the exponent of the instance, removing the bias.
`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.
`int`	`getOrder()` Get the derivation order.
`T`	`getPartialDerivative(int... orders)` Get a partial derivative.
`T`	`getPartialDerivative(int n)` Get the partial derivative with respect to one parameter.
`double`	`getReal()` Get the real value of the number.
`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>`	`log()` Natural logarithm.
`FieldGradient<T>`	`log10()` Base 10 logarithm.
`FieldGradient<T>`	`log1p()` Shifted natural logarithm.
`FieldGradient<T>`	`multiply(double a)` '×' operator.
`FieldGradient<T>`	`multiply(FieldGradient<T> a)` Compute this × a.
`FieldGradient<T>`	`multiply(int n)` Compute n × this.
`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 real value.
`FieldGradient<T>`	`pow(double p)` Power operation.
`static <T extends RealFieldElement<T>> FieldGradient<T>`	`pow(double a, FieldGradient<T> x)` Compute a^x where a is a double and x a `FieldGradient`
`FieldGradient<T>`	`pow(FieldGradient<T> e)` Power operation.
`FieldGradient<T>`	`pow(int n)` Integer power operation.
`FieldGradient<T>`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`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>`	`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.
`FieldGradient<T>`	`rootN(int n)` N^th root.
`FieldGradient<T>`	`scalb(int n)` Multiply the instance by a power of 2.
`FieldGradient<T>`	`signum()` Compute the signum of the instance.
`FieldGradient<T>`	`sin()` Sine operation.
`FieldSinCos<FieldGradient<T>>`	`sinCos()` Combined Sine and Cosine operation.
`FieldGradient<T>`	`sinh()` Hyperbolic sine operation.
`FieldGradient<T>`	`sqrt()` Square root.
`FieldGradient<T>`	`subtract(double a)` '-' operator.
`FieldGradient<T>`	`subtract(FieldGradient<T> a)` Compute this - a.
`FieldGradient<T>`	`subtract(T a)` '-' operator.
`FieldGradient<T>`	`tan()` Tangent operation.
`FieldGradient<T>`	`tanh()` Hyperbolic tangent operation.
`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 RealFieldElement<T>> FieldGradient<T>`	`variable(int freeParameters, int index, T 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.RealFieldElement
round

Methods inherited from interface org.hipparchus.CalculusFieldElement
isInfinite, isNaN

- 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 DerivativeStructure.
    
    Parameters:
    
    ds - derivative structure
    
    Throws:
    
    MathIllegalArgumentException - if ds order is not 1
- Method Detail
  - constant
```
public static <T extends RealFieldElement<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 RealFieldElement<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.
    The default implementation creates the instance by adding the value to getField().getZero(). This is not optimal and does not work when called with a negative zero as the sign of zero is lost with the addition. The default implementation should therefore be overridden in concrete classes. The default implementation will be removed at the next major version.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<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 real value.
    The default implementation creates the instance by adding the value to getField().getZero(). This is not optimal and does not work when called with a negative zero as the sign of zero is lost with the addition. The default implementation should therefore be overridden in concrete classes. The default implementation will be removed at the next major version.
    
    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 CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    real value
  - getValue
```
public T getValue()
```
    Get the value part of the function.
    
    Specified by:
    
    getValue in interface FieldDerivative<T extends RealFieldElement<T>,FieldGradient<T extends RealFieldElement<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 FieldDerivative<T extends RealFieldElement<T>,FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Get the derivation order.
    
    Specified by:
    
    getOrder in interface FieldDerivative<T extends RealFieldElement<T>,FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    derivation order
  - getPartialDerivative
```
public T getPartialDerivative(int... orders)
                       throws MathIllegalArgumentException
```
    Get a partial derivative.
    
    Specified by:
    
    getPartialDerivative in interface FieldDerivative<T extends RealFieldElement<T>,FieldGradient<T extends RealFieldElement<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(T a)
```
    '+' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - add
```
public FieldGradient<T> add(double a)
```
    '+' operator.
    
    Specified by:
    
    add in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<T>>>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - subtract
```
public FieldGradient<T> subtract(T a)
```
    '-' operator.
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - subtract
```
public FieldGradient<T> subtract(double a)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<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 FieldElement<FieldGradient<T extends RealFieldElement<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 × this = ∑_i=1ⁿ this.
    
    Specified by:
    
    multiply in interface FieldElement<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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 FieldElement<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    the opposite of this.
  - abs
```
public FieldGradient<T> abs()
```
    absolute value.
    
    Specified by:
    
    abs in interface RealFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    abs(this)
  - ceil
```
public FieldGradient<T> ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    ceil(this)
  - floor
```
public FieldGradient<T> floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    floor(this)
  - rint
```
public FieldGradient<T> rint()
```
    Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
    
    Specified by:
    
    rint in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - signum
```
public FieldGradient<T> signum()
```
    Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
    
    Specified by:
    
    signum in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  - 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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<T>>>
    
    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<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    exponent for the instance, without bias
  - scalb
```
public FieldGradient<T> scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<T>>>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
  - reciprocal
```
public FieldGradient<T> reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Specified by:
    
    reciprocal in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Specified by:
    
    reciprocal in interface FieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    the inverse of this.
  - compose
```
public FieldGradient<T> compose(T g0,
                                T g1)
```
    Compute composition of the instance by a function.
    
    Parameters:
    
    g0 - value of the function at the current point (i.e. at g(getValue()))
    
    g1 - first derivative of the function at the current point (i.e. at g'(getValue()))
    
    Returns:
    
    g(this)
  - sqrt
```
public FieldGradient<T> sqrt()
```
    Square root.
    
    Specified by:
    
    sqrt in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    square root of the instance
  - cbrt
```
public FieldGradient<T> cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public FieldGradient<T> rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static <T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<T>>>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - pow
```
public FieldGradient<T> pow(FieldGradient<T> e)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
  - exp
```
public FieldGradient<T> exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    exponential of the instance
  - expm1
```
public FieldGradient<T> expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public FieldGradient<T> log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public FieldGradient<T> log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    logarithm of one plus the instance
  - log10
```
public FieldGradient<T> log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public FieldGradient<T> cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    cos(this)
  - sin
```
public FieldGradient<T> sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<FieldGradient<T>> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public FieldGradient<T> tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    tan(this)
  - acos
```
public FieldGradient<T> acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    acos(this)
  - asin
```
public FieldGradient<T> asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    asin(this)
  - atan
```
public FieldGradient<T> atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    atan(this)
  - atan2
```
public FieldGradient<T> atan2(FieldGradient<T> x)
```
    Two arguments arc tangent operation.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
  - cosh
```
public FieldGradient<T> cosh()
```
    Hyperbolic cosine operation.
    
    Specified by:
    
    cosh in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    cosh(this)
  - sinh
```
public FieldGradient<T> sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    sinh(this)
  - tanh
```
public FieldGradient<T> tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    tanh(this)
  - acosh
```
public FieldGradient<T> acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    acosh(this)
  - asinh
```
public FieldGradient<T> asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    asin(this)
  - atanh
```
public FieldGradient<T> atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<T>>>
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public FieldGradient<T> toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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<FieldGradient<T extends RealFieldElement<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(Object, Object, Object, Object, Object, Object), CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
  - 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<FieldGradient<T extends RealFieldElement<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, Object, double, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - 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<FieldGradient<T extends RealFieldElement<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(Object, Object, Object, Object), CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
  - 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:
    
    CalculusFieldElement.linearCombination(double, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - 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<FieldGradient<T extends RealFieldElement<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, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
  - 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<FieldGradient<T extends RealFieldElement<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(Object, Object, Object, Object), CalculusFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)
  - 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<FieldGradient<T extends RealFieldElement<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, Object, double, Object), CalculusFieldElement.linearCombination(double, Object, double, Object, double, Object)
  - 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 RealFieldElement<T>>

Field Summary

Fields inherited from interface org.hipparchus.CalculusFieldElement

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.RealFieldElement

Methods inherited from interface org.hipparchus.CalculusFieldElement

Constructor Detail

FieldGradient

FieldGradient

Method Detail

constant

variable

getValueField

newInstance

newInstance

getReal

getValue

getGradient

getFreeParameters

getOrder

getPartialDerivative

getPartialDerivative

toDerivativeStructure

add

add

add

subtract

subtract

subtract

multiply

multiply

multiply

multiply

divide

divide

divide

remainder

remainder

remainder

negate

abs

ceil

floor

rint

signum

copySign

copySign

copySign

getExponent

scalb

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

tanh

acosh