FieldGradient (Hipparchus 2.0 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>>
```
public class FieldGradient<T extends CalculusFieldElement<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

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 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>`	`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.
`FieldGradient<T>`	`getPi()` Get the Archimedes constant π.
`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 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(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>`	`sign()` Compute the sign of the instance.
`FieldGradient<T>`	`sin()` Sine operation.
`FieldSinCos<FieldGradient<T>>`	`sinCos()` Combined Sine and Cosine operation.
`FieldGradient<T>`	`sinh()` Hyperbolic sine operation.
`FieldSinhCosh<FieldGradient<T>>`	`sinhCosh()` Combined hyperbolic sine and sosine 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
`FieldGradient<T>`	`ulp()` Compute least significant bit (Unit in Last Position) for a number.
`static <T extends CalculusFieldElement<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.CalculusFieldElement
isFinite, isInfinite, isNaN, norm, round

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 DerivativeStructure.
    
    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<FieldGradient<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 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 FieldElement<FieldGradient<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 FieldDerivative<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Get the derivation order.
    
    Specified by:
    
    getOrder in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    derivation order
  - 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(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 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<FieldGradient<T extends CalculusFieldElement<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 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 FieldElement<FieldGradient<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 × this = ∑_i=1ⁿ this.
    
    Specified by:
    
    multiply in interface FieldElement<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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 FieldElement<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    the opposite of this.
  - abs
```
public FieldGradient<T> abs()
```
    absolute value.
    Just another name for CalculusFieldElement.norm()
    
    Specified by:
    
    abs in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<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 CalculusFieldElement<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 CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - sign
```
public FieldGradient<T> 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<FieldGradient<T extends CalculusFieldElement<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 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<FieldGradient<T extends CalculusFieldElement<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 CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - ulp
```
public FieldGradient<T> 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<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    ulp(this)
    
    Since:
    
    2.0
  - 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 CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Specified by:
    
    reciprocal in interface FieldElement<FieldGradient<T extends CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Returns:
    
    square root of the instance
  - cbrt
```
public FieldGradient<T> cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<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 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<FieldGradient<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<FieldGradient<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<FieldGradient<T extends CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
  - exp
```
public FieldGradient<T> exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    exponential of the instance
  - expm1
```
public FieldGradient<T> expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public FieldGradient<T> log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    logarithm of the instance
  - log1p
```
public FieldGradient<T> log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Returns:
    
    base 10 logarithm of the instance
  - cos
```
public FieldGradient<T> cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    cos(this)
  - sin
```
public FieldGradient<T> sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<FieldGradient<T>> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public FieldGradient<T> tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    tan(this)
  - acos
```
public FieldGradient<T> acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    acos(this)
  - asin
```
public FieldGradient<T> asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    asin(this)
  - atan
```
public FieldGradient<T> atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    atan(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<FieldGradient<T extends CalculusFieldElement<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 CalculusFieldElement<T>>>
    
    Returns:
    
    cosh(this)
  - sinh
```
public FieldGradient<T> sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    sinh(this)
  - sinhCosh
```
public FieldSinhCosh<FieldGradient<T>> sinhCosh()
```
    Combined hyperbolic sine and sosine operation.
    
    Specified by:
    
    sinhCosh in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    [sinh(this), cosh(this)]
  - tanh
```
public FieldGradient<T> tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    tanh(this)
  - acosh
```
public FieldGradient<T> acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    acosh(this)
  - asinh
```
public FieldGradient<T> asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<T>>>
    
    Returns:
    
    asin(this)
  - atanh
```
public FieldGradient<T> atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<FieldGradient<T extends CalculusFieldElement<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 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<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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<FieldGradient<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)
  - 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<FieldGradient<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.FieldElement

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

sign

copySign

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