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

All Implemented Interfaces:

Serializable, Derivative<Gradient>, Derivative1<Gradient>, DifferentialAlgebra, CalculusFieldElement<Gradient>, FieldElement<Gradient>
```
public class Gradient
extends Object
implements Derivative1<Gradient>, Serializable
```
Class representing both the value and the differentials of a function.
This class is a stripped-down version of DerivativeStructure with derivation order limited to one. It should have less overhead than DerivativeStructure in its domain.

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

Gradient instances can be used directly thanks to the arithmetic operators to the mathematical functions provided as methods by this class (+, -, *, /, %, sin, cos ...).

Implementing complex expressions by hand using 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, FieldDerivativeStructure, FieldUnivariateDerivative1, FieldUnivariateDerivative2, FieldGradient, Serialized Form

Constructor Summary

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Gradient`	`abs()`	absolute value.
`Gradient`	`add(Gradient a)`	Compute this + a.
`Gradient`	`atan2(Gradient x)`	Two arguments arc tangent operation.
`Gradient`	`compose(double... f)`	Compute composition of the instance by a univariate function.
`Gradient`	`compose(double f0, double f1)`	Compute composition of the instance by a univariate function differentiable at order 1.
`static Gradient`	`constant(int freeParameters, double value)`	Build an instance corresponding to a constant value.
`Gradient`	`copySign(double sign)`	Returns the instance with the sign of the argument.
`Gradient`	`copySign(Gradient sign)`	Returns the instance with the sign of the argument.
`Gradient`	`divide(double a)`	'÷' operator.
`Gradient`	`divide(Gradient a)`	Compute this ÷ a.
`boolean`	`equals(Object other)`	Test for the equality of two univariate derivatives.
`Gradient`	`getAddendum()`	Get the addendum to the real value of the number.
`GradientField`	`getField()`	Get the `Field` to which the instance belongs.
`int`	`getFreeParameters()`	Get the number of free parameters.
`double[]`	`getGradient()`	Get the gradient part of the function.
`double`	`getPartialDerivative(int n)`	Get the partial derivative with respect to one parameter.
`double`	`getPartialDerivative(int... orders)`	Get a partial derivative.
`double`	`getValue()`	Get the value part of the function.
`int`	`hashCode()`	Get a hashCode for the univariate derivative.
`Gradient`	`hypot(Gradient y)`	Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`Gradient`	`linearCombination(double[] a, Gradient[] b)`	Compute a linear combination.
`Gradient`	`linearCombination(double a1, Gradient b1, double a2, Gradient b2)`	Compute a linear combination.
`Gradient`	`linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3)`	Compute a linear combination.
`Gradient`	`linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3, double a4, Gradient b4)`	Compute a linear combination.
`Gradient`	`linearCombination(Gradient[] a, Gradient[] b)`	Compute a linear combination.
`Gradient`	`linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2)`	Compute a linear combination.
`Gradient`	`linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3)`	Compute a linear combination.
`Gradient`	`linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3, Gradient a4, Gradient b4)`	Compute a linear combination.
`Gradient`	`multiply(double a)`	'×' operator.
`Gradient`	`multiply(int n)`	Compute n × this.
`Gradient`	`multiply(Gradient a)`	Compute this × a.
`Gradient`	`negate()`	Returns the additive inverse of `this` element.
`Gradient`	`newInstance(double c)`	Create an instance corresponding to a constant real value.
`Gradient`	`pow(double p)`	Power operation.
`static Gradient`	`pow(double a, Gradient x)`	Compute a^x where a is a double and x a `Gradient`
`Gradient`	`pow(int n)`	Integer power operation.
`Gradient`	`remainder(Gradient a)`	IEEE remainder operator.
`Gradient`	`scalb(int n)`	Multiply the instance by a power of 2.
`FieldSinCos<Gradient>`	`sinCos()`	Combined Sine and Cosine operation.
`FieldSinhCosh<Gradient>`	`sinhCosh()`	Combined hyperbolic sine and cosine operation.
`Gradient`	`stackVariable()`	Add an independent variable to the Taylor expansion.
`Gradient`	`subtract(Gradient a)`	Compute this - a.
`double`	`taylor(double... delta)`	Evaluate Taylor expansion a derivative structure.
`Gradient`	`toDegrees()`	Convert radians to degrees, with error of less than 0.5 ULP
`DerivativeStructure`	`toDerivativeStructure()`	Convert the instance to a `DerivativeStructure`.
`Gradient`	`toRadians()`	Convert degrees to radians, with error of less than 0.5 ULP
`static Gradient`	`variable(int freeParameters, int index, double value)`	Build a `Gradient` representing a variable.
`Gradient`	`withValue(double 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
ceil, floor, getPi, isFinite, isInfinite, isNaN, norm, rint, round, sign, ulp

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative
add, getExponent, getReal, pow, remainder, subtract

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative1
acos, acosh, asin, asinh, atan, atanh, cbrt, cos, cosh, exp, expm1, getOrder, log, log10, log1p, reciprocal, rootN, sin, sinh, sqrt, square, tan, tanh

Methods inherited from interface org.hipparchus.FieldElement
isZero

- Constructor Detail
  - Gradient
```
public Gradient(double value,
                double... gradient)
```
    Build an instance with values and derivative.
    
    Parameters:
    
    value - value of the function
    
    gradient - gradient of the function
  - Gradient
```
public Gradient(DerivativeStructure ds)
         throws MathIllegalArgumentException
```
    Build an instance from a DerivativeStructure.
    
    Parameters:
    
    ds - derivative structure
    
    Throws:
    
    MathIllegalArgumentException - if ds order is not 1
- Method Detail
  - constant
```
public static Gradient constant(int freeParameters,
                                double value)
```
    Build an instance corresponding to a constant value.
    
    Parameters:
    
    freeParameters - number of free parameters (i.e. dimension of the gradient)
    
    value - constant value of the function
    
    Returns:
    
    a Gradient with a constant value and all derivatives set to 0.0
  - variable
```
public static Gradient variable(int freeParameters,
                                int index,
                                double value)
```
    Build a Gradient representing a variable.
    Instances built using this method are considered to be the free variables with respect to which differentials are computed. As such, their differential with respect to themselves is +1.
    
    Parameters:
    
    freeParameters - number of free parameters (i.e. dimension of the gradient)
    
    index - index of the variable (from 0 to getFreeParameters() - 1)
    
    value - value of the variable
    
    Returns:
    
    a Gradient with a constant value and all derivatives set to 0.0 except the one at index which will be set to 1.0
  - newInstance
```
public Gradient newInstance(double c)
```
    Create an instance corresponding to a constant real value.
    
    Specified by:
    
    newInstance in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    c - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - withValue
```
public Gradient withValue(double 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 Derivative<Gradient>
    
    Parameters:
    
    v - zeroth-order derivative of new represented function
    
    Returns:
    
    new object with changed value
  - getAddendum
```
public Gradient 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<Gradient>
    
    Returns:
    
    real value
  - getValue
```
public double getValue()
```
    Get the value part of the function.
    
    Specified by:
    
    getValue in interface Derivative<Gradient>
    
    Returns:
    
    value part of the value of the function
  - getGradient
```
public double[] getGradient()
```
    Get the gradient part of the function.
    
    Returns:
    
    gradient part of the value of the function
    
    See Also:
    
    getPartialDerivative(int)
  - getFreeParameters
```
public int getFreeParameters()
```
    Get the number of free parameters.
    
    Specified by:
    
    getFreeParameters in interface DifferentialAlgebra
    
    Returns:
    
    number of free parameters
  - getPartialDerivative
```
public double getPartialDerivative(int... orders)
                            throws MathIllegalArgumentException
```
    Get a partial derivative.
    
    Specified by:
    
    getPartialDerivative in interface Derivative<Gradient>
    
    Parameters:
    
    orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)
    
    Returns:
    
    partial derivative
    
    Throws:
    
    MathIllegalArgumentException - if the numbers of variables does not match the instance
    
    See Also:
    
    Derivative.getValue()
  - getPartialDerivative
```
public double getPartialDerivative(int n)
                            throws MathIllegalArgumentException
```
    Get the partial derivative with respect to one parameter.
    
    Parameters:
    
    n - index of the parameter (counting from 0)
    
    Returns:
    
    partial derivative with respect to the n^th parameter
    
    Throws:
    
    MathIllegalArgumentException - if n is either negative or larger or equal to getFreeParameters()
  - toDerivativeStructure
```
public DerivativeStructure toDerivativeStructure()
```
    Convert the instance to a DerivativeStructure.
    
    Returns:
    
    derivative structure with same value and derivative as the instance
  - add
```
public Gradient add(Gradient a)
```
    Compute this + a.
    
    Specified by:
    
    add in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - subtract
```
public Gradient subtract(Gradient a)
```
    Compute this - a.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<Gradient>
    
    Specified by:
    
    subtract in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
  - multiply
```
public Gradient multiply(int n)
```
    Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]
    
    Specified by:
    
    multiply in interface CalculusFieldElement<Gradient>
    
    Specified by:
    
    multiply in interface FieldElement<Gradient>
    
    Parameters:
    
    n - Number of times this must be added to itself.
    
    Returns:
    
    A new element representing n × this.
  - multiply
```
public Gradient multiply(double a)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public Gradient multiply(Gradient a)
```
    Compute this × a.
    
    Specified by:
    
    multiply in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
  - divide
```
public Gradient divide(double a)
```
    '÷' operator.
    
    Specified by:
    
    divide in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - divide
```
public Gradient divide(Gradient a)
```
    Compute this ÷ a.
    
    Specified by:
    
    divide in interface CalculusFieldElement<Gradient>
    
    Specified by:
    
    divide in interface FieldElement<Gradient>
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
  - remainder
```
public Gradient remainder(Gradient a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - negate
```
public Gradient negate()
```
    Returns the additive inverse of this element.
    
    Specified by:
    
    negate in interface FieldElement<Gradient>
    
    Returns:
    
    the opposite of this.
  - abs
```
public Gradient abs()
```
    absolute value.
    
    Specified by:
    
    abs in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    abs(this)
  - copySign
```
public Gradient copySign(Gradient sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public Gradient copySign(double sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - scalb
```
public Gradient scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - hypot
```
public Gradient hypot(Gradient y)
```
    Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
    
    If either argument is infinite, then the result is positive infinity.
    
    else, if either argument is NaN then the result is NaN.
    Specified by:
    
    hypot in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
  - compose
```
public Gradient compose(double... f)
```
    Compute composition of the instance by a univariate function.
    
    Specified by:
    
    compose in interface Derivative<Gradient>
    
    Parameters:
    
    f - array of value and derivatives of the function at the current point (i.e. [f(Derivative.getValue()), f'(Derivative.getValue()), f''(Derivative.getValue())...]).
    
    Returns:
    
    f(this)
  - compose
```
public Gradient compose(double f0,
                        double f1)
```
    Compute composition of the instance by a univariate function differentiable at order 1.
    
    Specified by:
    
    compose in interface Derivative1<Gradient>
    
    Parameters:
    
    f0 - value of function
    
    f1 - first-order derivative
    
    Returns:
    
    f(this)
  - getField
```
public GradientField getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<Gradient>
    
    Returns:
    
    Field to which the instance belongs
  - pow
```
public static Gradient pow(double a,
                           Gradient x)
```
    Compute a^x where a is a double and x a Gradient
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - pow
```
public Gradient pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public Gradient pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - sinCos
```
public FieldSinCos<Gradient> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<Gradient>
    
    Specified by:
    
    sinCos in interface Derivative1<Gradient>
    
    Returns:
    
    [sin(this), cos(this)]
  - atan2
```
public Gradient atan2(Gradient x)
```
    Two arguments arc tangent operation.
    Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
  - sinhCosh
```
public FieldSinhCosh<Gradient> sinhCosh()
```
    Combined hyperbolic sine and cosine operation.
    
    Specified by:
    
    sinhCosh in interface CalculusFieldElement<Gradient>
    
    Specified by:
    
    sinhCosh in interface Derivative1<Gradient>
    
    Returns:
    
    [sinh(this), cosh(this)]
  - toDegrees
```
public Gradient toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public Gradient toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Specified by:
    
    toRadians in interface CalculusFieldElement<Gradient>
    
    Returns:
    
    instance converted into radians
  - taylor
```
public double taylor(double... delta)
```
    Evaluate Taylor expansion a derivative structure.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
  - linearCombination
```
public Gradient linearCombination(Gradient[] a,
                                  Gradient[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public Gradient linearCombination(double[] a,
                                  Gradient[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public Gradient linearCombination(Gradient a1,
                                  Gradient b1,
                                  Gradient a2,
                                  Gradient b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public Gradient linearCombination(double a1,
                                  Gradient b1,
                                  double a2,
                                  Gradient b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    Returns:
    
    a₁×b₁ + a₂×b₂
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public Gradient linearCombination(Gradient a1,
                                  Gradient b1,
                                  Gradient a2,
                                  Gradient b2,
                                  Gradient a3,
                                  Gradient b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public Gradient linearCombination(double a1,
                                  Gradient b1,
                                  double a2,
                                  Gradient b2,
                                  double a3,
                                  Gradient b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
  - linearCombination
```
public Gradient linearCombination(Gradient a1,
                                  Gradient b1,
                                  Gradient a2,
                                  Gradient b2,
                                  Gradient a3,
                                  Gradient b3,
                                  Gradient a4,
                                  Gradient b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    See Also:
    
    CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement), CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  - linearCombination
```
public Gradient linearCombination(double a1,
                                  Gradient b1,
                                  double a2,
                                  Gradient b2,
                                  double a3,
                                  Gradient b3,
                                  double a4,
                                  Gradient b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<Gradient>
    
    Parameters:
    
    a1 - first factor of the first term
    
    b1 - second factor of the first term
    
    a2 - first factor of the second term
    
    b2 - second factor of the second term
    
    a3 - first factor of the third term
    
    b3 - second factor of the third term
    
    a4 - first factor of the fourth term
    
    b4 - second factor of the fourth term
    
    Returns:
    
    a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
    
    See Also:
    
    CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement), CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
  - stackVariable
```
public Gradient stackVariable()
```
    Add an independent variable to the Taylor expansion.
    
    Returns:
    
    object with one more variable
    
    Since:
    
    4.0
  - equals
```
public boolean equals(Object other)
```
    Test for the equality of two univariate derivatives.
    univariate derivatives are considered equal if they have the same derivatives.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    
    other - Object to test for equality to this
    
    Returns:
    
    true if two univariate derivatives are equal
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the univariate derivative.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    a hash code value for this object

Class Gradient

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

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

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative1

Methods inherited from interface org.hipparchus.FieldElement

Constructor Detail

Gradient

Gradient

Method Detail

constant

variable

newInstance

withValue

getAddendum

getValue

getGradient

getFreeParameters

getPartialDerivative

getPartialDerivative

toDerivativeStructure

add

subtract

multiply

multiply

multiply

divide

divide

remainder

negate

abs

copySign

copySign

scalb

hypot

compose

compose

getField

pow

pow

pow

sinCos

atan2

sinhCosh

toDegrees

toRadians

taylor

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

stackVariable

equals

hashCode