SparseGradient (Hipparchus 1.7 API)

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

All Implemented Interfaces:

Serializable, CalculusFieldElement<SparseGradient>, FieldElement<SparseGradient>, RealFieldElement<SparseGradient>
```
public class SparseGradient
extends Object
implements RealFieldElement<SparseGradient>, Serializable
```
First derivative computation with large number of variables.
This class plays a similar role to DerivativeStructure, with a focus on efficiency when dealing with large number of independent variables and most computation depend only on a few of them, and when only first derivative is desired. When these conditions are met, this class should be much faster than DerivativeStructure and use less memory.

See Also:

Serialized Form

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`SparseGradient`	`abs()` absolute value.
`SparseGradient`	`acos()` Arc cosine operation.
`SparseGradient`	`acosh()` Inverse hyperbolic cosine operation.
`SparseGradient`	`add(double c)` '+' operator.
`SparseGradient`	`add(SparseGradient a)` Compute this + a.
`void`	`addInPlace(SparseGradient a)` Add in place.
`SparseGradient`	`asin()` Arc sine operation.
`SparseGradient`	`asinh()` Inverse hyperbolic sine operation.
`SparseGradient`	`atan()` Arc tangent operation.
`SparseGradient`	`atan2(SparseGradient x)` Two arguments arc tangent operation.
`static SparseGradient`	`atan2(SparseGradient y, SparseGradient x)` Two arguments arc tangent operation.
`SparseGradient`	`atanh()` Inverse hyperbolic tangent operation.
`SparseGradient`	`cbrt()` Cubic root.
`SparseGradient`	`ceil()` Get the smallest whole number larger than instance.
`SparseGradient`	`compose(double f0, double f1)` Compute composition of the instance by a univariate function.
`SparseGradient`	`copySign(double sign)` Returns the instance with the sign of the argument.
`SparseGradient`	`copySign(SparseGradient sign)` Returns the instance with the sign of the argument.
`SparseGradient`	`cos()` Cosine operation.
`SparseGradient`	`cosh()` Hyperbolic cosine operation.
`static SparseGradient`	`createConstant(double value)` Factory method creating a constant.
`static SparseGradient`	`createVariable(int idx, double value)` Factory method creating an independent variable.
`SparseGradient`	`divide(double c)` '÷' operator.
`SparseGradient`	`divide(SparseGradient a)` Compute this ÷ a.
`boolean`	`equals(Object other)` Test for the equality of two sparse gradients.
`SparseGradient`	`exp()` Exponential.
`SparseGradient`	`expm1()` Exponential minus 1.
`SparseGradient`	`floor()` Get the largest whole number smaller than instance.
`double`	`getDerivative(int index)` Get the derivative with respect to a particular index variable.
`Field<SparseGradient>`	`getField()` Get the `Field` to which the instance belongs.
`double`	`getReal()` Get the real value of the number.
`double`	`getValue()` Get the value of the function.
`int`	`hashCode()` Get a hashCode for the derivative structure.
`SparseGradient`	`hypot(SparseGradient y)` Returns the hypotenuse of a triangle with sides `this` and `y` - sqrt(this² +y²) avoiding intermediate overflow or underflow.
`static SparseGradient`	`hypot(SparseGradient x, SparseGradient y)` Returns the hypotenuse of a triangle with sides `x` and `y` - sqrt(x² +y²) avoiding intermediate overflow or underflow.
`SparseGradient`	`linearCombination(double[] a, SparseGradient[] b)` Compute a linear combination.
`SparseGradient`	`linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2)` Compute a linear combination.
`SparseGradient`	`linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3)` Compute a linear combination.
`SparseGradient`	`linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3, double a4, SparseGradient b4)` Compute a linear combination.
`SparseGradient`	`linearCombination(SparseGradient[] a, SparseGradient[] b)` Compute a linear combination.
`SparseGradient`	`linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2)` Compute a linear combination.
`SparseGradient`	`linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3)` Compute a linear combination.
`SparseGradient`	`linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3, SparseGradient a4, SparseGradient b4)` Compute a linear combination.
`SparseGradient`	`log()` Natural logarithm.
`SparseGradient`	`log10()` Base 10 logarithm.
`SparseGradient`	`log1p()` Shifted natural logarithm.
`SparseGradient`	`multiply(double c)` '×' operator.
`SparseGradient`	`multiply(int n)` Compute n × this.
`SparseGradient`	`multiply(SparseGradient a)` Compute this × a.
`void`	`multiplyInPlace(SparseGradient a)` Multiply in place.
`SparseGradient`	`negate()` Returns the additive inverse of `this` element.
`SparseGradient`	`newInstance(double v)` Create an instance corresponding to a constant real value.
`int`	`numVars()` Find the number of variables.
`SparseGradient`	`pow(double p)` Power operation.
`static SparseGradient`	`pow(double a, SparseGradient x)` Compute a^x where a is a double and x a `SparseGradient`
`SparseGradient`	`pow(int n)` Integer power operation.
`SparseGradient`	`pow(SparseGradient e)` Power operation.
`SparseGradient`	`reciprocal()` Returns the multiplicative inverse of `this` element.
`SparseGradient`	`remainder(double a)` IEEE remainder operator.
`SparseGradient`	`remainder(SparseGradient a)` IEEE remainder operator.
`SparseGradient`	`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.
`SparseGradient`	`rootN(int n)` N^th root.
`SparseGradient`	`scalb(int n)` Multiply the instance by a power of 2.
`SparseGradient`	`signum()` Compute the signum of the instance.
`SparseGradient`	`sin()` Sine operation.
`FieldSinCos<SparseGradient>`	`sinCos()` Combined Sine and Cosine operation.
`SparseGradient`	`sinh()` Hyperbolic sine operation.
`SparseGradient`	`sqrt()` Square root.
`SparseGradient`	`subtract(double c)` '-' operator.
`SparseGradient`	`subtract(SparseGradient a)` Compute this - a.
`SparseGradient`	`tan()` Tangent operation.
`SparseGradient`	`tanh()` Hyperbolic tangent operation.
`double`	`taylor(double... delta)` Evaluate Taylor expansion of a sparse gradient.
`SparseGradient`	`toDegrees()` Convert radians to degrees, with error of less than 0.5 ULP
`SparseGradient`	`toRadians()` Convert degrees to radians, with error of less than 0.5 ULP

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
getExponent, isInfinite, isNaN

- Method Detail
  - newInstance
```
public SparseGradient newInstance(double v)
```
    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<SparseGradient>
    
    Parameters:
    
    v - constant real value
    
    Returns:
    
    instance corresponding to a constant real value
  - createConstant
```
public static SparseGradient createConstant(double value)
```
    Factory method creating a constant.
    
    Parameters:
    
    value - value of the constant
    
    Returns:
    
    a new instance
  - createVariable
```
public static SparseGradient createVariable(int idx,
                                            double value)
```
    Factory method creating an independent variable.
    
    Parameters:
    
    idx - index of the variable
    
    value - value of the variable
    
    Returns:
    
    a new instance
  - numVars
```
public int numVars()
```
    Find the number of variables.
    
    Returns:
    
    number of variables
  - getDerivative
```
public double getDerivative(int index)
```
    Get the derivative with respect to a particular index variable.
    
    Parameters:
    
    index - index to differentiate with.
    
    Returns:
    
    derivative with respect to a particular index variable
  - getValue
```
public double getValue()
```
    Get the value of the function.
    
    Returns:
    
    value of the function.
  - getReal
```
public double getReal()
```
    Get the real value of the number.
    
    Specified by:
    
    getReal in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    real value
  - add
```
public SparseGradient add(SparseGradient a)
```
    Compute this + a.
    
    Specified by:
    
    add in interface FieldElement<SparseGradient>
    
    Parameters:
    
    a - element to add
    
    Returns:
    
    a new element representing this + a
  - addInPlace
```
public void addInPlace(SparseGradient a)
```
    Add in place.
    This method is designed to be faster when used multiple times in a loop.
    
    The instance is changed here, in order to not change the instance the add(SparseGradient) method should be used.
    
    Parameters:
    
    a - instance to add
  - add
```
public SparseGradient add(double c)
```
    '+' operator.
    
    Specified by:
    
    add in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    c - right hand side parameter of the operator
    
    Returns:
    
    this+a
  - subtract
```
public SparseGradient subtract(SparseGradient a)
```
    Compute this - a.
    
    Specified by:
    
    subtract in interface FieldElement<SparseGradient>
    
    Parameters:
    
    a - element to subtract
    
    Returns:
    
    a new element representing this - a
  - subtract
```
public SparseGradient subtract(double c)
```
    '-' operator.
    
    Specified by:
    
    subtract in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    c - right hand side parameter of the operator
    
    Returns:
    
    this-a
  - multiply
```
public SparseGradient multiply(SparseGradient a)
```
    Compute this × a.
    
    Specified by:
    
    multiply in interface FieldElement<SparseGradient>
    
    Parameters:
    
    a - element to multiply
    
    Returns:
    
    a new element representing this × a
  - multiplyInPlace
```
public void multiplyInPlace(SparseGradient a)
```
    Multiply in place.
    This method is designed to be faster when used multiple times in a loop.
    
    The instance is changed here, in order to not change the instance the add(SparseGradient) method should be used.
    
    Parameters:
    
    a - instance to multiply
  - multiply
```
public SparseGradient multiply(double c)
```
    '×' operator.
    
    Specified by:
    
    multiply in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    c - right hand side parameter of the operator
    
    Returns:
    
    this×a
  - multiply
```
public SparseGradient 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<SparseGradient>
    
    Parameters:
    
    n - Number of times this must be added to itself.
    
    Returns:
    
    A new element representing n × this.
  - divide
```
public SparseGradient divide(SparseGradient a)
```
    Compute this ÷ a.
    
    Specified by:
    
    divide in interface FieldElement<SparseGradient>
    
    Parameters:
    
    a - element to divide by
    
    Returns:
    
    a new element representing this ÷ a
  - divide
```
public SparseGradient divide(double c)
```
    '÷' operator.
    
    Specified by:
    
    divide in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    c - right hand side parameter of the operator
    
    Returns:
    
    this÷a
  - negate
```
public SparseGradient negate()
```
    Returns the additive inverse of this element.
    
    Specified by:
    
    negate in interface FieldElement<SparseGradient>
    
    Returns:
    
    the opposite of this.
  - getField
```
public Field<SparseGradient> getField()
```
    Get the Field to which the instance belongs.
    
    Specified by:
    
    getField in interface FieldElement<SparseGradient>
    
    Returns:
    
    Field to which the instance belongs
  - remainder
```
public SparseGradient remainder(double a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - remainder
```
public SparseGradient remainder(SparseGradient a)
```
    IEEE remainder operator.
    
    Specified by:
    
    remainder in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    a - right hand side parameter of the operator
    
    Returns:
    
    this - n × a where n is the closest integer to this/a
  - abs
```
public SparseGradient abs()
```
    absolute value.
    
    Specified by:
    
    abs in interface RealFieldElement<SparseGradient>
    
    Returns:
    
    abs(this)
  - ceil
```
public SparseGradient ceil()
```
    Get the smallest whole number larger than instance.
    
    Specified by:
    
    ceil in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    ceil(this)
  - floor
```
public SparseGradient floor()
```
    Get the largest whole number smaller than instance.
    
    Specified by:
    
    floor in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    floor(this)
  - rint
```
public SparseGradient 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<SparseGradient>
    
    Returns:
    
    a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  - signum
```
public SparseGradient 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<SparseGradient>
    
    Returns:
    
    -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  - copySign
```
public SparseGradient copySign(SparseGradient sign)
```
    Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
    
    Specified by:
    
    copySign in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - copySign
```
public SparseGradient 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<SparseGradient>
    
    Parameters:
    
    sign - the sign for the returned value
    
    Returns:
    
    the instance with the same sign as the sign argument
  - scalb
```
public SparseGradient scalb(int n)
```
    Multiply the instance by a power of 2.
    
    Specified by:
    
    scalb in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    n - power of 2
    
    Returns:
    
    this × 2ⁿ
  - hypot
```
public SparseGradient hypot(SparseGradient 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<SparseGradient>
    
    Parameters:
    
    y - a value
    
    Returns:
    
    sqrt(this² +y²)
  - hypot
```
public static SparseGradient hypot(SparseGradient x,
                                   SparseGradient y)
```
    Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +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.
    Parameters:
    
    x - a value
    
    y - a value
    
    Returns:
    
    sqrt(x² +y²)
  - reciprocal
```
public SparseGradient reciprocal()
```
    Returns the multiplicative inverse of this element.
    
    Specified by:
    
    reciprocal in interface CalculusFieldElement<SparseGradient>
    
    Specified by:
    
    reciprocal in interface FieldElement<SparseGradient>
    
    Returns:
    
    the inverse of this.
  - sqrt
```
public SparseGradient sqrt()
```
    Square root.
    
    Specified by:
    
    sqrt in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    square root of the instance
  - cbrt
```
public SparseGradient cbrt()
```
    Cubic root.
    
    Specified by:
    
    cbrt in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    cubic root of the instance
  - rootN
```
public SparseGradient rootN(int n)
```
    N^th root.
    
    Specified by:
    
    rootN in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    n - order of the root
    
    Returns:
    
    n^th root of the instance
  - pow
```
public SparseGradient pow(double p)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    p - power to apply
    
    Returns:
    
    this^p
  - pow
```
public SparseGradient pow(int n)
```
    Integer power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    n - power to apply
    
    Returns:
    
    thisⁿ
  - pow
```
public SparseGradient pow(SparseGradient e)
```
    Power operation.
    
    Specified by:
    
    pow in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    e - exponent
    
    Returns:
    
    this^e
  - pow
```
public static SparseGradient pow(double a,
                                 SparseGradient x)
```
    Compute a^x where a is a double and x a SparseGradient
    
    Parameters:
    
    a - number to exponentiate
    
    x - power to apply
    
    Returns:
    
    a^x
  - exp
```
public SparseGradient exp()
```
    Exponential.
    
    Specified by:
    
    exp in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    exponential of the instance
  - expm1
```
public SparseGradient expm1()
```
    Exponential minus 1.
    
    Specified by:
    
    expm1 in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    exponential minus one of the instance
  - log
```
public SparseGradient log()
```
    Natural logarithm.
    
    Specified by:
    
    log in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    logarithm of the instance
  - log10
```
public SparseGradient log10()
```
    Base 10 logarithm.
    
    Specified by:
    
    log10 in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    base 10 logarithm of the instance
  - log1p
```
public SparseGradient log1p()
```
    Shifted natural logarithm.
    
    Specified by:
    
    log1p in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    logarithm of one plus the instance
  - cos
```
public SparseGradient cos()
```
    Cosine operation.
    
    Specified by:
    
    cos in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    cos(this)
  - sin
```
public SparseGradient sin()
```
    Sine operation.
    
    Specified by:
    
    sin in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    sin(this)
  - sinCos
```
public FieldSinCos<SparseGradient> sinCos()
```
    Combined Sine and Cosine operation.
    
    Specified by:
    
    sinCos in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    [sin(this), cos(this)]
  - tan
```
public SparseGradient tan()
```
    Tangent operation.
    
    Specified by:
    
    tan in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    tan(this)
  - acos
```
public SparseGradient acos()
```
    Arc cosine operation.
    
    Specified by:
    
    acos in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    acos(this)
  - asin
```
public SparseGradient asin()
```
    Arc sine operation.
    
    Specified by:
    
    asin in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    asin(this)
  - atan
```
public SparseGradient atan()
```
    Arc tangent operation.
    
    Specified by:
    
    atan in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    atan(this)
  - atan2
```
public SparseGradient atan2(SparseGradient x)
```
    Two arguments arc tangent operation.
    
    Specified by:
    
    atan2 in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(this, x)
  - atan2
```
public static SparseGradient atan2(SparseGradient y,
                                   SparseGradient x)
```
    Two arguments arc tangent operation.
    
    Parameters:
    
    y - first argument of the arc tangent
    
    x - second argument of the arc tangent
    
    Returns:
    
    atan2(y, x)
  - cosh
```
public SparseGradient cosh()
```
    Hyperbolic cosine operation.
    
    Specified by:
    
    cosh in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    cosh(this)
  - sinh
```
public SparseGradient sinh()
```
    Hyperbolic sine operation.
    
    Specified by:
    
    sinh in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    sinh(this)
  - tanh
```
public SparseGradient tanh()
```
    Hyperbolic tangent operation.
    
    Specified by:
    
    tanh in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    tanh(this)
  - acosh
```
public SparseGradient acosh()
```
    Inverse hyperbolic cosine operation.
    
    Specified by:
    
    acosh in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    acosh(this)
  - asinh
```
public SparseGradient asinh()
```
    Inverse hyperbolic sine operation.
    
    Specified by:
    
    asinh in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    asin(this)
  - atanh
```
public SparseGradient atanh()
```
    Inverse hyperbolic tangent operation.
    
    Specified by:
    
    atanh in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    atanh(this)
  - toDegrees
```
public SparseGradient toDegrees()
```
    Convert radians to degrees, with error of less than 0.5 ULP
    
    Specified by:
    
    toDegrees in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    instance converted into degrees
  - toRadians
```
public SparseGradient toRadians()
```
    Convert degrees to radians, with error of less than 0.5 ULP
    
    Specified by:
    
    toRadians in interface CalculusFieldElement<SparseGradient>
    
    Returns:
    
    instance converted into radians
  - taylor
```
public double taylor(double... delta)
```
    Evaluate Taylor expansion of a sparse gradient.
    
    Parameters:
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
  - compose
```
public SparseGradient compose(double f0,
                              double f1)
```
    Compute composition of the instance by a univariate function.
    
    Parameters:
    
    f0 - value of the function at (i.e. f(getValue()))
    
    f1 - first derivative of the function at the current point (i.e. f'(getValue()))
    
    Returns:
    
    f(this)
  - linearCombination
```
public SparseGradient linearCombination(SparseGradient[] a,
                                        SparseGradient[] b)
                                 throws MathIllegalArgumentException
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
    
    Throws:
    
    MathIllegalArgumentException - if arrays dimensions don't match
  - linearCombination
```
public SparseGradient linearCombination(double[] a,
                                        SparseGradient[] b)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    Parameters:
    
    a - Factors.
    
    b - Factors.
    
    Returns:
    
    Σ_i a_i b_i.
  - linearCombination
```
public SparseGradient linearCombination(SparseGradient a1,
                                        SparseGradient b1,
                                        SparseGradient a2,
                                        SparseGradient b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    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 SparseGradient linearCombination(double a1,
                                        SparseGradient b1,
                                        double a2,
                                        SparseGradient b2)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    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 SparseGradient linearCombination(SparseGradient a1,
                                        SparseGradient b1,
                                        SparseGradient a2,
                                        SparseGradient b2,
                                        SparseGradient a3,
                                        SparseGradient b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    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 SparseGradient linearCombination(double a1,
                                        SparseGradient b1,
                                        double a2,
                                        SparseGradient b2,
                                        double a3,
                                        SparseGradient b3)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    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 SparseGradient linearCombination(SparseGradient a1,
                                        SparseGradient b1,
                                        SparseGradient a2,
                                        SparseGradient b2,
                                        SparseGradient a3,
                                        SparseGradient b3,
                                        SparseGradient a4,
                                        SparseGradient b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    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 SparseGradient linearCombination(double a1,
                                        SparseGradient b1,
                                        double a2,
                                        SparseGradient b2,
                                        double a3,
                                        SparseGradient b3,
                                        double a4,
                                        SparseGradient b4)
```
    Compute a linear combination.
    
    Specified by:
    
    linearCombination in interface CalculusFieldElement<SparseGradient>
    
    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 sparse gradients.
    Sparse gradients are considered equal if they have the same value and the same derivatives.
    
    Overrides:
    
    equals in class Object
    
    Parameters:
    
    other - Object to test for equality to this
    
    Returns:
    
    true if two sparse gradients are equal
  - hashCode
```
public int hashCode()
```
    Get a hashCode for the derivative structure.
    
    Overrides:
    
    hashCode in class Object
    
    Returns:
    
    a hash code value for this object

Class SparseGradient

Field Summary

Fields inherited from interface org.hipparchus.CalculusFieldElement

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.RealFieldElement

Methods inherited from interface org.hipparchus.CalculusFieldElement

Method Detail

newInstance

createConstant

createVariable

numVars

getDerivative

getValue

getReal

add

addInPlace

add

subtract

subtract

multiply

multiplyInPlace

multiply

multiply

divide

divide

negate

getField

remainder

remainder

abs

ceil

floor

rint

signum

copySign

copySign

scalb

hypot

hypot

reciprocal

sqrt

cbrt

rootN

pow

pow

pow

pow

exp

expm1

log

log10

log1p

cos

sin

sinCos

tan

acos

asin

atan

atan2

atan2

cosh

sinh

tanh

acosh

asinh

atanh

toDegrees

toRadians

taylor

compose

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination