FunctionUtils (Apache Commons Math 4.0-SNAPSHOT API)

java.lang.Object
- org.apache.commons.math4.analysis.FunctionUtils

```
public class FunctionUtils
extends Object
```
Utilities for manipulating function objects.

Since:

3.0

Method Summary

Methods
Modifier and Type	Method and Description
`static UnivariateDifferentiableFunction`	`add(UnivariateDifferentiableFunction... f)` Adds functions.
`static UnivariateFunction`	`add(UnivariateFunction... f)` Adds functions.
`static MultivariateFunction`	`collector(BivariateFunction combiner, double initialValue)` Returns a MultivariateFunction h(x[]) defined by
`static MultivariateFunction`	`collector(BivariateFunction combiner, UnivariateFunction f, double initialValue)` Returns a MultivariateFunction h(x[]) defined by
`static UnivariateFunction`	`combine(BivariateFunction combiner, UnivariateFunction f, UnivariateFunction g)` Returns the univariate function `h(x) = combiner(f(x), g(x))`.
`static UnivariateDifferentiableFunction`	`compose(UnivariateDifferentiableFunction... f)` Composes functions.
`static UnivariateFunction`	`compose(UnivariateFunction... f)` Composes functions.
`static MultivariateFunction`	`derivative(MultivariateDifferentiableFunction f, int[] orders)` Convert an `MultivariateDifferentiableFunction` to an `MultivariateFunction` computing n^th order derivative.
`static UnivariateFunction`	`derivative(UnivariateDifferentiableFunction f, int order)` Convert an `UnivariateDifferentiableFunction` to an `UnivariateFunction` computing n^th order derivative.
`static UnivariateFunction`	`fix1stArgument(BivariateFunction f, double fixed)` Creates a unary function by fixing the first argument of a binary function.
`static UnivariateFunction`	`fix2ndArgument(BivariateFunction f, double fixed)` Creates a unary function by fixing the second argument of a binary function.
`static UnivariateDifferentiableFunction`	`multiply(UnivariateDifferentiableFunction... f)` Multiplies functions.
`static UnivariateFunction`	`multiply(UnivariateFunction... f)` Multiplies functions.
`static double[]`	`sample(UnivariateFunction f, double min, double max, int n)` Samples the specified univariate real function on the specified interval.
`static MultivariateDifferentiableFunction`	`toDifferentiable(MultivariateFunction f, MultivariateVectorFunction gradient)` Convert regular functions to `MultivariateDifferentiableFunction`.
`static UnivariateDifferentiableFunction`	`toDifferentiable(UnivariateFunction f, UnivariateFunction... derivatives)` Convert regular functions to `UnivariateDifferentiableFunction`.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - compose
```
public static UnivariateFunction compose(UnivariateFunction... f)
```
    Composes functions.
    The functions in the argument list are composed sequentially, in the given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).
    
    Parameters:
    f - List of functions.
    
    Returns:
    the composite function.
  - compose
```
public static UnivariateDifferentiableFunction compose(UnivariateDifferentiableFunction... f)
```
    Composes functions.
    The functions in the argument list are composed sequentially, in the given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).
    
    Parameters:
    f - List of functions.
    
    Returns:
    the composite function.
    Since:
    
    3.1
  - add
```
public static UnivariateFunction add(UnivariateFunction... f)
```
    Adds functions.
    
    Parameters:
    f - List of functions.
    
    Returns:
    a function that computes the sum of the functions.
  - add
```
public static UnivariateDifferentiableFunction add(UnivariateDifferentiableFunction... f)
```
    Adds functions.
    
    Parameters:
    f - List of functions.
    
    Returns:
    a function that computes the sum of the functions.
    Since:
    
    3.1
  - multiply
```
public static UnivariateFunction multiply(UnivariateFunction... f)
```
    Multiplies functions.
    
    Parameters:
    f - List of functions.
    
    Returns:
    a function that computes the product of the functions.
  - multiply
```
public static UnivariateDifferentiableFunction multiply(UnivariateDifferentiableFunction... f)
```
    Multiplies functions.
    
    Parameters:
    f - List of functions.
    
    Returns:
    a function that computes the product of the functions.
    Since:
    
    3.1
  - combine
```
public static UnivariateFunction combine(BivariateFunction combiner,
                         UnivariateFunction f,
                         UnivariateFunction g)
```
    Returns the univariate function
    h(x) = combiner(f(x), g(x)).
    
    Parameters:
    combiner - Combiner function.
    f - Function.
    g - Function.
    
    Returns:
    the composite function.
  - collector
```
public static MultivariateFunction collector(BivariateFunction combiner,
                             UnivariateFunction f,
                             double initialValue)
```
    Returns a MultivariateFunction h(x[]) defined by
```
 
 h(x[]) = combiner(...combiner(combiner(initialValue,f(x[0])),f(x[1]))...),f(x[x.length-1]))
 
```
    Parameters:
    combiner - Combiner function.
    f - Function.
    initialValue - Initial value.
    
    Returns:
    a collector function.
  - collector
```
public static MultivariateFunction collector(BivariateFunction combiner,
                             double initialValue)
```
    Returns a MultivariateFunction h(x[]) defined by
```
 
 h(x[]) = combiner(...combiner(combiner(initialValue,x[0]),x[1])...),x[x.length-1])
 
```
    Parameters:
    combiner - Combiner function.
    initialValue - Initial value.
    
    Returns:
    a collector function.
  - fix1stArgument
```
public static UnivariateFunction fix1stArgument(BivariateFunction f,
                                double fixed)
```
    Creates a unary function by fixing the first argument of a binary function.
    
    Parameters:
    f - Binary function.
    fixed - Value to which the first argument of f is set.
    
    Returns:
    the unary function h(x) = f(fixed, x)
  - fix2ndArgument
```
public static UnivariateFunction fix2ndArgument(BivariateFunction f,
                                double fixed)
```
    Creates a unary function by fixing the second argument of a binary function.
    
    Parameters:
    f - Binary function.
    fixed - Value to which the second argument of f is set.
    
    Returns:
    the unary function h(x) = f(x, fixed)
  - sample
```
public static double[] sample(UnivariateFunction f,
              double min,
              double max,
              int n)
                       throws NumberIsTooLargeException,
                              NotStrictlyPositiveException
```
    Samples the specified univariate real function on the specified interval.
    The interval is divided equally into n sections and sample points are taken from min to max - (max - min) / n; therefore f is not sampled at the upper bound max.
    
    Parameters:
    f - Function to be sampled
    min - Lower bound of the interval (included).
    max - Upper bound of the interval (excluded).
    n - Number of sample points.
    
    Returns:
    the array of samples.
    
    Throws:
    
    NumberIsTooLargeException - if the lower bound min is greater than, or equal to the upper bound max.
    
    NotStrictlyPositiveException - if the number of sample points n is negative.
  - toDifferentiable
```
public static UnivariateDifferentiableFunction toDifferentiable(UnivariateFunction f,
                                                UnivariateFunction... derivatives)
```
    Convert regular functions to UnivariateDifferentiableFunction.
    This method handle the case with one free parameter and several derivatives. For the case with several free parameters and only first order derivatives, see toDifferentiable(MultivariateFunction, MultivariateVectorFunction). There are no direct support for intermediate cases, with several free parameters and order 2 or more derivatives, as is would be difficult to specify all the cross derivatives.
    
    Note that the derivatives are expected to be computed only with respect to the raw parameter x of the base function, i.e. they are df/dx, df²/dx², ... Even if the built function is later used in a composition like f(sin(t)), the provided derivatives should not apply the composition with sine and its derivatives by themselves. The composition will be done automatically here and the result will properly contain f(sin(t)), df(sin(t))/dt, df²(sin(t))/dt² despite the provided derivatives functions know nothing about the sine function.
    
    Parameters:
    f - base function f(x)
    derivatives - derivatives of the base function, in increasing differentiation order
    
    Returns:
    a differentiable function with value and all specified derivatives
    See Also:
    toDifferentiable(MultivariateFunction, MultivariateVectorFunction), derivative(UnivariateDifferentiableFunction, int)
  - toDifferentiable
```
public static MultivariateDifferentiableFunction toDifferentiable(MultivariateFunction f,
                                                  MultivariateVectorFunction gradient)
```
    Convert regular functions to MultivariateDifferentiableFunction.
    This method handle the case with several free parameters and only first order derivatives. For the case with one free parameter and several derivatives, see toDifferentiable(UnivariateFunction, UnivariateFunction...). There are no direct support for intermediate cases, with several free parameters and order 2 or more derivatives, as is would be difficult to specify all the cross derivatives.
    
    Note that the gradient is expected to be computed only with respect to the raw parameter x of the base function, i.e. it is df/dx₁, df/dx₂, ... Even if the built function is later used in a composition like f(sin(t), cos(t)), the provided gradient should not apply the composition with sine or cosine and their derivative by itself. The composition will be done automatically here and the result will properly contain f(sin(t), cos(t)), df(sin(t), cos(t))/dt despite the provided derivatives functions know nothing about the sine or cosine functions.
    
    Parameters:
    f - base function f(x)
    gradient - gradient of the base function
    
    Returns:
    a differentiable function with value and gradient
    See Also:
    toDifferentiable(UnivariateFunction, UnivariateFunction...), derivative(MultivariateDifferentiableFunction, int[])
  - derivative
```
public static UnivariateFunction derivative(UnivariateDifferentiableFunction f,
                            int order)
```
    Convert an UnivariateDifferentiableFunction to an UnivariateFunction computing n^th order derivative.
    This converter is only a convenience method. Beware computing only one derivative does not save any computation as the original function will really be called under the hood. The derivative will be extracted from the full DerivativeStructure result.
    
    Parameters:
    f - original function, with value and all its derivatives
    order - of the derivative to extract
    
    Returns:
    function computing the derivative at required order
    See Also:
    derivative(MultivariateDifferentiableFunction, int[]), toDifferentiable(UnivariateFunction, UnivariateFunction...)
  - derivative
```
public static MultivariateFunction derivative(MultivariateDifferentiableFunction f,
                              int[] orders)
```
    Convert an MultivariateDifferentiableFunction to an MultivariateFunction computing n^th order derivative.
    This converter is only a convenience method. Beware computing only one derivative does not save any computation as the original function will really be called under the hood. The derivative will be extracted from the full DerivativeStructure result.
    
    Parameters:
    f - original function, with value and all its derivatives
    orders - of the derivative to extract, for each free parameters
    
    Returns:
    function computing the derivative at required order
    See Also:
    derivative(UnivariateDifferentiableFunction, int), toDifferentiable(MultivariateFunction, MultivariateVectorFunction)

Class FunctionUtils

Method Summary

Methods inherited from class java.lang.Object

Method Detail

compose

compose

add

add

multiply

multiply

combine

collector

collector

fix1stArgument

fix2ndArgument

sample

toDifferentiable

toDifferentiable

derivative

derivative