public Class FunctionUtils

public static UnivariateFunction add(final UnivariateFunction... f)

Adds functions.

Parameters

f:UnivariateFunction[]: List of functions.

Returns:UnivariateFunction

a function that computes the sum of the functions.

add	back to summary
public static UnivariateDifferentiableFunction add(final UnivariateDifferentiableFunction... f) Adds functions. Parameters f:UnivariateDifferentiableFunction[] List of functions. Returns:UnivariateDifferentiableFunction a function that computes the sum of the functions. Since 3.1

add

public static UnivariateDifferentiableFunction add(final UnivariateDifferentiableFunction... f)

Adds functions.

Parameters

f:UnivariateDifferentiableFunction[]: List of functions.

a function that computes the sum of the functions.

Since

3.1

add back to summary

add	back to summary
public static DifferentiableUnivariateFunction add(final DifferentiableUnivariateFunction... f) Deprecated as of 3.1 replaced by `add(UnivariateDifferentiableFunction...)` Adds functions. Parameters f:DifferentiableUnivariateFunction[] List of functions. Returns:DifferentiableUnivariateFunction a function that computes the sum of the functions. Annotations @Deprecated

public static DifferentiableUnivariateFunction add(final DifferentiableUnivariateFunction... f)

Deprecated

as of 3.1 replaced by add(UnivariateDifferentiableFunction...)

Adds functions.

Parameters

f:DifferentiableUnivariateFunction[]: List of functions.

a function that computes the sum of the functions.

Annotations

@Deprecated

collector back to summary

collector	back to summary
public static MultivariateFunction collector(final BivariateFunction combiner, final UnivariateFunction f, final 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:BivariateFunction Combiner function. f:UnivariateFunction Function. initialValue:double Initial value. Returns:MultivariateFunction a collector function.

public static MultivariateFunction collector(final BivariateFunction combiner, final UnivariateFunction f, final 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:BivariateFunction: Combiner function.
f:UnivariateFunction: Function.
initialValue:double: Initial value.

Returns:MultivariateFunction

a collector function.

collector back to summary

collector	back to summary
public static MultivariateFunction collector(final BivariateFunction combiner, final 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:BivariateFunction Combiner function. initialValue:double Initial value. Returns:MultivariateFunction a collector function.

public static MultivariateFunction collector(final BivariateFunction combiner, final 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:BivariateFunction: Combiner function.
initialValue:double: Initial value.

Returns:MultivariateFunction

a collector function.

combine back to summary

combine	back to summary
public static UnivariateFunction combine(final BivariateFunction combiner, final UnivariateFunction f, final UnivariateFunction g) Returns the univariate function `h(x) = combiner(f(x), g(x)).` Parameters combiner:BivariateFunction Combiner function. f:UnivariateFunction Function. g:UnivariateFunction Function. Returns:UnivariateFunction the composite function.

public static UnivariateFunction combine(final BivariateFunction combiner, final UnivariateFunction f, final UnivariateFunction g)

Returns the univariate function h(x) = combiner(f(x), g(x)).

Parameters

combiner:BivariateFunction: Combiner function.
f:UnivariateFunction: Function.
g:UnivariateFunction: Function.

Returns:UnivariateFunction

the composite function.

compose	back to summary
public static UnivariateFunction compose(final 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:UnivariateFunction[] List of functions. Returns:UnivariateFunction the composite function.

compose

public static UnivariateFunction compose(final 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:UnivariateFunction[]: List of functions.

Returns:UnivariateFunction

the composite function.

compose	back to summary
public static UnivariateDifferentiableFunction compose(final 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:UnivariateDifferentiableFunction[] List of functions. Returns:UnivariateDifferentiableFunction the composite function. Since 3.1

compose

public static UnivariateDifferentiableFunction compose(final 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:UnivariateDifferentiableFunction[]: List of functions.

the composite function.

Since

3.1

compose back to summary

compose	back to summary
public static DifferentiableUnivariateFunction compose(final DifferentiableUnivariateFunction... f) Deprecated as of 3.1 replaced by `compose(UnivariateDifferentiableFunction...)` 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:DifferentiableUnivariateFunction[] List of functions. Returns:DifferentiableUnivariateFunction the composite function. Annotations @Deprecated

public static DifferentiableUnivariateFunction compose(final DifferentiableUnivariateFunction... f)

Deprecated

as of 3.1 replaced by compose(UnivariateDifferentiableFunction...)

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:DifferentiableUnivariateFunction[]: List of functions.

the composite function.

Annotations

@Deprecated

fix1stArgument back to summary

fix1stArgument	back to summary
public static UnivariateFunction fix1stArgument(final BivariateFunction f, final double fixed) Creates a unary function by fixing the first argument of a binary function. Parameters f:BivariateFunction Binary function. fixed:double value to which the first argument of `f` is set. Returns:UnivariateFunction the unary function h(x) = f(fixed, x)

public static UnivariateFunction fix1stArgument(final BivariateFunction f, final double fixed)

Creates a unary function by fixing the first argument of a binary function.

Parameters

f:BivariateFunction: Binary function.
fixed:double: value to which the first argument of f is set.

Returns:UnivariateFunction

the unary function h(x) = f(fixed, x)

fix2ndArgument back to summary

fix2ndArgument	back to summary
public static UnivariateFunction fix2ndArgument(final BivariateFunction f, final double fixed) Creates a unary function by fixing the second argument of a binary function. Parameters f:BivariateFunction Binary function. fixed:double value to which the second argument of `f` is set. Returns:UnivariateFunction the unary function h(x) = f(x, fixed)

public static UnivariateFunction fix2ndArgument(final BivariateFunction f, final double fixed)

Creates a unary function by fixing the second argument of a binary function.

Parameters

f:BivariateFunction: Binary function.
fixed:double: value to which the second argument of f is set.

Returns:UnivariateFunction

the unary function h(x) = f(x, fixed)

multiply	back to summary
public static UnivariateFunction multiply(final UnivariateFunction... f) Multiplies functions. Parameters f:UnivariateFunction[] List of functions. Returns:UnivariateFunction a function that computes the product of the functions.

multiply

public static UnivariateFunction multiply(final UnivariateFunction... f)

Multiplies functions.

Parameters

f:UnivariateFunction[]: List of functions.

Returns:UnivariateFunction

a function that computes the product of the functions.

multiply	back to summary
public static UnivariateDifferentiableFunction multiply(final UnivariateDifferentiableFunction... f) Multiplies functions. Parameters f:UnivariateDifferentiableFunction[] List of functions. Returns:UnivariateDifferentiableFunction a function that computes the product of the functions. Since 3.1

multiply

public static UnivariateDifferentiableFunction multiply(final UnivariateDifferentiableFunction... f)

Multiplies functions.

Parameters

f:UnivariateDifferentiableFunction[]: List of functions.

a function that computes the product of the functions.

Since

3.1

multiply back to summary

multiply	back to summary
public static DifferentiableUnivariateFunction multiply(final DifferentiableUnivariateFunction... f) Deprecated as of 3.1 replaced by `multiply(UnivariateDifferentiableFunction...)` Multiplies functions. Parameters f:DifferentiableUnivariateFunction[] List of functions. Returns:DifferentiableUnivariateFunction a function that computes the product of the functions. Annotations @Deprecated

public static DifferentiableUnivariateFunction multiply(final DifferentiableUnivariateFunction... f)

Deprecated

as of 3.1 replaced by multiply(UnivariateDifferentiableFunction...)

Multiplies functions.

Parameters

f:DifferentiableUnivariateFunction[]: List of functions.

a function that computes the product of the functions.

Annotations

@Deprecated

sample back to summary

sample	back to summary
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:UnivariateFunction Function to be sampled min:double Lower bound of the interval (included). max:double Upper bound of the interval (excluded). n:int Number of sample points. Returns:double[] the array of samples. Exceptions 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.

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:UnivariateFunction: Function to be sampled
min:double: Lower bound of the interval (included).
max:double: Upper bound of the interval (excluded).
n:int: Number of sample points.

Returns:double[]

the array of samples.

Exceptions

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.

toDifferentiableMultivariateFunction back to summary

toDifferentiableMultivariateFunction	back to summary
public static DifferentiableMultivariateFunction toDifferentiableMultivariateFunction(final MultivariateDifferentiableFunction f) Deprecated this conversion method is temporary in version 3.1, as the `DifferentiableMultivariateFunction` interface itself is deprecated Convert a `MultivariateDifferentiableFunction` into a `DifferentiableMultivariateFunction`. Parameters f:MultivariateDifferentiableFunction function to convert Returns:DifferentiableMultivariateFunction converted function Annotations @Deprecated

public static DifferentiableMultivariateFunction toDifferentiableMultivariateFunction(final MultivariateDifferentiableFunction f)

Deprecated

this conversion method is temporary in version 3.1, as the DifferentiableMultivariateFunction interface itself is deprecated

Convert a MultivariateDifferentiableFunction into a DifferentiableMultivariateFunction.

Parameters

f:MultivariateDifferentiableFunction: function to convert

Returns:DifferentiableMultivariateFunction

converted function

Annotations

@Deprecated

toDifferentiableMultivariateVectorFunction back to summary

toDifferentiableMultivariateVectorFunction	back to summary
public static DifferentiableMultivariateVectorFunction toDifferentiableMultivariateVectorFunction(final MultivariateDifferentiableVectorFunction f) Deprecated this conversion method is temporary in version 3.1, as the `DifferentiableMultivariateVectorFunction` interface itself is deprecated Convert a `MultivariateDifferentiableVectorFunction` into a `DifferentiableMultivariateVectorFunction`. Parameters f:MultivariateDifferentiableVectorFunction function to convert Returns:DifferentiableMultivariateVectorFunction converted function Annotations @Deprecated

public static DifferentiableMultivariateVectorFunction toDifferentiableMultivariateVectorFunction(final MultivariateDifferentiableVectorFunction f)

Deprecated

this conversion method is temporary in version 3.1, as the DifferentiableMultivariateVectorFunction interface itself is deprecated

Convert a MultivariateDifferentiableVectorFunction into a DifferentiableMultivariateVectorFunction.

Parameters

f:MultivariateDifferentiableVectorFunction: function to convert

Returns:DifferentiableMultivariateVectorFunction

converted function

Annotations

@Deprecated

toDifferentiableUnivariateFunction back to summary

toDifferentiableUnivariateFunction	back to summary
public static DifferentiableUnivariateFunction toDifferentiableUnivariateFunction(final UnivariateDifferentiableFunction f) Deprecated this conversion method is temporary in version 3.1, as the `DifferentiableUnivariateFunction` interface itself is deprecated Convert a `UnivariateDifferentiableFunction` into a `DifferentiableUnivariateFunction`. Parameters f:UnivariateDifferentiableFunction function to convert Returns:DifferentiableUnivariateFunction converted function Annotations @Deprecated

public static DifferentiableUnivariateFunction toDifferentiableUnivariateFunction(final UnivariateDifferentiableFunction f)

Deprecated

this conversion method is temporary in version 3.1, as the DifferentiableUnivariateFunction interface itself is deprecated

Convert a UnivariateDifferentiableFunction into a DifferentiableUnivariateFunction.

Parameters

f:UnivariateDifferentiableFunction: function to convert

converted function

Annotations

@Deprecated

toMultivariateDifferentiableFunction back to summary

toMultivariateDifferentiableFunction	back to summary
public static MultivariateDifferentiableFunction toMultivariateDifferentiableFunction(final DifferentiableMultivariateFunction f) Deprecated this conversion method is temporary in version 3.1, as the `DifferentiableMultivariateFunction` interface itself is deprecated Convert a `DifferentiableMultivariateFunction` into a `MultivariateDifferentiableFunction`. Note that the converted function is able to handle `DerivativeStructure` elements that all have the same number of free parameters and order, and with order at most 1. If the function is called with inconsistent numbers of free parameters or higher order, a `DimensionMismatchException` or a `NumberIsTooLargeException` will be thrown. Parameters f:DifferentiableMultivariateFunction function to convert Returns:MultivariateDifferentiableFunction converted function Annotations @Deprecated

public static MultivariateDifferentiableFunction toMultivariateDifferentiableFunction(final DifferentiableMultivariateFunction f)

Deprecated

this conversion method is temporary in version 3.1, as the DifferentiableMultivariateFunction interface itself is deprecated

Convert a DifferentiableMultivariateFunction into a MultivariateDifferentiableFunction.

Note that the converted function is able to handle DerivativeStructure elements that all have the same number of free parameters and order, and with order at most 1. If the function is called with inconsistent numbers of free parameters or higher order, a DimensionMismatchException or a NumberIsTooLargeException will be thrown.

Parameters

f:DifferentiableMultivariateFunction: function to convert

Returns:MultivariateDifferentiableFunction

converted function

Annotations

@Deprecated

toMultivariateDifferentiableVectorFunction back to summary

toMultivariateDifferentiableVectorFunction	back to summary
public static MultivariateDifferentiableVectorFunction toMultivariateDifferentiableVectorFunction(final DifferentiableMultivariateVectorFunction f) Deprecated this conversion method is temporary in version 3.1, as the `DifferentiableMultivariateFunction` interface itself is deprecated Convert a `DifferentiableMultivariateVectorFunction` into a `MultivariateDifferentiableVectorFunction`. Note that the converted function is able to handle `DerivativeStructure` elements that all have the same number of free parameters and order, and with order at most 1. If the function is called with inconsistent numbers of free parameters or higher order, a `DimensionMismatchException` or a `NumberIsTooLargeException` will be thrown. Parameters f:DifferentiableMultivariateVectorFunction function to convert Returns:MultivariateDifferentiableVectorFunction converted function Annotations @Deprecated

public static MultivariateDifferentiableVectorFunction toMultivariateDifferentiableVectorFunction(final DifferentiableMultivariateVectorFunction f)

Deprecated

this conversion method is temporary in version 3.1, as the DifferentiableMultivariateFunction interface itself is deprecated

Convert a DifferentiableMultivariateVectorFunction into a MultivariateDifferentiableVectorFunction.

Parameters

f:DifferentiableMultivariateVectorFunction: function to convert

Returns:MultivariateDifferentiableVectorFunction

converted function

Annotations

@Deprecated

toUnivariateDifferential back to summary

toUnivariateDifferential	back to summary
public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) Deprecated this conversion method is temporary in version 3.1, as the `DifferentiableUnivariateFunction` interface itself is deprecated Convert a `DifferentiableUnivariateFunction` into a `UnivariateDifferentiableFunction`. Note that the converted function is able to handle `DerivativeStructure` up to order one. If the function is called with higher order, a `NumberIsTooLargeException` is thrown. Parameters f:DifferentiableUnivariateFunction function to convert Returns:UnivariateDifferentiableFunction converted function Annotations @Deprecated

public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f)

Deprecated

this conversion method is temporary in version 3.1, as the DifferentiableUnivariateFunction interface itself is deprecated

Convert a DifferentiableUnivariateFunction into a UnivariateDifferentiableFunction.

Note that the converted function is able to handle DerivativeStructure up to order one. If the function is called with higher order, a NumberIsTooLargeException is thrown.

Parameters

f:DifferentiableUnivariateFunction: function to convert