User manual

Algorithms for optimal step

DumontetVignes(function, x[, ...])

Compute an approximately optimal step for the central F.D.

GillMurraySaundersWright(function, x[, ...])

Compute an approximately optimal step for the forward F.D.

SteplemanWinarsky(function, x[, beta, args, ...])

Compute an approximately optimal step for the central F.D.

SteplemanWinarskyInitialize(algorithm[, ...])

Compute an initial step for a search algorithm

ShiXieXuanNocedalForward(function, x[, ...])

Compute an approximately optimal step for the forward F.D.

ShiXieXuanNocedalGeneral(...[, ...])

Compute an approximately optimal step for the forward F.D.

Finite Differences

FunctionWithArguments(function[, args])

Evaluate a function with extra arguments.

FiniteDifferenceFormula(function, x[, args])

Compute a derivative of the function using finite difference formula

FirstDerivativeForward(function, x[, args])

Compute the first derivative using forward finite difference formula

FirstDerivativeCentral(function, x[, args])

Compute the first derivative using central finite difference formula

SecondDerivativeCentral(function, x[, args])

Compute the second derivative using central finite difference formula

ThirdDerivativeCentral(function, x[, args])

Compute the third derivative using central finite difference formula

GeneralFiniteDifference(function, x, ...[, ...])

Create a general finite difference formula

Benchmark problems

DerivativeBenchmarkProblem(name, function, ...)

Create a benchmark problem for numerical derivatives of a function

PolynomialProblem([alpha, x, interval])

Create a polynomial derivative benchmark problem

InverseProblem([x, interval])

Create an inverse derivative benchmark problem

ExponentialProblem([x, interval])

Create an exponential derivative benchmark problem

LogarithmicProblem([x, interval])

Create a logarithmic derivative benchmark problem

SquareRootProblem([x, interval])

Create a square root derivative benchmark problem

AtanProblem([x, interval])

Create an arctangent derivative benchmark problem

SinProblem([x, interval])

Create a sine derivative benchmark problem

ScaledExponentialProblem([alpha, x, interval])

Create a scaled exponential derivative benchmark problem

GMSWExponentialProblem([x, interval])

Create an exponential derivative benchmark problem

SXXNProblem1([x, interval])

Create an exponential derivative benchmark problem

SXXNProblem2([alpha, x, interval])

Create an exponential derivative benchmark problem

SXXNProblem3([x, interval])

Create an exponential derivative benchmark problem

SXXNProblem4([x, interval])

Create an exponential derivative benchmark problem

OliverProblem1([alpha, x, interval])

Create an exponential derivative benchmark problem

OliverProblem2([x, interval])

Create an exponential derivative benchmark problem

OliverProblem3([x, interval])

Create an logarithmic derivative benchmark problem

Benchmark features

build_benchmark()

Create a list of benchmark problems.

benchmark_method(function, ...[, verbose])

Compute the first derivative on a set of test points