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Up-> CppAD AD ADValued MathOther erf

AD-> Default ad_copy Convert ADValued BoolValued VecAD base_require

ADValued-> Arithmetic std_math_ad MathOther CondExp Discrete user_atomic

MathOther-> abs sign atan2 epsilon erf pow

erf-> Erf.cpp

Headings-> Syntax Description x Operation Sequence Method Example

The AD Error Function
Syntax
y = erf(x)

Description
Returns the value of the error function which is defined by $$\mathrm{erf}(\mathit{x})=\frac{2}{\sqrt{\mathrm{\pi }}}{\int }_0^{\mathit{x}}\exp (-\mathit{t}*\mathit{t})\mathbf{d}\mathit{t}$$
x
The argument x , and the result y have one of the following paris of prototypes:
     const float                  &x,     float    y
     const double                 &x,     double   y
     const AD<Base>               &x,     AD<Base> y
     const VecAD<Base>::reference &x,     AD<Base> y

Operation Sequence
The AD of Base operation sequence used to calculate y is independent of x .

Method
This is a fast approximation (few numerical operations) with relative error bound $4\times {10}^{-4}$ ; see Vedder, J.D., Simple approximations for the error function and its inverse, American Journal of Physics, v 55, n 8, 1987, p 762-3.

Example
The file Erf.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.

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Input File: cppad/local/erf.hpp