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Up-> CppAD AD ADValued unary_standard_math erf

AD-> ad_ctor ad_assign Convert ADValued BoolValued VecAD base_require

ADValued-> Arithmetic unary_standard_math binary_math CondExp Discrete numeric_limits atomic

unary_standard_math-> acos asin atan cos cosh exp log log10 sin sinh sqrt tan tanh abs acosh asinh atanh erf expm1 log1p sign

erf-> erf.cpp

Headings-> Syntax Description x, y CPPAD_USE_CPLUSPLUS_2011 CPPAD_USE_CPLUSPLUS_2011.true CPPAD_USE_CPLUSPLUS_2011.false Example

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@The Error Function
Syntax
y = erf(x)

Description
Returns the value of the error function which is defined by @[@ {\rm erf} (x) = \frac{2}{ \sqrt{\pi} } \int_0^x \exp( - t * t ) \; {\bf d} t @]@

x, y
See the possible types for a unary standard math function.

CPPAD_USE_CPLUSPLUS_2011

true
If this preprocessor symbol is true (1), and x is an AD type, this is an atomic operation .

false
If this preprocessor symbol is false (0), CppAD uses 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/core/erf.hpp