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MathsSpecial

Error Fn Inv

viewed 2829 times and licensed 63 times
Evaluates the inverse of the error function.
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Dependents

Info

Interface

C++

ErrorFn Inv

 
doubleerrorFn_invdoubley )[inline]
The inverse error function is defined as the function \mathrm{erf}^{-1}:(-1,1) \rightarrow \mathbb{R} which satisfies:

\left\{ \begin{array}{rcll} \mathrm{erf}\left(\mathrm{erf}^{-1}(x)\right) &=& x, &\qquad \forall x \in (-1,1)\\ \mathrm{erf}^{-1}\left(\mathrm{erf}(x)\right) &=& x, &\qquad \forall x \in \mathbb{R} \end{array}

where \displaystyle \mathrm{erf} is the error function. Some special values are:

The graph of this function is shown below.
There is an error with your graph parameters for errorFn_inv with options y=-0.99:0.99

Error Message:Function errorFn_inv failed. Ensure that: Invalid C++

The following property also holds:

where \displaystyle \mathrm{erfc}^{-1} is the inverse of the complementary error function. Based on this last formula, you may notice how the output of the example code below is linked to the example output in the errorFnC_inv module.

References:

Mathworld, http://mathworld.wolfram.com/InverseErf.html

Example 1

#include <codecogs/maths/special/errorfn_inv.h>
#include <stdio.h>
 
int main(  )
{
  // display the value of the function at important points
  printf("x = -1    y = %.15lf\n",   Maths::Special::errorFn_inv(-1.0));
  printf("x = 0     y = %.15lf\n",   Maths::Special::errorFn_inv( 0.0));
  printf("x = 1     y = %.15lf\n\n", Maths::Special::errorFn_inv( 1.0));
 
  // display several values of the function
  // at equally spaced abscissas with a step of 0.1
  for (double x = 0.1; x < 0.99; x += 0.1)
    printf("x = %.1lf   y = %.15lf\n", 
    x, Maths::Special::errorFn_inv(x));
 
  return 0;
}

Output

x = -1    y = -1.#INF00000000000
x = 0     y = 0.000000000000000
x = 1     y = 1.#INF00000000000
 
x = 0.1   y = 0.088855990494258
x = 0.2   y = 0.179143454621292
x = 0.3   y = 0.272462714726755
x = 0.4   y = 0.370807158593558
x = 0.5   y = 0.476936276204470
x = 0.6   y = 0.595116081449995
x = 0.7   y = 0.732869077959217
x = 0.8   y = 0.906193802436823
x = 0.9   y = 1.163087153676674

Parameters

ythe value at which to evaluate the function (-1 \leq y \leq 1)

Returns

The inverse of the error function.

Authors

Lucian Bentea (September 2006)
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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