Name

assert_atancond — Computes the condition number of the atan function.

Calling Sequence

   [c,y] = assert_atancond ( x )
   
   

Parameters

x :

a n-by-m matrix of doubles

c :

a n-by-m matrix of doubles, the condition number

y :

a n-by-m, matrix of doubles, the function values

Description

Computes the condition number of the atan function. The atan function is well conditionned: it always has a condition number lower than 1.

<latex> \begin{eqnarray} c(x) = \left| \frac{x}{\sqrt{1+x^2}\arctan(x)} \right| \end{eqnarray} </latex>

Examples

[c,y] = assert_atancond ( 0 )        // c=1
[c,y] = assert_atancond ( 0.5 )      // c~1

assert_plotcond ( "atan" , linspace(-10,10,1000) );

   

Authors

Michael Baudin, DIGITEO, 2010