Math E and function Sigmoid()

[Antonio Linares]

https://www.lemoda.net/c/maths-constants/

Code: Select all  Expand view

#include "FiveWin.ch"

function Main()

   MsgInfo( Math_E() )

return nil

#pragma BEGINDUMP

#include <hbapi.h>
#include <math.h>

HB_FUNC( MATH_E )
{
   hb_retnd( M_E );
}

#pragma ENDDUMP

[Antonio Linares]

function Sigmoid( nValue )

return 1 / ( 1 + Math_E() ^ ( -nValue / 1 ) )

[Antonio Linares]

Sigmoid demo:

sigmoid.prg

Code: Select all  Expand view

#include "FiveWin.ch"

function Main()

   local n

   for n = 1 to 20
      MsgInfo( Sigmoid( If( n % 2 == 0, -1, 1 ) * nRandom() / nRandom() ) )
   next  
 
return nil

function Sigmoid( nValue )

return 1 / ( 1 + Math_E() ^ ( -nValue / 1 ) )

#pragma BEGINDUMP

#include <hbapi.h>
#include <math.h>

HB_FUNC( MATH_E )
{
   hb_retnd( M_E );
}

#pragma ENDDUMP

[Antonio Linares]

https://en.wikipedia.org/wiki/Sigmoid_function

A wide variety of sigmoid functions have been used as the activation function of artificial neurons

[Enrico Maria Giordano]

function Sigmoid( nValue )

return 1 / ( 1 + Math_E() ^ ( -nValue / 1 ) )

Simplified:

Code: Select all  Expand view

return 1 / ( 1 + Math_E()  ^ -nValue )

EMG

[Antonio Linares]

thanks

[Antonio Linares]

function dSigmoid( n ) --> returns the derivative of the sigmoid function

Code: Select all  Expand view

function dSigmoid( nValue )

   local n := Sigmoid( nValue )

return n * ( 1 - n )

[Antonio Linares]

Example

Code: Select all  Expand view

function Main()

   local n

   SET DECIMALS TO 10

   for n = 1 to 10
      ? Sigmoid( n ), dSigmoid( n )
   next

return nil

function Sigmoid( nValue )

return 1 / ( 1 + Math_E()  ^ -nValue )

function dSigmoid( nValue ) // returns the derivative of the sigmoid function

   local n := Sigmoid( nValue )

return n * ( 1 - n )
 

0.7310585786 0.19661193324148180000
0.8807970780 0.10499358540350660000
0.9525741268 0.04517665973091220000
0.9820137900 0.01766270621329111000
0.9933071491 0.00664805667079003200
0.9975273768 0.00246650929135993100
0.9990889488 0.00091022118012178410
0.9996646499 0.00033523767075636810
0.9998766054 0.00012337934976493020
0.9999546021 0.00004539580773590766