[pstricks] si-function

[José Emilio Vila Forcén]

Dear Herbert,

  I found very impressive your example with integration. I did't know 
that it was possible to do that. I have modified slightly the code: my 
objective is to calculate:

y(x) = \int_a^b f(x,t)dt

  In my example it is working, but I didn't test it extensively. the new 
macro is

\integrate{x_min}{x_max}(a,b){function}

where function takes two arguments: t x FUNC. For example, 1 GAUSS takes 
first the value of 'x' and lately the mean of the distribution.

a and b are the limits of integration and x_min and x_max the limits for 
the x-axis of the plot.

Regards
Jose

\documentclass{article}
\usepackage{pst-plot}
\usepackage{pst-math,pst-func}
\makeatletter
\def\cummulativeI{\pst at object{cummulativeI}}
\def\cummulativeI at i#1#2#3{%
   \begin at SpecialObj%
   \addto at pscode{
     /a #1  def
     /dx #2 #1 sub \psk at plotpoints\space div def
     /b a dx add def
     /scx { \pst at number\psxunit mul } def
     /scy { \pst at number\psyunit mul } def
     tx at FuncDict begin /SFunc { #3 } def end
     a scx 0 moveto
     \psk at plotpoints 1 sub {
       a b \psk at Simpson % a b M on Styack
       tx at FuncDict begin Simpson I end % y value on stack
       scy b scx exch lineto
       /b b dx add def
     } repeat
     stroke
   }%
   \end at SpecialObj%
}
\def\integrate{\pst at object{integrate}}
\def\integrate at i#1#2(#3,#4)#5{%
   \begin at SpecialObj%
   \addto at pscode{
     /a #3  def
     /dx #4 #3 sub \psk at plotpoints\space div def
     /b #4 def
     /aa #1 def
     /dd #2 #1 sub \psk at plotpoints\space div def
     /bb aa dd add def
     /scx { \pst at number\psxunit mul } def
     /scy { \pst at number\psyunit mul } def
     tx at FuncDict begin /SFunc { bb #5 } def end
       a b \psk at Simpson % a b M on Stack
       tx at FuncDict begin Simpson I end % y value on stack
       scy bb scx exch moveto
       /bb bb dd add def
     \psk at plotpoints 1 sub {
       a b \psk at Simpson % a b M on Stack
       tx at FuncDict begin Simpson I end % y value on stack
       scy bb scx exch lineto
       /bb bb dd add def
     } repeat
     stroke
   }%
   \end at SpecialObj%
}
\makeatother
\begin{document}

\psset{xunit=0.5cm,yunit=1cm}
\begin{pspicture}(-10,-.5)(10,4)
    \psaxes[dx=1cm,Dx=2]{->}(0,0)(-10,0)(10,4)
    \cummulativeI[plotpoints=200,Simpson=10]{-10}{10}{0 1 GAUSS}
 
\integrate[plotpoints=200,Simpson=10,linecolor=red]{-10}{10}(-10,10){1 
GAUSS}
\end{pspicture}

\end{document}