Maple procedure issue

This is a discussion on Maple procedure issue within the Tech Board forums, part of the Community Boards category; I know some of you are into maple so I figured that perhaps someone might be able to help me ...

  1. #1
    and the Hat of Clumsiness GanglyLamb's Avatar
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    Maple procedure issue

    I know some of you are into maple so I figured that perhaps someone might be able to help me with the issue that I am currently having.

    Code:
    restart; 
    calcDistributionFunc := proc (f) 
        cdf := unapply(int(int(f(x)*sin(x), x = 0 .. x2), phi = 0 .. phi2), x2); 
        phi2 := 2*Pi; 
        
        cte := cdf((1/2)*Pi); 
    
        if 1 < evalf(cte) then 
            cte := 1/cte 
        end if; 
    
        cdf := apply(cdf, x); 
        cdf := cte*cdf; 
        cdf := unapply(cdf, x); 
    
        s := solve(y = cdf(x), x); 
    
        if 1 < nops([s]) then 
            b := unapply(s[1], y) 
        else 
            b := unapply(s, y) 
        end if 
    end proc
    
    calcDistributionFunc(cos(x));
    The above code works fine as long as you do not put in into a procedure, from the moment I try to put the code into a procedure and call it using calcDistributionFunc(cos(x)); I get the error:

    Error, (in solve) cannot solve expressions with int((cos(x))(x)*sin(x), x = 0 .. (1/2)*Pi) for x

    For example a function f(x) = cos(x) will yield a distribution function: arccos(sqrt(-y+1))

    In case you are wondering what it is that I am trying to do, I have a userdefined distribution function and I want to generate random numbers using this distribution by generating uniform random numbers between 0 and 1 and evaluating this random number using the calculated distribution function. This in turn is used for Monte Carlo based simulations...

    Probably I am just missing some basic tips/pointers on how to use procedures in maple. I have to admit I am more a matlab person then a maple one, but I need an analytical solution and not a numerical one. I know that using Matlab I can also perform analytical math using the symbolic link toolbox, but that would be like driving around in a Porsche 959 trying to get to the finishline of Paris-Dakar.

    Thanks in advance for any help .

  2. #2
    Epy
    Epy is offline
    Fortran lover Epy's Avatar
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    Just looking at that error message, I would guess that

    Code:
    cdf := unapply(int(int(f(x)*sin(x), x = 0 .. x2), phi = 0 .. phi2), x2);
    should really be

    Code:
    cdf := unapply(int(int(f*sin(x), x = 0 .. x2), phi = 0 .. phi2), x2);
    since it seems to be dumping cos(x) in place of "f", not "f(x)"

  3. #3
    and the Hat of Clumsiness GanglyLamb's Avatar
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    Wow, that I have been looking over this so many times... Thanks!

    Anyhow, I will have to move away from the analytical solution as finding the inverse of a function is not that straightforward anymore as soon as the function to be inverted gets quite complicated (which is the case as I am trying to fit functions to measured BSDF data).

    Seems I'm back where I started by performing my monte carlo simulations using distribution functions that are being sampled instead of using an analytical solution.

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