
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 ParisDakar.
Thanks in advance for any help :).

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)"

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.