Re: numerical Lua?

I am pleased at how complete your port is.  You've overloaded arithmetic operators and have even included support for N-d arrays. It is almost as easy to use as Matlab!  However there is still a performance issue which surprised me.  On my windows xp box  (amd x2 3800) I ran a simple benchmark that inverts some matrices and performs some other calculations.  I then ran the equivalent code in Matlab 6.5.

The results are
NumLua 24 sec.s
Matlab. 15.2 sec.s

here's the code for each

LUA

u0 = os.time()
x = matrix(100,100)
I = matrix.eye(100)
for i,j in x:entries() do
                x[i][j] = math.random()
end
for q=1,1000 do
        x = I + matrix.inv(x)
end
u1 = os.time()
print(u1-u0)

Matlab
tic ;
x = rand(100,100) ;
I = eye(100) ;
for q=1:1000
    x = I + inv(x) ;
end
toc


Now since I used your binary distribution I'm not using tuned BLAS libraries, but then again neither is Matlab.  (I think 6.5 uses Atlas but I'm not sure).  Your code does a lot of type checking, but then again so does Matlabs.  I would have expected Matlab to incur more overhead and therefore the LUA code to be more competitive.  

One of the big attractions for using LUA for numerical applications is it's easy interface to C, (with the help of maybe tolua or SWIG).  With C doing the heavy number crunching, one can get a factor of 5 or 6 improvment in speed over Matlab.  (Contrary to the claims of some speed is still of huge importance for numerical applications.  I have Matlab scripts that take 2 days to run, even on my overclocked dual core athlon)

LUA is great for configuration and high level logic.  I have used it this way before with great success.  The problem now with the NumLua approach,  with all the syntactic sugar, is that an overhead penalty is being paid that defeats the purpose of using LUA.  If we want free numerical software,  SciPy is a lot more mature and also has a nice C interface.