Few questions (convolutions, 'mapping', linspace)

[Przemek Klosowski]

Hi,

I have a couple of questions that came in my recent using of Octave; I wonder
if anyone could help:

 - I want to convolute the theoretical function S(Q,w) with the experimental 
   resolution r(w), to compare the resulting Sr(Q,w) with experimental data. 
   The formula is:
                  w0
                  /
      Sr(Q,w) =   |  S(Q,w-v) r(v) dv 
                  /
                 -w0

   I was hoping to use the quad("fun",-w0,w0), where fun would be defined
   as 'function y=fun(x); y=S(Q,w-x)*r(x); endfunction'. This didn't quite
   work, as I need to access Q,w from within that function. I can't pass
   them as parameters of fun() because quad() expects only one-parameter fun;
   I couldn't figure the way to pass them as globals either.

 - I often find myself defining a function (y=fun(x)), and hoping to be able
   to 'map' (in the LISP sense) the vectors/matrices with this function, for 
   instance to plot it. The naive approach, y=f(x) for a vector/matrix 'x', 
   does not result in 

         y = [f(x(1)),  f(x(2)),  f(x(3)) ... f(x(N))],

   which is fine because the arithmetic operators in the function definition 
   have meaning for matrices as well. For vector 'x' I can always do 

         for i=1:length(x); y(i)=f(x(i)); endfor

   but I wonder if there is a neater, general way. I suppose I could be defining
   my functions to do the explicitly recognize vector arguments, but
   that still leaves the question whether I have to write explicit 'for' loops
   or is there a better way.
   
 - I noticed that the linspace operator is fairly slow: linspace(-1,1, 10000) 
takes
   25 seconds on a 150MHz r4400, while the a=(0:.0001:1); is very quick, and 
the 
   FFT of the resulting matrix is only few seconds. What is the advantage of 
linspace 
   over the range operator, and why is it so slow?



        Greetings
                        przemek