RE: [Visualpython-users] Speeding up a wave propagation simulation

[David S. <dsc...@vi...>]

> (Even looking back, I still don't see in the NumPy 
> documentation just why this works.  It looks to me from the 
> documentation that only "ufuncs" operate on arrays 
> element-by-element, not arbitrary user-defined functions.  
> Yet the actual behavior is exactly what I want in this case.)

Python will of course allow you to call a function with parameters of
any type, including arrays.  So the call

    pulse.gcurve.pos[:,1] = yt(x, t)

to the function

    def yt(x,t):
        ytotal = 0.0
        for k in arange(1.0, 4.0, 0.05):
            ytotal = ytotal + sin(k * x - w(k) * t)
        return ytotal

is just like writing

    ytotal = 0.0
    for k in arange(1.0, 4.0, 0.05):
        ytotal = ytotal + sin(k * x - w(k) * t)
    pulse.gcurve.pos[:,1] = ytotal

The only operations that operate on the array x in this code are
arithmetic operators and sin, which is a ufunc.  So it works fine.  If
yt() attempted to do something with x that isn't supported for arrays,
you would get a TypeError at that point.

Incidentally, if you wanted to eliminate the "for k" loop as well, you
can do it with more Numeric code:

def yt(x,t):
    k = arange(1.0, 4.0, 0.05)[:,NewAxis]
    return sum( sin(k * x - w(k) * t) )

and, of course, you could calculate k and w(k) just once.  But since
readability was one of your goals, I didn't recommend it.  (If you want
to use this code, you will have to change the first call yt(x,t) in the
plotting loop to yt(x,t)[0], since ytotal comes back a rank-1 array
instead of a scalar)

Dave