[SciPy-User] vectorizing a function with non scalar arguments

[David Warde-Farley]

On 10-Aug-09, at 5:28 PM, Luke wrote:

> I have a function of the following form:
> def f(q, qd, parameter_list):
>    # Unpacking the parameters
>    m, g, I11, I22, I33 = parameter_list
>    # Unpacking the qdots
>    q1, q2, q3, q4, q5, q6 = q
>    q1p, q2p, q3p, q4p, q5p, q6p = qd
>    ....Some calculations to determine u1,u2,u3,u4,u5,u6....
>    return [u1, u2, u3, u4, u5, u6]

We'd really need to see "...Some calculations..." but if it's  
something that's expressible as simple arithmetic/calls to numpy  
ufuncs, then it's probable that you can pull this off.

> I would like to vectorize this function so that I could pass it:
> 1)  q and qd as a 2-d numpy arrays of shape (n, 6)
> 2) parameter_list as a 1-d numpy array of shape (5,)

hsplit() and hstack() to unpack/pack the 2D arrays, respectively  
(though there are more memory efficient/cache friendly ways, if you  
care about speed).

> and it would return a 2-d numpy array of shape (n, 6)
>
> parameter_list is a bunch of constants that don't change, while q and
> qd are the things that are different between say q[n, :] and q[n+1,
> :].

> I realize that I can use a for loop to loop from 0 to n-1.
>
> My question is whether there a way to use vectorize (or some other
> decorator), to obtain the behavior?  Or is there another nice method
> that people might be able to recommend?

Again, if you split into 1d arrays and are just doing arithmetic on  
them (or you use numpy functions that can take scalar or vector  
arguments) then it should "vectorize itself". But it might be helpful  
if you have any helper functions of one scalar variable that you need  
to evaluate across an entire array of q1's, etc.

> The documentation for vectorize is very sparse and seems like it is
> geared only towards function which have scalar arguments.

Yes, 'vectorize' won't do it for you in this case.

David