numpy performance and list comprehension

[irstas at gmail.com]

On Apr 3, 5:42 pm, "TG" <gir... at gmail.com> wrote:
> Hi there.
>
> Reading the page on python performance (http://scipy.org/PerformancePython
> ) made me realize that I can achieve tremendous code acceleration with
> numpy just by using "u[:,:]" kind of syntax the clever way.
>
> Here is a little problem (Oja's rule of synaptic plasticity)
>
> * W is a matrix containing the weights of connections between elements
> i
> and j
> * V is an array containing the values of elements
>
> I want to make W evolve with this rule :
>
> dW[i,j] / dt = alpha * (V[i] * V[j] - W[i,j] * V[i]^2)
>
> (don't pay attention to the derivate and stuff)
>
> So, how would you write it in this nifty clever way ?
>
> As a begining I wrote this :
>
>   W += V.flatten().reshape((V.size,1)) *
> V.flatten().reshape((1,V.size))
>
> But it is not complete and, I guess, not efficient.

alpha * (V[i] * V[j] - W[i,j] * V[i]^2) =
alpha * V[i] * (V[j] - W[i,j] * V[i])

Assuming that V is a column vector, you could do it like this:

V = array([[5],[3],[7]])
W = array([[1,5,3],[2,2,7],[3,9,8]])
W += alpha * V * (transpose(V) - W * V)