numpy performance and list comprehension

[TG]

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.

[irstas]

On Apr 3, 5:42 pm, "TG" <[e-mail]:

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)

[Robert Kern]

TG 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 ?

irstas is correct. I'm just going to show off another feature of numpy,
numpy.newaxis.

import numpy as np

V = np.array([1, 2, 3])
VT = V[:, np.newaxis] # VT.shape == (3, 1)

W = np.array([[1,2,3], [4,5,6], [7,8,9]])

dWdt = alpha * VT*(V - W*VT)

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco