# [Numpy-discussion] [Matplotlib-users] Vectorization

Benjamin Root ben.root@ou....
Fri Jul 2 13:33:28 CDT 2010

```I am moving this over to numpy-discussion maillist...

I don't have a firm answer for you, but I did notice one issue in your
code.  You call arange(len(dx) - 1) for your loops, but you probably really
need arange(1, len(dx) - 1) because you are accessing elements both after
*and* before the current index.  An index of -1 is actually valid because
that means the last element of the array, and may not be what you intended.

Ben Root

On Fri, Jul 2, 2010 at 1:15 PM, Nicolas Bigaouette <nbigaouette@gmail.com>wrote:

> Hi all,
>
> I don't really know where to ask, so here it is.
>
> I was able to vectorize the normalization calculation in quantum mechanics:
> <phi|phi>. Basically it's a volume integral of a scalar field. Using:
>
>> norm = 0.0
>> for i in numpy.arange(len(dx)-1):
>>     for j in numpy.arange(len(dy)-1):
>>         for k in numpy.arange(len(dz)-1):
>>             norm += psi[k,j,i]**2 * dx[i] * dy[j] * dz[k]
>>
> if dead slow. I replaced that with:
>
>> norm = (psi**2 *
>> dx*dy[:,numpy.newaxis]*dz[:,numpy.newaxis,numpy.newaxis]).sum()
>>
> which is almost instantanious.
>
> I want to do the same for the calculation of the kinetic energy:
> <phi|p^2|phi>/2m. There is a laplacian in the volume integral which
> complicates things:
>
>> K = 0.0
>> for i in numpy.arange(len(dx)-1):
>>     for j in numpy.arange(len(dy)-1):
>>         for k in numpy.arange(len(dz)-1):
>>             K += -0.5 * m * phi[k,j,i] * (
>>                   (phi[k,j,i-1] - 2.0*phi[k,j,i] + phi[k,j,i+1]) /
>> dx[i]**2
>>                 + (phi[k,j-1,i] - 2.0*phi[k,j,i] + phi[k,j+1,i]) /
>> dy[j]**2
>>                 + (phi[k-1,j,i] - 2.0*phi[k,j,i] + phi[k+1,j,i]) /
>> dz[k]**2
>>             )
>>
>
> My question is, how would I vectorize such loops? I don't know how I would
> manage the "numpy.newaxis" code-foo with neighbours dependency... Any idea?
>
> Thanx!
>
>
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