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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