 # Vectorization

I would first create a 3d array of the integrand, probably using scipy.signal.convolve to convolve phi with a kernel such as
[[[0,0,0],[0,1,0],[0,0,0]],
[[0,1,0],[1,-6,1],[0,1,0]],
[[0,0,0],[0,1,0],[0,0,0]]]

Then just multiply by whatever factors of dx, dy, dz, and m, and sum the 3d integrand. If dx,dy,dz are non-uniform, it is a harder problem...

Hope that helps,
-Jeff

P.S. Careful, the code you wrote will multiply by the mass instead of dividing by it.

···

On Jul 2, 2010, at 2:15 PM, Nicolas Bigaouette 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?