[SciPy-user] 3D density calculation

[Bernhard Voigt]

Hi Chris!

you could try a grid of unit cells that cover your phase space (x,y,z,t).
Count the number of photons per unit cell of your initial configuration and
track photons leaving and entering a particular cell. A dictionary with a
tuple of x,y,z,t coordinates obtained from integer division of the x,y,z,t
coordinates could serve as keys.

Example for 2-D:

from numpy import *
# phase space in x,y
x = arange(-100,100.1,.1)
y = arange(-100,100.1,.1)
# cell dimension in both dimensions the same
GRID_WIDTH=7.5

# computes the grid key from x,y coordinates
def gridKey(x,y):
    '''return the a tuple of x,y integer divided by GRID_WIDHT'''
    return (int(x // GRID_WIDTH), int(y // GRID_WIDTH))

# setup your grid dictionary
gridLowX, gridHighX = gridKey(min(x), max(x))
gridLowY, gridHighY = gridKey(min(y), max(y))
keys = [(i,j) for i in xrange(gridLowX, gridHighX + 1) \
            for j in xrange(gridLowY, gridHighY + 1)]
grid = dict().fromkeys(keys, 0)

# random photons
photons = random.uniform(-100.,100., (100000,2))

# count photons in each grid cell
for p in photons:
    grid[gridKey(*p)] += 1

#########################################
# in your simulation you have to keep track of where your photons
# are going to...
# (the code below won't run, it's just an example)
#########################################
oldKey = gridKey(photon)
propagate(photon)  # changes x,y coordinates of photon
newKey = gridKey(photon)
if oldKey != newKey:
    grid[oldKey] -= 1
    grid[newKey] += 1

I hope this helps! Bernhard

On 6/15/07, Chris Lee <c.j.lee at tnw.utwente.nl> wrote:
>
> Hi everyone,
>
> I was hoping this list could point me in the direction of a more
> efficient solution to a problem I have.
>
> I have 4 vectors: x, y, z, and t that are about 1 million in length
> that describe the positions of photons.  As my simulation progresses
> it updates the positions so x, y, z, and t change by an unknown (and
> unknowable) amount every update.
>
> This worked very well for its original purpose but now I need to
> calculate the photon density change over time.  Currently after each
> update, I iterate over time slices, x slices, and y slices and then
> make an histogram of z which I then stitch together to create a
> density.  However, this becomes very slow as the photons spread out
> in space and time.
>
> Does anyone know how to take such a large vector set and return a
> density efficiently?
>
>
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