[Numpy-discussion] Multiple Boolean Operations

[Angus McMorland]

2008/5/22 Andrea Gavana <andrea.gavana at gmail.com>:
> Hi All,
>
>    I am building some 3D grids for visualization starting from a much
> bigger grid. I build these grids by satisfying certain conditions on
> x, y, z coordinates of their cells: up to now I was using VTK to
> perform this operation, but VTK is slow as a turtle, so I thought to
> use numpy to get the cells I am interested in.
> Basically, for every cell I have the coordinates of its center point
> (centroids), named xCent, yCent and zCent. These values are stored in
> numpy arrays (i.e., if I have 10,000 cells, I have 3 vectors xCent,
> yCent and zCent with 10,000 values in them). What I'd like to do is:
>
> # Filter cells which do not satisfy Z requirements:
> zReq = zMin <= zCent <= zMax
>
> # After that, filter cells which do not satisfy Y requirements,
> # but apply this filter only on cells who satisfy the above condition:
>
> yReq = yMin <= yCent <= yMax
>
> # After that, filter cells which do not satisfy X requirements,
> # but apply this filter only on cells who satisfy the 2 above conditions:
>
> xReq = xMin <= xCent <= xMax
>
> I'd like to end up with a vector of indices which tells me which are
> the cells in the original grid that satisfy all 3 conditions. I know
> that something like this:
>
> zReq = zMin <= zCent <= zMax
>
> Can not be done directly in numpy, as the first statement executed
> returns a vector of boolean. Also, if I do something like:
>
> zReq1 = numpy.nonzero(zCent <= zMax)
> zReq2 = numpy.nonzero(zCent[zReq1] >= zMin)
>
> I lose the original indices of the grid, as in the second statement
> zCent[zReq1] has no more the size of the original grid but it has
> already been filtered out.
>
> Is there anything I could try in numpy to get what I am looking for?
> Sorry if the description is not very clear :-D
>
> Thank you very much for your suggestions.

How about (as a pure numpy solution):

valid = (z >= zMin) & (z <= zMax)
valid[valid] &= (y[valid] >= yMin) & (y[valid] <= yMax)
valid[valid] &= (x[valid] >= xMin) & (x[valid] <= xMax)
inds = valid.nonzero()

?
-- 
AJC McMorland, PhD candidate
Physiology, University of Auckland

(Nearly) post-doctoral research fellow
Neurobiology, University of Pittsburgh