Projecting Coordinates in Numpy array

Question

So I have come across a rather large bottle neck in my software. I have a set of co-ordinates in cords where each row corresponds to X,Y,Z co-ordinates. Each co-ordinate in cords has a defined area in atom_proj. The atoms variable corresponds to the cords variable and provides the key to the atom_proj.

I project the co-ordinates onto the grid array then rotate and repeat until the number of rotations is satisfied. I only project the X and Z co-ordinates ignoring the Y.

I have simplified version of my code below. The code runs relatively quick for small co-ordinate sets and number of rotations. But can take a long time if both co-ordinate set and rotation list is large. The number of co-ordinates can vary from a few hundred to tens of thousands. I project the area on the grid over a number or rotations to produce a heat map. An example of the heat map for a co-ordinate set is also shown below.

Question:

(i) - How can I decrease the projection time of the co-ordinates onto the matrix

(ii) - Is there a more pythonic way of applying the co-ordinate area to the grid rather than array splicing?

import numpy as np
cords = np.array([[5,4,5],[5,4,3],[6,4,6]])
atoms = np.array([['C'],['H'],['C']])
atom_proj = {'H':np.array([[0,0,0,0,0],[0,0,1,0,0],[0,1,1,1,0],[0,0,1,0,0],[0,0,0,0,0]]),'C':np.array([[0,0,0,0,0,0,0],[0,0,0,0,0,0,0],[0,0,1,1,1,0,0],[0,0,1,1,1,0,0],[0,0,1,1,1,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0,0]])}

grid = np.zeros((10,10))

for rot in xrange(1,10): 
    # This for loop would contain a list of list of rotations to apply which are calculated before hand.
    # apply rotation
    for values in zip(cords, atoms):
        atom_shape = np.shape(atom_proj[values[1][0]])
        rad = (atom_shape[0]-1)/2                                
        grid[values[0][2]-rad:values[0][2]+rad+1,values[0][0]-rad:values[0][0]+rad+1] += atom_proj[values[1][0]]    
print grid

Heat map:

Answer 1

Something like this should work for the inner loop

extruded = np.zeros((N, 10,10))
extruded[range(N), cords[:,2], cords[:,0]] = 1

grid = np.zeros((10,10))
for atom, proj in atom_proj.iteritems():
    centers = extruded[atoms==atom].sum(0)
    projected = nd.convolve(centers, proj)
    grid += projected

A couple notes:

• There's still a loop, but it is through the length-2 array of atom types, not the length-N array of individual atoms.
• I've left out the for rot in [] loop, since it wasn't doing anything here, but it should fit back in just fine.
• This works by putting a one at the central location of each atom, in a stack of grids. Then, for each atom type, those ones are all added. Then, as @Joe suggested, the atom projection is convolved with those centers.
• For testing, my atoms is 1d, yours is 2d. Not sure if this was on purpose or not.
• Below, I've also added a third version, which is your algorithm but with variables that I was able to understand, it's called OP_simplified

Here's the full suite:

import numpy as np
import scipy.ndimage as nd

N = 1000
cords = np.random.randint(3, 7, (N, 3)) #np.array([[5,4,5],[5,4,3],[6,4,6]])
atoms = np.random.choice(list('HC'), N) #np.array([['C'],['H'],['C']])
atom_proj = {'H': np.array([[0,0,0,0,0],
                            [0,0,1,0,0],
                            [0,1,1,1,0],
                            [0,0,1,0,0],
                            [0,0,0,0,0]]),
             'C': np.array([[0,0,0,0,0,0,0],
                            [0,0,0,0,0,0,0],
                            [0,0,1,1,1,0,0],
                            [0,0,1,1,1,0,0],
                            [0,0,1,1,1,0,0],
                            [0,0,0,0,0,0,0],
                            [0,0,0,0,0,0,0]])}

def project_atom(cords, atoms, atom_proj):
    extruded = np.zeros((N, 10,10))
    extruded[range(N), cords[:,2], cords[:,0]] = 1
    grid = np.zeros((10,10))
    for atom, proj in atom_proj.iteritems():
        grid += nd.convolve(extruded[atoms.squeeze()==atom].sum(0), proj, mode='constant')
    return grid

def OP_simplified(cords, atoms, atom_proj):
    rads = {atom: (proj.shape[0] - 1)/2 for atom, proj in atom_proj.iteritems()}
    grid = np.zeros((10,10))
    for (x,y,z), atom in zip(cords, atoms):
        rad = rads[atom]
        grid[z-rad:z+rad+1, x-rad:x+rad+1] += atom_proj[atom]
    return grid

def OP(cords, atoms, atom_proj):
    grid = np.zeros((10,10))
    for values in zip(cords, atoms):
        atom_shape = np.shape(atom_proj[values[1][0]])
        rad = (atom_shape[0]-1)/2
        grid[values[0][2]-rad:values[0][2]+rad+1,values[0][0]-rad:values[0][0]+rad+1] += atom_proj[values[1][0]]
    return grid

It works!

In [957]: np.allclose(OP(cords, atoms, atom_proj), project_atom(cords, atoms, atom_proj))
Out[957]: True

And timing:

In [907]: N = 1000

In [910]: timeit OP(cords, atoms, atom_proj)
10 loops, best of 3: 30.7 ms per loop

In [911]: timeit project_atom(cords, atoms, atom_proj)
100 loops, best of 3: 2.97 ms per loop

In [913]: N = 10000

In [916]: timeit project_atom(cords, atoms, atom_proj)
10 loops, best of 3: 33.3 ms per loop

In [917]: timeit OP(cords, atoms, atom_proj)
1 loops, best of 3: 314 ms per loop