Mapping a 3-dimensional coordinate to a 1-dimensional index

I have a 3-dimensional coordinate. I'd like to map it to a 1-dimensional index. As I understand, one can use a pairing function to handle this in the 2-dimensional case. However, I've come up with the following naive implementation for the 3D case:

from numpy import *

# the size of the coordinate space
xn = 100
yn = 100
zn = 100

# make a 3 dimensional matrix of zeros
m = zeros((xn,yn,zn))

def xyz_to_index(m,x,y,z):
    # set a particular coordinate to 1
    m[x,y,z] = 1
    # find its index
    i = argmax(m)
    # rezero matrix
    m开发者_如何学Go[x,y,z] = 0
    # return 1D index
    return i

This code allows me to map from the 3D point to a 1D index as the following ipython log indicates:

In [40]: xyz_to_index(m,34,56,2)
Out[40]: 345602

So now my question is, is there a better way to do this? I suppose that traversing a matrix is not the most efficient way of going about this coordinate conversion. What would you do instead?

---

You can implement a function ravel_index() for NumPy arrays of arbitrary dimension:

def ravel_index(x, dims):
    i = 0
    for dim, j in zip(dims, x):
        i *= dim
        i += j
    return i

This function is the inverse of the function numpy.unravel_index().

For your application, you can call this function as ravel_index((x, y, z), m.shape).

---

There is a general solution provided here:

Numpy interconversion between multidimensional and linear indexing

but basically if you know the shape of your multidimensional space:

def ravel_index(x, dims):
    c = np.cumprod([1] + dims[::-1])[:-1][::-1]
    return np.dot(c,x)


s = [100,100,100] # shape of dims
ii = [34,56,2] # 3d index
jj = ravel_index(ii,s) # 1d index

---

If you know beforehand that all coordinates are in the range 0..99 you can easily calculated the index via the following function:

def xyz_to_index(x,y,z):
    return ((x * 100) + y) * 100 + z