How to convert the output of meshgrid to the corresponding array of points?
numpy, python
Solution
I just noticed that the documentation in numpy provides an even faster way to do this:
X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = np.vstack([X.ravel(), Y.ravel()])
This can easily be generalized to more dimensions using the linked meshgrid2 function and mapping 'ravel' to the resulting grid.
g = meshgrid2(x, y, z)
positions = np.vstack(map(np.ravel, g))
The result is about 35 times faster than the zip method for a 3D array with 1000 ticks on each axis.
Source: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html#scipy.stats.gaussian_kde
To compare the two methods consider the following sections of code:
Create the proverbial tick marks that will help to create the grid.
In [23]: import numpy as np
In [34]: from numpy import asarray
In [35]: x = np.random.rand(100,1)
In [36]: y = np.random.rand(100,1)
In [37]: z = np.random.rand(100,1)
Define the function that mgilson linked to for the meshgrid:
In [38]: def meshgrid2(*arrs):
....: arrs = tuple(reversed(arrs))
....: lens = map(len, arrs)
....: dim = len(arrs)
....: sz = 1
....: for s in lens:
....: sz *= s
....: ans = []
....: for i, arr in enumerate(arrs):
....: slc = [1]*dim
....: slc[i] = lens[i]
....: arr2 = asarray(arr).reshape(slc)
....: for j, sz in enumerate(lens):
....: if j != i:
....: arr2 = arr2.repeat(sz, axis=j)
....: ans.append(arr2)
....: return tuple(ans)
Create the grid and time the two functions.
In [39]: g = meshgrid2(x, y, z)
In [40]: %timeit pos = np.vstack(map(np.ravel, g)).T
100 loops, best of 3: 7.26 ms per loop
In [41]: %timeit zip(*(x.flat for x in g))
1 loops, best of 3: 264 ms per loop
Problem
I want to create a list of points that would correspond to a grid. So if I want to create a grid of the region from `(0, 0)` to `(1, 1)`, it would contain the points `(0, 0)`, `(0, 1)`, `(1, 0)` and `(1, 0)`. I know that that this can be done with the following code: ``` g = np.meshgrid([0,1],[0,1]) np.append(g[0].reshape(-1,1),g[1].reshape(-1,1),axis=1) ``` Yielding the result: ``` array([[0, 0], [1, 0], [0, 1], [1, 1]]) ``` My question is twofold: - Is there a better way of doing this? - Is there a way of generalizing this to higher dimensions?