Franz - 1 year ago 68
Python Question

# Variable dimensionality of a meshgrid with numpy

I try to create a meshgrid with n dimensions.
Is there a nicer way to call meshgrid with n column vectors than with the if clause I am using?

Edit: The goal is to use it for user-defined n (2-100) without writing 100 if clauses.

The second line in the if clauses reduces the grid so column(n) < column(n+1)

Example:

``````import numpy as np
dimension = 2
range = np.arange(0.2,2.4,0.1)
if dimension == 2:
grid = np.array(np.meshgrid(range,range)).T.reshape(-1,dimension)
grid = np.array(grid[[i for i in range(grid.shape[0]) if grid[i,0]<grid[i,1]]])
elif dimension == 3:
grid = np.array(np.meshgrid(range,range,range)).T.reshape(-1,dimension)
grid = np.array(grid[[i for i in range(grid.shape[0]) if grid[i,0]<grid[i,1]]])
grid = np.array(grid[[i for i in range(grid.shape[0]) if grid[i,1]<grid[i,2]]])
``````

Edit: The solution was posted below:

``````dimension = 2
r = np.arange(0.2,2.4,0.1)
grid=np.array(np.meshgrid(*[r]*n)).T.reshape(-1,n)

for i in range(0,n-1):
grid = [g for g in grid if g[i]<g[i+1]]
``````

I haven't fully absorbed your approach and goals, but here's a partial simplification

``````In [399]: r=np.arange(3)           # simpler range for example
In [400]: grid=np.meshgrid(*[r]*2)   # use `[r]*3` for 3d case
In [401]: grid=np.array(grid).T.reshape(-1,2)
In [402]: np.array([g for g in grid if g[0]<g[1]])  # simpler comprehensions
Out[402]:
array([[0, 1],
[0, 2],
[1, 2]])
``````

`itertools.product` makes that 2 column grid easier:

``````In [403]: from itertools import product
In [404]: np.array([g for g in product(r,r) if g[0]<g[1]])
Out[404]:
array([[0, 1],
[0, 2],
[1, 2]])
``````

That is, your `grid` before filtering is

``````In [407]: grid
Out[407]:
array([[0, 0],
[0, 1],
[0, 2],
[1, 0],
[1, 1],
[1, 2],
[2, 0],
[2, 1],
[2, 2]])
``````

and `product` is

``````In [406]: list(product(r,r))
Out[406]: [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
``````

`product` has a `repeat` parameter that makes this even easier:

``````In [411]: list(product(r,repeat=2))
Out[411]: [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
``````

You still need the `if` clause to apply the 2 step filtering for dim=3. I guess the could written iteratively

``````for i in range(0,dimension-1):
grid = [g for g in grid if g[i]<g[i+1]]
``````
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