Creating a numpy array of 3D coordinates from three 1D arrays

Question

Suppose I have three arbitrary 1D arrays, for example:

x_p = np.array((1.0, 2.0, 3.0, 4.0, 5.0))
y_p = np.array((2.0, 3.0, 4.0))
z_p = np.array((8.0, 9.0))
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Answer 1

To use numpy mesh grid on the above example the following will work:

np.vstack(np.meshgrid(x_p,y_p,z_p)).reshape(3,-1).T

Numpy meshgrid for grids of more then two dimensions require numpy 1.7. To circumvent this and pulling the relevant data from the source code.

def ndmesh(*xi,**kwargs):
    if len(xi) < 2:
        msg = 'meshgrid() takes 2 or more arguments (%d given)' % int(len(xi) > 0)
        raise ValueError(msg)

    args = np.atleast_1d(*xi)
    ndim = len(args)
    copy_ = kwargs.get('copy', True)

    s0 = (1,) * ndim
    output = [x.reshape(s0[:i] + (-1,) + s0[i + 1::]) for i, x in enumerate(args)]

    shape = [x.size for x in output]

    # Return the full N-D matrix (not only the 1-D vector)
    if copy_:
        mult_fact = np.ones(shape, dtype=int)
        return [x * mult_fact for x in output]
    else:
        return np.broadcast_arrays(*output)

Checking the result:

print np.vstack((ndmesh(x_p,y_p,z_p))).reshape(3,-1).T

[[ 1.  2.  8.]
 [ 1.  2.  9.]
 [ 1.  3.  8.]
 ....
 [ 5.  3.  9.]
 [ 5.  4.  8.]
 [ 5.  4.  9.]]

For the above example:

%timeit sol2()
10000 loops, best of 3: 56.1 us per loop

%timeit np.vstack((ndmesh(x_p,y_p,z_p))).reshape(3,-1).T
10000 loops, best of 3: 55.1 us per loop

For when each dimension is 100:

%timeit sol2()
1 loops, best of 3: 655 ms per loop
In [10]:

%timeit points = np.vstack((ndmesh(x_p,y_p,z_p))).reshape(3,-1).T
10 loops, best of 3: 21.8 ms per loop

Depending on what you want to do with the data, you can return a view:

%timeit np.vstack((ndmesh(x_p,y_p,z_p,copy=False))).reshape(3,-1).T
100 loops, best of 3: 8.16 ms per loop