坐标的数字矩阵 [英] Numpy matrix of coordinates

问题描述

我正在尝试获取坐标数组矩阵.这与numpy.meshgrid不同.例如，对于2x2的尺寸，我想要2x2x2的输出

I'm trying to get a matrix of coordinate-arrays. This is different from numpy.meshgrid. For example, for a 2x2 size I'd want the 2x2x2 output

[[[0,0],[0,1]],
 [[1,0],[1,1]]]

作为一个numpy数组.这可能看起来更清晰地读取了一个2x2元组矩阵:

as a numpy array. This probably looks and reads cleaner a 2x2 matrix of tuples:

[[(0,0),(0,1)],
 [(1,0),(1,1)]]

(除了我不认为您可以在numpy数组中包含元组，而这不是重点)

(except I don't think you can have tuples in a numpy array, and it's not the point here)

这个简单的示例可以通过切换numpy-meshgrid的输出轴(具体来说，将第一个轴移动到最后一个轴)来完成:

This simple example can be done by switching the axes of numpy-meshgrid's output (specifically, moving the first axis to be last):

np.array(np.meshgrid([0,1],[0,1])).transpose([1,2,0])

这可以很容易地推广到任意尺寸，除了meshgrid的行为不像我期望的多于2个输入.具体来说，返回的矩阵的坐标值沿轴以奇数顺序变化:

This could be easily generalized to arbitrary dimensions, except that meshgrid doesn't behave as I would expect for more than 2 inputs. Specifically, the returned matrices have coordinate values that vary along axes in an odd order:

In [627]: np.meshgrid([0,1],[0,1],[0,1])
Out[627]:
[array([[[0, 0],
        [1, 1]],

       [[0, 0],
        [1, 1]]]),
 array([[[0, 0],
        [0, 0]],

       [[1, 1],
        [1, 1]]]),
 array([[[0, 1],
        [0, 1]],

       [[0, 1],
        [0, 1]]])]

请注意，此输出的元素分别沿轴1、0和2变化.这将建立不正确的坐标矩阵；我需要输出沿轴0、1和2以此顺序变化.所以我可以做

Notice that the elements of this output vary along axes 1, 0, and 2, respectively. This will build an incorrect coordinate matrix; I would need the output to vary along axes 0, 1, and 2, in that order. So I could do

In [642]: np.array(np.meshgrid([0,1],[0,1],[0,1])).swapaxes(1,2)
Out[642]:
array([[[[0, 0],
         [0, 0]],

        [[1, 1],
         [1, 1]]],


       [[[0, 0],
         [1, 1]],

        [[0, 0],
         [1, 1]]],


       [[[0, 1],
         [0, 1]],

        [[0, 1],
         [0, 1]]]])

但是，这真的开始变得困难了，我不知道我是否可以在高维网状网格输出中依靠这个顺序. numpy.mgrid给出正确的顺序，但似乎不允许使用我需要的任意值.因此，这归结为两个问题:

But this is starting to get really hacky and I don't know if I can count on this order in higher-dimension meshgrid outputs. numpy.mgrid gives the right order, but doesn't seem to allow arbitrary values, which I will need. So this boils down to two questions:

1)是否有一种更简洁的方法，也许会缺少numpy中的某些函数，该函数会生成所描述的坐标矢量矩阵? 2)这种奇怪的排序真的是我们对Meshgrid的期望吗?关于这一点，我是否可以依靠某个规范?

1) Is there a cleaner way, maybe some function in numpy I'm missing, that will generate a matrix of coordinate-vectors as described? 2) Is this odd ordering really what we expect from meshgrid? Is there a spec to this point that I can count on?

跟着Jaime的解决方案，以下是一个更通用的函数，可以对感兴趣的任何人进行更明确的构建:

Following up on Jaime's solution, here's a more generalized function to build it a little more explicitly for anyone interested:

def build_coords(*vecs):
    coords = numpy.empty(map(len,vecs)+[len(vecs)])
    for ii in xrange(len(vecs)):
        s = np.hstack((len(vecs[ii]), np.ones(len(vecs)-ii-1)))
        v = vecs[ii].reshape(s)
        coords[...,ii] = v
    return coords

推荐答案

尝试np.meshgrid([0, 1], [0, 1], [0, 1], indexing="ij"). meshgrid文档实际上非常清楚地说明了默认的indexing="xy"与非默认的indexing="ij"相比如何产生有趣的轴顺序，因此您可以检查更多细节. (他们对为什么如此工作还不太清楚，a ...)

Try np.meshgrid([0, 1], [0, 1], [0, 1], indexing="ij"). The meshgrid docs are actually pretty explicit about how the default indexing="xy" produces a funny axis ordering as compared to the non-default indexing="ij", so you can check that for more details. (They're not as clear on why it works this way, alas...)

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