在使用numpy进行矩阵运算的时候踩到的坑，原因是不能正确区分numpy.concatenate和numpy.stack在功能上的差异。
先说numpy.concatenate，直接看文档：
numpy.concatenate((a1, a2, ...), axis=0, out=None)
Join a sequence of arrays along an existing axis.
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Parameters
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- a1, a2, … : sequence of array_like
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The arrays must have the same shape, except in the dimension corresponding to axis (the first, by default).
axis : int, optional
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The axis along which the arrays will be joined. If axis is None, arrays are flattened before use. Default is 0.
out : ndarray, optional
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If provided, the destination to place the result. The shape must be correct, matching that of what concatenate would have returned if no out argument were specified.
Returns
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- res : ndarray
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The concatenated array.
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重点在这一句：在一个已经存在的维度上连接数组列。可见numpy.concatenate可以同时连接好几个数组，并且不会生成新的维度: along an existing axis。示例如下：
>>> a = np.array([[1, 2], [3, 4]])
>>> b = np.array([[5, 6]])
>>> np.concatenate((a, b), axis=0)
array([[1, 2],
[3, 4],
[5, 6]])
>>> np.concatenate((a, b.T), axis=1)
array([[1, 2, 5],
[3, 4, 6]])
>>> np.concatenate((a, b), axis=None)
array([1, 2, 3, 4, 5, 6])
再说numpy.stack:
numpy.stack(arrays, axis=0, out=None)
Join a sequence of arrays along a new axis.
The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension.
New in version 1.10.0.
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Parameters
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- arrays : sequence of array_like
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Each array must have the same shape.
axis : int, optional
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The axis in the result array along which the input arrays are stacked.
out : ndarray, optional
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If provided, the destination to place the result. The shape must be correct, matching that of what stack would have returned if no out argument were specified.
Returns
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- stacked : ndarray
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The stacked array has one more dimension than the input arrays.
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和concatenate不同的是，stack Joins a sequence of arrays along a new axis.也就是说stack会生成一个新的维度。而且stack适用的条件很强，数组序列必须全部有相同的shape。用例子来说明，使用最多的大概是在第0维stack：
>>> arrays = [np.random.randn(3, 4) for _ in range(10)] # arrays是一个长度为10的List，每一个元素都是(3,4)的ndarray >>> np.stack(arrays, axis=0).shape (10, 3, 4) >>> np.stack(arrays, axis=1).shape (3, 10, 4) >>> np.stack(arrays, axis=2).shape (3, 4, 10)
一个清晰的区别是返回的数组比输入数组多了一维。