为什么Numpy数组中的第二维为空？ [英] Why the second dimension in a Numpy array is empty?
问题描述
为什么在这里输出
array = np.arange(3)
array.shape
是
(3,)
而不是
(1,3)
缺少维度是什么意思或等于？
What does the missing dimension means or equals?
推荐答案
如果出现混乱，（3，）不会表示缺少尺寸。逗号是单个元素元组的标准Python表示法的一部分。形状（1,3），（3，）和（3,1）是不同的，
In case there's confusion, (3,) doesn't mean there's a missing dimension. The comma is part of the standard Python notation for a single element tuple. Shapes (1,3), (3,), and (3,1) are distinct,
它们可以包含相同的3个元素，它们在计算中的使用（广播）不同，它们的打印格式不同，并且等效列表也不同：
While they can contain the same 3 elements, their use in calculations (broadcasting) is different, their print format is different, and their list equivalent is different:
In [21]: np.array([1,2,3])
Out[21]: array([1, 2, 3])
In [22]: np.array([1,2,3]).tolist()
Out[22]: [1, 2, 3]
In [23]: np.array([1,2,3]).reshape(1,3).tolist()
Out[23]: [[1, 2, 3]]
In [24]: np.array([1,2,3]).reshape(3,1).tolist()
Out[24]: [[1], [2], [3]]
我们不必停止添加一个单例尺寸：
And we don't have to stop at adding just one singleton dimension:
In [25]: np.array([1,2,3]).reshape(1,3,1).tolist()
Out[25]: [[[1], [2], [3]]]
In [26]: np.array([1,2,3]).reshape(1,3,1,1).tolist()
Out[26]: [[[[1]], [[2]], [[3]]]]
在 numpy 中，数组可以有0、1 2个或更多尺寸。 1维和2维一样逻辑。
In numpy an array can have 0, 1, 2 or more dimensions. 1 dimension is just as logical as 2.
在MATLAB中，矩阵始终具有2个dim（或更多），但是不必那样。严格来说，MATLAB甚至没有标量。仅当以MATLAB为标准时，形状为（3，）的数组才缺少维。
In MATLAB a matrix always has 2 dim (or more), but it doesn't have to be that way. Strictly speaking MATLAB doesn't even have scalars. An array with shape (3,) is missing a dimension only if MATLAB is taken as the standard.
numpy 是建立在标量和列表（可以嵌套）的Python上的。 Python列表有多少个维度？
numpy is built on Python which as scalars, and lists (which can nest). How many dimensions does a Python list have?
如果想了解历史，MATLAB是作为Fortran线性代数例程集的前端开发的。考虑到这些问题，这些例程解决了二维矩阵的概念，并且行向量和列向量很有意义。直到版本3为止，在1990年代后期，MATLAB普遍适用于2个以上的维度。
If you want to get into history, MATLAB was developed as a front end to a set of Fortran linear algebra routines. Given the problems those routines solved the concept of matrix with 2 dimensions, and row vs column vectors made sense. It wasn't until version 3.something that MATLAB was generalized to allow more than 2 dimensions (in the late 1990s).
numpy 是基于多次尝试向Python提供数组的尝试（例如数字）。这些开发人员对数组采取了更通用的方法，其中2d是人为约束。在计算机语言和数学（以及物理学）中，这是优先的。 APL于1960年代开发，最初是作为一种数学符号，然后是一种计算机语言。像 numpy 一样，其数组可以为0d或更高。 （由于在使用MATLAB之前先使用APL，所以 numpy 的方法感觉很自然。）
numpy is based on several attempts to provide arrays to Python (e.g. numeric). Those developers took a more general approach to arrays, one where 2d was an artificial constraint. That has precedence in computer languages and mathematics (and physics). APL was developed in the 1960s, first as a mathematical notation, and then as a computer language. Like numpy its arrays can be 0d or higher. (Since I used APL before I used MATLAB, the numpy approach feels quite natural.)
在 APL 中没有单独的列表或元组。因此，数组， rho A 的形状本身就是数组，而 rho rho A 是A的维数，也称为 rank 。
In APL there aren't separate lists or tuples. So the shape of an array, rho A is itself an array, and rho rho A is the number of dimensions of A, also called the rank.
http://docs.dyalog.com/14.0/Dyalog%20APL%20Idioms.pdf
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