numpy中的broadcast

关于broadcast，官方文档描述如下：

Each universal function takes array inputs and produces array outputs by performing the core function element-wise
on the inputs. Standard broadcasting rules are applied so that inputs not sharing exactly the same shapes can still be
usefully operated on. Broadcasting can be understood by four rules:
1. All input arrays with ndim smaller than the input array of largest ndim, have 1’s prepended to their shapes.
2. The size in each dimension of the output shape is the maximum of all the input sizes in that dimension.
3. An input can be used in the calculation if its size in a particular dimension either matches the output size in that
dimension, or has value exactly 1.
4. If an input has a dimension size of 1 in its shape, the first data entry in that dimension will be used for all
calculations along that dimension. In other words, the stepping machinery of the ufunc will simply not step
along that dimension (the stride will be 0 for that dimension).
Broadcasting is used throughout NumPy to decide how to handle disparately shaped arrays; for example, all arith-
metic operations (+, -, * , ...) between ndarrays broadcast the arrays before operation. A set of arrays is called
“broadcastable” to the same shape if the above rules produce a valid result, i.e., one of the following is true:
1. The arrays all have exactly the same shape.
2. The arrays all have the same number of dimensions and the length of each dimensions is either a common length
or 1.
3. The arrays that have too few dimensions can have their shapes prepended with a dimension of length 1 to satisfy
property 2.

Example
If a.shape is (5,1), b.shape is (1,6), c.shape is (6,) and d.shape is () so that d is a scalar, then a, b, c, and d
are all broadcastable to dimension (5,6); and
• a acts like a (5,6) array where a[:,0] is broadcast to the other columns,
• b acts like a (5,6) array where b[0,:] is broadcast to the other rows,
• c acts like a (1,6) array and therefore like a (5,6) array where c[:] is broadcast to every row, and finally,

这里面对于形状的描述都是很完整的，但是有时候我们也见到这样的定义
a = np.zeros((2,))

print(a)

array([0.,0.0])

注意只有一个中括号，但是我们定义

a = np.zeros((2,1))的时候

print(a)

array([[0,],[0.]])

默认情况下，a = np.zeros((2,))定义的是一个向量，它的形状跟(2,1)是不一样的，要转型的话，默认是转成（1,2）的！！！

numpy的数组存储默认是跟C 语言一样，行优先的，所以向量默认是行向量，也可以修改成FORTRAN那种列优先的方式！