python - 矩阵和数组的 NumPy 点积

Question

来自 numpy 的文档:https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot

numpy.dot(a, b, out=None)

Dot product of two arrays. Specifically,

• If both a and b are 1-D arrays, it is inner product of vectors (without complex conjugation).

• If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred.

• If either a or b is 0-D (scalar), it is equivalent to multiply and using numpy.multiply(a, b) or a * b is preferred.

• If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.

• If a is an N-D array and b is an M-D array (where M>=2), it is a sum product over the last axis of a and the second-to-last axis of b:

根据第四点，如果我们取二维数组 A 和一维数组 B 的点积，我们应该取 A 列和 B 行的和积，因为 A 的最后一个轴是列，对吗？
然而，当我在 Python IDLE 中尝试这个时，这是我的输出:

>>> a
    array([[1, 2],
           [3, 4],
           [5, 6]])
>>> b
    [1, 2]
>>> a.dot(b)
    array([ 5, 11, 17])

我预计这会引发错误，因为 a 的列的维度大于 b 的行的维度。

Answer 1

If a is an N-D array and b is a 1-D array, it is a sum product over the last axis of a and b.

a的最后一个轴有尺寸 2:

>>> a.shape
(3, 2)

匹配 b s 大小。
请记住:numpy 中多维数组的第一个轴是“向下”。一维数组在 numpy 中水平显示，但我认为通常最好将它们视为垂直向量。这是正在计算的内容: