Python Numpy 之廣播機制

對兩個數組使用廣播機制要遵守下列規則：

1. 如果數組的秩不同，使用1來將秩較小的數組進行擴展，直到兩個數組的尺寸的長度都一樣。
2. 如果兩個數組在某個維度上的長度是一樣的，或者其中一個數組在該維度上長度為1，那么我們就說這兩個數組在該維度上是相容的。
3. 如果兩個數組在所有維度上都是相容的，他們就能使用廣播。
4. 如果兩個輸入數組的尺寸不同，那么注意其中較大的那個尺寸。因為廣播之后，兩個數組的尺寸將和那個較大的尺寸一樣。
5. 在任何一個維度上，如果一個數組的長度為1，另一個數組長度大於1，那么在該維度上，就好像是對第一個數組進行了復制。

作者：杜客
鏈接：https://zhuanlan.zhihu.com/p/20878530
來源：知乎
著作權歸作者所有。商業轉載請聯系作者獲得授權，非商業轉載請注明出處。

import numpy as np

# Compute outer product of vectors
v = np.array([1,2,3])  # v has shape (3,)
w = np.array([4,5])    # w has shape (2,)
# To compute an outer product, we first reshape v to be a column
# vector of shape (3, 1); we can then broadcast it against w to yield
# an output of shape (3, 2), which is the outer product of v and w:
# [[ 4  5]
#  [ 8 10]
#  [12 15]]
print np.reshape(v, (3, 1)) * w

# Add a vector to each row of a matrix
x = np.array([[1,2,3], [4,5,6]])
# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),
# giving the following matrix:
# [[2 4 6]
#  [5 7 9]]
print x + v

# Add a vector to each column of a matrix
# x has shape (2, 3) and w has shape (2,).
# If we transpose x then it has shape (3, 2) and can be broadcast
# against w to yield a result of shape (3, 2); transposing this result
# yields the final result of shape (2, 3) which is the matrix x with
# the vector w added to each column. Gives the following matrix:
# [[ 5  6  7]
#  [ 9 10 11]]
print (x.T + w).T

# Another solution is to reshape w to be a row vector of shape (2, 1);
# we can then broadcast it directly against x to produce the same
# output.
print x + np.reshape(w, (2, 1))

# Multiply a matrix by a constant:
# x has shape (2, 3). Numpy treats scalars as arrays of shape ();
# these can be broadcast together to shape (2, 3), producing the
# following array:
# [[ 2  4  6]
#  [ 8 10 12]]
print x * 2