import numpy as np
a = np.arange(6) # [0 1 2 3 4 5]
a + a # [ 0 2 4 6 8 10]
a - 1 # [-1 0 1 2 3 4]
a * 6 # [ 0 6 12 18 24 30]
# gradient
x = np.array([2, 4, 5]) # [2 4 5]
y = np.array([6, 2, 8]) # [6, 2, 8]
np.gradient(x) # [ 2. 1.5 1. ] (i.e. (4 - 2) / 1, (5 - 2) / 2, (5 - 4)/ 1)
np.gradient(y) # [-4. 1. 6.] (i.e. (2 - 6) / 1, (8 - 6) / 2, (8 - 2)/ 1)
# numerical derivative
np.gradient(y) / np.gradient(x) # [-2. 0.66666667 6. ]
# broadcasting
b = np.arange(4)
b.shape = (2, 2)
# [[0 1]
# [2 3]]
v = np.array([[2],[4]])
# [[2]
# [4]]
# scalar (multiplication)
b * v
# [[ 0 2]
# [ 8 12]]
# dot product
np.dot(b, v)
# [[ 4]
# [16]]
# operations on higher dimensions
matrix = np.arange(12)
matrix.shape = (4, 3)
# [[ 0 1 2]
# [ 3 4 5]
# [ 6 7 8]
# [ 9 10 11]]
row = np.array([16, 17, 18])
# [16 17 18]
matrix + row
# [[16 18 20]
# [19 21 23]
# [22 24 26]
# [25 27 29]]