NumPy for numerical computing

NumPy provides the ndarray, a fixed-type, contiguous n-dimensional array. Vectorised operations run in compiled C over contiguous memory, which is why they are usually much faster than equivalent Python loops over lists.

Useful functions: np.arange(n) for integers 0 to n-1, np.linspace(a, b, k) for k evenly spaced values from a to b, reshape to change shape, np.eye(n) for an identity matrix, np.argsort for sorting indices.

Broadcasting lets arithmetic work on arrays of different shapes by stretching dimensions of size 1 without copying data.

import numpy as np
a = np.arange(12).reshape(3, 4)
print(a.sum(axis=0))
print(a.sum(axis=1))
x = np.arange(5)
s = x[1:4]
s[0] = 99
print(x.tolist())

Output: [12 15 18 21], then [ 6 22 38], then [0, 99, 2, 3, 4]. The axis argument names the dimension that is collapsed: axis=0 sums down the rows giving one value per column, axis=1 sums across columns giving one value per row.

Basic slices are views, so writing into s changes x; use .copy() for an independent array.

Exam trap: confusing axis=0 with row sums, and assuming a slice is a copy.