Indexing and slicing

From a data table you almost always need only a part: one column, the first rows, the objects priced above a threshold. A numpy array returns such parts by index, like a list, but it can do more:

import numpy as np

a = np.array([120, 95, 300, 210, 80])
print(a[0], a[-1])  # 120 80
print(a[1:3])  # [ 95 300]
print(a[:2], a[3:])  # [120  95] [210  80]

The index 0 is the first element, and -1 is the last. The slice a[1:3] takes the elements from index 1 up to index 3, not including it. An omitted start means "from the first element", and an omitted end means "to the last". A slice of an array is an array too, and it has shape, sum and mean as well.

Rows and columns

A two-dimensional array takes two indices separated by a comma: the row first, then the column. A colon in place of an index means "all": X[:, 1] is the second column of every row. A slice of rows keeps all the columns, so X[1:] is the table without its first row.

X = np.array([[1.5, 20.0], [2.0, 35.0], [0.5, 12.0]])
print(X[1, 0])  # 2.0
print(X[:, 1])  # [20. 35. 12.]
print(X[1:].shape)  # (2, 2)

In machine learning, a row is usually an object and a column is a feature. So X[:, 1] reads as "the second feature of every object". A slice and an index can be combined: X[:2, 1] is the second feature of the first two objects.

Boolean mask

Comparing an array with a number runs for each element and gives an array of True and False. Such an array is called a boolean mask. If you pass a mask in place of an index, the elements marked True remain:

mask = a > 100
print(mask)  # [ True False  True  True False]
print(a[mask])  # [120 300 210]
print(mask.sum(), a[mask].sum())  # 3 630
print(a[(a > 100) & (a < 250)])  # [120 210]

A mask keeps the order: a[mask] lists the matching values as they stood in a. The sum of a mask counts True as 1 and False as 0. So mask.sum() is the number of matching elements, and a[mask].sum() is the sum of their values.

The & operator ("and") joins two conditions. Each comparison goes in parentheses: without them the expression raises ValueError.

Common mistake

The first feature is taken with a single index:

first_feature = X[0]  # ✗
print(first_feature)  # [ 1.5 20. ]

Python reports no error, but X[0] is the first row, that is, every feature of the first object. The first index always selects rows, even when the second is omitted. The first feature of every object is X[:, 0].