Course 1.1Lesson 3 of 5

Indexing, slices and masks

Indexing and slicing work for arrays as for lists: a[0] is the first, a[-1] the last, a[1:4] is a slice, a[::2] takes every second one and a[::-1] reverses. A slice of an array is a view of the same numbers and not a copy, so changing the slice changes the original, and copy makes a real copy. A boolean mask such as a[a greater than 50] picks the numbers for which the condition is True. Conditions combine with & for and, | for or and ~ for not, and each condition needs brackets. Assigning to a mask changes only the chosen places. np.where chooses between two values for every place, or gives the places where a condition is True, and np.clip keeps the numbers between two limits.

about 35 min1 simulation2 practice questions

Lesson 3 of 5Show all lessons

Try the code and the simulations beside the lesson.

What you will be able to do

After this lesson you can

pick numbers from an array by place, with indexes and slices,
know when a slice changes the original array,
pick the numbers that pass a test with a boolean mask, and
use np.where and np.clip.

Indexing and slices

Predict first. What does a[::-1] give? Then run it.

If you know lists, there is nothing new here.

a[0] is the first number, and a[-1] is the last.
a[1:4] is a slice: the places 1, 2 and 3. The stop (4) is not included.
a[:3] is the first three, and a[3:] is everything from place 3.
a[::2] takes every second number, and a[::-1] goes backwards.
You can assign to a slice. a[1:3] = 0 puts zero in two places at once.

A slice is a window, not a copy

For a list, a slice is a new list. For an array, a slice is a view: a window on the same numbers. When the program sets window[0] = 99, the first place of the window is the place 1 of the original, and the original changes too: [ 1 99 3 4 5].

This is by design. It saves memory, because a big array is not copied. But it means that you must be careful. If you want a slice that you can change without touching the original, ask for a copy: original[1:4].copy(). After that, changing safe does not change original.

A rule to remember: a slice is a view. A copy is a copy. Use .copy() when in doubt.

Picking with a mask

Three rows of boxes. The first row is the marks 45, 82, 67, 91, 30 and 75. Arrows lead down to the second row, the mask marks greater than or equal to 50, which is False, True, True, True, False, True, with the False boxes red and the True boxes green. Green arrows lead from the True boxes to the third row, marks of mask, which holds only 82, 67, 91 and 75.

Predict first. Which marks are 50 or more? Then run it.

In the last lesson, marks >= 50 gave an array of True and False. Used inside the square brackets, this mask picks the numbers where it is True.

marks[marks >= 50] gives [82 67 91 75], the marks of those who passed.
To use two conditions, join them with & (and), | (or), and ~ (not). Each condition must have brackets: (marks >= 60) & (marks < 90). The reason is that & binds tighter than >=, so without brackets Python does the wrong thing and gives an error. Do not use the words and and or with arrays. They work on one True or False, and raise a ValueError for an array.
~(marks >= 50) is the opposite: the marks of those who did not pass, [45 30].
You can also change only the chosen places: marks_copy[marks_copy < 50] = 50 raises every low mark to 50. The original marks was not touched, because we worked on a copy.

Masks are the tool for questions such as "How many readings are above the limit?" and "Remove the faulty values".

Use & and | between masks, with brackets round each comparison. The words and and or do not work on arrays.

np.where and np.clip

Common mistakes

Changing a slice and forgetting that the original changes. Use .copy().
Writing marks[marks >= 60 & marks < 90]. Each condition needs its own brackets.
Using and or or between arrays. Use & and |.
Thinking that a mask changes the array. It only picks. To change, assign to the chosen places.
Counting the stop in a slice. a[1:4] has 3 numbers.

Practice

Start with two quick questions. Each New numbers gives you a fresh one, so you can practise as long as you like.

Then the labs and the problems:

Warm-up. Open the lab Pick with a mask. You pick, count and change numbers with masks.
Build. Open the problem Slices on paper and the problem Why did the original change?

Remember these

Indexes and slices work as for lists. A slice of an array is a view of the same numbers.
.copy() makes a real copy.
A mask such as a[a > 5] picks the numbers for which the condition is True.
Combine conditions with &, | and ~, and put each condition in brackets.
np.where(c, a, b) chooses for every place. np.clip keeps numbers between two limits.