Course 1.1Lesson 2 of 5

Maths on whole arrays

An array works with a number or with another array of the same length place by place, so one formula serves all the values at once. Writing v equal to g times t for an array of times gives an array of speeds, with no loop. Functions of NumPy such as np.sqrt, np.sin, np.exp, np.abs and np.round work on every number of an array, and np.deg2rad changes degrees to radians because the trigonometric functions need radians. The math module takes one number only, so math.sqrt of an array is an error. Arrays of different lengths do not fit, and give a ValueError. A comparison such as temps greater than 32 gives an array of True and False, and sum counts the True values.

about 35 min1 simulation2 practice questions

Lesson 2 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

write a formula once and use it on a whole array of values,
use np.sqrt, np.sin, np.exp, np.abs and np.round on arrays,
convert degrees to radians, and
compare an array with a number and count the results.

One formula, many values

In science, you often have a formula and many values. A ball falls from rest. After a time $t$ , its speed is $v = gt$ and the distance it has fallen is $s = \tfrac{1}{2}gt^2$ . For the times 0, 1, 2, 3 and 4 seconds, you would calculate five speeds and five distances. With a list, that is a loop. With an array, you write the formula once.

Predict first. What is the distance fallen after 2 seconds? Then run it.

A number with an array works on every place. A scalar (one number) is stretched to fit. This is a first example of broadcasting, which you meet again in lesson 4.

Two arrays together

Functions for the whole array

NumPy has its own versions of the maths functions, and they work on a whole array in one call.

np.sqrt, np.exp (the power of $e$ ), np.log, np.abs, and np.round(x, 3) which rounds to 3 decimals.
np.sin, np.cos and np.tan need the angle in radians, as in the maths class. To change degrees to radians, use np.deg2rad. Then np.sin(np.deg2rad(30)) is 0.5. (And np.rad2deg goes back.) Forgetting this conversion is the most common mistake in physics programs.
The math module works on one number only. math.sqrt(16) is fine, and math.sqrt(x) with an array of four numbers is a TypeError. When you work with arrays, use np.sqrt, not math.sqrt. (For one single number, either one is fine.)

With a list, this would need a loop or a comprehension. With an array, the formula is written once, like the mathematics.

Comparisons give True and False

Use == to compare for equality (two equals signs), as in temps == 28.

Common mistakes

Using math.sqrt or math.sin on an array. Use np.sqrt and np.sin.
Forgetting the radians. np.sin(30) is not 0.5. Write np.sin(np.deg2rad(30)).
Arrays of different lengths. Read the two shapes in the error message.
Writing ^ for a power. In Python, the power is **. The symbol ^ is something else.
Using and and or between arrays. Use & and |, with brackets. This is explained in the next lesson.

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 Convert the units. You write functions for the conversion of arrays.
Build. Open the problem Free fall table and the problem Temperature scales.

Remember these

A formula written for one number works on a whole array. No loop is needed.
Two arrays work place by place, and must have the same length.
Use the NumPy functions (np.sqrt, np.sin, np.exp) for arrays, and np.deg2rad for angles.
A comparison gives an array of True and False, and .sum() counts the True values.