Course 1.2Lesson 4 of 5

Several graphs in one picture

fig, ax = plt.subplots() makes a figure and its axes, and the object style calls the methods of ax, such as ax.plot, ax.set_title, ax.set_xlabel and ax.set_ylabel. plt.subplots with a number of rows and columns gives several axes in one picture, which are used to compare graphs side by side, and fig.tight_layout stops the labels from touching, figsize sets the size, and sharex shares the x axis. Error bars from ax.errorbar show the uncertainty of each point, and for counts the usual size is the square root of the count. ax.set_yscale with log turns an exponential decay into a straight line, which is how decay is tested. fig.savefig saves the picture in a file, and plt.close frees the memory.

about 35 min1 simulation2 practice questions

Lesson 4 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

put several graphs side by side in one picture,
use the object style, fig, ax = plt.subplots(),
add error bars and use a log scale, and
save a graph in a file.

Figure and axes

A matplotlib picture has two parts. The figure is the whole sheet. The axes are one plotting area on the sheet, with its own x axis and y axis. A figure can have several axes, side by side or one above the other.

So far, you used plt.plot and plt.title, which work on the "current" axes. When there are several axes, you must say which one you mean. For this, you keep the axes in a variable: fig, ax = plt.subplots(). Then you call the methods of ax. This is the object style, and it is what professionals use.

plt style	object style
`plt.plot(x, y)`	`ax.plot(x, y)`
`plt.title("...")`	`ax.set_title("...")`
`plt.xlabel("...")`	`ax.set_xlabel("...")`
`plt.ylabel("...")`	`ax.set_ylabel("...")`
`plt.xlim(a, b)`	`ax.set_xlim(a, b)`
`plt.legend()`	`ax.legend()`
`plt.grid(True)`	`ax.grid(True)`

Two graphs side by side

Predict first. A ball is thrown up at 20 m/s. What is its speed at the top of the path? Then run it.

Read the program.

- plt.subplots(1, 2, figsize=(9, 3.6)) makes a figure with 1 row and 2 columns of axes. figsize is the width and height in inches. It returns the figure and the two axes, and the line fig, (left, right) = ... gives each one a name.

- left.plot(...) and right.plot(...) draw on the left and on the right.

- fig.tight_layout() moves the graphs so that the labels and the titles do not touch each other. Use it nearly every time.

- The two graphs tell one story. On the left, the height rises and falls in an arch, and the top is at about 2.06 s, which the last line of the program prints. On the right, the speed falls steadily from 20 m/s, crosses zero at the top, and goes negative as the ball comes down. The point where the speed is zero on the right is the top of the arch on the left.

For a table of graphs, use more rows and columns. plt.subplots(2, 3) gives 6 axes in a 2 by 3 array, and you reach one with axes[1, 0].

Error bars and the log scale

Two graphs of radioactive counts against time, with error bars. On the left, with a linear scale, the counts fall from 1000 to about 125 in a curve that flattens out. On the right, with a log scale, the same points fall along an almost straight line.

Run it. A Geiger counter counts the radioactive particles from a sample, each second, at several times.

- ax.errorbar(t, counts, yerr=error, fmt="o", capsize=3) plots the points with error bars: a small vertical line above and below each point. The bar shows the uncertainty: the number could easily be a little higher or lower. For counting, the usual size of the scatter is the square root of the count. A count of 1000 has a typical scatter of about 32. A graph with error bars tells the reader how far to trust each point.

- A for loop draws the same data on both axes, so the two graphs match. This is the way to avoid repeating the same lines.

- log.set_yscale("log") changes the vertical axis to a logarithmic scale, where equal steps mean equal ratios: from 100 to 1000 is the same distance as from 1000 to 10 000.

- On the linear scale (left), the counts fall in a curve. On the log scale (right), they fall along an almost straight line. This is the sign of an exponential decay, in which the count loses the same fraction in each equal time. Scientists use this trick: if the points of a log graph are on a straight line, the law is exponential, and the slope of the line gives the rate of decay.

A count of 100 is uncertain by 10 percent; a count of 10,000 by only 1 percent.

Saving a graph

Common mistakes

Mixing the two styles. plt.title after you made several axes works on the last one only. In a picture with several axes, use ax.set_title.
Forgetting tight_layout. The labels overlap.
Putting a log scale on data with zero or negative numbers. The logarithm of zero does not exist.
Showing a point without its error bar when the measurement is uncertain.
Forgetting that ax is an array when subplots has more than one row and column. Use ax[0], or ax[1, 0].

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 Two panels. You write a function that makes a figure with two graphs.
Build. Open the problem Cooling curve on a log scale and the problem Show it in two panels.

Remember these

fig, ax = plt.subplots(rows, columns) gives a figure and its axes. Call the methods of ax.
fig.tight_layout() keeps the labels apart. figsize sets the size.
ax.errorbar shows the uncertainty. For a count, the usual error is its square root.
A log scale turns an exponential decay into a straight line.
fig.savefig("name.png") saves, and plt.close(fig) frees the memory.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

What does plt.subplots(2, 3) give?

What is the usual uncertainty of a count of 400?

What does a straight line on a log graph tell you?

What is the object-style call for the title of the axes ax?

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Problems (2)

A cup of tea is 60 degrees hotter than the room at time 0.Hard · High School (11–12) · by StemPy Lab

A savings account starts with 1000 dollars and grows by 8 percent each year: after n years it has…Medium · High School (11–12) · by StemPy Lab

Python Labs (1)

Next: lesson 5Project: motion graphs from data

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