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How can I plot error bars for functions?

asked 2019-04-15 08:55:37 -0500

stockh0lm gravatar image

updated 2019-04-15 16:45:55 -0500

So far i plotted an upper and lower bound to my functions (as separate overlayed functions) and I liked that solution a lot. Now a colleague said that error bars were nicer. Can sage plot those? I searched and didnt find any.

The code I use currently is from this helpful comment from rburing: https://ask.sagemath.org/question/454...

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Can you provide code for a function you would like such a plot for?

slelievre gravatar imageslelievre ( 2019-04-15 10:37:00 -0500 )edit

i meant to do so, thanks for the reminder.

stockh0lm gravatar imagestockh0lm ( 2019-04-15 11:40:49 -0500 )edit

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answered 2019-04-15 16:37:06 -0500

dsejas gravatar image

updated 2019-04-15 23:27:29 -0500

Hello, @stockh0lm. You ask a very interesting question. I just found a solution, but I don't think it's the most elegant one. I would suggest you to keep looking for another option, but meanwhile...

We are going to mix SageMath plots with pure Matplotlib plots, so you need to import Matplotlib with the line

import matplotlib.pyplot as mpl

I took the following from another of your questions, and made a few changes (the colors and line styles). We will work with this. We are also going to take advantage of your already defined f(), f_lower() and f_upper().

plot([f, f_lower, f_upper],(x,0.2,0.99), color=['blue', 'green', 'green'], linestyle=['-', '--', ':'],
     legend_label=['without error',  'lower margin of error', 'upper margin of error'], 
     axes_labels=['cable\'s burial depth in [m]','Potential in [V]'], 
     figsize=8, axes_labels_size=1, title='$U$ is without error', title_pos=(0.5,1.1)
).matplotlib(figure=mpl.gcf())

Note the ".matplotlib(figure=mpl.gcf())" at the end. this is because, as you know, "plot" is a purely SageMath command. So this is directive to convert it to a Matplotlib-compatible figure. In particular, saying "figure=mpl.gcf()" indicates to add this plot to the current graphic (gcf="get current graphics").

You'll probably need to adjust the axis ranges a little bit to make a more elegant figure. In this case, after some try-and-error, i figured this will make it:

mpl.axis([0.2, 1.1, 0.21, 0.37])

Now we are going to create some lists for the $x$ and $y$ coordinates of the error, and the lower and upper length of the bars:

xx = [] # this will contain the $x$ coordinate
yy = [] # this will contain the $y$ coordinate
el = [] # the lower length of the error box
eu = [] # the upper length of the error box

Now we will fill them. I am assuming that your $x$-axis is from 0.2 to 1.0, and I will use a step of 0.1: for i in range(2, 11): t = 0.1 * i v = N(f(t)) # I use the function N() to convert to RIF to float xx += [t] yy += [v] el += [v - f_lower(t)] eu += [f_upper(t) - v]

Now we use the errorbar() function from Matplotlib:

mpl.errorbar(xx, yy, [el, eu], ecolor='r', elinewidth=1, marker='s', fmt=' ')

Note there is a space between the last quotation marks. This es in order to ask Matplotlib to only draw the error bars and not the lines linking them, since we don't want lines, but the the original function, which we plot next. The argument "ecolor" defines the color of the error bars (b = "blue"), the "elinewidth" define its thickness, and the "marker" indicates a marker for the location of the error bar (s = "square").

Now you have to plot it, not using SageMath, but Matplotlib:

mpl.savefig('Error_bars.png')

That's it! Phew. Quite cumbersome, but effective. The result should look like follows, but you can adjust it at your convenience. image description

You can read more about Matplotlib's errorbar() here. You can check a mix of my code with yours (the one that produced the image) here.

Best regards!

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wow, thank you for your comprehensive answer!

stockh0lm gravatar imagestockh0lm ( 2019-04-15 16:44:58 -0500 )edit

of course i now want to incorporate this style of plot into the graphics array i just created. However, i am not sure how to have mpl return a figure object that i can append(l), to adjust y-axis etc and decorate it etc. How is that possible? can the x-axis be scaled in this kind of plot?

stockh0lm gravatar imagestockh0lm ( 2019-04-16 15:53:40 -0500 )edit

I am not completely sure what you mean. Do you want to add this plot as a subplot in a figure?

dsejas gravatar imagedsejas ( 2019-04-16 18:24:46 -0500 )edit

No, i want to add this plot as part of the mega plot created in this answer: https://ask.sagemath.org/question/461...

stockh0lm gravatar imagestockh0lm ( 2019-04-17 00:21:27 -0500 )edit

i tried to use l.append(p) and l.append(mpl.gcf()), but those objects dont have the attribute get_minmax_data anymore. So i guess i cant rescale them anymore like it is needed to create the equally scaled graphics_array in my other question. That would mean i cant easily combine this and the other plot type, can I?

stockh0lm gravatar imagestockh0lm ( 2019-04-17 00:55:00 -0500 )edit

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Asked: 2019-04-15 08:55:37 -0500

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Last updated: Apr 15