{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Plotting in python for Physics students\n", "\n", "
plot()
from that library and pass our vectors to it"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"*
) from two very large libraries, and now our python session knows a lot of cool commands and functions. If you were to do\n",
"\n",
" dir()
\n",
"\n",
"at this point, a very long list of functions would appear.\n",
"\n",
"Some functions are about plotting (matplotlib
), some are about numerics (numpy
) like sin()
and cos()
or multiply()
:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"multiply()
function from the numpy toolbox/library because multiplying two vectors is tricky: you need to specify whether it's a dot-product, a cross-product, or as here: an element-by-element product.\n",
"\n",
"Also, we can start making our plot a bit better-looking, as well as telling a more complex story from the same experimental data. After all, we performed the measurement in the laboratory by changing the value of the load resistance, which of course is $R=V/I$, so how does power depends on the load resistance?"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"array()
, not a python list [a, b, ...]
. Lists are more general objects in python and may include mixtures of things, like numbers and strings intermixed, but arrays are of numbers only. The side benefit of converting to arrays is that we no longer need to use multiply()
and divide()
, the usual *
and /
will suffice.\n",
"\n",
"Since we want our theoretical curve to look smooth, we will also generate another array of all possible $R$ values, from the minimum to the maximum of the values we used in the experiment, but at a much finer step size, using function arange(min,max,step)
. The resulting curve should look smooth in-between the data points, so we use a \"blue line\" plot 'b-'
instead of a \"red point\" 'r.'
scatter plot we used for the experimental data."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"numpy
already has some linear algebra tools (from the numpy toolbox) that we could use, but we can also import another toolbox, scipy
, that has some more powerful and flexible tools, including non-linear least-squares curve fitting function. When you follow the link to read up on how to call this tool, you will see a lot of powerful options available to you that control the exact details of how the fit is performed. In our case, we will use only the simplest form of the call to our Swiss-army-knife of a function, curve_fit()
. Putting it all together:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"label='string'
should be entered with every plot()
command, but will only show up when legend()
has been called;\n",
" * defining a function is useful for both plotting a guesstimate and to supply in the curve_fit()
call;\n",
" * LaTeX symbols can be included in text strings, surrounded by $\\$ $ signs, but each backslash needs to be doubled-up, e.g. \\$\\\\\\\\Omega\\$
for $\\Omega$;\n",
" * in python, {:d}
for integers or {:f}
for floating-point numbers, etc. are format designators, and they allow you to include values in strings;\n",
" * arrows are just one type of annotation: xy=(__,__)
places the tip and xytext=(__,__)
places the start of the arrow, which is where the annotation text goes;\n",
" * the format of the output file is inferred from the extension specified (.pdf, .png, .svg). Whenever possible, and especially if you are planning to insert the resulting figure into your LaTeX document, use vector formats (.svg, .pdf) which scale smoothly at different display and paper resolutions, and not rasterized bitmap files (.png, .jpg).\n",
" \n",
"\n",
"## Other useful things"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Reading data from files\n",
"Using jupyter magic, create a data file on the fly, then read it into python. This is equivalent to the first two lines of the above script, and allows one to separate the actions of the script from the data these actions apply to. If the script has a simple loop over a list of file names, it can perform the same actions on a large number of data files in one go."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting VI.dat\n"
]
}
],
"source": [
"%%file VI.dat\n",
"# V I,mA\n",
" 0 0.468\n",
" 1 0.405\n",
" 2 0.342\n",
" 3 0.279\n",
" 4 0.216\n",
" 5 0.153\n",
" 6 0.090\n",
" 6.4 0.064"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"data=loadtxt('VI.dat')\n",
"V = data[:,0] # first column\n",
"I = data[:,1] # second column"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Error bars\n",
"\n",
"In the same manner, if the third column in the file were to contain error bars for every data point, is would be easy to add dI = data[:,2]
, and use errorbar()
instead of plot()
with yerr = dI
included in the calling sequence:\n",
"\n",
" dI = data[:,2]\n",
" errorbar(V,I, fmt='ro', yerr = dI);\n",
"
\n",
"\n",
"In other cases, only the instrumental error is known, the same for all measurements. errorbar()
is flexible enough that is can accept both a vector and a scalar for errorbars, it automatically assigns the same scalar number (say, 0.02 i.e. 2 in the second digit after the decimal of $I$) to all errorbars: \n",
"\n",
" errorbar(V,I, fmt='ro', yerr = 0.02);\n",
"
\n",
"\n",
"Alternatively, one could create a vector of the same size as the data vector, but with all values set to that instrumental error. One can use standard python declarattions, like this:\n",
"\n",
" dI = array([0.02]*len(I))\n",
"
\n",
"\n",
"or one might prefer to do this vector multiplication by a scalar to achieve the same goal:\n",
"\n",
" dI = 0.0*I + 0.02\n",
"
\n",
"\n",
"You can also have asymmetric errorbars, different below and above the data values. And, of course, you can also add xerr = ...
in the same way."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"c=
(colour) or to s=
(size) settings in the scatter()
command changes colour or size to marker symbols at every data point.\n",
"\n",
"### Many more things\n",
"\n",
"Many other aspects of the graph appearance can be controlled. For some of them, control is simply a matter of inserting a pair keyword=value
into the calling sequence of one of the plotting commands, for some it requires invoking a different command altogether (e.g. contour()
). This simple introduction just covered the basics; for more - RTFM (\"read the fine manual\").\n",
"\n",
"Happy trails!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.3"
}
},
"nbformat": 4,
"nbformat_minor": 1
}