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diff --git a/lecture-notes/advanced-python/plotting.rst b/lecture-notes/advanced-python/plotting.rst new file mode 100644 index 0000000..ad246d4 --- /dev/null +++ b/lecture-notes/advanced-python/plotting.rst @@ -0,0 +1,816 @@ +Interactive Plotting +==================== + +We have looked at the basics of Python. In this section we shall look at the +basics of plotting. + +Lets start our IPython interpreter, by + +:: + + $ ipython -pylab + +Pylab is a python library which provides plotting functionality. It also +provides many other important mathematical and scientific functions. After +running ``ipython -pylab`` in your shell if at the top of the output, you see +something like + +:: + + `ERROR: matplotlib could NOT be imported! Starting normal IPython.` + + +Then you have to install ``python-matplotlib`` and run this command again. + +Let us get started directly and try plotting a cosine curve in the range -pi +to pi. + +:: + + p = linspace(-pi,pi,100) + plot(p, cos(p)) + +As you can see we have obtained a cosine curve in the required range. Let's +try and understand what we have done here. + +The variable ``p`` has a hundred points in the range -pi to pi. To see this, +check the documentation of the linspace command. + +:: + + linspace? + +As you can see, it returns ``num`` evenly spaced samples, calculated over the +interval start and stop. + +You can verify this, by looking at the first and last points of ``p`` and the +length of ``p`` + +:: + + print p[0], p[-1], len(p) + +Now, let's clear the plot we obtained and plot a sine curve in the same +range. + +:: + + clf() + plot(p, sin(p)) + +``clf`` command clears the plot, and the plot command following it, plots the +required curve. + +Let's briefly explore the plot window and look at what features it has. + +Firstly, note that moving the mouse around gives us the point where mouse +points at. + +Also we have some buttons the right most among them is for saving the file. + +Left to the save button is the slider button to specify the margins. + +Left to this is zoom button to zoom into the plot. Just specify the region to +zoom into. + +The button left to it can be used to move the axes of the plot. + +The next two buttons with a left and right arrow icons change the state of +the plot and take it to the previous state it was in. It more or less acts +like a back and forward button in the browser. + +The last one is 'home', which returns the plot to the original view. + +Embellishing Plots +================== + +Now that we know how to make simple plots, let us look at embellishing the +plots. We shall look at how to modify the colour, thickness and line-style of +a plot. We shall then learn how to add title to a plot and then look at +adding labels to x and y axes. We shall also look at adding annotations to the plot and setting the limits on the axes. + +Let us decorate the sine curve that we have already plotted. If you have closed that window or your IPython terminal, redo the plot. + +:: + + p = linspace(-pi,pi,100) + plot(p, sin(p)) + + +As we can see, the default colour and the default thickness of the line is as +decided by pylab. Wouldn't it be nice if we could control these parameters in +the plot? This is possible by passing additional arguments to the plot +command. + +The additional argument that we shall be passing in here now is the color +argument. We shall first clear the figure and plot the same in red color. + +:: + + clf() + plot(p, sin(p), 'r') + +As we can see we have the same plot but now in red color. + +To alter the thickness of the line, we use the ``linewidth`` argument +in the plot command. + +:: + + plot(p, cos(p), linewidth=2) + +produces a plot with a thicker line, to be more precise plot with line +thickness 2. + +Occasionally we would also want to alter the style of line. Sometimes all we +want is just a bunch of points not joined. This is possible by passing the +linestyle argument along with or instead of the colour argument. + +:: + + clf() + plot(p, sin(p), '.') + +produces a plot with only points. + +To produce the same plot but now in blue colour, we do + +:: + + clf() + plot(p, sin(p), 'b.') + +Other available options can be seen in the documentation of plot. + +:: + + plot? + +Now that we know how to produce a bare minimum plot with colour, style and +thickness of our interest, we shall look at decorating the plot. + +Let us start with a plot of the function -x^2 + 4x - 5 in the range -2 to 4. + +:: + + x = linspace(-2, 4, 50) + plot(x, -x*x + 4*x - 5, 'r', linewidth=2) + +We now have the plot in a colour and linewidth of our interest. As you can +see, the figure does not have any description describing the plot. + +We will now add a title to the plot by using the ``title`` command. + +:: + + title("Parabolic function -x^2+4x-5") + +The figure now has a title which describes what the plot is. The ``title`` +command as you can see, takes a string as an argument and sets the title +accordingly. + +The formatting in title is messed and it does not look clean. You can imagine +what would be the situation if there were fractions and more complex +functions like log and exp. Wouldn't it be good if there was LaTeX like +formatting? + +That is also possible by adding a $ sign before and after the part of the +string that should be in LaTeX style. For instance, + +:: + + title("Parabolic function $-x^2+4x-5$") + +gives us the polynomial formatted properly. + +Although we have title, the plot is not complete without labelling x and y +axes. Hence we shall label x-axis to "x" and y-axis to "f(x)" :: + + xlabel("x") + +As you can see, ``xlabel`` command takes a string as an argument, +similar to the ``title`` command and sets it as the label to x-axis. + +.. #[See the diff] + +Similarly, + +:: + + ylabel("f(x)") + +sets the name of the y-axis as "f(x)" + +Let us now see how to name or annotate a point on the plot. For example the +point (2, -1) is the local maxima. We would like to name the point +accordingly. We can do this by using + +:: + + annotate("local maxima", xy=(2, -1)) + +As you can see, the first argument to ``annotate`` command is the name we +would like to mark the point as and the second argument is the co-ordinates +of the point at which the name should appear. It is a sequence containing two +numbers. The first is x co-ordinate and second is y co-ordinate. + +As we can see, every annotate command makes a new annotation on the figure. + +Now we have everything we need to decorate a plot. But, it would be nice to +change the limits of the plot area, so that it looks better. + +We shall look at how to get and set them from the script. We shall first get +the existing limits and then change them as required. + +:: + + xlim() + ylim() + +We see that ``xlim`` function returns the current x axis limits and ylim +function returns the current y-axis limits. + +Let us look at how to set the limits. + +:: + + xlim(-4, 5) + +We see the limits of x-axis are now set to -4 and 5. + +Similarly + +:: + + ylim(-15, 2) + +sets the limits of y-axis appropriately. + +Saving to Scripts +================= + +While we are at it, let's look at how to save all the things we typed into +our interpreter into scripts that can be used anytime we like. + +Let's now look at the history of the commands we have typed. The history can +be retreived by using ``%hist`` command. + +:: + + %hist + + +As you can see, it displays a list of recent commands that we typed. Every +command has a number in front, to specify in which order and when it was +typed. + +Please note that there is a % sign before the hist command. This implies that +``%hist`` is a command that is specific to IPython and not available in the +vanilla Python interpreter. These type of commands are called as magic +commands. + +Also note that, the ``%hist`` itself is a command and is displayed as the +most recent command. We should note that anything we type in is stored as +history, irrespective of whether it is a valid command or an error or an +IPython magic command. + +If we want only the recent 5 commands to be displayed, we pass the number as +an argument to ``%hist`` command. + +:: + + %hist 5 + +displays the recent 5 commands, inclusive of the ``%hist`` command. The +default number is 40. + +To list all the commands between 5 and 10, type + +:: + + %hist 5-10 + +Now that we have the history, we would like to save the required lines of +code from history to reproduce the plot of the parabolic function. This is +possible by using the ``%save`` command. + +Before we do that, let us first look at history and identify what lines of +code we require. + +:: + + %hist + +The first command is linspace. But second command is a command that gave us +an error. Hence we do not need second command. The commands from third to +sixth and eighth are required. + +:: + + %save plot_script.py 1 3-6 8 + +The command saves first and then third to sixth and eighth lines of code into +the specified file. + +The first argument to %save is the path of file to save the commands and the +arguments there after are the commands to be saved in the given order. + +Now that we have the required lines of code in a file, let us learn how to +run the file as a python script. We use the IPython magic command ``%run`` to +do this. + +:: + + %run -i plot_script.py + +The script runs but we do not see the plot. This happens because when we are +running a script and we are not in interactive mode anymore. + +Hence on your IPython terminal type + +:: + + show() + +to show the plot. + +The reason for including a ``-i`` after ``run`` is to tell the interpreter +that if any name is not found in script, search for it in the interpreter. +Hence all these ``sin``, ``plot``, ``pi`` and ``show`` which are not +available in script, are taken from the interpreter and used to run the +script. + +Saving Plots +============ + +Let us now learn to save the plots, from the command line, in different +formats. + +Let us plot a sine curve from minus 3pi to 3pi. + +:: + + x = linspace(-3*pi,3*pi,100) + plot(x,sin(x)) + +As, you can see we now have a sine curve. Let's now see how to save the plot. + +For saving the plot, we will use ``savefig()`` function, and it has to be +done with the plot window open. The statement is, :: + + savefig('sine.png') + +Notice that ``savefig`` function takes one argument which is the filename. +The last 3 characters after the ``.`` in the filename is the extension or +type of the file which determines the format in which you want to save. + +Also, note that we gave the full path or the absolute path to which we +want to save the file. + +Here we have used an extension ``.png`` which means the plot gets saved as a +PNG image. + +You can check file which has been saved as ``sine.png`` + +``savefig`` can save the plot in many formats, such as pdf, ps, eps, svg and +png. + + + +Multiple Plots +============== + +Let us now learn, how to draw more than one plot, how to add legends to each +plot to indicate what each plot represents. We will also learn how to switch +between the plots and create multiple plots with different regular axes which +are also called as subplots. + +Let us first create set of points for our plot. For this we will use the +command called linspace:: + + x = linspace(0, 50, 10) + +As we know, x has 10 points in the interval between 0 and 50 both inclusive. + +Now let us draw a plot simple sine plot using these points + +:: + + plot(x, sin(x)) + +This should give us a nice sine plot. + +Oh! wait! It isn't as nice, as we expected. The curve isn't very smooth, why? +In the ``linspace`` command, we chose too few points in a large interval +between 0 and 50 for the curve to be smooth. So now let us use linspace again +to get 500 points between 0 and 50 and draw the sine plot + +:: + + y = linspace(0, 50, 500) + plot(y, sin(y)) + +Now we see a smooth curve. We can also see that, we have two plots, one +overlaid upon another. Pylab overlays plots by default. + +Since, we have two plots now overlaid upon each other we would like to have a +way to indicate what each plot represents to distinguish between them. This +is accomplished using legends. Equivalently, the legend command does this for +us + +:: + + legend(['sine-10 points', 'sine-500 points']) + +Now we can see the legends being displayed for the respective plots. The +legend command takes a single list of parameters where each parameter is the +text indicating the plots in the order of their serial number. + +Additionally, we could give the ``legend`` command an additional argument to +choose the location of the placement, manually. By default, ``pylab`` places +it in the location it thinks is the best. The example below, places it in the +center of the plot. Look at the doc-string of ``legend`` for other locations. + +:: + + legend(['sine-10 points', 'sine-500 points'], loc='center') + +We now know how to draw multiple plots and use legends to indicate which plot +represents what function, but we would like to have more control over the +plots we draw. Like plot them in different windows, switch between them, +perform some operations or labeling on them individually and so on. Let us +see how to accomplish this. Before we move on, let us clear our screen. + +:: + + clf() + +To accomplishing this, we use the figure command + +:: + + x = linspace(0, 50, 500) + figure(1) + plot(x, sin(x), 'b') + figure(2) + plot(x, cos(x), 'g') + +Now we have two plots, a sine plot and a cosine plot in two different +figures. + +The figure command takes an integer as an argument which is the serial number +of the plot. This selects the corresponding plot. All the plot commands we +run after this are applied to the selected plot. In this example figure 1 is +the sine plot and figure 2 is the cosine plot. We can, for example, save each +plot separately + +:: + + savefig('cosine.png') + figure(1) + title('sin(y)') + savefig('sine.png') + +We also titled our first plot as 'sin(y)' which we did not do for the second +plot. + +Let us now do the following. Draw a line of the form y = x as one figure and +another line of the form y = 2x + 3. Switch back to the first figure, +annotate the x and y intercepts. Now switch to the second figure and annotate +its x and y intercepts. Save each of them. + +To solve this problem we should first create the first figure using +the figure command. Before that, let us first run clf command to make +sure all the previous plots are cleared + +:: + + clf() + figure(1) + x = linspace(-5, 5, 100) + plot(x, x) + +Now we can use figure command to create second plotting area and plot +the figure + +:: + + figure(2) + plot(x, ((2 * x) + 3)) + +Now to switch between the figures we can use figure command. So let us +switch to figure 1. We are asked to annotate x and y intercepts of the +figure 1 but since figure 1 passes through origin we will have to +annotate the origin. We will annotate the intercepts for the second +figure and save them as follows + +:: + + figure(1) + annotate('Origin', xy=(0.0, 0.0) + figure(2) + annotate('x-intercept', xy=(0, 3)) + annotate('y-intercept', xy=(0, -1.5)) + savefig('plot2.png') + figure(1) + savefig('plot1.png') + +We can close the figures from the terminal by using the ``close()`` command. + +:: + + close() + close() + +The first ``close`` command closes figure 1, and the second one closes the +figure 2. We could have also use the ``close`` command with an argument +'all', to close all the figures. + +:: + + close('all') + +At times we run into situations where we want to compare two plots and in +such cases we want to draw both the plots in the same plotting area. The +situation is such that the two plots have different regular axes which means +we cannot draw overlaid plots. In such cases we can draw subplots. + +We use subplot command to accomplish this + +:: + + subplot(2, 1, 1) + +``subplot`` command takes three arguments, number of rows, number of columns +and the plot number, which specifies what subplot must be created now in the +order of the serial number. In this case we passed 1 as the argument, so the +first subplot that is top half is created. If we execute the subplot command +as + +:: + + subplot(2, 1, 2) + +the lower subplot is created. Now we can draw plots in each of the subplot +area using the plot command. + +:: + + x = linspace(0, 50, 500) + plot(x, cos(x)) + + subplot(2, 1, 1) + y = linspace(0, 5, 100) + plot(y, y ** 2) + +This created two plots one in each of the subplot area. The top subplot holds +a parabola and the bottom subplot holds a cosine curve. + +As seen here we can use subplot command to switch between the subplot +as well, but we have to use the same arguments as we used to create +that subplot, otherwise the previous subplot at that place will be +automatically erased. It is clear from the two subplots that both have +different regular axes. For the cosine plot x-axis varies from 0 to +100 and y-axis varies from 0 to 1 where as for the parabolic plot the +x-axis varies from 0 to 10 and y-axis varies from 0 to 100 + +Plotting Data +============= + +We often require to plot points obtained from experimental observations, +instead of the analytic functions that we have been plotting, until now. We +shall now learn to read data from files and read it into sequences that can +later be used to plot. + +We shall use the ``loadtxt`` command to load data from files. We will be +looking at how to read a file with multiple columns of data and load each +column of data into a sequence. + +Now, Let us begin with reading the file ``primes.txt``, which contains just a +list of primes listed in a column, using the loadtxt command. The file, in +our case, is present in ``primes.txt``. + +Now let us read this list into the variable ``primes``. + +:: + + primes = loadtxt('primes.txt') + +``primes`` is now a sequence of primes, that was listed in the file, +``primes.txt``. + +We now type, ``print primes`` to see the sequence printed. + +We observe that all of the numbers end with a period. This is so, because +these numbers are actually read as ``floats``. + +Now, let us use the ``loadtxt`` command to read a file that contains two +columns of data, ``pendulum.txt``. This file contains the length of the +pendulum in the first column and the corresponding time period in the second. +Note that ``loadtxt`` needs both the columns to have equal number of rows. + +Let us, now, read the data into the variable ``pend``. Again, it is +assumed that the file is in our current working directory. + +:: + + pend = loadtxt('pendulum.txt') + +Let us now print the variable ``pend`` and see what's in it. + +:: + + print pend + +Notice that ``pend`` is not a simple sequence like ``primes``. It has a +sequence of items in which each item contains two values. Let us use an +additional argument of the ``loadtxt`` command, to read it into two separate, +simple sequences. We add the argument ``unpack=True`` to the ``loadtxt`` +command. + +:: + + L, T = loadtxt('pendulum.txt', unpack=True) + +Let us now, print the variables L and T, to see what they contain. + +:: + + print L + print T + +Notice, that L and T now contain the first and second columns of data +from the data file, ``pendulum.txt``, and they are both simple +sequences. ``unpack=True`` has given us the two columns into two +separate sequences instead of one complex sequence. + +Now that we have the required data in sequences, let us see how to plot it. + +Since we already have the values of L and T as two different sequences, we +now need to calculate T squared. We shall be plotting L vs. T^2 values. + +To obtain the square of sequence T we will use the function ``square`` + +:: + + Tsq = square(T) + +Now to plot L vs T^2 we will simply type + +:: + + plot(L, Tsq, '.') + +For any experimental data, there is always an error in measurements due to +instrumental and human constraints. Now we shall try and take into account +error into our plots. + +We shall read the read the error values from the file ``pendulum_error.txt`` +along with the L and T values. + +:: + + L, T, L_err, T_err = loadtxt('pendulum_error.txt', unpack=True) + + +Now to plot L vs T^2 with an error bar we use the function ``errorbar()`` + +:: + + errorbar(L, Tsq , xerr=L_err, yerr=T_err, fmt='b.') + +This gives a plot with error bar for x and y axis. The dots are of blue +color. The parameters ``xerr`` and ``yerr`` are error on x and y axis and +``fmt`` is the format of the plot. + + +You can explore other options of ``errorbar`` by looking at it's +documentation. + +:: + + errorbar? + + +Other kinds of Plots +==================== + +We shall now briefly look at a few other kinds of plots, namely, the scatter +plot, the pie chart, the bar chart and the log-log plot. + +Let us start with scatter plot. + +In a scatter plot, the data is displayed as a collection of points, each +having the value of one variable determining the position on the horizontal +axis and the value of the other variable determining the position on the +vertical axis. This kind of plot is also called a scatter chart, a scatter +diagram or a scatter graph. + +Now, let us plot a scatter plot showing the percentage profit of a company A +from the year 2000-2010. The data for the same is available in the file +``company-a-data.txt``. + +The data file has two lines with a set of values in each line, the first line +representing years and the second line representing the profit percentages. + +To produce the scatter plot, we first need to load the data from the file +using ``loadtxt``. + +:: + + year,profit = loadtxt('company-a-data.txt', dtype=int) + +By default loadtxt converts the value to float. The ``dtype=type(int())`` +argument in loadtxt converts the value to integer as we require the data as +integers. + +In-order to generate the scatter graph we will use the function ``scatter()`` + +:: + + scatter(year, profit) + +Notice that we passed two arguments to ``scatter()`` function, first one the +values in x-coordinate, year, and the other the values in y-coordinate, the +profit percentage. + +Now let plot a pie chart for the same data. A pie chart or a circle graph is +a circular chart divided into sectors, illustrating proportion. + +Plot a pie chart representing the profit percentage of company A, with the +same data from file ``company-a-data.txt``. We shall reuse the data we have +already read from the file. + +We can plot the pie chart using the function ``pie()``. + +:: + + pie(profit, labels=year) + +Notice that we passed two arguments to the function ``pie()``. First one the +values and the next one the set of labels to be used in the pie chart. + +Now let us move on to the bar charts. A bar chart or bar graph is a chart +with rectangular bars with lengths proportional to the values that they +represent. + +Plot a bar chart representing the profit percentage of company A, with the +same data from file ``company-a-data.txt``. + +We can plot the bar chart using the function ``bar()``. + +:: + + bar(year, profit) + +Note that the function ``bar()`` needs at least two arguments one the values +in x-coordinate and the other values in y-coordinate which is used to +determine the height of the bars. + +Now let us move on to the log-log plot. A log-log graph or a log-log plot is +a two-dimensional graph of numerical data that uses logarithmic scales on +both the horizontal and vertical axes. + +Due to the nonlinear scaling of the axes, a function of the form y = ax^b +will appear as a straight line on a log-log graph. + +Plot a ``log-log`` chart of y=5*x^3 for x from 1-20. + +Before we actually plot let us calculate the points needed for that. + +:: + + x = linspace(1,20,100) + y = 5*x**3 + +Now we can plot the log-log chart using ``loglog()`` function, + +:: + + loglog(x, y) + +For the sake of clarity, let us make a linear plot of x vs. y. + +:: + + plot(x, y) + +Observing the two plots together should give you some clarity about the +``loglog`` plot. + +Help about matplotlib can be obtained from +http://matplotlib.sourceforge.net/contents.html + +That brings us to the end of the discussion on plots and matplotlib. We have +looked a making simple plots, embellishing plots, saving plots, making +multiple plots, plotting data from files, and a few varieties of plots. + +.. + Local Variables: + mode: rst + indent-tabs-mode: nil + sentence-end-double-space: nil + fill-column: 77 + End: + + |