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-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
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-   End:
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-