multiple-plots/script.rst
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.. Objectives
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.. ----------
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..  * How to draw multiple plots which are overlaid
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..  * the figure command
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..  * the legend command
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..  * how to switch between the plots and perform some operations on each
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..    of them like saving the plots and
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..  * creating and switching between subplots
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.. Prerequisites
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.. -------------
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.. 1. using the plot command interactively
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.. 2. embellishing a plot
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.. 3. saving plots
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.. Author              : Madhu
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   Internal Reviewer 1 :         [potential reviewer: Puneeth]
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   Internal Reviewer 2 : Nishanth
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   External Reviewer   :
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Script
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------
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{{{ Show the slide containing the title }}}
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Hello friends. Welcome to this spoken tutorial on Multiple plots.
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{{{ Show the slide containing the outline }}}
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In this tutorial, we will learn how to draw more than one plot, how to
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add legends to each plot to indicate what each plot represents. We
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will also learn how to switch between the plots and create multiple
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plots with different regular axes which are also called as subplots.
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.. #[Nishanth]: See diff - edited a grammatical mistake
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.. #[Madhu: Done]
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{{{ Shift to terminal and start ipython -pylab }}}
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To begin with let us start ipython with pylab, by typing::
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  ipython -pylab
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on the terminal
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Let us first create set of points for our plot. For this we will use
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the command called linspace::
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  x = linspace(0, 50, 10)
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linspace command creates 10 points in the interval between 0 and 50
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both inclusive. We assign these values to a variable called x.
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.. #[Nishanth]: pre requisite for this LO is basic plotting which
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                covers linspace and plot. So you may not need to 
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                specify all that again. But not a problem if it is
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                there also.
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.. #[Madhu: Since I thought the LOs are disconnected, I thought it is
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     better to give a very short intro to it]
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Now let us draw a plot simple sine plot using these points::
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  plot(x, sin(x))
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This should give us a nice sine plot.
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{{{ Switch to the plot window }}}
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Oh! wait! Is that a nice sine plot? Does a sine plot actually look
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like that? We know that a sine plot is a smooth curve. Is it not? What
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really caused this?
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.. #[Nishanth]: See diff
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.. #[Madhu: Done]
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{{{ pause for a while }}}
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A small investigation on linspace tells us that we chose too few
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points in a large interval between 0 and 50 for the curve to be
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smooth. This should also indicate that the plot command actually plots
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the set of points given by x and sin(x) and it doesn't plot the
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analytical function itself i.e. it plots the points given by
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Analytical functions. So now let us use linspace again to get 500
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points between 0 and 100 and draw the sine plot
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.. #[Nishanth]: Here specify that when we do plot(x, sin(x) 
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                it is actually plotting two sets of points
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                and not analytical functions. Hence the sharp 
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                curve.
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.. #[Madhu: Incorporated]
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{{{ Switch to ipython andtype }}} ::
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  y = linspace(0, 50, 500)
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  plot(y, sin(y))
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{{{ Change to the plot window }}}
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Now we see what we remember as a sine plot. A smooth curve. If we
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carefully notice we also have two plots now one overlaid upon
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another. In pylab, by default all the plots are overlaid.
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Since we have two plots now overlaid upon each other we would like to
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have a way to indicate what each plot represents to distinguish
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between them. This is accomplished using legends. Equivalently, the
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legend command does this for us
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{{{ Switch to ipython }}}::
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  legend(['sin(x)', 'cos(x)'])
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.. #[Nishanth]: This legend may go up in the script. May be before 
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                introducing the figure command itself.
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.. #[Madhu: brought up]
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The legend command takes a single list of parameters where each
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parameter is the text indicating the plots in the order of their
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serial number.
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{{{ Switch to plot window }}}
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Now we can see the legends being displayed for the respective sine and
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cosine plots on the plot area.
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We have learnt quite a lot of things now, so let us take up an
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exercise problem.
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%% 1 %% Draw two plots overlaid upon each other, with the first plot
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   being a parabola of the form y = 4(x ^ 2) and the second being a
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   straight line of the form y = 2x + 3 in the interval -5 to 5. Use
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   colors to differentiate between the plots and use legends to
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   indicate what each plot is doing.
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{{{ pause for a while and continue from paused state }}}
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We can obtain the two plots in different colors using the following
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commands::
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  x = linspace(-5, 5, 100)
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  plot(x, 4 * (x * x), 'b')
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  plot(x, (2 * x) + 3, 'g')
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Now we can use the legend command as::
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  legend(['Parabola', 'Straight Line'])
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Or we can also just give the equations of the plot::
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  legend(['y = 4(x ^ 2)', 'y = 2x + 3'])
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We now know how to draw multiple plots and use legends to indicate
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which plot represents what function, but we would like to have more
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control over the plots we draw. Like switch between them, perform some
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operations or labelling on them individually and so on. Let us see how
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to accomplish this. Before we move on, let us clear our screen.
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{{{ Switch to ipython }}}::
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  clf()
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To accomplishing more control over individual plots we use the figure
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command::
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  x = linspace(0, 50, 500)
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  figure(1)
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  plot(x, sin(x), 'b')
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  figure(2)
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  plot(x, cos(x), 'g')
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{{{ Switch to plot window }}}
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Now we have two plots, a sine plot and a cosine plot in two different
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figures.
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.. #[Nishanth]: figure(1) and figure(2) give two different plots.
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                The remaining script moves on the fact that they 
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                give overlaid plots which is not the case.
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                So clear the figure and plot cos and sin without
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                introducing figure command. Then introduce legend
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                and finish off the everything on legend.
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                Then introduce figure command.
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.. #[Madhu: I have just moved up the text about legend command. I
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     think that should take care of what you suggested. If there is
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     some mistake with it, Punch please let me know in your next
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     review.]
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{{{ Have both plot window and ipython side by side }}}
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The figure command takes an integer as an argument which is the serial
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number of the plot. This selects the corresponding plot. All the plot
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commands we run after this are applied to the selected plot. In this
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example figure 1 is the sine plot and figure 2 is the cosine plot. We
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can, for example, save each plot separately
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{{{ Switch to ipython }}}::
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  savefig('/home/user/cosine.png')
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  figure(1)
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  title('sin(y)')
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  savefig('/home/user/sine.png')
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{{{ Have both plot window and ipython side by side }}}
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We also titled the our first plot as 'sin(y)' which we did not do for
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the second plot.
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Let us attempt another exercise problem
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%% 2 %% Draw a line of the form y = x as one figure and another line
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   of the form y = 2x + 3. Switch back to the first figure, annotate
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   the x and y intercepts. Now switch to the second figure and
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   annotate its x and y intercepts. Save each of them.
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{{{ Pause for a while and continue from the paused state }}}
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To solve this problem we should first create the first figure using
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the figure command. Before that, let us first run clf command to make
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sure all the previous plots are cleared::
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  clf()
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  figure(1)
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  x = linspace(-5, 5, 100)
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  plot(x, x)
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Now we can use figure command to create second plotting area and plot
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the figure::
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  figure(2)
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  plot(x, ((2 * x) + 3))
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Now to switch between the figures we can use figure command. So let us
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switch to figure 1. We are asked to annotate x and y intercepts of the
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figure 1 but since figure 1 passes through origin we will have to
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annotate the origin. We will annotate the intercepts for the second
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figure and save them as follows::
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  figure(1)
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  annotate('Origin', xy=(0.0, 0.0)
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  figure(2)
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  annotate('x-intercept', xy=(0, 3))
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  annotate('y-intercept', xy=(0, -1.5))
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  savefig('/home/fossee/plot2.png')
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  figure(1)
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  savefig('/home/fossee/plot1.png')
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At times we run into situations where we want to compare two plots and
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in such cases we want to draw both the plots in the same plotting
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area. The situation is such that the two plots have different regular
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axes which means we cannot draw overlaid plots. In such cases we can
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draw subplots.
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We use subplot command to accomplish this
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{{{ Switch to ipython }}}::
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  subplot(2, 1, 1)
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subplot command takes three arguments, the first being the number of
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rows of subplots that must be created,
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{{{ Have both plot window and ipython side by side }}}
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in this case we have 2 so it spilts the plotting area horizontally for
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two subplots. The second argument specifies the number of coloumns of
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subplots that must be created. We passed 1 as the argument so the
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plotting area won't be split vertically and the last argument
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specifies what subplot must be created now in the order of the serial
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number. In this case we passed 1 as the argument, so the first subplot
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that is top half is created. If we execute the subplot command as
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{{{ Switch to ipython }}}::
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  subplot(2, 1, 2)
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{{{ Switch to plot window }}}
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The lower subplot is created. Now we can draw plots in each of the
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subplot area using the plot command.
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{{{ Switch to ipython }}}::
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  x = linspace(0, 50, 500)
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  plot(x, cos(x))
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  subplot(2, 1, 1)
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  y = linspace(0, 5, 100)
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  plot(y, y ** 2)
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{{{ Have both plot window and ipython side by side }}}
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This created two plots one in each of the subplot area. The top
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subplot holds a parabola and the bottom subplot holds a cosine
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curve.
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As seen here we can use subplot command to switch between the subplot
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as well, but we have to use the same arguments as we used to create
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that subplot, otherwise the previous subplot at that place will be
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automatically erased. It is clear from the two subplots that both have
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different regular axes. For the cosine plot x-axis varies from 0 to
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100 and y-axis varies from 0 to 1 where as for the parabolic plot the
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x-axis varies from 0 to 10 and y-axis varies from 0 to 100
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.. #[Nishanth]: stress on the similarity between subplot and figure
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     commands
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.. #[Madhu: I think they are not really similar. Trying to bring in
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     the similarity will confuse people I think.]
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%% 3 %% We know that the Pressure, Volume and Temperatures are held by
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the equation PV = nRT where nR is a constant. Let us assume nR = .01
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Joules/Kelvin and T = 200K. V can be in the range from 21cc to
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100cc. Draw two different plots as subplots, one being the Pressure
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versus Volume plot and the other being Pressure versus Temparature
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plot.
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{{{ Pause for a while and continue }}}
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To start with, we have been given the range of Volume using which we
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can define the variable V::
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  V = linspace(21, 100, 500)
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Now we can create first subplot and draw Pressure versus Volume graph
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using this V. We know that nRT is a constant which is equal to 2.0
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since nR = 0.01 Joules/Kelvin and T = 200 Kelvin::
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  subplot(2, 1, 1)
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  plot(V, 2.0/V)
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Now we can create the second subplot and draw the Pressure versus
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Temparature plot as follows::
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  subplot(2, 1, 2)
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  plot(200, 2.0/V)
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Unfortunately we have an error now, telling x and y dimensions don't
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match. This is because our V contains a set of values as returned by
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linspace and hence 2.0/V which is the pressure also contains a set of
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values. But the first argument to the plot command is a single
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value. So to plot this data we need to create as many points as there
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are in Pressure or Volume data for Temperature too, all having the
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same value. This can be accomplished using::
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  T = linspace(200, 200, 500)
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We now have 500 values in T each with the value 200 Kelvin. Plotting
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this data we get the required plot::
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  plot(T, 2.0/V)
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It is left as a homework to label both X and Y axes for each of the
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two subplots. 
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{{{ Show summary slide }}}
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.. #[Nishanth]: Exercises are missing in the script
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                one exercise for overlaid plot and legend
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                one for figure command
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                one for subplot must do
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This brings us to the end of another session. In this tutorial session
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we learnt
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 * How to draw multiple plots which are overlaid
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 * the figure command
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 * the legend command
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 * how to switch between the plots and perform some operations on each
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   of them like saving the plots and
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 * creating and switching between subplots
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.. #[Nishanth]: legend command can be told right after overlaid plots
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.. #[Madhu: Incorporated]
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{{{ Show the "sponsored by FOSSEE" slide }}}
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This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
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Hope you have enjoyed and found it useful.
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Thank you!
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