1 .. Objectives

     2 .. ----------

     3 

     4 ..  * How to draw multiple plots which are overlaid

     5 ..  * the figure command

     6 ..  * the legend command

     7 ..  * how to switch between the plots and perform some operations on each

     8 ..    of them like saving the plots and

     9 ..  * creating and switching between subplots

    10 

    11 

    12 .. Prerequisites

    13 .. -------------

    14 

    15 .. 1. using the plot command interactively

    16 .. 2. embellishing a plot

    17 .. 3. saving plots

    18      

    19 .. Author              : Madhu

    20    Internal Reviewer 1 :         [potential reviewer: Puneeth]

    21    Internal Reviewer 2 : Nishanth

    22    External Reviewer   :

    23 

    24 Script

    25 ------

    26 

    27 {{{ Show the slide containing the title }}}

    28 

    29 Hello friends. Welcome to this spoken tutorial on Multiple plots.

    30 

    31 {{{ Show the slide containing the outline }}}

    32 

    33 In this tutorial, we will learn how to draw more than one plot, how to

    34 add legends to each plot to indicate what each plot represents. We

    35 will also learn how to switch between the plots and create multiple

    36 plots with different regular axes which are also called as subplots.

    37 

    38 .. #[Nishanth]: See diff - edited a grammatical mistake

    39 .. #[Madhu: Done]

    40 

    41 {{{ Shift to terminal and start ipython -pylab }}}

    42 

    43 To begin with let us start ipython with pylab, by typing::

    44 

    45   ipython -pylab

    46 

    47 on the terminal

    48 

    49 Let us first create set of points for our plot. For this we will use

    50 the command called linspace::

    51 

    52   x = linspace(0, 50, 10)

    53 

    54 linspace command creates 10 points in the interval between 0 and 50

    55 both inclusive. We assign these values to a variable called x.

    56 

    57 .. #[Nishanth]: pre requisite for this LO is basic plotting which

    58                 covers linspace and plot. So you may not need to 

    59                 specify all that again. But not a problem if it is

    60                 there also.

    61 .. #[Madhu: Since I thought the LOs are disconnected, I thought it is

    62      better to give a very short intro to it]

    63 

    64 Now let us draw a plot simple sine plot using these points::

    65 

    66   plot(x, sin(x))

    67 

    68 This should give us a nice sine plot.

    69 

    70 {{{ Switch to the plot window }}}

    71 

    72 Oh! wait! Is that a nice sine plot? Does a sine plot actually look

    73 like that? We know that a sine plot is a smooth curve. Is it not? What

    74 really caused this?

    75 

    76 .. #[Nishanth]: See diff

    77 .. #[Madhu: Done]

    78 

    79 {{{ pause for a while }}}

    80 

    81 A small investigation on linspace tells us that we chose too few

    82 points in a large interval between 0 and 50 for the curve to be

    83 smooth. This should also indicate that the plot command actually plots

    84 the set of points given by x and sin(x) and it doesn't plot the

    85 analytical function itself i.e. it plots the points given by

    86 Analytical functions. So now let us use linspace again to get 500

    87 points between 0 and 100 and draw the sine plot

    88 

    89 .. #[Nishanth]: Here specify that when we do plot(x, sin(x) 

    90                 it is actually plotting two sets of points

    91                 and not analytical functions. Hence the sharp 

    92                 curve.

    93 .. #[Madhu: Incorporated]

    94 

    95 {{{ Switch to ipython andtype }}} ::

    96 

    97   y = linspace(0, 50, 500)

    98   plot(y, sin(y))

    99 

   100 {{{ Change to the plot window }}}

   101 

   102 Now we see what we remember as a sine plot. A smooth curve. If we

   103 carefully notice we also have two plots now one overlaid upon

   104 another. In pylab, by default all the plots are overlaid.

   105 

   106 Since we have two plots now overlaid upon each other we would like to

   107 have a way to indicate what each plot represents to distinguish

   108 between them. This is accomplished using legends. Equivalently, the

   109 legend command does this for us

   110 

   111 {{{ Switch to ipython }}}::

   112 

   113   legend(['sin(x)', 'cos(x)'])

   114 

   115 .. #[Nishanth]: This legend may go up in the script. May be before 

   116                 introducing the figure command itself.

   117 .. #[Madhu: brought up]

   118 

   119 The legend command takes a single list of parameters where each

   120 parameter is the text indicating the plots in the order of their

   121 serial number.

   122 

   123 {{{ Switch to plot window }}}

   124 

   125 Now we can see the legends being displayed for the respective sine and

   126 cosine plots on the plot area.

   127 

   128 We have learnt quite a lot of things now, so let us take up an

   129 exercise problem.

   130 

   131 %% 1 %% Draw two plots overlaid upon each other, with the first plot

   132    being a parabola of the form y = 4(x ^ 2) and the second being a

   133    straight line of the form y = 2x + 3 in the interval -5 to 5. Use

   134    colors to differentiate between the plots and use legends to

   135    indicate what each plot is doing.

   136 

   137 {{{ pause for a while and continue from paused state }}}

   138 

   139 We can obtain the two plots in different colors using the following

   140 commands::

   141 

   142   x = linspace(-5, 5, 100)

   143   plot(x, 4 * (x * x), 'b')

   144   plot(x, (2 * x) + 3, 'g')

   145 

   146 Now we can use the legend command as::

   147 

   148   legend(['Parabola', 'Straight Line'])

   149 

   150 Or we can also just give the equations of the plot::

   151 

   152   legend(['y = 4(x ^ 2)', 'y = 2x + 3'])

   153 

   154 We now know how to draw multiple plots and use legends to indicate

   155 which plot represents what function, but we would like to have more

   156 control over the plots we draw. Like switch between them, perform some

   157 operations or labelling on them individually and so on. Let us see how

   158 to accomplish this. Before we move on, let us clear our screen.

   159 

   160 {{{ Switch to ipython }}}::

   161 

   162   clf()

   163 

   164 To accomplishing more control over individual plots we use the figure

   165 command::

   166 

   167   x = linspace(0, 50, 500)

   168   figure(1)

   169   plot(x, sin(x), 'b')

   170   figure(2)

   171   plot(x, cos(x), 'g')

   172 

   173 {{{ Switch to plot window }}}

   174 

   175 Now we have two plots, a sine plot and a cosine plot in two different

   176 figures.

   177 

   178 .. #[Nishanth]: figure(1) and figure(2) give two different plots.

   179                 The remaining script moves on the fact that they 

   180                 give overlaid plots which is not the case.

   181                 So clear the figure and plot cos and sin without

   182                 introducing figure command. Then introduce legend

   183                 and finish off the everything on legend.

   184                 Then introduce figure command.

   185 

   186 .. #[Madhu: I have just moved up the text about legend command. I

   187      think that should take care of what you suggested. If there is

   188      some mistake with it, Punch please let me know in your next

   189      review.]

   190 

   191 {{{ Have both plot window and ipython side by side }}}

   192 

   193 The figure command takes an integer as an argument which is the serial

   194 number of the plot. This selects the corresponding plot. All the plot

   195 commands we run after this are applied to the selected plot. In this

   196 example figure 1 is the sine plot and figure 2 is the cosine plot. We

   197 can, for example, save each plot separately

   198 

   199 {{{ Switch to ipython }}}::

   200 

   201   savefig('/home/user/cosine.png')

   202   figure(1)

   203   title('sin(y)')

   204   savefig('/home/user/sine.png')

   205 

   206 {{{ Have both plot window and ipython side by side }}}

   207 

   208 We also titled the our first plot as 'sin(y)' which we did not do for

   209 the second plot.

   210 

   211 Let us attempt another exercise problem

   212 

   213 %% 2 %% Draw a line of the form y = x as one figure and another line

   214    of the form y = 2x + 3. Switch back to the first figure, annotate

   215    the x and y intercepts. Now switch to the second figure and

   216    annotate its x and y intercepts. Save each of them.

   217 

   218 {{{ Pause for a while and continue from the paused state }}}

   219 

   220 To solve this problem we should first create the first figure using

   221 the figure command. Before that, let us first run clf command to make

   222 sure all the previous plots are cleared::

   223 

   224   clf()

   225   figure(1)

   226   x = linspace(-5, 5, 100)

   227   plot(x, x)

   228 

   229 Now we can use figure command to create second plotting area and plot

   230 the figure::

   231 

   232   figure(2)

   233   plot(x, ((2 * x) + 3))

   234 

   235 Now to switch between the figures we can use figure command. So let us

   236 switch to figure 1. We are asked to annotate x and y intercepts of the

   237 figure 1 but since figure 1 passes through origin we will have to

   238 annotate the origin. We will annotate the intercepts for the second

   239 figure and save them as follows::

   240 

   241   figure(1)

   242   annotate('Origin', xy=(0.0, 0.0)

   243   figure(2)

   244   annotate('x-intercept', xy=(0, 3))

   245   annotate('y-intercept', xy=(0, -1.5))

   246   savefig('/home/fossee/plot2.png')

   247   figure(1)

   248   savefig('/home/fossee/plot1.png')

   249 

   250 At times we run into situations where we want to compare two plots and

   251 in such cases we want to draw both the plots in the same plotting

   252 area. The situation is such that the two plots have different regular

   253 axes which means we cannot draw overlaid plots. In such cases we can

   254 draw subplots.

   255 

   256 We use subplot command to accomplish this

   257 

   258 {{{ Switch to ipython }}}::

   259 

   260   subplot(2, 1, 1)

   261 

   262 subplot command takes three arguments, the first being the number of

   263 rows of subplots that must be created,

   264 

   265 {{{ Have both plot window and ipython side by side }}}

   266 

   267 in this case we have 2 so it spilts the plotting area horizontally for

   268 two subplots. The second argument specifies the number of coloumns of

   269 subplots that must be created. We passed 1 as the argument so the

   270 plotting area won't be split vertically and the last argument

   271 specifies what subplot must be created now in the order of the serial

   272 number. In this case we passed 1 as the argument, so the first subplot

   273 that is top half is created. If we execute the subplot command as

   274 

   275 {{{ Switch to ipython }}}::

   276 

   277   subplot(2, 1, 2)

   278 

   279 {{{ Switch to plot window }}}

   280 

   281 The lower subplot is created. Now we can draw plots in each of the

   282 subplot area using the plot command.

   283 

   284 {{{ Switch to ipython }}}::

   285 

   286   x = linspace(0, 50, 500)

   287   plot(x, cos(x))

   288   subplot(2, 1, 1)

   289   y = linspace(0, 5, 100)

   290   plot(y, y ** 2)

   291 

   292 {{{ Have both plot window and ipython side by side }}}

   293 

   294 This created two plots one in each of the subplot area. The top

   295 subplot holds a parabola and the bottom subplot holds a cosine

   296 curve.

   297 

   298 As seen here we can use subplot command to switch between the subplot

   299 as well, but we have to use the same arguments as we used to create

   300 that subplot, otherwise the previous subplot at that place will be

   301 automatically erased. It is clear from the two subplots that both have

   302 different regular axes. For the cosine plot x-axis varies from 0 to

   303 100 and y-axis varies from 0 to 1 where as for the parabolic plot the

   304 x-axis varies from 0 to 10 and y-axis varies from 0 to 100

   305 

   306 .. #[Nishanth]: stress on the similarity between subplot and figure

   307      commands

   308 

   309 .. #[Madhu: I think they are not really similar. Trying to bring in

   310      the similarity will confuse people I think.]

   311 

   312 %% 3 %% We know that the Pressure, Volume and Temperatures are held by

   313 the equation PV = nRT where nR is a constant. Let us assume nR = .01

   314 Joules/Kelvin and T = 200K. V can be in the range from 21cc to

   315 100cc. Draw two different plots as subplots, one being the Pressure

   316 versus Volume plot and the other being Pressure versus Temparature

   317 plot.

   318 

   319 {{{ Pause for a while and continue }}}

   320 

   321 To start with, we have been given the range of Volume using which we

   322 can define the variable V::

   323 

   324   V = linspace(21, 100, 500)

   325 

   326 Now we can create first subplot and draw Pressure versus Volume graph

   327 using this V. We know that nRT is a constant which is equal to 2.0

   328 since nR = 0.01 Joules/Kelvin and T = 200 Kelvin::

   329 

   330   subplot(2, 1, 1)

   331   plot(V, 2.0/V)

   332 

   333 Now we can create the second subplot and draw the Pressure versus

   334 Temparature plot as follows::

   335 

   336   subplot(2, 1, 2)

   337   plot(200, 2.0/V)

   338 

   339 Unfortunately we have an error now, telling x and y dimensions don't

   340 match. This is because our V contains a set of values as returned by

   341 linspace and hence 2.0/V which is the pressure also contains a set of

   342 values. But the first argument to the plot command is a single

   343 value. So to plot this data we need to create as many points as there

   344 are in Pressure or Volume data for Temperature too, all having the

   345 same value. This can be accomplished using::

   346 

   347   T = linspace(200, 200, 500)

   348 

   349 We now have 500 values in T each with the value 200 Kelvin. Plotting

   350 this data we get the required plot::

   351 

   352   plot(T, 2.0/V)

   353 

   354 It is left as a homework to label both X and Y axes for each of the

   355 two subplots. 

   356 

   357 {{{ Show summary slide }}}

   358 

   359 .. #[Nishanth]: Exercises are missing in the script

   360                 one exercise for overlaid plot and legend

   361                 one for figure command

   362                 one for subplot must do

   363 

   364 This brings us to the end of another session. In this tutorial session

   365 we learnt

   366 

   367  * How to draw multiple plots which are overlaid

   368  * the figure command

   369  * the legend command

   370  * how to switch between the plots and perform some operations on each

   371    of them like saving the plots and

   372  * creating and switching between subplots

   373 

   374 .. #[Nishanth]: legend command can be told right after overlaid plots

   375 .. #[Madhu: Incorporated]

   376 

   377 {{{ Show the "sponsored by FOSSEE" slide }}}

   378 

   379 This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India

   380 

   381 Hope you have enjoyed and found it useful.

   382 Thank you!

   383