Matlab usage - short (may be too short) introduction
by EugeniyMikhailov



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= Why Matlab =

At the very least, it is a great replacement of a  hand held calculator. Once
you need  to process multiple  data point it  became tedious with  a simple
calculator. Once  you master Matlab  it will not matter  if it is  one data
point or millions of them. It  can do complex math, plotting, fitting, etc.
It is also the complete programming language which can stand by itself.
Also, Matlab has excellent help documentation and a lot of tutorials at the web.

There are free alternatives. [Octave  http://www.gnu.org/software/octave/]
is  one example. This what I personally use
instead of Matlab all the time. But it is a bit difficult with installation
and it  might be  scary to  see no  GUI and  only a  command prompt  for a
beginner.

= Getting Matlab =

Please visit W&M IT [software support page http://www.wm.edu/offices/it/a-z/software/]
and download Matlab from appropriate "Licensed Software >> Math & Statistics
Software" section. They have several available versions. Either one is fine.
Since we are learning Matlab, we will not  have time to go to fancy toolboxes
which Matlab provides/removes with new releases. 


= How to make a simple plot =
Suppose during the measurements we obtain the following data
for each current value 'I' we measured voltage 'V' 
with some uncertainty in voltage measurement dV.
Our experimental data is represented in the following table.

|| I   | V   | dV  |
|  0.1 | 1.0 | 0.2 |
|  1.0 | 2.2 | 0.1 |
|  1.8 | 3.2 | 0.2 |
|  3.3 | 3.8 | 0.2 |
|  4.0 | 4.9 | 0.3 |

First of all,  we need to transfer  it to the Matlab  vector variables. Pay
attention to the delimiter **;** between numbers

``` 
I  = [  .1; 1.0; 1.8; 3.3; 4.0 ]
V  = [ 1.0; 2.2; 3.2; 3.8; 4.9 ]
dV = [ 0.2; 0.1; 0.2; 0.2; 0.3 ]
```

Now we make a simple plot without error bars to get  the basic, text after
**%** is considered as a comment and Matlab will disregard it.

```
figure(1) % all plotting output will go to the particular window
plot(I,V) 
```

Easy, is not it?

[simple_labeled_plot.png]


But  **every plot  must be  present with  title, proper  axes labels  and units**.
Note **'** for the string specifiers


No our plot is nice and pretty.

[simple_unlabeled_plot.png]

= Fixing the range of the axes =

Have a look at above plot. We see that one of the axes (y) does not contain
origin point  (y=0). Such plots are  very common in finances  and design to
fool a reader, but they are  generally not acceptable in scientific reports
and  definitely not  in  my class  unless  you  have a  good  reason to  do
otherwise.

The fix is very easy. Note that we are actually sending a vector [0,5] to the
**``ylim``** function (fir x-axis we need to use **``xlim``** function).
``` ylim([0,5])

Now our plot is good to present

[simple_labeled_and_proper_limits_plot.png]


= Plotting with error bars =
Let's open a new window for the plot

``` figure(2)

Now we make plot with error bars assuming that they are the same for up and down parts

``` errorbar(I,V,dV)

Yet again we need proper labeling

``` 
title('Dependence of voltage on current')
xlabel('Voltage (V)')
ylabel('Current (A)')
``` 

[errorbar_plot.png]

= Fixing plots font size =

Honestly Matlab is not the best tool to do presentation quality plots, it
requires a quite a bit of messing with their GUI. But at least for a quick font
size fix do the following. This might look like  a magic spell so do read documentation
on **``set``** command.

```
fontSize=24;
set(gca,'FontSize',fontSize );

errorbar(I,V,dV)
title('Dependence of voltage on current')
xlabel('Voltage (V)')
ylabel('Current (A)')
```

[errorbar_with_large_font_plot.png]


= Saving you Matlab plots =

Well it nice to have Matlab  plots.  But as soon as you close Matlab they will go away.
How to save them for a future use? Actually, quite easy with **``print``** command. Unlike the name suggest it does not make a carbon copy but actually an electronic one.

For figure saved in png format do
``` print('V_vs_I.png')

or if you need a pdf (Matlab usually make very bad pdfs without a lot of tweaking)
``` print('V_vs_I.pdf')

Make sure that you read documentation for **``print``** command there are some
useful parameters.


= Where to learn more =

At W&M Physics 256 class teaches how scientists use computers. Matlab was a language of
choice for this class. Feel free to read and use
[my Physics 256 materials http://physics.wm.edu/~evmik/classes/2012_fall_practical_computing_for_scientists/]
make sure that you read at least Lecture 02 slides. Also lecture 15 slides discuss
data reduction and fitting.