Tim Hoar's Matlab Demo
February 2012

The (unix/linux/mac) Environment for Matlab:

Nothing is really required, but there are some things that make life nicer, naturally.

mkdir ~/matlab
mkdir ~/matlab/data/

Matlab automatically searches for a ~/matlab directory upon startup, this is a nice place to have general purpose scripts/functions. If there exists a ~/matlab/startup.m file, it is automatically executed upon startup. The file may contain any sequence of valid Matlab commands. If there are directories that contain certain third-party toolboxes, the obvious way to add them is with your startup.m file, which could be as simple as this:

%% Startup.m  is executed by the matlabrc script automatically at startup.
% append this directory to your MATLABPATH
%
addpath('~/matlab/data');

To start Matlab:

Simply type matlab & at the UNIX prompt or click on the Matlab icon if you're a person who likes that sort of thing. If your (unix) PATH is correct, this will work. Windows and Mac users may have a little Matlab icon on the desktop/dock ... that works too, naturally. You can fire up Matlab from any directory and your MATLABPATH will be set to search the normal Matlab installation, anything specified in your ~/matlab/startup.m file, and the current working directory (which, for the icon startups, is a bit obfuscated).

The matlab prompt is:

>>

To quit Matlab:

>> quit

Matlab Help

Matlab's syntax:

Matlab is short for Matrix Laboratory. If you can think of the algebra in 2D, it will probably work exactly as you expect. The thing to get used to is that any command without a ";" at the end will print the result of the command to the screen. Not particularly desirable for large results. I am in the habit of terminating every command with a ";", whether it needs one or not.

General help for all the relational operators can be had with help relops. The only tricky part is that the square brackets are used for defining arrays, parentheses are for indexing, and the variables MUST be conformable.

Example

a = [0:127];                            % "a" is a row vector
b = cos(2*pi*a/length(a));              % so is "b"
plot(b(1:64));                          % only plot the first 64 elements
title('My mental retention prowess.');
xlabel('(minutes)');
ylabel('fraction of capacity');

Conformable?

For example, multiplying a 10x3 matrix by a 10x3 matrix will generate an error message, unless you want the operator to work on an element-by-element basis. Here is another example of trying to multiply a 1xN matrix by another 1xN matrix ... simply not possible ...

size(a)
size(b)
a*b

c = a.*b;           % should be reminiscent of the "dot product"
size(c)
d = sum(c);         % wow

c = a'*b;           % transpose a to make it 128-x-1 * 1-x-128 -> 128-x-128
size(c)

Thinking like vectors and matrices

It is best to simply ignore the existence of vectors and just admit they are really N x 1 or 1 x N matrices. All the rules of matrix algebra apply. Some functions are tailored for 1D matrices and can be used on higher-dimensional matrices, like sum.

c = b'*b;           % premultiplying b by its transpose -> 128-x-128
d = sum(c)          % what is "d"? (semicolon intentionally left off)
imagesc(c);         % color-code the result and plot
colorbar;           % plot a legend
title('Not Quite Psychedelic')
xlabel('X index')
ylabel('Y index')

The classic one is fft. Taking the fft of a 1D variable is pretty clear. What happens if you feed fft a M x N matrix? Matlab grew from Fortran beginnings, so it takes ffts of each column, since these are stored sequentially in memory (and it can take unit strides). If you want a real 2D fft, use fft2. This is a common theme in Matlab. Operations that have a different connotation for 2D as opposed to 1D have an additional "2" in the function name.

load topo;
wow = topo - mean(topo(:));
C = fft(wow);      % take the fft of each column of "c"
whos               % "who and size" (semicolon intentionally left off)
D = fft2(wow);
subplot(2,2,1)
  imagesc(real(C))
  title('Real part of FFT of each column')
  colorbar
subplot(2,2,2)
  imagesc(fftshift(real(D)))
  title('Real part of 2DFFT')
  colorbar
subplot(2,2,3)
  imagesc(imag(C))
  title('Imaginary part of FFT of each column')
  colorbar
subplot(2,2,4)
  imagesc(fftshift(imag(D)))
  title('Imaginary part of 2DFFT')
  colorbar

Public-domain functions/tools:

Import an ascii file (of a matrix):

Handle Graphics:

Perhaps the best part of Matlab. Infinitely customizable graphics.

Contour Plots:

The only thing tricky about contour plots in matlab is the resulting orientation. (1,1) is at the bottom left.

clear			% clears all variables in your workspace!!!!!
load topo		% a default dataset
whos
contour(topo)
colorbar

Changing the number of contour lines is easy.

contour(topo,5)
colorbar

Specifying which contour levels is also easy.

contour(topo,[0:500:4500])
colorbar

Personally, I like the imageplots a lot better, they give clues as to the original resolution. However, the plot has (1,1) in the upper left.

imagesc(topo)
colorbar

imagesc(topo)
set(gca,'YDir','normal')	% GetCurrentAxis attribute "YDir"; set to ...
colorbar

get(gca)

Meridional/Zonal means:

[x,y,z] = peaks(360);		% CREATE SOME FAKE DATA (z is 360x360)
imagesc(z);			% TAKE A QUICK LOOK AT THE DATA

newz = z(1:2:360,:);		% GRAB EVERY OTHER ROW OF DATA
imagesc(newz);			% IMAGE THE SUBSETTED MATRIX
set(gca,'YDir','normal');	% PLOT 1,1 IN THE LOWER LEFT

clf;				% CLEAR OUT THE FIGURE WINDOW (GOOD STYLE)
subplot(2,2,1);			% CHOP PLOT WINDOW INTO A 2X2 MATRIX
imagesc(newz);			% CHEAP PLOT OF DATA
set(gca,'YDir','normal');	% PLOT 1,1 IN THE LOWER LEFT
title('Peak data');

subplot(2,2,4);			% use the 4th window of the 2x2 
contour(newz);			% duhhhhhhhh
title('Contoured peak data');

subplot(2,2,3);			% USE THE THIRD WINDOW OF THE 2x2 set
mmeans = mean(newz);		% CREATE MEANS OF EACH COLUMN (ALL LATITUDES)
plot(mmeans);			% PLOT THEM (versus their index [1,360])
title('Meridional means');

subplot(2,2,2);
zmeans = mean(newz');		% TRANSPOSE THE MATRIX AND FIND THE MEANS
plot(zmeans);			% PLOT THEM (versus their index [1,180]
title('Zonal means');

Labelled contour plots

[cs,h] = contour(peaks); 	% this is kinda sneaky
clabel(cs,h,'fontsize',15,'color','r','rotation',0)

Weighted Averages

clf;				% CLEAR OUT THE FIGURE WINDOW (GOOD STYLE)
t = 0.5:1:179.5;                % Just making a digital frequency for 'sin' 
a = sin(2*pi*t/(2*length(t)));  % create half a sinusoid.
w = a.^2;	                % CREATE WEIGHTING FUNCTION (column vector)
c = w.*zmeans;			% CREATE THE WEIGHTED AVERAGE
lats = [-89:1:90];		% CREATE A "REALISTIC" LATITUDE AXIS
plot(lats,zmeans,'-.',lats,c,'-');
grid;				% PUTS A GRID ON THE AXIS
legend('unweighted zonal mean','weighted zonal mean')

Linear Least Squares:

The solution to A*X = B is simply X = A\B; Pretty boring, but true.

help \

help relop

Masking (a bunch of color-coded matrix elements):

Masked Contour Plots:

Cheap Projections:

clf;
load topo
[x,y,z] = sphere(35);					% MAKE A 3D SURFACE
h = surface(x,y,z,'FaceColor','texture','Cdata',topo)	% DO TEXTURE MAP,
							% KEEP GRAPHICS HANDLE
set(h,'EdgeColor','none')				% USE HANDLE TO CHANGE
							% AN ATTRIBUTE
axis square;						% MAKE AXES EQUAL
axis off;						% TURN OFF LABELLING
colormap(jet);						% A DIFFERENT PALETTE

Scripts:

By now, you should be sick of cutting and pasting. Enter the script, generically called a ".m" file. By inserting your matlab commands into a file called (for example) foo.m, you can simply type "foo" at the Matlab prompt and the entire file is checked for syntax and executed. Put the following lines in a file called ~/matlab/foo.m:

% This is a generic matlab script.
%

  load topo;                            % GET [180x360] ELEVATION DATASET
  lats = [-89.5:89.5];                  % CREATE LAT ARRAY FOR TOPO MATRIX
  lons = [0.5:359.5];                   % CREATE LON ARRAY FOR TOPO MATRIX
  imagesc(lons,lats,topo);              % CREATE SOME PLOT w/ true x,y limits
  set(gca,'YDir','normal');             % CORRECT ORIENTATION
 
  worldmap; 

Then, (one at a time) from Matlab's command line:

which foo
help foo
type foo
foo

Functions:

A Matlab Function is a special .m file. The first line of the file is the function declaration.

You can peruse most functions with type.

The FIRST line of the help file should contain some keywords. This is the only line searched by the lookfor function.

copy and paste this into a text file in your ~/matlab directory. Call the file ... Imagesc.m ... or bob.m

function h = Imagesc(x,y,datmat)
% Imagesc is the same as imagesc except the YDir is normal.

% Brilliantly devised and executed by Tim. 1 Jan 1601

h = imagesc(x,y,datmat);
set(h,'YDir','normal')

From the Matlab command line,

help Imagesc

Tinker with the help line, screw up the syntax, call it with the wrong number of arguments ... knock yourself out.

Profiling:

profile your favorite script/function --- VERY impressive. follow the example from "help profile"

Importing binary:

Printing:

To a particular printer:

• Color Postscript:
  

  print -dpsc -P[printer]

• Black & White Postscript:
  

  print -dps -P[printer]

To a file:

• Color Postscript:
  

  print -dpsc [filename]

• Black & White Postscript:
  

  print -dps [filename]

Making Matlab do the rasterization

Lots of postscript files are simply ascii files of postscript commands. You can view and change the source with your favorite editor. This shifts the burden of rendering the figure from the computer to the printer. There can be some relatively small postscript files that take an extremely long time to print because of this. By making the computer render the figures to some finite raster density, the computational burden stays on the computer at the expense of making potentially large (but simple and relatively fast to print) postscript files for the printer. This is particularly true for maps.

If you have figures that are taking too long to print, you may consider having Matlab do the rendering. There is a huge tradeoff between size of the file and the raster level (dots per inch).

print -dpsc2 -zbuffer -r200 [filename]

NetCDF

Matlab and netCDF:

Reading a (known) variable from an existing netCDF file

Creating a netCDF file.

Reading a hyperslab of a variable instead of the WHOLE variable.

ncid  = netcdf.open('/fs/image/home/thoar/public_html/Prior_Diag.nc','NC_NOWRITE');
netcdf.inq(ncid)
lonmat  = netcdf.getVar(ncid, netcdf.inqVarID(ncid,'XLONG_d01'));
latmat  = netcdf.getVar(ncid, netcdf.inqVarID(ncid,'XLAT_d01'));
times   = netcdf.getVar(ncid, netcdf.inqVarID(ncid,'time'));
copy    = netcdf.getVar(ncid, netcdf.inqVarID(ncid,'copy'));
varid   = netcdf.inqVarID(ncid,'T2_d01');

% Read in the whole variable at once:

temps   = netcdf.getVar(ncid, varid,'double');

size(temps)

% temps is a 4D variable: 221-x-127-x-3-x-4

datmat = temps(:,:,1,2);

clf;
h = pcolor(lonmat, latmat, datmat);
set(h,'LineStyle','none');

title('Hunh?')
h2 = colorbar('vert');
set(get(h2,'YLabel'),'String','degrees')

disp('What''s going on? the matrix is being plotted ''correctly''')
disp('but there is one element that is in the wrong hemisphere.')
disp('The longitudes in lonmat are [-180,180] so the wraparound')
disp('point is problematic. Just change the longitudes to be ')
disp('[0,360] by finding those elements that are less than zero')
disp('and adding 360 to them.\n')
disp('Pausing, hit any key to continue ...')
pause

inds = find(lonmat < 0.0);
lonmat(inds) = lonmat(inds) + 360.0;

h = pcolor(lonmat, latmat, datmat);
set(h,'LineStyle','none');

title('Ta DA','Interpreter','none')
h2 = colorbar('vert');
set(get(h2,'YLabel'),'String','degrees')

disp('Let''s only read in a 2D slab of data')
disp('Pausing, hit any key to continue ...')
pause

% For simplicity, we are exploting the fact that we KNOW the size/shape of the variable.
% If you do not, the best way is to use netcdf.inqVar and then loop over
% al the varDimIDs to find their size.
% [varname, xtype, varDimIDs, varAtts] = netcdf.inqVar(ncid,varid) 
%
% remember that the Matlab netCDF routines are implemented with the C-style addressing,
% so the first element is zero, not one. The rest of Matlab, as far as I can tell,
% has always started counting at one ... so the break from their own standard is disturbing
% and annoying.

start = [  0,  0,0,1];
count = [221,127,1,1];
bob   = netcdf.getVar(ncid, varid, start, count, 'double');
size(bob)

clf
subplot(3,1,1)

   h = pcolor(lonmat, latmat, datmat);
   set(h,'LineStyle','none');
   title('Whole Variable at Once')
   h2 = colorbar('vert');
   set(get(h2,'YLabel'),'String','degrees')

subplot(3,1,2)

   h = pcolor(lonmat, latmat, bob);
   set(h,'LineStyle','none');
   title('Just a 2D hyperslab')
   h2 = colorbar('vert');
   set(get(h2,'YLabel'),'String','degrees')

subplot(3,1,3)

   h = pcolor(lonmat, latmat, (datmat-bob) );
   set(h,'LineStyle','none');
   title('Difference')
   h2 = colorbar('vert');
   set(get(h2,'YLabel'),'String','degrees')

Mapping / Projections

Movies / Animations

I used to use the matlab getframe, movie commands ... but then I moved to a Mac and realized that for really nice animations, i just needed to dump each frame to a .png file and make the animation in QuickTime.

Movie Documentation

Ingesting animations

Creating a movie.

Low Level Examples

Tim Hoar thoar 'at' ucar 'dot' edu