chapter04b.m

%% Analyzing Neural Time Series Data
% Matlab code for Chapter 4 script B
% Mike X Cohen
% 
% This code accompanies the book, titled "Analyzing Neural Time Series Data" 
% (MIT Press). Using the code without following the book may lead to confusion, 
% incorrect data analyses, and misinterpretations of results. 
% Mike X Cohen assumes no responsibility for inappropriate or incorrect use of this code. 

%% Basic plotting

% Matlab visual windows are called figures. Make a new figure with the command figure. 

figure % opens a new figures
plot(1:10,(1:10).^2); % plot X by Y

% run this line after the previous one. note that it overwrites the
% previous plot
plot(1:10,log(1:10))

% now try this: 
plot(1:10,(1:10).^2,'linewidth',3);
hold on % this command enables overwriting
plot(1:10,log(1:10)*30,'r-d') % plot in red and with thicker lines. type "help plot" to learn more

% Drawing a line is simple, but can be a bit tricky at first. You need to
% define the start and end points in the X and Y (and also Z if you are
% plotting in 3D) axes:
plot([2 9],[60 60],'k')
plot([1 10],[0 100],'m:')

% now release the hold, and plot something else
hold off
plot(1:10,(1:10)*3)

% Of course, you can plot the information in variables:
x = 0:.1:1;
y = exp(x);
plot(x,y,'.-')

% x and y need to be of equal length, otherwise you'll get an error:
x = 0:.1:1;
y = [0 exp(x)];
plot(x,y,'.-')

% you can plot multiple lines simultaneously if they are in a matrix
clf % stands for clear-figure
plot(100:100:1000,rand(10,3))
% now let's add some extra features...
title('Random lines')
xlabel('x-axis label... maybe time? maybe space?')
ylabel('voltage (\muV)') % note that the "\mu" is converted to the greek lower-case character
legend({'line 1';'line 2';'line 3'}) % this is a cell array!

% close a figure:
close

% if you know the figure number, or have a handle to it (we'll get to this
% later), you can also open and close specific figures.
figure(10)
figure(100)
figure(103)

close([100 ...  An elipse at the end of a line allows you to write comments and continue the code on the next line. This is convenient for long lines of code that you want to be visible on a single screen without using the horizontal scrollbar. 
    103])

%% plotting lines in 3D space

% If you feel constrained by two dimensions, fear not! Matlab also allows you to 
% plot data in three dimensions. This becomes useful in chapters 11-13 when
% introducing complex wavelets. 

% Plotting a line in a 3D space is easy. First, define data in 3 dimensions. 
n = 10;
dataX = rand(1,n);
dataY = randn(1,n);
dataZ = rand(1,n)*10;

% Now simply use plot3 the same way you would use plot, 
% but with three inputs:
figure
plot3(dataX,dataY,dataZ)

grid on % sometimes useful

rotate3d % this command will allow you to click-and-drag on the figure to spin the data around

% adding other features to the plot works the same as with a normal plot,
% e.g.,
xlabel('X-axis')
ylabel('Y-axis')
zlabel('Z-axis')


% You might instead have a 3D matrix, e.g.,
data3d = randn(3,30);
plot3(data3d)
% Although the previous line seems like it should work, it unfortunately
% doesn't. You'll need to input each dimension separately:
plot3(data3d(1,:),data3d(2,:),data3d(3,:),'ko-','linew',3,'markerface','m') % you can use the same extra inputs to define line features as you would with the normal plot function
axis off
axis square % also try tight and normal

%% slightly more advanced: get and set
% "set" allows you to access specific properties of graphics. 
% set uses "parameter-value pair" operations, which you will use
% often in plotting, as well as in some other advanced functions.
plot(1:10,rand(10,3))
set(gca,'xtick',1:2:9); % gca = "get current axis"; note the parameter-value pair afterwards
set(gca,'xtick',1:2:9,'xticklabel',{'one';'three';'five';'seven';'nine'}) % can put multiple parameter-value pairs in one function

% the complement to set is get. type "get(gca)" to see a list of parameters
% you can change
get(gca)
% you can also access (and return output from) axis properties:
axis_ylim = get(gca,'YLim'); % axis_ylim is the lower and upper bounds of the y-axis

% you can also assign axis properties using variables or functions:
the_ylim_i_want = [-.3 -cos(pi)];
set(gca,'YLim',the_ylim_i_want);

% If you have multiple axes or plotting objects, you can assign pointers (called handles) to
% the objects. It is good practice to include a lower-case 'h' in the name
% of the variable, to make it clear that these are handles:
figure
ploth = axes;
plot(ploth,1:10,randn(10,3));
title('Random lines')
set(ploth,'ydir','reverse') % this makes positive up, useful for ERP plotting
set(gca,'xlim',[5 10]); % you can also change the x-axis limits

% note that 'gca' points to the "current" axis, or the one most recently used. 
% You can mouse-click on an axis to make it current.

% you can also change properties of figures, e.g.: 
set(gcf,'Color',[.6 0 .8],'name','My purple figure!','numberTitle','off')

% Things can get slightly confusing, so make sure you use informative variable names.
title('Hello there')
titleh = get(gca,'Title'); % the "title" property is a handle to the title object
get(titleh)
set(titleh,'FontSize',40)
set(titleh,'String','LARGE TITLE')

% Let's touch up the figure with some lines showing the 0 crossings. 
% We can do this without needing to know the exact axis limits:
hold on
plot(get(gca,'xlim'),[0 0],'k')
plot([6 6],get(gca,'ylim'),'k:')

% More generally, type "get(gca)" or "get(gcf)" to see what properties you
% can change and how to access them.

%% subplots

% so far we've been putting all the data into one plot in the center of the
% figure. you can also use multiple plots:
figure
subplot(1,2,1) % 1 row, 2 columns, make the first subplot active
plot(randn(10,2))
subplot(1,2,2) % 1 row, 2 columns, make the second subplot active
plot(randn(10,2))

edgecolors='rgmk';

clf % clear figure
for subploti=1:4
    subplot(2,2,subploti)
    plot(1:subploti,(1:subploti)*2+1,'m-p','linewidth',3,'markerEdgeColor',edgecolors(subploti))
    set(gca,'xlim',[.5 4.5],'ylim',[1 10]) % fix X- and Y-axis ranges
    title([ 'Subplot ' num2str(subploti) repmat('!',1,subploti) ])
end

%% basic image plotting

% You can also plot images in 2D. This is useful for 2D data such as
% time-frequency maps, connectivity matrices, etc.

figure
imagesc(randn(100,100))

% imagesc can also take x,y,z inputs, to make x- and y-axis values:
imagesc(1:10:100,0:.1:1,randn(100))

% now let's make this a bit smoother by convoling it with a 2D gaussian
xyrange = -1:.1:1;
[X,Y]   = meshgrid(xyrange); % this creates a grid of X and Y values
gaus2d  = exp(-(X.^2 + Y.^2));

% let's look at the Gaussian
imagesc(gaus2d)

imagesc(xyrange,xyrange,conv2(gaus2d,randn(100),'same'));

% you can toggle the colorbar, which shows you the mapping between color
% and value
colorbar

% you can also change the colormap (type "help graph3d" to see a list of
% default colormaps; you can also create your own)
colormap bone
colormap spring
colormap hot
colormap jet % this is the default
% hint for how to create your own: type "cmap=jet;" columns are RGB values


% there are other functions you can use for 2D data, including:
figure
data = conv2(gaus2d,randn(100),'same'); % 2D convolution

subplot(221) % that if you don't use variables and have fewer than 10 subplots, commas are not necessary
imagesc(xyrange,xyrange,data)
title('function: imagesc')

subplot(222)
surf(xyrange,xyrange,data)
shading interp
title('function: surf')

subplot(223)
contourf(xyrange,xyrange,data)
title('function: contourf')

subplot(224)
contourf(xyrange,xyrange,data,40,'linecolor','none')
title('function: contourf (with more parameters)')

% note how imagesc flips the y-axis! (this can be changed: " set(gca,'YDir','normal') ")

% now let's change the color scaling
set(gca,'clim',[-1 1])
set(gca,'clim',[-10 2])
set(gca,'clim',[-10 20])


% There are many more ways to plot data and manipulate plots;
% this should get you started with the basics. 

% to save the figure, go File -> Save As...
%   you can save as .fig (readable in matlab only), pixelated formats like
%   .bmp or .png, or vector format like .eps (useful for importing into
%   Illustrator or Correl Draw)

%% a bit more about images

% Images are just matrices of numbers. So are pictures. Load in the picture
% of amsterdam (note: Matlab must be in the directory in which the file lives).
amsterdam = imread('amsterdam.bmp');
whos amsterdam

% note that this picture is a 2 (rows) x 2 (columns) x 3 (RGB) matrix
figure
imagesc(amsterdam)
axis image
axis off % or axis on
grid on  % only if axis is on
grid minor

% try plotting the individual values separately:
title_color_components='RGB';
for subploti=1:4
    subplot(2,2,subploti)
    if subploti<4
        imagesc(amsterdam(:,:,subploti))
        title([ 'Plotting just the ' title_color_components(subploti) ' dimension.' ])
    else
        imagesc(amsterdam)
        title('Plotting all colors')
    end
end

%% end.

% Continue on to script c...