%CNS120
%matlab tutorial
%
%

%functions and keywords needed for HW5 are:

%find, bar, histc/hist, load, subplot, length, xlim/ylim, xlabel, ylabel,
%title, for, ttest2

%select lines in editor and press F9 to execute.

%---- variables, datastructures


cd('/home/urut/caltech/classes/TA/cns120/'); %go to dir where you put all the stuff from the HP

%don't need to declare variables, is automatic
a=10;
b=50;

a+b

c1=1:100;  %make array of length 100, with elements 1...100

c2=1:20:100; %make array of length 5, with elements 1,21,41,61,81

c2

c2(5)  % access by index

c2([1 2 3]) %access by index

c2(1:3)   %access by index


c2=[c2 55 66 77];  %add elements


c2=c2-10; %subtract 10 from each element

c3=[c1 c2];


%---- how to make figures
randNumbers = randn(1000,1);  %1000 random numbers, mean zero, std 1

%mean and standard deviation
mean(randNumbers)
std(randNumbers)

%plot x-y points, connected by lines
figure(1)
plot( 1:1000, randNumbers );

%plot histograms
figure(2)
hist( randNumbers, 100);  %histogram, 100 bins

xlabel('random number');
ylabel('frequency');
title('Histogram xx');

%---- use find  and subplot

%find all random numbers smaller -1
inds = find( randNumbers < -1 );
randNumbersSmall = randNumbers(inds);

%how many numbers were smaller than -1
length(inds)

%more complicated find: how many numbers are between -1 and -0.5 ?

inds2 = find( randNumbers < -0.5 & randNumbers > -1.0 );
length(inds2)

%---- how to make barplots
figure(20)
bar( 1:2, [length(inds) length(inds2)]);

ylabel('# entries');
set(gca,'XTickLabel',{'< -1', '-1<x<-0.5'});

%use of histc to make this more automatic
figure(21)
N=histc(randNumbers,-2:0.5:2);   %counts the number of entries for -2..-1.5, -1.5..-1 ... etc
bar(-2:0.5:2, N, 'histc');


%---- how to use subplot
figure(3)
subplot(1,2,1)   %1 row, 2 columns; select first plot
hist( randNumbers, 100);  %histogram, 100 bins
subplot(1,2,2)   %1 row, 2 columns; select second plot
hist( randNumbersSmall, 100);
xlim([-3 3]);


%---- how to access data in structures, loops etc
for i=1:10
    i    
end

for i=1:2:10
    i    
end


%---- statistical tests

%are the means of two population of normally distributed numbers different?

pop1 = randn(1000,1); %mean 0
pop2 = randn(1000,1); %mean 0

mean(pop1)
mean(pop2)

%is this significant?  (yes if p < 0.05 )
[h,p] = ttest2(pop1,pop2);
p           % not significant

pop2 = pop2+0.1;        % pop2 theoretical mean is 0.1 now

mean(pop1)
mean(pop2)

[h,p] = ttest2(pop1,pop2);
p           % now is significant

%load supplied data file
load 'N1.mat'