TWODIM.M    1/17/2005

Let's make a two-dimensional data set to illustrate EOF analysis

Run this over and over again with the graphic window open and see how little the eigenvectors move, even though the data are jumping all over the place.  Increase and reduce the sample size. 

Vary the parameter c1 [ 1 -1 2 ] to change the slope of the cloud of points.

clear all

echo on

loop on time

tap space bar to go to next set of data

echo off

for ii=1:10

Set the sample size to num

num=120;

set the parameter controlling the amplitude of the first variablea1=2.0;

set the parameter controlling the noise of the second variablea2=2.5;

set the parameter scaling the second variable on the firstc1=0.5;

Make data setfor i=1:num 

First number is Gaussian noise with an amplitude of a1x(1,i)=randn(1)*a1;

Second number is the first times a slope c1,

plus more noise of amplitude a2x(2,i)=c1*x(1,i)+randn(1)*a2;end

Remove mean

xm=x;

for i=1,2

xm(1,:)=x(1,:)-mean(x(1,:));

xm(2,:)=x(2,:)-mean(x(1,:));

end

Compute covariance matrixc=xm*xm'/num;

do SVD of covariance matrix[u s v]=svd(c)

make a scatter diagram of the data

scatter(xm(1,1:num),xm(2,1:num),10)

set(get(1,'CurrentAxes'),'FontSize',14)

xlabel('X1','Fontsize',14)

ylabel('X2','Fontsize',14)

Write the eigenvectors and eigenvalues on the plot

es=num2str(u,'%8.4g')

xtitle=strcat('e1=',es(1,1),es(2,1),',e2=',es(1,2),es(2,2))

xtitle=strcat(es);

ss=num2str(s,'%8.2g')

ytitle=strcat(ss);title(xtitle)

h=text(-8,8,xtitle)

set(h,'fontsize',14)

h2=text(-8,6,ytitle)

set(h2,'fontsize',14)

Plot the eigenvectors in red on this plot

Make them 10 units long instead of 1, so you can see them better 

u=u*10;

xx(1,1)=0.0;

xx(2,1)=u(1,1);

xx(1,2)=0.0;

xx(2,2)=u(1,2);

yy(1,1)=0.0;

yy(2,1)=u(2,1);

yy(1,2)=0.0;

yy(2,2)=u(2,2);

line(xx,yy,'color','red')

set the axis limits

axis([-10 10 -10 10])

make the plot square, so the eigenvectors look orthogonalset (gca,'DataAspectRatio',[1 1 1])

echo on

press space bar to continue

echo off

pause

clear all

end

echo on

FINISHED!