Some good blog posts

I ran into a blog yesterday, which is a very good source for Matlab fans. And i found some posts are really useful.

This one tells you how to better manage the memory:
http://obasic.net/preallocate-before-you-loop-it-in-matlab

This one shows how to conveniently set up the interface and default settings by using startup file.
http://obasic.net/set-your-customized-startup-file-for-matlab

Though some of them are geeky:
Twitter from Matlab?
http://obasic.net/how-to-twitter-from-matlab
Sending email using Matlab?
http://obasic.net/how-to-send-e-mail-from-matlab

Anyway, very nice job.

how to calculate payments on a loan using MS Excel?

Excel has lots of useful built-in functions, and PMT is one of them that can calculate payments on a loan for you. Here is a simple example:

If I get a loan of $5000 from a bank, with the annual interest rate of 8%, and I am supposed to pay it off in 3 years, how much should I pay (OR they will ask me to pay) each month?

And here is how to do the calculation:
Input following into any cell of a Excel worksheet:

=PMT(0.08/12, 3*12, 5000)

and press Enter.

The value shown in the cell ($156.68 ) is the money I am going to pay to the bank each month. Here 0.08/12 is used because the 8% is annual rate, so divide it by 12 to get the monthly rate. And in 3 years, there are 3*12 months, which means the number of payment is 36.

Then, what is the total I pay to the bank? As you might have guessed, it is $156.68*36 (=$5640.55). So the bank will earn $640.55 in this deal at the end. Well, that is a lot of money. Now I am thinking about how to own a bank...


P.S: If you didn't buy MS Excel, that's OK! The Google Docs spreadsheet will do the same thing for you! It is right here: docs.google.com


P.S: this has nothing to do with Matlab, but it is still interesting (at least to me) and useful.

Linear least-square regression

Of course, the linear least-square regression is an easy thing to do in Excel. Just adding a linear trend-line to the plot will do that for you. Anyway, I wrote this piece of code to do it in Matlab. 

% Single least-square linear regression
%Created on 02/17
x=input ('x='); %use [] to input a row
y=input ('y='); %use [] to input a row
X=mean(x);
Y=mean(y);
beta=(sum((x-X).*(y-Y)))/sum((x-X).^2);
alpa=Y-beta*X;
Equation=strcat('y=',num2str(beta), 'x+',num2str(alpa))

The num2str function was used to convert the beta and alpa, which are numbers, into strings.
The strcat function was used to concatenate the strings.

Give curves random color, just for fun

A few days ago, I drew some curves on a same plot. And now I want to randomize the curve color.

Because the color syntax can be expressed as letters such as k, g, b etc. and also as a three element row, which indicate the RBG mode, such as [1, 0, 1], [0.1,0.7, 0.4] and so on.

So here I wrote a M-file to randomize the color and plot 10 curves in each subplot.

%this code produce a three element row
%which can be used to specify a random color
%created on 02/15/2010
function rndclr=f()
rndclr=[rand, rand, rand];
%this code draws some curves
%of random color
clf
t=0:0.01:100*pi;
for j=1:9
for i=1:10
hold all;
x=(i+2)*cos(t/i)+cos((i-1)*t);
y=i*sin(t/i)+sin((i-3)*t);
subplot (3,3,j);
plot(x,y,'color',rndclr)
axis('equal')
axis off
end
end

And here is the figure:

Yahoo META Tag

I'm not sure if this will work or not. Let's see!

M-file, single-variable function integration and boundary on fixed interval

%This is a simple f(x) function
function y =bumpy(x)
%this function draws a bumpy curve

y=1/(4*pi)*(1./((x-2).^2+1)+1./((x+0.5).^4+32)+1./((x+1).^2+2));
%This is how to integrate the function on (-3,3), with tolerance of 10^(-6)
quad('bumpy', -3, 3, 10^(-6))
%This is how to find the minimum boundary of x and y, on (-1.2, 1)
xmin=fminbnd('bumpy',-1.2, 1)
ymin=bumpy(xmin)
%How to find the maximun boundary?
%find minimum boundary for y=-f(x)



%This is example is from Introduction to Matlab with numerical preliminaries by Alexander Stanoyevitch.

How do I know if the file name already exist or not?

I tried to save a M-file and was told the file name already exist. How do i know that before I start saving it?
This function would help:

exist ('file_name_you_want_to_check')

Possible output are 0,1,2,3,4,5,6,7,8. However, only 0 means that the file name does not exist and is available to you.

Factorial in Matlab

To calculate the factorial of n in Matlab, that's simple:

factorial (n)

will do it.

plotting some curves, just for fun

%this code draws some curves
clf
t=0:0.01:100*pi;
for i=1:10
    hold all;
x=(i+2)*cos(t/i)+cos((i-1)*t);
y=i*sin(t/i)+sin((i-3)*t);
plot (x,y,'red')
end
axis('equal')

Find the element you want in matrix

a =

     1     2     3
     1     3     4
     1     4     5
     2     5     6
     2     6     7
     3     7     8
     2     8     9
     1     0     1
     2     1     2
the command:
b = find ( a ( : , 1 )= =2)
returns following results:

b =

     4
     5
     7
     9

the coomand:
c= a ( b , : )
returns following results:

c =

     2     5     6
     2     6     7
     2     8     9
     2     1     2

This is how to pick out all the rows in which the first element is 2 in matrix a and put them into c. I could have used this to handle my ozone historic data and it will be much easier.  

Use stopwatch to measure the time elapsed

 run 3D random walk for 30 times and get the average time of each run.

% random walk
for k=1:30
tic;
x=[];
y=[];
z=[];
x(1)=0;
y(1)=0;
z(1)=0;
tTotal=0;
for i=1:1000
    J=rand*6;
if J<1
    x(i+1)=x(i)+1;
    y(i+1)=y(i);
    z(i+1)=z(i);
elseif (J>1)&(J<2)
    x(i+1)=x(i)-1;
    y(i+1)=y(i);
    z(i+1)=z(i);
elseif (J>2)&(J<3)
    x(i+1)=x(i);
    y(i+1)=y(i)+1;
    z(i+1)=z(i);
elseif (J>3)&(J<4)
    x(i+1)=x(i);
    y(i+1)=y(i)-1;
    z(i+1)=z(i);
elseif (J>4)&(J<5)
    x(i+1)=x(i);
    y(i+1)=y(i);
    z(i+1)=z(i)+1;
else
    x(i+1)=x(i);
    y(i+1)=y(i);
    z(i+1)=z(i)-1;
end
end
plot3(x,y,z)
t(i)=toc;
tTotal=tTotal+t(i);
end
tAve=tTotal/10;

Resutls:

when i=1:1000, tAve=0.0012s
when i=1:2000, tAve=0.0032s
when i=1:4000, tAve=0.0114s
when i=1:6000, tAve=0.0506s
when i=1:12000, tAve=0.1882s
when i=1:24000, tAve=0.8823s.
when i=1:48000, tAve=2.7501s.

3D Random walk

% random walk
x=[];
y=[];
z=[];
x(1)=0;
y(1)=0;
z(1)=0;
for i=1:20000
J=rand*6;
if J<1>1)&(J<2)>2)&(J<3)>3)&(J<4)>4)&(J<5)
x(i+1)=x(i);
y(i+1)=y(i);
z(i+1)=z(i)+1;
else
x(i+1)=x(i);
y(i+1)=y(i);
z(i+1)=z(i)-1;
end
end

plot3(x,y,z)

Result:

2D Random walk program

Why I want to do this?
http://en.wikipedia.org/wiki/Random_walk

Here's the code I wrote:

% random walk
x=[];
y=[];
x(1)=0;
y(1)=0;
for i=1:100000
J=rand;
if J<0.25
x(i+1)=x(i)+1;
y(i+1)=y(i);
elseif (J>0.25)&(J<0.5)
x(i+1)=x(i)-1;
y(i+1)=y(i);
elseif (J>0.5)&(J<0.75)
x(i+1)=x(i);
y(i+1)=y(i)+1;
else
x(i+1)=x(i);
y(i+1)=y(i)-1;
end
end

plot(x,y)

And here are the figure I got: