generate random numbers with a given correlation in matlab

Q. How to generate random numbers with a pre specified correlation in Matlab?

Ans. Use mvnrnd() function.This function takes mean (vector of 1xk), covariance (matrix of k x k), number of points (n). The output is an nxk matrix which corresponds to the multivariate normal distribution with the specified mean, covariance.

>> n=1000; mu=[-2,2]; sigma=[1 0.5; 0.5 1]; X = mvnrnd(mu, sigma, n);
>> size(X)
ans =
        1000           2

>> mean(X)
ans =
   -2.0350    2.0157

>> cov(X)
ans =
    0.9950    0.4898
    0.4898    0.9894

>> plot(X(:,1), X(:,2), '.')
>> grid

The problem is underspecified if only the correlation matrix is known. In this case, set the mean to a zero vector, covariance to the given correlation matrix.

Tested in MATLAB 7.14.0.739 (R2012a),  Octave 3.6.2

passing functions as arguments in octave

It is possible to pass functions as arguments to another function in Octave. Consider the following sample code

$ls
cube.m  dynamic.m  script.m  square.m

$cat square.m
function [sq] = square(x)
sq = x**2;
endfunction

$cat cube.m
function [cu] = cube(x)
cu = x**3;
endfunction

$cat dynamic.m
function [ ret ] = dynamic (fh, x)
# fh is a function name passed as a string
# ex:-    b = dynamic("cube", a);
# fh can also be a handle
#         handle = @square;
#         b = dynamic(handle, a);
ret = feval(fh, x);
endfunction

$cat script.m
a=5.0

# bh = b obtained by using handle as arguments
handle=@square;
bh = dynamic( handle, a)

# bs = b obtained by using strings as arguments
bs = dynamic("square", a)

# ch = c obtained by using handle as arguments
handle=@cube;
ch = dynamic( handle, a)

# cs = c obtained by using strings as arguments
cs = dynamic("cube", a)

Run the script.m in octave

$octave3.2 -qf script.m

a =  5
bh =  25
bs =  25
ch =  125
cs =  125

Tested using Debian Lenny (stable), Octave 3.2.4

Further Reading:
1) The section on "Function handles, Inline Functions, and Anonymous Functions" in the octave manual http://www.gnu.org/software/octave/doc/interpreter/Function-Handles-Inline-Functions-and-Anonymous-Functions.html

2) http://rosettacode.org/wiki/Higher-order_functions explains how to do this kind of "calling functions from functions" in various programming languages

load data file with header lines in octave

When a data file contains some header lines before the actual data matrix, octave's dlmread function can be used to read the matrix of data and ignore the headers.

For example,

$cat input_data.m
col1 col2 col3
1, 2, 3
4, 5, 6
7, 8, 9
10, 11, 12

This file contains one header line and a 4x3 data matrix. To read it into octave, create a script called

$cat read_data.m
1;
A = dlmread("input_data.m", SEP=',', R0=1, C0=0);
A

$octave3.2 -qf
octave3.2:1> read_data
A =

1 2 3
4 5 6
7 8 9
10 11 12


For more information on dlmread function, use 'help dlmread' inside octave.

Tested using octave 3.2.4-3 on Debian stable (Lenny).

running external commands

1. To run external commands while editing a file in vim, use the '!' in the normal mode. For example
   

   :!ls -al
   

   will list the files
   

   :!date
   

   will display the current date.
   
   
2. To read the output of external commands into the current file, do
   

   :r !date
   

   All the commands are run in normal mode. Press ESC key to enter the normal mode in vim.
   
   Further reading:- :help :!
   
   
3. To run external commands in octave, use the system command. Sample octave session looks as
   

   $octave -q
   octave:1> system("date")
   Thu Jun  4 23:49:23 EDT 2009
   ans = 0
   octave:2> [ret_code output] = system("date");
   octave:3> ret_code
   ret_code = 0
   octave:4> output
   output = Thu Jun  4 23:49:40 EDT 2009
   
   octave:5> exit

   Further reading :- "doc system" shows the relevant help pages in octave.
   
   
4. To run external commands in Fortran 90 programs, use the system command. Sample code looks as below
   

   $cat system.f90
   program callsystem
          implicit none
          !to examine the behaviour of the system command
          character (len=100)::cmd
          cmd="echo Wake up Neo"
          !if u are using ifc compiler use -Vaxlib during compilation
          call system(cmd//achar(0))
          call system(cmd)
          call system("date")
          ! The next line also works.
          ! call system("ls")
   end program callsystem
   
   $gfortran system.f90
   
   $./a.out
   Wake up Neo
   Wake up Neo
   Thu Jun  4 23:55:07 EDT 2009

5. To run the external commands in C, use the system command available in stdlib.h. Sample code will be
   

   $cat system.c
   #include stdio.h
   #include stdlib.h
   
   int main() {
        /* Fixme :- <, > in the header files are not showing up on blogspot */
        int ret_code;
        ret_code = system("date");
   
        printf("%d\n", ret_code);
        return 0;
   }
   
   $gcc -Wall system.c
   
   $./a.out
   Fri Jun  5 00:04:14 EDT 2009
   0

   
   Further reading :- man system
   
   All the above are tested in Debian Lenny using vim 7.1, octave 3.0.1, gfortran 4.3.1, gcc 4.3.1