xrwalk.m

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%                                xrwalk.m
%  Scope:   This MATLAB program generates a random walk process, and plots the
%           random walk sequence and the normalized auto-correlation sequence
%           (optional).
%  Usage:   xrwalk
%  Inputs:  - number of random number to be generated
%           - value of the noise covariance, q*dt 
%           - value of the initial seed, e.g. 0
%           - name of the output file (optional), if the generated data are saved
%  Outputs: - plot of the random walk sequence
%           - plot of the normalized auto-correlation sequence
%  External Matlab macros used:  genrn, rms, rwalk, xcorr (from Signal 
%                                Processing Toolbox) - optional
%  Last update:  06/27/00
%  Copyright (C) 1996-00 by LL Consulting. All Rights Reserved.

clear 

yes = 'y';
answer1 = yes;
disp('  ');

while (strcmp(answer1,yes) == 1)

   clear  x
   close all

%  Specify the input data

   nstep = input('Specify the number of random numbers to be generated --> ');
   disp('  ');
   qdt = input('Specify the value of the noise covariance, q*dt --> ');
   disp('  ');
   iseed = input('Specify the value of the initial seed, iseed, e.g. 0 --> ');
   disp('  ');

%  Generate the random walk process (zero mean and standard deviation equals 
%  to  q*dt)

   x = rwalk(nstep,qdt,iseed);

%  Determine mean, standard deviation and root mean square (rms) for the 
%  generated random numbers

   xmean = mean(x);
   xstd = std(x);
   xrms = rms(x);
   temp1 = ['mean = ',num2str(xmean)];
   temp2 = ['st.dev. = ',num2str(xstd)];
   temp3 = ['rms = ',num2str(xrms)];
   g = [temp1,' ;   ',temp2,' ;   ',temp3];
   
%  Save the generated data into a specified file if desired

   answer2 = input('Do you want to save the generated data? (y/n)[y] --> ','s');
   if  isempty(answer2)
      answer2 = 'y';
   end
   if strcmp(answer2,yes) == 1
      disp('  ');
      f2 = input('Specify the output file name  --> ','s');
      for  k = 1:nstep
         fprintf(f2,'%24.14e\n',x(k));
      end
   end
   
%  Plot the random walk sequence 
   
   dd = num2str(nstep);
   aa = 'Random walk process - with ';
   aa = [aa dd ' time sequences'];
   ee = 'Random walk sequence';
   ff = 'Time sequence';
   disp('  ');
   disp('Execute random walk graph ... ');
   disp('Select the mouse position to insert statistics text on the graph...');
   temp = input('Press a key to start ...');
   figure(1)
   plot(x),...
   title(aa), ylabel(ee), xlabel(ff), grid,...
   gtext(g);                   %  mouse placement of the text on a graph
   disp('  ');
   disp('Check the window containing the Random Walk Graph and  . . .');
   disp('Press a key to continue . . .   ');
   pause

%  Plot the normalized auto-correlation sequence

   disp('  ');
   disp('For the auto-correlation sequence - the function XCORR from  ');
   disp('Signal Processing Toolbox is required');
   answer3 = input('Plot the auto-correlation sequence? (y/n)[y] --> ','s');
   if  isempty(answer3)
      answer3 = 'y';
   end
   if strcmp(answer3,yes) == 1
      b = -(nstep-1):1:(nstep-1);
      a = xcorr(x','coeff');
      bb = 'Normalized auto-correlation sequence';
      cc = 'Sequence lag';
      figure(2)
      plot(b,a'),...
      title(aa), ylabel(bb), xlabel(cc), grid;
      disp('  ');
      disp('Check the window containing the Auto-correlation Graph and . . .');
      disp('Press a key to continue . . .  ');
      pause
   end
   
%  Select another computation, if desired
   
   disp('  ');
   answer1 = input('Do you want another computation? (y/n)[y] --> ','s');
   disp('  ');
   if  isempty(answer1)
      answer1 = 'y';
   end
   
end

disp('End of the program XRWALK');
disp('  ');