fig_2_9_simulate_hom_profiles_gaussian

% Fig. 2.9 page 51 and Fig 16.11 page 742 
 simulate homgeneous/inhomogeneous 1D gaussian process

 Wolfgang Förstner 2015
 last changes: Susanne Wenzel 09/16
 [email protected], [email protected]

0001 %% Fig. 2.9 page 51 and Fig 16.11 page 742
0002 % simulate homgeneous/inhomogeneous 1D gaussian process
0003 %
0004 % Wolfgang Förstner 2015
0005 % last changes: Susanne Wenzel 09/16
0006 % [email protected], [email protected]
0007 
0008 close all
0009 clearvars
0010 
0011 addpath(genpath('../General-Functions'));
0012 
0013 %% set your parameters ------------------------------------------
0014 NoSample = 3;       % number of smaples for the plot, <5
0015 N = 300;            % number of grid points
0016 
0017 % parameters for homogeneous  gaussian process
0018 d0 = 20;            % reference distance
0019 sigma = 1;          % standard deviation
0020 
0021 % parameters for inhomogeneous  gaussian process
0022 d0l = 10;               % left reference distance
0023 sigma_l = 0.5;          % left std
0024 d0r = 40;               % right reference distance
0025 sigma_r = 3;            % right standard deviation
0026 dc = 30;                % smearing constant
0027 
0028 %---------------------------------------------------------------
0029 
0030 %% prepare visualization
0031 % line spec
0032 col=['k','b','r','c','m'];
0033 lin=['-','-','-','-','-'];
0034 
0035 % get current screensize, for proper positioning of figures and set default
0036 % plot settings
0037 ss = plot_init;
0038   
0039 %% homogeneous GP
0040 
0041 % initiate covariance matrix
0042 Sigma=zeros(N);  
0043 % generate 300x300 covariance matrix
0044 for n = 1:N
0045     for m = 1:N
0046         d = (n-m)/d0;
0047         Sigma(n,m) = sigma^2*exp(-d^2/2);
0048     end
0049 end
0050 
0051 % generate three samples
0052 y = rand_gauss(zeros(N,1),Sigma,NoSample);
0053 
0054 % plot samples
0055 figure('name','homogeneous GP','color','w','Position',[0.1*ss(1),0.2*ss(2),0.35*ss(1),0.60*ss(2)]); hold on
0056 for s = 1:NoSample
0057     plot(1:N,y(:,s),strcat(lin(s),col(s)),'LineWidth',2);
0058 end
0059 plot(1:N, -3*sigma*ones(1,N),'--k')
0060 plot(1:N, +3*sigma*ones(1,N),'--k')
0061 xlim([-25,N+25])
0062 ylim([-4.5,+4.5]*sigma)
0063 xlabel('$t$');ylabel('$x$')
0064 title('Fig. 2.9: Samples of homogeneous Gaussian Process')
0065 
0066