File: fbmlevinson.sci

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function [x,y,r] = fbmlevinson(N,H,seed) ;

// This Software is ( Copyright INRIA . 1998  1 )
// 
// INRIA  holds all the ownership rights on the Software. 
// The scientific community is asked to use the SOFTWARE 
// in order to test and evaluate it.
// 
// INRIA freely grants the right to use modify the Software,
// integrate it in another Software. 
// Any use or reproduction of this Software to obtain profit or
// for commercial ends being subject to obtaining the prior express
// authorization of INRIA.
// 
// INRIA authorizes any reproduction of this Software.
// 
//    - in limits defined in clauses 9 and 10 of the Berne 
//    agreement for the protection of literary and artistic works 
//    respectively specify in their paragraphs 2 and 3 authorizing 
//    only the reproduction and quoting of works on the condition 
//    that :
// 
//    - "this reproduction does not adversely affect the normal 
//    exploitation of the work or cause any unjustified prejudice
//    to the legitimate interests of the author".
// 
//    - that the quotations given by way of illustration and/or 
//    tuition conform to the proper uses and that it mentions 
//    the source and name of the author if this name features 
//    in the source",
// 
//    - under the condition that this file is included with 
//    any reproduction.
//  
// Any commercial use made without obtaining the prior express 
// agreement of INRIA would therefore constitute a fraudulent
// imitation.
// 
// The Software beeing currently developed, INRIA is assuming no 
// liability, and should not be responsible, in any manner or any
// case, for any direct or indirect dammages sustained by the user.
// 
// Any user of the software shall notify at INRIA any comments 
// concerning the use of the Sofware (e-mail : FracLab@inria.fr)
// 
// This file is part of FracLab, a Fractal Analysis Software"


oldrnd=rand('info');
if length(H) > 1
  error('Time-dependant regularity not allowed yet.')
end

[nargout,nargin] = argn(0) ;
tmax = N-1 ;  
shift = 1 ;
if nargin < 3 ; rand ('uniform') ; seed = rand(1) * 1e6 ; end
t = linspace(0,tmax,N) ;
s = 0 ;
alpha = 2*H ; sigma = 1 ;
r = sigma^2*(abs(t+shift-s).^alpha + abs(t-s-shift).^alpha - 2*abs(t-s).^alpha)/2 ;

rand('normal') ;
rand('seed',seed) ;
y = rand(N,1) ;

inter1(1) = r(1) ;
x = zeros(1,N) ;

inter1 = r ;
inter2 = [0 r(2:N) 0] ;
Y = y(1)*r ;

k = -inter2(2) ;
aa = sqrt(r(1)) ;

for j = 2:N

  aa = aa*sqrt(1-k^2) ;
  inter = k*inter2(j:N) + inter1(j-1:N-1) ;
  inter2(j:N) = inter2(j:N) + k*inter1(j-1:N-1) ;	
  inter1(j:N) = inter ;					
  bb = y(j)/aa ; ;
  x(j:N) = x(j:N) + bb*inter1(j:N) ;
  k = -inter2(j+1)/(aa^2) ;

end

coef = 1/(N^H) * sigma ;
x = cumsum(x(:)).*coef ;
rand(oldrnd)