1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
|
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)
|