File: MFAG_eta.sci

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function MFAG_eta(mu_n,s,e,norm_type);

// 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



// function MFAG_eta(mu_n,s,e,norm_type)
//
// Computes a vector of Continuous Large Deviation spectrum 
// with fixed precision epsilon (e) 
// and varying scale eta (related to the scale factor (s: eta=s*eta_n)
//
// inputs : 	mu_n: input 1d pre-mu_nltifractal measure
//		(normalized strictly positive vector)
//		s: scale factor 
//		(strictly positive vector)
//		e: set the precision epsilon of the pdf 
//		(strictly positive scalar)
//		norm_type: type of the Lp norm
//		(1,2,inf,-inf,P)
// outputs : 
//

// set nu_n, eta_n, eta_i, n, m, f
[height,width]=size(mu_n);
nu_n=max([height,width]);
eta_n=1./nu_n;
eta_i=eta_n.*s;
[height,n]=size(s);
[height m]=size(e);
f=zeros(n,200);

// compute first spectrum 
i=1;
[a,f,p,oe]=mcfge(mu_n,200,2,s(i),e);
f(i,:)=f;
// plot first spectrum
plot(a,f(i,:));

// compute other spectra 
for i=2:n
	[a,f,p,oe]=mcfge(mu_n,200,2,s(i),e);
	f(i,:)=f;
	plot(a,f(i,:)); 
	norm_diff(i)=norm(f(i,:)-f(i-1,:),norm_type);
end


// plot norm_diff
plot(eta_i(2:n),norm_diff(2:n),'-');