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.TH " linearlt" 2 " March 10, 1998" "Fractales Group" "Scilab Function"
.so ../sci.an
.SH NAME
linearlt - linear time legendre transform
.sp
Author: Christophe Canus
.sp
This C_LAB routine the Legendre transform of a function using the linear time Legendre transform algorithm.
.sp
.sp
.SH Usage
\f(CR[\fPs,u_star_s\f(CR]\fP=linearlt(x,u_x)
.SH Input parameters
.RS
.TP
o
\fBx\fP : real vector \f(CR[\fP1,N\f(CR]\fP or
\f(CR[\fPN,1\f(CR]\fP
Contains the abscissa.
.TP
o
\fBy\fP : real vector \f(CR[\fP1,N\f(CR]\fP or
\f(CR[\fPN,1\f(CR]\fP
Contains the function to be transformed.
.RE
.SH Output parameters
.RS
.TP
o
\fBs\fP : real vector \f(CR[\fP1,M\f(CR]\fP
Contains the abscissa of the regularized function.
.TP
o
\fBu_star_s\fP : real vector \f(CR[\fP1,M\f(CR]\fP
Contains the Legendre conjugate function.
.RE
.SH Description
.SH Parameters
The abscissa \fIx\fP and the function \fIu_x\fP to be transformed must
be of the same size \f(CR[\fP1,N\f(CR]\fP or \f(CR[\fPN,1\f(CR]\fP.
The abscissa \fIs\fP and the Legendre conjugate function \fIu_star_s\fP
are of the same size \f(CR[\fP1,M\f(CR]\fP with \fIM\fP\f(CR<=\fP\fIN\fP.
.SH Algorithm details
The linear time Legendre transform algorithm is based on the use of a
concave regularization before slopes' computation.
.SH Examples
.SH Matlab
.sp
.ft CR
.nf
x=linspace(-5.,5.,1024);
u_x=-1+log(6+x);
plot(x,u_x);
% looks like a Reyni exponents function, isn't it ?
[s,u_star_s]=linearlt(x,u_x);
plot(s,u_star_s);
.fi
.ec
.ft P
.sp
.SH Scilab
.sp
.ft CR
.nf
//
.fi
.ec
.ft P
.sp
.SH References
None..SH See Also
\fBbbch\fP (C_LAB routine).
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