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linearlt(2) Scilab Function linearlt(2)
NAME
linearlt - linear time legendre transform
Author: Christophe Canus
This C_LAB routine the Legendre transform of a function using the linear
time Legendre transform algorithm.
Usage
[s,u_star_s]=linearlt(x,u_x)
Input parameters
o x : real vector [1,N] or [N,1] Contains the abscissa.
o y : real vector [1,N] or [N,1] Contains the function to be
transformed.
Output parameters
o s : real vector [1,M] Contains the abscissa of the regularized func-
tion.
o u_star_s : real vector [1,M] Contains the Legendre conjugate func-
tion.
Description
Parameters
The abscissa x and the function u_x to be transformed must be of the same
size [1,N] or [N,1]. The abscissa s and the Legendre conjugate function
u_star_s are of the same size [1,M] with M<=N.
Algorithm details
The linear time Legendre transform algorithm is based on the use of a con-
cave regularization before slopes' computation.
Examples
Matlab
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);
Scilab
//
References
None..SH See Also bbch (C_LAB routine).
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