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flt(2) Scilab Function flt(2)
NAME
flt - Fast Legendre transform
Author: Paulo Goncalves
Computes the Legendre transform of y y*(s) = sup_{x in X}[s.x - y(x)]
Usage
[u,s] = flt(x,y[,ccv])
Input parameters
o x : real valued vector [1,N] samples support of the function y
o y : real valued vector [1,N] samples of function y = y(x)
o ccv : optional argument to choose between convex (ccv = 0) and con-
cave (ccv = 1) envelope. Default value is ccv = 1 (concave)
Output parameters
o u : real valued vector [1,M] Legendre transform of input y. Note
that, since u stems from the envelope of y, in general M <= N.
o s : real valued vector [1,M] Variable of the Legendre transform of
y.
See also:
Example:
Function synthesis
m0 = .55 ; m1 = 1 - m0 ;
m2 = .95 ; m3 = 1 - m2 ;
q = linspace(-20,20,201) ;
tau1 = - log2(exp(q.*log(m0)) + exp(q.*log(m1))) ;
tau2 = - log2(exp(q.*log(m2)) + exp(q.*log(m3))) ;
tau3 = min(tau1 , tau2) ;
Legendre Transforms
[u1,s1] = flt(q,tau1) ;
[u2,s2] = flt(q,tau2) ;
[u3,s3] = flt(q,tau3) ;
Vizualisation - Matlab
plot(s1,u1,'g',s2,u2,'b',s3,u3,'r') ; grid ;
legend('u(tau1(q))','u(tau2(q))','u(tau3(q))') ;
Vizualisation - Scilab
plot2d(s3,u3,17) ; plot2d(s1,u1,18,'001') ; plot2d(s2,u2,19,'001') ;
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