!Finding the minimum of a given external nonlinear function with dimension n using
!the Downhill Simplex method.

program NONLIN_EQUATIONS_min
use MY_STUFF
use FUNCTION_TEST
Implicit none

     integer, parameter :: n=2   !Dim. of problem
     integer :: M 
     real(KIND=dbl) :: tolf, tolx
     real(KIND=dbl), dimension(n) :: x_final
     real(KIND=dbl), dimension(n+1,n) ::sim
!Tolerance on f(x1,x2) and simplex:
tolf = 0.0000001 ; tolx = 0.00001

!Initial simplex:
sim(1,1) = 37.0 ; sim(1,2) = -15.0
sim(2,1) = 20.0 ; sim(2,2) = 27.0
sim(3,1) = 43.0 ; sim(3,2) = -25.0

call SIMPLEX(sim, n, tolf, tolx, x_final, M)


print  '("Minimum at (x,y) = ", f12.6, " ,", f9.6)', x_final(1), x_final(2)
print  '("Function value of final point:", f12.6)', f(x_final(1))
print *, "Total number of iterations:", M
print "(/)"
print '("Tolerance on function value:", e10.2)', tolf
print '("Tolerance on Simplex size:  ", e10.2)', tolx

end program NONLIN_EQUATIONS_min