'Program NNMAP.BAS trains a neural network to a 1-D map
'(c) 2004 by J. C. Sprott <http://sprott.physics.wisc.edu>
'Compile with PowerBASIC for DOS <http://www.powerbasic.com>
defext a-z
randomize timer
np&=2		'Number of parameters
dim a(np&), abest(np&)
for i&=1 to np&: abest(i&)=1: next i&
eps=1: ebest=1e6
while inkey$<>chr$(27)
    for i&=1 to np&
    	a(i&)=abest(i&)+eps*gauss
    next i&
    c=-a(2)*tanh(a(1))
    f1=a(2)*tanh(a(1)/2##) + c/2## - 1##
    f2=a(1)*a(2)*sech(a(1)/2##)^2 + c
    e=f1*f1+f2*f2
    if e<=ebest then
    	ebest=e
        cls
        print"Error =";e
        print"Neighborhood =";eps
        print"Slope @ zero =";a(1)*a(2)+c
        print
        print"a =";a(1)
        print"b =";a(2)
        print"c =";c
        for i&=1 to np&
            abest(i&)=a(i&)
        next i&
        eps=min(2*eps,1)
    else
    	eps=0.9999*eps
    end if
wend

'plot results
screen 12
color 8,63
cls
line(0,0)-(639,479),,b
y1=rnd: y2=y1
while inkey$<>chr$(27)
    x=y1
    y1=4##*x*(1##-x)
    pset(639*x,479-479*y1)
    x=y2
    y2=a(2)*tanh(a(1)*x)+c*x
    pset(639*x,479-479*y2),3
    le=le+log(abs(a(1)*a(2)*sech(a(1)*x)^2+c))
    incr n&&
    if (n&& mod 1000)=0 then locate 2,2: print"LE =";csng(le/n&&)
wend

end

FUNCTION tanh (x)
    'Returns hyperbolic tangent of x
    tanh = 1## - 2## / (EXP(2## * x) + 1##)
END FUNCTION

FUNCTION sech (x)
    'Returns hyperbolic cosecant of x
    sech = 2## / (EXP(x) + EXP(-x))
END FUNCTION

FUNCTION gauss
    'Returns a normally (Gaussian) distributed random deviate
    'with mean of zero and standard deviation of 1.0
    DO
        V1 = 2## * RND - 1##
        V2 = 2## * RND - 1##
        R = V1 * V1 + V2 * V2
    LOOP WHILE R >= 1## OR R = 0##
    GAUSS = V2 * SQR(-2## * LOG(R) / R)
END FUNCTION