/* Simulatior for Probability Distribution */
% 19 Nov 2002.
% 21 Dec 2011. minor bugfix (last/2 was worngly used in gen_histogram/4. why?)


:-write('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'),nl,
   write(' A Simulatior for Probabilities'),nl,
   write('%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'),nl,
   write('type ``gen_dist(uniform,[0,1],100,P)." or ``menu."'),nl.

wn(Z):-write(Z),nl.
nw(Z):-nl,write(Z).
menu:-
 nl,
 tab(2),wn('1. model a distribution.'),
 tab(2),wn('2. calculate the frequency (i.e., build the histogram).'),
 tab(2),wn('3. draw a graph of the histogram.'),
 tab(2),wn('4. exit this menu.'),
 tab(1),write('input number>'),
 read(Y),
 (
   (
     member([Y,A],[[1,dist],[2,freq],[3,draw],[4,exit]]),
     write('You selected '),write((Y,(A))),write('. OK? (y/n)'),
     read(y)
   )
   ->
    (
     (Y=1->set_gen_dist(D,[L,U],_N,_P);true),
     ((\+var(L),\+var(U))->(G=..[D,L,U],write(G));true),
     (Y=2->set_gen_histogram(G,_Class,_M,cum);true),
     (Y=3->draw_histogram;true),
     (Y=4->!, fail; true) % to exit the menu (modified: Dec 2011)
    )
   ; menu
 ),
 menu.
select_dist:-select_dist(_).
select_dist(N):-
 nl,
 tab(2),wn('1. uniform distribution.'),
 tab(2),wn('2. trianglar distribution.'),
 tab(2),wn('3. binominal distribution.'),
 tab(2),wn('4. normal distribution.'),
 tab(1),write('input number>'),
 read(Y),
 (
   (
     member([Y,A],[[1,uniform],[2,triangle],[3,binominal],[4,normal]]),
     write('Will you generate a '),write(A),write(' distribution?(y/n)'),
     read(y)
   )
   ->set_gen_dist(A,_,_,_)
   ; select_dist(N)
 ),
 menu.

p(dummy,nul,0,0).
p_init:- abolish(p,4), assert(p(dummy,nul,0,0)).

sampling_limit(1000).
set_gen_dist(X,no,no,abend):-
  \+ member(X,[uniform]),
  wn('Not yet.').
set_gen_dist(A,B,N,D):-
  var(N),
  write('Type the sample size. '),
  read(N),
  set_gen_dist(A,B,N,D).
set_gen_dist(_,_,N,abend):-
  sampling_limit(T),
  N > T,
  wn('Too large sample size. Please try a smaller.').
set_gen_dist(A,[L,U],N,D):-
  %(var(L);var(U)),
  var(L),
  write('Type the lower bound. '),
  read(Y),
  L is integer(Y),
  set_gen_dist(A,[L,U],N,D).
set_gen_dist(A,[L,U],N,D):-
  %(var(L);var(U)),
  var(U),
  write('Type the upper bound. '),
  read(Y),
  U is integer(Y),wn(gen_dist(A,[L,U],N,D)),
  gen_dist(A,[L,U],N,D).
gen_dist(uniform,[L,U],_,abend):-
  \+ (integer(L),integer(U)),write([L,U]),
  wn('Each of the lower and upper bounds must be an integer.').
gen_dist(uniform,[L,U],N,ok):-
  sampling_limit(T),
  N =< T,
  integer(U),
  integer(L),
  length(X,N),
  p_init,
  forall(
    nth1(K,X,A),
    (
     G=..[p,uniform,[L,U],K,A],
     B is integer(U - L + 1),
     A is random(B) + L, %wn(A),
     assert(G)
    )
  ),
  trim_stacks,
  listing(p).
set_gen_histogram(_G,_Class,_M,_cum):-
  \+ (clause(p(X,_,_,_),_),X \= dummy),
  wn('You have need to create a distribution before do this.').
set_gen_histogram(G,Class,M,cum):-
  G=..[uniform,L,_U],
  var(L),
  write('Type the lower bound. '),
  read(Y),
  L is integer(Y),
  set_gen_histogram(G,Class,M,cum).
set_gen_histogram(G,Class,M,cum):-
  G=..[uniform,_L,U],
  var(U),
  write('Type the upper bound. '),
  read(Y),
  U is integer(Y),
  set_gen_histogram(G,Class,M,cum).
set_gen_histogram(G,Class,M,cum):-
  var(Class),
  write('Input the boundaries as a list.'),
  read(Y),
  (length(Y,_)->(Class=Y,gen_histogram(G,Class,M,cum)); fail).
gen_histogram(G,Class,M,cum):-
  abolish(histogram,4),
  (G=uniform(L,U)->true;(wn('illegal goal format.'),fail)),
  ((Class=[Lc|_], Lc >= L)->true;(wn('illegal for the lower bound.'),fail)),
  ((last(Class, Uc), Uc =< U)->true;(wn('illegal for the upper boud.'),fail)),
  (length(Class,M)->true;(wn('illegal partitioning.'),fail)),
  bagof(K,A^p(uniform,[L,U],K,A),All),
  length(All,N),wn(num_of_samples(N)),
  forall(
    (
     nth1(J,Class,Ub)%,wn(ub(Ub))
    ),
    (
     bagof(K1,B^(p(uniform,[L,U],K1,B),B =< Ub),Ks),
     length(Ks,Freq),%wn(lev(Ks,Freq)),
     Perc is integer(Freq * 100 / N),
     assert(histogram(J,Ub,Freq,Perc))
    )
  ),
  trim_stacks,
  listing(histogram).
draw_histogram:-
  \+clause(histogram(_J,_B,_F,_P),_),
  wn('Before do this, you have need to create a histogram.').
draw_histogram:-
  wn([class,frequency,percentile]),
  write_ruler(10),
  findall(J,histogram(J,_B,_F,_P),Js),
  sort(Js,N),%wn(N),
  forall(
    (
     member(J,N)%,write(J)
    ),
    (
     histogram(J,B,F,P),
     iteratively_draw(P,'*'),
     wn((B,F,P))
    )
  ),trim_stacks.
iteratively_draw(M,X):-
  length(L,50),
  forall(nth1(K,L,_),(M >= 2*K->write(X);true)),
  write('|').
write_ruler(N):-
  length(L,N),
  forall(member(_A,L),iteratively_draw(8,'-')),
  nl.
counter(N,M,L):-
    length(L,_),
    findall(M,member(M,L),Mx),
    length(Mx,N).


% end