function [x,fval,flag,iteration]=original******m(c,a,b)
%原始單純形法(大m法，無需給出初始基變數)
%programmed by liyang(faruto's studio~!) bnu math
%last modified 2008.4.27
%求解標準型線性規劃:max c*x;s.t. a*x=b
(b>=0);x>=0;
%輸入：c是n維行向量，a是m*n的係數矩陣，b是m維列向量
%輸出：x最優解(如果有的話)，fval最優值，flag解的狀態說明，interation求解時的迴圈次數
%flag 最終解的狀態說明：
%flag = 0 lp converged to a
solution x
%flag = 1 inf feasible
solutions
%flag = 2 lp is
unbounded
%flag = 3 no feasible point
was found
m = 1e5;
[m,n] = size(a);
a = [a,eye(m)];
for run = 1:1:m
c =[c,-m];
endxb = (n+1:n+m);%xb承裝初始基變數的下標
n = n+m;
iteration = 0;
while 1
iteration
= iteration +1;
flag =
0;sigma =
zeros(1,n);
for col =
1:ntemp = 0;
for row = 1:m
temp = temp + c(xb(row))*a(row,col);
endsigma(col) = c(col)-temp;
endif
sigma<=0
x = zeros(1,n);
for row = 1:m
x(xb(row)) = b(row);
endfval = c*x';
for row = 1:m
for temp = n-m+1:n
if xb(row)==temp && x(temp)~=0
flag = 3;
x = 0;
fval = 0;
break;
endend
if flag == 3
break;
endend
if flag == 3
break;
endfor col = 1:n
tflag = 0;
for row = 1:m
if col == xb(row)
tflag = 1;
break;
endend
if tflag == 0
if sigma(col) == 0
flag =
1;break;
endend
endif flag == 1
x = x(:,1:n-m);
break;
endif flag == 0;
x = x(:,1:n-m);
fval;
break;
endelse
for col = 1:n
if sigma(col)>0 &
a(:,col)<=0
flag = 2;
x = 0;
fval = 0;
break;
endend
if flag == 2
break;
endtemp = 0;
for col = 1:n
if sigma(col)>temp
temp = sigma(col);
intobase = col;%入基變數的下標
endend
theta = zeros(1,m);
for row = 1:m
if a(row,intobase)>0
theta(row) = b(row)/a(row,intobase);
endend
temp = inf;
for row = 1:m
if theta(row)>0 & theta(row)
temp = theta(row);
outbase = xb(row);%出基變數的下標
outrow
= row;%出基變數在基變數中的位置
endend
b(outrow) = b(outrow)/a(outrow,intobase);
a(outrow,:) = a(outrow,:)/a(outrow,intobase);
for row = 1:m
if row ~= outrow
b(row) = b(row) - b(outrow)*a(row,intobase);
a(row,:) = a(row,:) - a(outrow,:)*a(row,intobase);
endend
for row = 1:m
if xb(row) == outbase;
xb(row) = intobase;
endend
endend
if flag == 0
disp('lp
converged to a solution x!');
x;fval;
endif flag == 1
disp('inf
feasible solutions!');
disp('one
of the solutions is:');
endif flag == 2
disp('lp
is unbounded!');
endif flag == 3
disp('no
feasible point was found!');
end
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