I have this huge fucntion which work as expected
def bigM_init(A,signs,b,c,M,cond):
# lines: will be the rows of the matrix
lines = []
var=[]
# column: where to put the next nonzero entry
column = 0
# total number of columns in matrix
size = len(signs)+signs.count(">=")
for s in signs:
if s == '=':
new = column * [0] + [1] + (size - column - 1) * [0]
wen=['$a_{}$'.format({column+A.ncols()})]
column += 1
elif s == '>=':
new = column * [0] + [-1, 1] + (size - column - 2) * [0]
wen=['$\\varepsilon_{}$'.format({column+A.ncols()}),'$a_{}$'.format({column+A.ncols()+1})]
column += 2
elif s == '<=':
new = column * [0] + [1] + (size - column - 1) * [0]
wen=['$\\varepsilon_{}$'.format({column+A.ncols()})]
column += 1
lines.append(new)
var.append(wen)
mat = matrix(lines)
hr=flatten(['$x_{}$'.format({i}) for i in range(0,A.ncols())]+var)
b1=list(b)
c1=list(c)
C0=block_matrix([[A,mat]],subdivide=false)
C1=list(C0)
C2=[list(v) for v in C1]
[C2[i].append(-b1[i]) for i in range(len(C1))]
H=[v for v in hr if v.startswith('$a_')]
HH=[hr.index(v) for v in H]
C3=[flatten([c for c in C2 if c[i]==1]) for i in HH]
C4=[v[:i] for v,i in zip(C3,HH)]
C5=[v[i+1:] for v,i in zip(C3,HH)]
C6=[v+[0]+w for v,w in zip(C4,C5)]
C7= [[-M*_ for _ in C6[i]] for i in range(len(C6))]
C8=matrix(C7)
C9=list(sum(C8))
cf= c1+list(zero_vector(SR, len(new)+1))
C10=[-v+w for v,w in zip(C9,cf)]
C0p=matrix([list(C0[i])+[b1[i]] for i in range(len(b1))])
C11m=block_matrix([[C0p],[-matrix(C10)]],subdivide=false)
C11l=list(block_matrix([[C0p],[-matrix(C10)]],subdivide=false))
#hc=['']+list(HH)+['$z$']
base_init=[]
for j in range(len(signs)) :
if signs[j]==">=" :
base_init.append('$a_{}$'.format({j}))
if signs[j]=="=" :
base_init.append('$a_{}$'.format({j}))
if signs[j]=="<=" :
base_init.append('$\\varepsilon_{}$'.format({j+len(H)}))
hr=list(hr)+list(['$b$'])
hc=['']+list(base_init)+['$z$']
t = table(C11l, header_row=hr, header_column=hc,frame=True)
if cond==0:
return t
if cond==1:
return C11m
if cond==2:
return hc
if cond==3:
return hr
It can be applied on the following exemple
b=vector([8,6,4])
c=vector([5,4,2])
A=matrix(3,3, [3,2,1,4,3,-1,1,2,2])
signs1 = ['=','>=','<=']
M=100
var=bigM_init(A,signs1,b,c,M,3)
base=bigM_init(A,signs1,b,c,M,2)
show(base)
My first problem is the following, the show(base) output seems weird [,$𝚊⎯{𝟶}$,$𝚊⎯{𝟷}$,$\𝚟𝚊𝚛𝚎𝚙𝚜𝚒𝚕𝚘𝚗⎯{𝟺}$}}$𝚣$], (look at the two brakets which must be a coma). But if you ask for show(base[i]) for $i \in {0,..., 4}$ the return is correct. Now I have an other function :
def base_after_pivot(base, veb, vsb):
#base = base
#veb = variable entrant dans la base
#vsb = variable sortant de la base
hc=[sub.replace(vsb, veb) for sub in base]
return hc
whose object is to change the name of the elements of the base. In the following context it works
base1=base_after_pivot(base, '$x_0$', '$a_{1}$')
show(base1)
gives the expected output (one more time seeming weird but correct) [,$𝚊⎯{𝟶}$,$𝚊⎯{𝟷}$,$\𝚟𝚊𝚛𝚎𝚙𝚜𝚒𝚕𝚘𝚗⎯{𝟺}$}}$𝚣$].
So now I try
base2=base_after_pivot(base, '$x_1$', '$\varepsilon_{4}$')
show(base2)
which doesn't change the base. I hope that some on will find my mistake.
