def run(self, lb, ub):
self.PzSeq = []
self.PzPrimes = []
self.nPzPrimes = []
self.numSeq = []
self.tpSeq = []
self.lBound = lb
self.uBound = ub
self.size = self.uBound - self.lBound
for i in range(self.lBound, self.uBound):
PzTmp = self.Pz(i)
self.PzSeq.append((fract(PzTmp).limit_denominator(),
fract(1 - PzTmp).limit_denominator()))
for (Pz, nPz) in self.PzSeq:
if self.verbosity > 0: print '--------------------'
if self.verbosity > 0: print '{0}, {1}'.format(Pz, nPz)
# check if numerator prime
if self.isPrime(Pz.numerator):
self.PzPrimes.append(Pz.numerator)
self.numSeq.append(Pz.numerator)
if self.isPrime(nPz.numerator):
self.nPzPrimes.append(nPz.numerator)
self.numSeq.append(nPz.numerator)
if self.verbosity > 0: print '--------------------'
self.tpSeq = self.findTwins(self.numSeq)
print '--------------------'
print self.numSeq
print '--------------------'
return {
'PzPrimes': self.PzPrimes,
'nPzPrimes': self.nPzPrimes,
'numSeq': self.numSeq
}
def _init_base(self):
self.rows = self.origrows[:]
for i, row in enumerate(self.rows):
if not row: continue
self.rows[i] = row[:]
self.m = len(self.rows)-1 #excluding objective row
self.b = [v[0] for v in self.rows if v] #initial b
nvars = len(self.vars)
self.base = list(range(nvars-self.m-1, nvars))
self.base[0] = 0 #reserved for the objective row
self.cols = nvars #0 for RHS
for vi in range(nvars-self.m, nvars):
if self.vars[vi][0]=='@': break
else: #no artificial variables
self.rows[0] = self.fobj[:]
self.phase = 2
return
#with artificial variables
self.phase = 1
sigma = [fract(-1) if self.vars[i][0]=='@' else fract(0)
for i, a in enumerate(self.fobj)]
for b, row in zip(self.base, self.rows):
if row is None: continue
if self.vars[b][0]!='@': continue
sigma = [c+v for c,v in zip(sigma,row)]
self.rows[0] = sigma
def getX(i, v):
if i==0: return '(Obj)', self.getObj()
if i in self.base:
return v,self.rows[self.base.index(i)][0]
if i+1 < len(self.vars) and\
self.vars[i+1][0]=='!' and i+1 in self.base:
return v,-self.rows[self.base.index(i)][0]
return v, fract(0)
def _best_objective(self):
best, idx, sigma = fract(-1), 0, self.rows[0]
for i in range(1, self.cols):
if sigma[i] <= 0: continue
imp = self._improvement(i)
if imp is None: return i #infinity
if imp <= best: continue #infty can't be converted
best, idx = imp, i
return idx #0: reached optimality
def fractions(s):
lst = s.split()
n1 = n2 = x1 = x2 = 0
y1 = y2 = 1
if "+" in lst:
mid = lst.index("+")
mark = "+"
else:
mid = lst.index("-")
mark = "-"
for i in range(mid):
if len(lst[i]) == 1:
n1 = lst[i]
else:
[x1, y1] = lst[i].split('/')
for i in range(mid, len(lst)):
if len(lst[i]) == 1:
n2 = lst[i]
else:
[x2, y2] = lst[i].split('/')
[x1, x2, y1, y2, n1, n2] = list(map(int, [x1, x2, y1, y2, n1, n2]))
if n1:
num1 = n1 * y1 + x1
else:
num1 = x1
if n2:
num2 = n2 * y2 + x2
else:
num2 = x2
if mark == '+':
result = fract(num1, y1) + fract(num2, y2)
else:
result = fract(num1, y1) - fract(num2, y2)
n = int(result)
dem = result - n
if n and not float(dem):
print('{}'.format(n))
elif n:
print('{} {}'.format(n, str(dem)))
else:
print('{}'.format(str(dem)))
def _pivot_row(self, col):
'''always use "smallest_index" to break tie.'''
if self.degenerated:
rows = self.degenerated
puts("degenerated rows:"+ repr(rows))
else: rows = list(range(1,self.m+1))
rhs = [self.rows[i][0] for i in rows]
lhs = [self.rows[i][col] for i in rows]
ratio = [r/l for l,r in zip(lhs,rhs) if l>0]
if len(ratio) == 0:
if not self.degenerated: return 0 #infinite solution
#OK, we found a way out of degeneracy!
self._restore()
return self._pivot_row(col)
mrat = min(ratio) #ratio==0: degenerated!
nrat = sum(1 for r in ratio if r==mrat)
needcare = (mrat == 0 and nrat > 1)
if needcare and self.virtual_perturbation:
lmin, idx = max(lhs)+1, 0
for i, l, r in zip(rows, lhs, rhs):
if r == 0 and (lmin > l > 0):
lmin, idx = l, i
return idx #which has lmin, to break cycle
if needcare and self.flat_wolf:
if not self.degenerated:
self.vobj = self.rows[0][0] #remember objective value
self.degenerated = [i for i in rows if self.rows[i][0]==0]
for i in self.degenerated:
if self.rows[i][0]: continue #re-randomize?
#wolf randomization, without recursion (flat)
self.rows[i][0] = fract(1)/randint(2,10)
return self._pivot_row(col)
smallest, ri = len(self.vars) + 1, -1
for i, l, r in zip(rows, lhs, rhs): #min ratio
if l <= 0: continue
if r == mrat * l: #fractions
if self.base[i] < smallest:
smallest, ri = self.base[i], i #smallest_index
assert ri >= 0, "row index should never be negative!"
return ri #smallest_index
from fractions import Fraction as fract
x = set()
for i in range(100,1,-1):
for z in range(i-1,0, -1):
if z/i in x:
z-=1
else:
x.add(z/i)
print(fract(z,i))
print(len(x))#1 to 8 should give len 21
from fractions import Fraction as fract
x = set()
for i in range(1, 80001):
for z in range(int((fract(3, 7) * i) - 1 / i), i):
if z / i >= 3 / 7:
i += 1
else:
print(fract(z, i))
x.add(fract(z, i))
x = sorted(x)
print('---', x.pop(), '---')
def _largest_sigma(self):
best, idx, sigma = fract(0), 0, self.rows[0]
for i in range(1, self.cols):
if sigma[i] <= best: continue
best, idx = sigma[i], i
return idx #0: reached optimality
def terms(td):
ts = {}
for v,c in td.items(): ts[v] = fract(c)
return ts
def __init__(self, prob, interactive=True):
'''no variable name should start with '@' in prob.'''
self.text = str(prob)
self.vars = [''] #reserved
def terms(td):
ts = {}
for v,c in td.items(): ts[v] = fract(c)
return ts
sts = [(terms(t),r, fract(b)) for t,r,b,p in prob.sts]
self.rownames = [p for t,r,b,p in prob.sts]
for i, (t,r,b) in enumerate(sts):
if i==0: self.obj_dir = r
if i==0 and r<0 or i and b < 0: #minimize or b<0
for v in t: t[v] = -t[v]
sts[i] = t, -r, -b
for v in prob.fvs: #free vars
if v not in t: continue
t['!%s'%v] = - t[v] #negate coefficient
for v in t:
if v not in self.vars:
self.vars.append(v)
self.vars = prob.sortvars(self.vars) #sort by var name
self.vars[0] = '(RHS)'
#add surplus vars
for idx, (t,r,b) in enumerate(sts):
if r>=0: continue
v = '#%i'%idx
t[v] = -1
self.vars.append(v)
#add slack vars
for idx, (t,r,b) in enumerate(sts):
if idx==0 or r<=0: continue
v = '$%i'%idx #slack
t[v] = 1
self.vars.append(v)
#add artificial vars, in the end.
#NOTE: not matrix I
for idx, (t,r,b) in enumerate(sts):
if idx==0 or r>0: continue
v = '@%i'%idx #artificial
t[v] = 1
self.vars.append(v)
#ready for tableau
fobj = sts[0][0]
self.fobj = [fobj.get(v,0) for v in self.vars]
self.origrows = [None]
for i, (t,r,b) in enumerate(sts):
if i==0: continue #ignore objective
row = [t.get(v,0) for v in self.vars]
row[0] = b
self.origrows.append(row)
self._method = Tableau._largest_sigma
self.interactive = interactive
#The virtual perturbation is not proven
self.virtual_perturbation = False
#we may also use flat wolf randomization
self.flat_wolf = not interactive
#degenerated rows for wolf randomization
self.degenerated = ()
self.hist = [] #history, to undo