def get_initial_guess(S, enzymeInfo, concLB, concUB):
nMetabs = len(S.index)
ini = []
for i, metab in enumerate(S.index):
f = np.zeros(nMetabs)
f[i] = 1
A = R * T * S.T
b = -np.array([
-R * T * np.log(item[0]) for item in enzymeInfo.loc[:, 'Keq']
])
lb = [np.log(concLB)] * nMetabs
ub = [np.log(concUB)] * nMetabs
meth = 'pclp'
p = LP(f=f, A=A, b=b, lb=lb, ub=ub, iprint=-1)
r = p.solve(meth, plot=0)
ini.append(r.xf[i])
ini = np.array(ini)
return ini
def optimize_minimal_driving_force(S, Vss, enzymeInfo, concLB, concUB):
'''
Parameters
S: df, stoichiometric matrix, metabolite in rows, reaction in columns. negative for substrates, positive for products
Vss: ser, net fluxes in steady state (including in and out fluxes)
enzymeInfo: df, reaction in rows
concLB: float, concentration lower bound (mM) for all metabolites
concUB: float, concentration upper bound (mM) for all metabolites
Returns
optConcs: ser, optimal log(concentrations)
optDeltaGs: ser, optimal minimal driving forces
refDeltaGs: float, reference minimal driving forces (all concentrations at 1 mM)
'''
from openopt import LP
from constants import R, T
f = np.zeros(S.shape[0] + 1)
f[0] = -1
S = S * Vss[S.columns]
A = np.concatenate((np.ones((S.shape[1], 1)), R * T * S.T), axis=1)
b = -np.array(
[-R * T * np.log(item[0]) for item in enzymeInfo.loc[:, 'Keq']])
b = b * Vss[S.columns].values
lb = [-np.inf] + [np.log(concLB)] * S.shape[0]
ub = [np.inf] + [np.log(concUB)] * S.shape[0]
meth = 'cvxopt_lp'
p = LP(f=f,
A=A,
b=b,
lb=lb,
ub=ub,
iprint=-1,
name='Maximize minimal driving force')
r = p.solve(meth, plot=0)
optLogConcs = r.xf[1:]
optConcs = pd.Series(np.exp(optLogConcs), index=S.index)
optDeltaGs = pd.Series(-b + R * T * np.dot(S.T, optLogConcs),
index=S.columns)
refDeltaGs = pd.Series(-b, index=S.columns)
return optConcs, optDeltaGs, refDeltaGs
def minimize(self, **kwargs):
""" solve the linear problem with the solver given in self.solver
Returns:
obj_value, solution
obj_value -- value of the objective function at the discovered solution
solution -- the solution flux vector (indexed like matrix columns)
"""
if self.solver == _GLPK:
# Use pyMathProg interface to GLPK solver
self.glpkP.solve()
self.istop = self.glpkP.status()
# print "istop:", self.istop
self.status = glpkToSolverStatus(self.istop)
if self.status == SolverStatus.OPTIMAL:
self.obj_value = self.glpkP.vobj()
self.solution = [
self.glpkVar[i].primal for i in range(len(self.glpkVar))
]
else:
self.obj_value = 0.
self.solution = []
else:
# Use OpenOpt interface
lp = LP(self.obj,
A=self.Aineq,
Aeq=self.Aeq,
b=self.bineq,
beq=self.beq,
lb=self.lb,
ub=self.ub,
**kwargs)
lp.debug = 1
# lp.iprint=-1 # suppress solver output
r = lp.solve(self.solver if self.solver != _OOGLPK else 'glpk')
if r.istop <= 0. or r.ff != r.ff: # check halting condition
self.obj_value = 0.
self.solution = []
self.istop = r.istop
else:
self.obj_value = r.ff
self.solution = r.xf
self.istop = r.istop
# print self.istop
return self.obj_value, self.solution
def delete_dom_act_Pi(game, i):
no_a_game = list(
game.shape) #will contain number of actions available for each player
no_a_game.pop(
) #removes last element of list which simply was n: the number of payoffs in each action profile
#as the first number is number of actions of last player etc., we turn the list around
no_a_game = no_a_game[::-1]
no_a_i = no_a_game.pop(
i
) #remove the number of actions of player i from no_a_game and put it in no_a_i
if no_a_i == 1: #if a single action remains it cannot be dominated
return game
var_no = np.prod(no_a_game) #size of the support of mu
if var_no == 1: #special case: the support of mu has a single elment
return del_dom_a_Pi_point_belief(game, i, no_a_i)
temp_game = game
f = [0.] * var_no #dummy objective used below
lb = [0.] * var_no
ub = [1.] * var_no
Aeq = [[1.] * var_no]
beq = (1., )
j = 0
while j < no_a_i:
u_action = payoffi_builder(game, j, i)
A = []
b = []
k = 0
while k < no_a_i:
u_other_action = payoffi_builder(game, k, i)
A.append(u_other_action - u_action) #elementwise difference
b.append(0.)
k += 1
p = LP(
f, A=A, b=b, lb=lb, ub=ub, Aeq=Aeq, beq=beq
) #we use the artificial minimization problem under the constraint that action gives a weakly higher payoff than any other action; if no feasible solution is obtained than action is dominated
p.iprint = -1
r = p.minimize('pclp')
if r.stopcase != 1: #if no feasible solution was obtained then action is dominated...
temp_game = np.delete(
temp_game, j, n - i - 1
) #...and therefore action j is removed; recall that players are "in the wrong order"
count = 0
z = -1
while count <= j:
z += 1
if undominated[i][z] != -1:
count += 1
undominated[i][z] = -1
j += 1
return temp_game
def compressed_sensing2(x1, trans):
"""L1 compressed sensing
:Parameters:
x1 : array-like, shape=(n_outputs,)
input sparse vector
trans : array-like, shape=(n_outputs, n_inputs)
transformation matrix
:Returns:
decoded vector, shape=(n_inpus,)
:RType:
array-like
"""
# obrain sizes of inputs and outputs
(n_outputs, n_inputs) = trans.shape
# define variable
t = fd.oovar('t', size=n_inputs)
x = fd.oovar('x', size=n_inputs)
# objective to minimize: f x^T -> min
objective = fd.sum(t)
# init constraints
constraints = []
# equality constraint: a_eq x^T = b_eq
constraints.append(fd.dot(trans, x) == x1)
# inequality constraint: -t < x < t
constraints.append(-t <= x)
constraints.append(x <= t)
# start_point
start_point = {x:np.zeros(n_inputs), t:np.zeros(n_inputs)}
# solve linear programming
prob = LP(objective, start_point, constraints=constraints)
result = prob.minimize('pclp') # glpk, lpSolve... if available
# print result
# print "x =", result.xf # arguments at mimimum
# print "objective =", result.ff # value of objective
return result.xf[x]
def compressed_sensing(x1, trans):
"""L1 compressed sensing
:Parameters:
x1 : array-like, shape=(n_outputs,)
input sparse vector
trans : array-like, shape=(n_outputs, n_inputs)
transformation matrix
:Returns:
decoded vector, shape=(n_inpus,)
:RType:
array-like
"""
# obrain sizes of inputs and outputs
(n_outputs, n_inputs) = trans.shape
# objective to minimize: f x^T -> min
f = np.zeros((n_inputs * 2), dtype=np.float)
f[n_inputs:2 * n_inputs] = 1.0
# constraint: a x^T == b
a_eq = np.zeros((n_outputs, 2 * n_inputs), dtype=np.float)
a_eq[:, 0:n_inputs] = trans
b_eq = x1
# constraint: -t <= x <= t
a = np.zeros((2 * n_inputs, 2 * n_inputs), dtype=np.float)
for i in xrange(n_inputs):
a[i, i] = -1.0
a[i, n_inputs + i] = -1.0
a[n_inputs + i, i] = 1.0
a[n_inputs + i, n_inputs + i] = -1.0
b = np.zeros(n_inputs * 2)
# solve linear programming
prob = LP(f, Aeq=a_eq, beq=b_eq, A=a, b=b)
result = prob.minimize('pclp') # glpk, lpSolve... if available
# print result
# print "x =", result.xf # arguments at mimimum
# print "objective =", result.ff # value of objective
return result.xf[0:n_inputs]
def delete_dom_act_Pi(game,i):
no_a_game = list(game.shape) #will contain number of actions available for each player
no_a_game.pop()#removes last element of list which simply was n: the number of payoffs in each action profile
#as the first number is number of actions of last player etc., we turn the list around
no_a_game = no_a_game[::-1]
no_a_i = no_a_game.pop(i)#remove the number of actions of player i from no_a_game and put it in no_a_i
if no_a_i==1:#if a single action remains it cannot be dominated
return game
var_no = np.prod(no_a_game)#size of the support of mu
if var_no == 1:#special case: the support of mu has a single elment
return del_dom_a_Pi_point_belief(game, i,no_a_i)
temp_game = game
f = [0.]*var_no #dummy objective used below
lb = [0.]*var_no
ub = [1.]*var_no
Aeq = [[1.]*var_no]
beq = (1.,)
j = 0
while j<no_a_i:
u_action = payoffi_builder(game,j,i)
A = []
b = []
k = 0
while k<no_a_i:
u_other_action = payoffi_builder(game,k,i)
A.append(u_other_action - u_action)#elementwise difference
b.append(0.)
k+=1
p = LP(f, A=A,b=b,lb=lb,ub=ub,Aeq=Aeq,beq=beq)#we use the artificial minimization problem under the constraint that action gives a weakly higher payoff than any other action; if no feasible solution is obtained than action is dominated
p.iprint = -1
r = p.minimize('pclp')
if r.stopcase!=1:#if no feasible solution was obtained then action is dominated...
temp_game = np.delete(temp_game,j,n-i-1)#...and therefore action j is removed; recall that players are "in the wrong order"
count = 0
z = -1
while count<=j:
z+=1
if undominated[i][z]!=-1 :
count+=1
undominated[i][z] = -1
j+=1
return temp_game
8x1 + 80x2 + 15x3 <=150 (4)
100x1 + 10x2 + x3 >= 800 (5)
80x1 + 8x2 + 15x3 = 750 (6)
x1 + 10x2 + 100x3 = 80 (7)
x1 >= 4 (8)
-8 >= x2 >= -80 (9)
"""
from numpy import *
from openopt import LP
f = array([15, 8, 80])
A = mat(
'1 2 3; 8 15 80; 8 80 15; -100 -10 -1') # numpy.ndarray is also allowed
b = [15, 80, 150, -800] # numpy.ndarray, matrix etc are also allowed
Aeq = mat('80 8 15; 1 10 100') # numpy.ndarray is also allowed
beq = (750, 80)
lb = [4, -80, -inf]
ub = [inf, -8, inf]
p = LP(f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
#or p = LP(f=f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
#r = p.minimize('glpk') # CVXOPT must be installed
#r = p.minimize('lpSolve') # lpsolve must be installed
r = p.minimize('pclp')
#search for max: r = p.maximize('glpk') # CVXOPT & glpk must be installed
#r = p.minimize('nlp:ralg', ftol=1e-7, xtol=1e-7, goal='min', plot=1)
print('objFunValue: %f' % r.ff) # should print 204.48841578
print('x_opt: %s' % r.xf) # should print [ 9.89355041 -8. 1.5010645 ]
from FuncDesigner import *
N = 100
a = oovars(N) # create array of N oovars
b = oovars(N) # another array of N oovars
some_lin_funcs = [i * a[i] + 4 * i + 5 * b[i] for i in range(N)]
f = some_lin_funcs[15] + some_lin_funcs[80] - sum(a) + sum(b)
point = {}
for i in range(N):
point[a[i]] = 1.5 * i**2
point[b[i]] = 1.5 * i**3
# BTW we could use 1-dimensional arrays here, eg point[a[25]] = [2,3,4,5], point[a[27]] = [1,2,5] etc
print f(point) # prints 40899980.
from openopt import LP
# define prob
p = LP(f, point)
# add some box-bound constraints
aLBs = [a[i] > -10 for i in range(N)]
bLBs = [b[i] > -10 for i in range(N)]
aUBs = [a[i] < 15 for i in range(N)]
bUBs = [b[i] < 15 for i in range(N)]
p.constraints = aLBs + bLBs + aUBs + bUBs
# add some general linear constraints
p.constraints.append(a[4] + b[15] + a[20].size - f.size >
-9) # array size, here a[20].size = f.size = 1
# or p.constraints += [a[4] + b[15] + a[20].size - f.size>-9]
for i in range(N):
p.constraints.append(2 * some_lin_funcs[i] + a[i] < i / 2.0 +
some_lin_funcs[N - i - 1] + 1.5 * b[i])
def __solver__(self, p):
n = p.n
x0 = copy(p.x0)
xPrev = x0.copy()
xf = x0.copy()
xk = x0.copy()
p.xk = x0.copy()
f0 = p.f(x0)
fk = f0
ff = f0
p.fk = fk
df0 = p.df(x0)
#####################################################################
## #handling box-bounded problems
## if p.__isNoMoreThanBoxBounded__():
## for k in range(int(p.maxIter)):
##
## #end of handling box-bounded problems
isBB = p.__isNoMoreThanBoxBounded__()
## isBB = 0
H = diag(ones(p.n))
if not p.userProvided.c:
p.c = lambda x: array([])
p.dc = lambda x: array([]).reshape(0, p.n)
if not p.userProvided.h:
p.h = lambda x: array([])
p.dh = lambda x: array([]).reshape(0, p.n)
p.use_subproblem = 'QP'
#p.use_subproblem = 'LLSP'
for k in range(p.maxIter + 4):
if isBB:
f0 = p.f(xk)
df = p.df(xk)
direction = -df
f1 = p.f(xk + direction)
ind_l = direction <= p.lb - xk
direction[ind_l] = (p.lb - xk)[ind_l]
ind_u = direction >= p.ub - xk
direction[ind_u] = (p.ub - xk)[ind_u]
ff = p.f(xk + direction)
## print 'f0', f0, 'f1', f1, 'ff', ff
else:
mr = p.getMaxResidual(xk)
if mr > p.contol: mr_grad = p.getMaxConstrGradient(xk)
lb = p.lb - xk #- p.contol/2
ub = p.ub - xk #+ p.contol/2
c, dc, h, dh, df = p.c(xk), p.dc(xk), p.h(xk), p.dh(xk), p.df(
xk)
A, Aeq = vstack((dc, p.A)), vstack((dh, p.Aeq))
b = concatenate((-c, p.b - p.matmult(p.A, xk))) #+ p.contol/2
beq = concatenate((-h, p.beq - p.matmult(p.Aeq, xk)))
if b.size != 0:
isFinite = isfinite(b)
ind = where(isFinite)[0]
A, b = A[ind], b[ind]
if beq.size != 0:
isFinite = isfinite(beq)
ind = where(isFinite)[0]
Aeq, beq = Aeq[ind], beq[ind]
if p.use_subproblem == 'LP': #linear
linprob = LP(df, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
linprob.iprint = -1
r2 = linprob.solve(
'cvxopt_glpk') # TODO: replace lpSolve by autoselect
if r2.istop <= 0:
p.istop = -12
p.msg = "failed to solve LP subproblem"
return
elif p.use_subproblem == 'QP': #quadratic
qp = QP(H=H,
f=df,
A=A,
Aeq=Aeq,
b=b,
beq=beq,
lb=lb,
ub=ub)
qp.iprint = -1
r2 = qp.solve(
'cvxopt_qp') # TODO: replace solver by autoselect
#r2 = qp.solve('qld') # TODO: replace solver by autoselect
if r2.istop <= 0:
for i in range(4):
if p.debug:
p.warn("iter " + str(k) + ": attempt Num " +
str(i) +
" to solve QP subproblem has failed")
#qp.f += 2*N*sum(qp.A,0)
A2 = vstack((A, Aeq, -Aeq))
b2 = concatenate(
(b, beq, -beq)) + pow(10, i) * p.contol
qp = QP(H=H, f=df, A=A2, b=b2, iprint=-5)
qp.lb = lb - pow(10, i) * p.contol
qp.ub = ub + pow(10, i) * p.contol
# I guess lb and ub don't matter here
try:
r2 = qp.solve(
'cvxopt_qp'
) # TODO: replace solver by autoselect
except:
r2.istop = -11
if r2.istop > 0: break
if r2.istop <= 0:
p.istop = -11
p.msg = "failed to solve QP subproblem"
return
elif p.use_subproblem == 'LLSP':
direction_c = getConstrDirection(p,
xk,
regularization=1e-7)
else:
p.err('incorrect or unknown subproblem')
if isBB:
X0 = xk.copy()
N = 0
result, newX = chLineSearch(p, X0, direction, N, isBB)
elif p.use_subproblem != 'LLSP':
duals = r2.duals
N = 1.05 * abs(duals).sum()
direction = r2.xf
X0 = xk.copy()
result, newX = chLineSearch(p, X0, direction, N, isBB)
else: # case LLSP
direction_f = -df
p2 = NSP(LLSsubprobF, [0.8, 0.8],
ftol=0,
gtol=0,
xtol=1e-5,
iprint=-1)
p2.args.f = (xk, direction_f, direction_c, p, 1e20)
r_subprob = p2.solve('ralg')
alpha = r_subprob.xf
newX = xk + alpha[0] * direction_f + alpha[1] * direction_c
# dw = (direction_f * direction_c).sum()
# cos_phi = dw/p.norm(direction_f)/p.norm(direction_c)
# res_0, res_1 = p.getMaxResidual(xk), p.getMaxResidual(xk+1e-1*direction_c)
# print cos_phi, res_0-res_1
# res_0 = p.getMaxResidual(xk)
# optimConstrPoint = getDirectionOptimPoint(p, p.getMaxResidual, xk, direction_c)
# res_1 = p.getMaxResidual(optimConstrPoint)
#
# maxConstrLimit = p.contol
#xk = getDirectionOptimPoint(p, p.f, optimConstrPoint, -optimConstrPoint+xk+direction_f, maxConstrLimit = maxConstrLimit)
#print 'res_0', res_0, 'res_1', res_1, 'res_2', p.getMaxResidual(xk)
#xk = getDirectionOptimPoint(p, p.f, xk, direction_f, maxConstrLimit)
#newX = xk.copy()
result = 0
# x_0 = X0.copy()
# N = j = 0
# while p.getMaxResidual(x_0) > Residual0 + 0.1*p.contol:
# j += 1
# x_0 = xk + 0.75**j * (X0-xk)
# X0 = x_0
# result, newX = 0, X0
# print 'newIterResidual = ', p.getMaxResidual(x_0)
if result != 0:
p.istop = result
p.xf = newX
return
xk = newX.copy()
fk = p.f(xk)
p.xk, p.fk = copy(xk), copy(fk)
#p._df = p.df(xk)
####################
p.iterfcn()
if p.istop:
p.xf = xk
p.ff = fk
#p._df = g FIXME: implement me
return
def schedule_all(self, timelimit=None):
if not self.reservation_list:
return self.schedule_dict
self.build_data_structures()
# allocate A & b
# find the row size of A:
# first find the number of reservations participating in oneofs
oneof_reservation_num = 0
for c in self.oneof_constraints:
oneof_reservation_num += len(c)
A_numrows = len(self.reservation_list) + len(self.aikt) + len(
self.oneof_constraints) - oneof_reservation_num
A_rows = []
A_cols = []
A_data = []
# try:
# A = numpy.zeros((A_numrows, len(self.Yik)), dtype=numpy.int)
# except ValueError:
# print("Number of A rows: {}".format(A_numrows))
b = numpy.zeros(A_numrows, dtype=numpy.int16)
# build A & b
row = 0
# constraint 5: oneof
for c in self.oneof_constraints:
for r in c:
for entry in r.Yik_entries:
A_rows.append(row)
A_cols.append(entry)
A_data.append(1)
# A[row,entry] = 1
r.skip_constraint2 = True
b[row] = 1
row += 1
# constraint 2: each res should have one start:
# optimization:
# if the reservation participates in a oneof, then this is
# redundant with the oneof constraint added above, so don't add it.
for r in self.reservation_list:
if hasattr(r, 'skip_constraint2'):
continue
for entry in r.Yik_entries:
A_rows.append(row)
A_cols.append(entry)
A_data.append(1)
# A[row,entry] = 1
b[row] = 1
row += 1
# constraint 3: each slice should only have one sched. reservation:
for s in self.aikt.keys():
for entry in self.aikt[s]:
A_rows.append(row)
A_cols.append(entry)
A_data.append(1)
# A[row,entry] = 1
b[row] = 1
row += 1
A = coo_matrix((A_data, (A_rows, A_cols)),
shape=(A_numrows, len(self.Yik)))
# constraint 6: and
# figure out size of constraint matrix
if not self.and_constraints:
Aeq = []
beq = []
else:
Aeq_numrows = 0
for c in self.and_constraints:
Aeq_numrows += len(c) - 1
# allocate Aeq and beq
# Aeq = numpy.zeros((Aeq_numrows, len(self.Yik)), dtype=numpy.int)
Aeq_rows = []
Aeq_cols = []
Aeq_data = []
beq = numpy.zeros(Aeq_numrows, dtype=numpy.int16)
row = 0
for c in self.and_constraints:
constraint_size = len(c)
left_idx = 0
right_idx = 1
while right_idx < constraint_size:
left_r = c[left_idx]
right_r = c[right_idx]
for entry in left_r.Yik_entries:
# Aeq[row, entry] = 1
Aeq_rows.append(row)
Aeq_cols.append(entry)
Aeq_data.append(1)
for entry in right_r.Yik_entries:
Aeq_rows.append(row)
Aeq_cols.append(entry)
Aeq_data.append(-1)
# Aeq[row, entry] = -1
left_idx += 1
right_idx += 1
row += 1
# print(Aeq_numrows)
Aeq = coo_matrix((Aeq_data, (Aeq_rows, Aeq_cols)),
shape=(Aeq_numrows, len(self.Yik)))
# bounds:
lb = numpy.zeros(len(self.Yik), dtype=numpy.int16)
ub = numpy.ones(len(self.Yik), dtype=numpy.int16)
# objective function:
f = numpy.zeros(len(self.Yik))
f = numpy.zeros(len(self.Yik), dtype=numpy.int16)
row = 0
for entry in self.Yik:
f[row] = entry[2] # priority
row += 1
dump_matrix_sizes(f, A, Aeq, b, beq, lb, ub,
len(self.compound_reservation_list))
p = LP(f=f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
# r = p.minimize('pclp')
r = p.maximize('glpk', iprint=-1)
# r = p.minimize('lpsolve')
return self.unpack_result(r)
"""
Sparse LP example
for Nvariables = 25000
(hence Nconstraints = 75000)
glpk peak memory ~70 Mb,
time elapsed = 35.79, CPU time elapsed = 35.0
"""
from openopt import LP
from numpy import arange
from FuncDesigner import *
N = 25000
x, y, z = oovars(3)
startPoint = {x:0, y:[0]*N, z:[0]*(2*N)} # thus x from R, y from R^N, z from R^2N
objective = sum(x) + 2*sum(y) + 3*sum(z)
cons = [x<100, x>-100, y<arange(N), y>-10-arange(N), z<arange(2*N), z>-100-arange(2*N), x+y>2-3*arange(N), x+z>4-5*arange(2*N)]
p = LP(objective, startPoint, constraints = cons)
solver = 'glpk' # CVXOPT & glpk must be installed
r = p.minimize(solver)
print('objFunValue:%f' % r.ff)
from FuncDesigner import *
N = 100
a = oovars(N) # create array of N oovars
b = oovars(N) # another array of N oovars
some_lin_funcs = [i*a[i]+4*i + 5*b[i] for i in range(N)]
f = some_lin_funcs[15] + some_lin_funcs[80] - sum(a) + sum(b)
point = {}
for i in range(N):
point[a[i]] = 1.5 * i**2
point[b[i]] = 1.5 * i**3
# BTW we could use 1-dimensional arrays here, eg point[a[25]] = [2,3,4,5], point[a[27]] = [1,2,5] etc
print f(point) # prints 40899980.
from openopt import LP
# define prob
p = LP(f, point)
# add some box-bound constraints
aLBs = [a[i]>-10 for i in range(N)]
bLBs = [b[i]>-10 for i in range(N)]
aUBs = [a[i]<15 for i in range(N)]
bUBs = [b[i]<15 for i in range(N)]
p.constraints = aLBs + bLBs + aUBs + bUBs
# add some general linear constraints
p.constraints.append(a[4] + b[15] + a[20].size - f.size>-9) # array size, here a[20].size = f.size = 1
# or p.constraints += [a[4] + b[15] + a[20].size - f.size>-9]
for i in range(N):
p.constraints.append(2 * some_lin_funcs[i] + a[i] < i / 2.0 + some_lin_funcs[N-i-1] + 1.5*b[i])
# or p.constraints += [2 * some_lin_funcs[i] + a[i] < i / 2.0 + some_lin_funcs[N-i-1] + 1.5*b[i] for i in range(N]
def __solver__(self, p):
n = p.n
x0 = copy(p.x0)
xPrev = x0.copy()
xf = x0.copy()
xk = x0.copy()
p.xk = x0.copy()
f0 = p.f(x0)
fk = f0
ff = f0
p.fk = fk
df0 = p.df(x0)
#####################################################################
## #handling box-bounded problems
## if p.__isNoMoreThanBoxBounded__():
## for k in range(int(p.maxIter)):
##
## #end of handling box-bounded problems
isBB = p.__isNoMoreThanBoxBounded__()
## isBB = 0
H = diag(ones(p.n))
if not p.userProvided.c:
p.c = lambda x : array([])
p.dc = lambda x : array([]).reshape(0, p.n)
if not p.userProvided.h:
p.h = lambda x : array([])
p.dh = lambda x : array([]).reshape(0, p.n)
p.use_subproblem = 'QP'
#p.use_subproblem = 'LLSP'
for k in range(p.maxIter+4):
if isBB:
f0 = p.f(xk)
df = p.df(xk)
direction = -df
f1 = p.f(xk+direction)
ind_l = direction<=p.lb-xk
direction[ind_l] = (p.lb-xk)[ind_l]
ind_u = direction>=p.ub-xk
direction[ind_u] = (p.ub-xk)[ind_u]
ff = p.f(xk + direction)
## print 'f0', f0, 'f1', f1, 'ff', ff
else:
mr = p.getMaxResidual(xk)
if mr > p.contol: mr_grad = p.getMaxConstrGradient(xk)
lb = p.lb - xk #- p.contol/2
ub = p.ub - xk #+ p.contol/2
c, dc, h, dh, df = p.c(xk), p.dc(xk), p.h(xk), p.dh(xk), p.df(xk)
A, Aeq = vstack((dc, p.A)), vstack((dh, p.Aeq))
b = concatenate((-c, p.b-p.matmult(p.A,xk))) #+ p.contol/2
beq = concatenate((-h, p.beq-p.matmult(p.Aeq,xk)))
if b.size != 0:
isFinite = isfinite(b)
ind = where(isFinite)[0]
A, b = A[ind], b[ind]
if beq.size != 0:
isFinite = isfinite(beq)
ind = where(isFinite)[0]
Aeq, beq = Aeq[ind], beq[ind]
if p.use_subproblem == 'LP': #linear
linprob = LP(df, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
linprob.iprint = -1
r2 = linprob.solve('cvxopt_glpk') # TODO: replace lpSolve by autoselect
if r2.istop <= 0:
p.istop = -12
p.msg = "failed to solve LP subproblem"
return
elif p.use_subproblem == 'QP': #quadratic
qp = QP(H=H,f=df, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub = ub)
qp.iprint = -1
r2 = qp.solve('cvxopt_qp') # TODO: replace solver by autoselect
#r2 = qp.solve('qld') # TODO: replace solver by autoselect
if r2.istop <= 0:
for i in range(4):
if p.debug: p.warn("iter " + str(k) + ": attempt Num " + str(i) + " to solve QP subproblem has failed")
#qp.f += 2*N*sum(qp.A,0)
A2 = vstack((A, Aeq, -Aeq))
b2 = concatenate((b, beq, -beq)) + pow(10,i)*p.contol
qp = QP(H=H,f=df, A=A2, b=b2, iprint = -5)
qp.lb = lb - pow(10,i)*p.contol
qp.ub = ub + pow(10,i)*p.contol
# I guess lb and ub don't matter here
try:
r2 = qp.solve('cvxopt_qp') # TODO: replace solver by autoselect
except:
r2.istop = -11
if r2.istop > 0: break
if r2.istop <= 0:
p.istop = -11
p.msg = "failed to solve QP subproblem"
return
elif p.use_subproblem == 'LLSP':
direction_c = getConstrDirection(p, xk, regularization = 1e-7)
else: p.err('incorrect or unknown subproblem')
if isBB:
X0 = xk.copy()
N = 0
result, newX = chLineSearch(p, X0, direction, N, isBB)
elif p.use_subproblem != 'LLSP':
duals = r2.duals
N = 1.05*abs(duals).sum()
direction = r2.xf
X0 = xk.copy()
result, newX = chLineSearch(p, X0, direction, N, isBB)
else: # case LLSP
direction_f = -df
p2 = NSP(LLSsubprobF, [0.8, 0.8], ftol=0, gtol=0, xtol = 1e-5, iprint = -1)
p2.args.f = (xk, direction_f, direction_c, p, 1e20)
r_subprob = p2.solve('ralg')
alpha = r_subprob.xf
newX = xk + alpha[0]*direction_f + alpha[1]*direction_c
# dw = (direction_f * direction_c).sum()
# cos_phi = dw/p.norm(direction_f)/p.norm(direction_c)
# res_0, res_1 = p.getMaxResidual(xk), p.getMaxResidual(xk+1e-1*direction_c)
# print cos_phi, res_0-res_1
# res_0 = p.getMaxResidual(xk)
# optimConstrPoint = getDirectionOptimPoint(p, p.getMaxResidual, xk, direction_c)
# res_1 = p.getMaxResidual(optimConstrPoint)
#
# maxConstrLimit = p.contol
#xk = getDirectionOptimPoint(p, p.f, optimConstrPoint, -optimConstrPoint+xk+direction_f, maxConstrLimit = maxConstrLimit)
#print 'res_0', res_0, 'res_1', res_1, 'res_2', p.getMaxResidual(xk)
#xk = getDirectionOptimPoint(p, p.f, xk, direction_f, maxConstrLimit)
#newX = xk.copy()
result = 0
# x_0 = X0.copy()
# N = j = 0
# while p.getMaxResidual(x_0) > Residual0 + 0.1*p.contol:
# j += 1
# x_0 = xk + 0.75**j * (X0-xk)
# X0 = x_0
# result, newX = 0, X0
# print 'newIterResidual = ', p.getMaxResidual(x_0)
if result != 0:
p.istop = result
p.xf = newX
return
xk = newX.copy()
fk = p.f(xk)
p.xk, p.fk = copy(xk), copy(fk)
#p._df = p.df(xk)
####################
p.iterfcn()
if p.istop:
p.xf = xk
p.ff = fk
#p._df = g FIXME: implement me
return
t = time()
# Define some oovars
drugs = oovar(2)
material = oovar(2)
budgets = oovar(3)
# Let's define some linear functions
f1 = 4*x+5*y + 3*z + 5
f2 = f1.sum() + 2*x + 4*y + 15
f3 = 5*f1 + 4*f2 + 20
# Define objective; sum(a) and a.sum() are same as well as for numpy arrays
obj = x.sum() + y - 50*z + sum(f3) + 2*f2.sum() + 4064.6
# Define some constraints via Python list or tuple or set of any length, probably via while/for cycles
constraints = [x+5*y<15, x[0]<4, f1<[25, 35], f1>-100, 2*f1+4*z<[80, 800], 5*f2+4*z<100, -5<x, x<1, -20<y, y<20, -4000<z, z<4]
# Start point - currently matters only size of variables, glpk, lpSolve and cvxopt_lp use start val = all-zeros
startPoint = {x:[8, 15], y:25, z:80} # however, using numpy.arrays is more recommended than Python lists
# Create prob
p = LP(obj, startPoint, constraints = constraints)
# Solve
r = p.solve('glpk') # glpk is name of solver involved, see OOF doc for more arguments
# Decode solution
print('Solution: x = %s y = %f z = %f' % (str(x(r)), y(r), z(r)))
# Solution: x = [-4.25 -4.25] y = -20.000000 z = 4.000000
print "elapsed %.3f secs"%(time() - t)
# Example of export OpenOpt LP to MPS file
# you should have lpsolve and its Python binding properly installed
# (you may take a look at the instructions from openopt.org/LP)
# You can solve problems defined in MPS files
# with a variety of solvers at NEOS server for free
# http://neos.mcs.anl.gov/
# BTW they have Python API along with web API and other
from numpy import *
from openopt import LP
f = array([15,8,80])
A = mat('1 2 3; 8 15 80; 8 80 15; -100 -10 -1') # numpy.ndarray is also allowed
b = [15, 80, 150, -800] # numpy.ndarray, matrix etc are also allowed
Aeq = mat('80 8 15; 1 10 100') # numpy.ndarray is also allowed
beq = (750, 80)
lb = [4, -80, -inf]
ub = [inf, -8, inf]
p = LP(f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub, name = 'lp_1')
# or p = LP(f=f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
# if file name not ends with '.MPS' or '.mps'
# then '.mps' will be appended
success = p.exportToMPS('asdf')
# success is False if a error occurred (read-only file system, no write access, etc)
# elseware success is True
# objFunValue should be 204.48841578
# x_opt should be [ 9.89355041 -8. 1.5010645 ]
f1 = 4 * x + 5 * y + 3 * z + 5
f2 = f1.sum() + 2 * x + 4 * y + 15
f3 = 5 * f1 + 4 * f2 + 20
# Define objective; sum(a) and a.sum() are same as well as for numpy arrays
obj = sum(f1) + x.sum() + y - 50 * z + 2 * f2.sum() + 4064.6
# Start point - currently matters only size of variables
startPoint = {
x: [8, 15],
y: 25,
z: 80
} # however, using numpy.arrays is more recommended than Python lists
# Create prob
p = LP(obj, startPoint)
# Define some constraints
p.constraints = [
x + 5 * y < 15, x[0] < 4, f1 < [25, 35], f1 > -100,
2 * f1 + 4 * z < [80, 800], 5 * f2 + 4 * z < 100, -5 < x, x < 1, -20 < y,
y < 20, -4000 < z, z < 4
]
# Solve
r = p.solve(
'lpSolve', fixedVars=t
) # glpk is name of solver involved, see OOF doc for more arguments
# Decode solution
print('Solution: x = %s y = %f z = %f' % (r(x), r(y), r(z)))
# you should have lpsolve and its Python binding properly installed
# (you may take a look at the instructions from openopt.org/LP)
# You can solve problems defined in MPS files
# with a variety of solvers at NEOS server for free
# http://neos.mcs.anl.gov/
# BTW they have Python API along with web API and other
from numpy import *
from openopt import LP
f = array([15, 8, 80])
A = mat(
'1 2 3; 8 15 80; 8 80 15; -100 -10 -1') # numpy.ndarray is also allowed
b = [15, 80, 150, -800] # numpy.ndarray, matrix etc are also allowed
Aeq = mat('80 8 15; 1 10 100') # numpy.ndarray is also allowed
beq = (750, 80)
lb = [4, -80, -inf]
ub = [inf, -8, inf]
p = LP(f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub, name='lp_1')
# or p = LP(f=f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
# if file name not ends with '.MPS' or '.mps'
# then '.mps' will be appended
success = p.exportToMPS('asdf')
# success is False if a error occurred (read-only file system, no write access, etc)
# elseware success is True
# objFunValue should be 204.48841578
# x_opt should be [ 9.89355041 -8. 1.5010645 ]
from FuncDesigner import *
from openopt import LP
# Define some oovars
x, y, z = oovars(3)
# Let's define some linear functions
f1 = 4*x+5*y + 3*z + 5
f2 = f1.sum() + 2*x + 4*y + 15
f3 = 5*f1 + 4*f2 + 20
# Define objective; sum(a) and a.sum() are same as well as for numpy arrays
obj = sum(f1)+ x.sum()+ y - 50*z + 2*f2.sum() + 4064.6
# Start point - currently matters only size of variables
startPoint = {x:[8, 15], y:25, z:80} # however, using numpy.arrays is more recommended than Python lists
# Create prob
p = LP(obj, startPoint)
# Define some constraints
p.constraints = [x+5*y<15, x[0]<4, f1<[25, 35], f1>-100, 2*f1+4*z<[80, 800], 5*f2+4*z<100, -5<x, x<1, -20<y, y<20, -4000<z, z<4]
# Solve
r = p.solve('lpSolve', fixedVars=t) # glpk is name of solver involved, see OOF doc for more arguments
# Decode solution
print('Solution: x = %s y = %f z = %f' % (r(x), r(y), r(z)))
# Solution: x = [-4.25 -4.25] y = -20.000000 z = 4.000000
ub = [1.]*len(Ulist)
Aeq = [[1.]*len(Ulist)]
beq = (1.,)
A = []
b = []
player = 0
while player<len(no_action):
action = 0
while action < no_action[player]:
for k in range(0,no_action[player]):
A.append(multiply(udiff(player,action,k),aik_indicator(player,action)))
b.append(0.)
action = action + 1
player = player +1
#print A,b
p = LP(neg_welfare, A=A,b=b,lb=lb,ub=ub,Aeq=Aeq,beq=beq)#we use the artificial minimization problem under the constraint that action gives a weakly higher payoff than any other action; if no feasible solution is obtained than action is dominated
p.iprint = -1
try:
r = p.minimize('pclp')
pminw = LP(welfare, A=A,b=b,lb=lb,ub=ub,Aeq=Aeq,beq=beq)
pminw.iprint = -1
rminw = pminw.minimize('pclp')
except:
print "Solver returns error. Probably, each player has a unique rationalizable action (check with rationalizability solver)."
quit()
###formatting the result back into the same format as the game input
# first: rounding
outr = []
for item in r.xf:
def solve(self):
p=LP(self.cost_function,Aeq=self.Aeq,beq=self.beq,lb=self.lb)
p.iprint = -1
r=p.solve('pclp')
return [r.xf,r.ff]
print len(s.matrix)
# for m in bMets:
# s.add_reaction(Reaction('R_'+m.identifier+'_Transp', (m,), (), ()))
# A_eq = numpy.delete(numpy.array(s.matrix, dtype=float), bIndices, 0)
transpColumn = numpy.zeros((len(s.matrix), len(bIndices)))
for i, elem in enumerate(bIndices):
transpColumn[elem,i] = 1
A_eq = numpy.append(numpy.array(s.matrix, dtype=float), transpColumn, 1)
print A_eq
print numpy.shape(A_eq)
b_eq = numpy.zeros(len(A_eq))
print numpy.shape(A_eq)[1]
print len(b_eq)
print len(numpy.random.randint(-10, -5, numpy.shape(A_eq)[1]))
print len(numpy.random.randint(5, 10, numpy.shape(A_eq)[1]))
lp = LP(f=obj, Aeq=A_eq, beq=b_eq, lb=numpy.random.randint(-6, -0, numpy.shape(A_eq)[1]), ub=numpy.random.randint(0, 6, numpy.shape(A_eq)[1]))
lp.exportToMPS
# print help(lp.manage)
# lp.solve('cvxopt_lp')
# print help(lp.solve)
r = lp.solve('glpk', goal='max')
# print dir(r)
# print r.ff
# print r.evals
# print r.isFeasible
# print r.msg
# print r.xf
# print r.duals
# print r.rf
# print r.solverInfo
# problem = openopt.LP(f=objective, Aeq=A_eq, beq=b_eq, lb=lb, ub=ub)
(hence Nconstraints = 75000)
glpk peak memory ~70 Mb,
time elapsed = 35.79, CPU time elapsed = 35.0
"""
from openopt import LP
from numpy import arange
from FuncDesigner import *
N = 25000
x, y, z = oovars(3)
startPoint = {
x: 0,
y: [0] * N,
z: [0] * (2 * N)
} # thus x from R, y from R^N, z from R^2N
objective = sum(x) + 2 * sum(y) + 3 * sum(z)
cons = [
x < 100, x > -100, y < arange(N), y > -10 - arange(N), z < arange(2 * N),
z > -100 - arange(2 * N), x + y > 2 - 3 * arange(N),
x + z > 4 - 5 * arange(2 * N)
]
p = LP(objective, startPoint, constraints=cons)
solver = 'glpk' # CVXOPT & glpk must be installed
r = p.minimize(solver)
print('objFunValue:%f' % r.ff)
8x1 + 80x2 + 15x3 <=150 (4)
100x1 + 10x2 + x3 >= 800 (5)
80x1 + 8x2 + 15x3 = 750 (6)
x1 + 10x2 + 100x3 = 80 (7)
x1 >= 4 (8)
-8 >= x2 >= -80 (9)
"""
from numpy import *
from openopt import LP
f = array([15, 8, 80])
A = mat("1 2 3; 8 15 80; 8 80 15; -100 -10 -1") # numpy.ndarray is also allowed
b = [15, 80, 150, -800] # numpy.ndarray, matrix etc are also allowed
Aeq = mat("80 8 15; 1 10 100") # numpy.ndarray is also allowed
beq = (750, 80)
lb = [4, -80, -inf]
ub = [inf, -8, inf]
p = LP(f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
# or p = LP(f=f, A=A, Aeq=Aeq, b=b, beq=beq, lb=lb, ub=ub)
# r = p.minimize('glpk') # CVXOPT must be installed
# r = p.minimize('lpSolve') # lpsolve must be installed
r = p.minimize("pclp")
# search for max: r = p.maximize('glpk') # CVXOPT & glpk must be installed
# r = p.minimize('nlp:ralg', ftol=1e-7, xtol=1e-7, goal='min', plot=1)
print("objFunValue: %f" % r.ff) # should print 204.48841578
print("x_opt: %s" % r.xf) # should print [ 9.89355041 -8. 1.5010645 ]