def create_problem(cobra_model, **kwargs):
"""Solver-specific method for constructing a solver problem from
a cobra.Model. This can be tuned for performance using kwargs
"""
metabolite_to_index = {r: i for i, r in enumerate(cobra_model.metabolites)}
lp = LPX() # Create empty problem instance
lp.name = 'cobra' # Assign symbolic name to problem
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
for r, the_metabolite in zip(lp.rows, cobra_model.metabolites):
r.name = the_metabolite.id
b = float(the_metabolite._bound)
c = the_metabolite._constraint_sense
if c == 'E':
r.bounds = b, b # Set metabolite to steady state levels
elif c == 'L':
r.bounds = None, b
elif c == 'G':
r.bounds = b, None
else:
raise ValueError("invalid constraint sense")
objective_coefficients = []
linear_constraints = []
for c, the_reaction in zip(lp.cols, cobra_model.reactions):
c.name = the_reaction.id
c.kind = variable_kind_dict[the_reaction.variable_kind]
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(float(
the_reaction.objective_coefficient))
for metabolite, coefficient in iteritems(the_reaction._metabolites):
metabolite_index = metabolite_to_index[metabolite]
linear_constraints.append((metabolite_index, c.index, coefficient))
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
#Need to assign lp.matrix after constructing the whole list
#linear_constraints.sort() # if we wanted to be 100% deterministic
lp.matrix = linear_constraints
# make sure the objective sense is set in create_problem
objective_sense = kwargs.get("objective_sense", "maximize")
set_parameter(lp, "objective_sense", objective_sense)
return lp
def create_problem(cobra_model, **kwargs):
"""Solver-specific method for constructing a solver problem from
a cobra.Model. This can be tuned for performance using kwargs
"""
metabolite_to_index = {r: i for i, r in enumerate(cobra_model.metabolites)}
lp = LPX() # Create empty problem instance
lp.name = 'cobra' # Assign symbolic name to problem
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
for r, the_metabolite in zip(lp.rows, cobra_model.metabolites):
r.name = the_metabolite.id
b = float(the_metabolite._bound)
c = the_metabolite._constraint_sense
if c == 'E':
r.bounds = b, b # Set metabolite to steady state levels
elif c == 'L':
r.bounds = None, b
elif c == 'G':
r.bounds = b, None
else:
raise ValueError("invalid constraint sense")
objective_coefficients = []
linear_constraints = []
for c, the_reaction in zip(lp.cols, cobra_model.reactions):
c.name = the_reaction.id
c.kind = variable_kind_dict[the_reaction.variable_kind]
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(float(the_reaction.objective_coefficient))
for metabolite, coefficient in iteritems(the_reaction._metabolites):
metabolite_index = metabolite_to_index[metabolite]
linear_constraints.append((metabolite_index, c.index, coefficient))
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
#Need to assign lp.matrix after constructing the whole list
#linear_constraints.sort() # if we wanted to be 100% deterministic
lp.matrix = linear_constraints
# make sure the objective sense is set in create_problem
objective_sense = kwargs.get("objective_sense", "maximize")
set_parameter(lp, "objective_sense", objective_sense)
return lp
def create_problem(cobra_model, objective_sense="maximize", lp=None):
if lp is None:
lp = LPX() # Create empty problem instance
lp.name = cobra_model.id
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
if objective_sense == 'maximize':
lp.obj.maximize = True
elif objective_sense == 'minimize':
lp.obj.maximize = False
else:
raise ValueError("objective_sense not 'maximize' or 'minimize'")
# create metabolites/constraints as rows
for i, r in enumerate(lp.rows):
metabolite = cobra_model.metabolites[i]
r.name = metabolite.id
b = float(metabolite._bound)
c = metabolite._constraint_sense
# constraint sense is set by changing the bounds
if c == 'E':
r.bounds = (b, b)
elif c == 'L':
r.bounds = (None, b)
elif c == 'G':
r.bounds = (b, None)
else:
raise ValueError("%s is not a valid constraint_sense" % c)
# create reactions/variables as columns
for i, c in enumerate(lp.cols):
reaction = cobra_model.reactions[i]
c.name = reaction.id
c.kind = variable_kind_dict[reaction.variable_kind]
c.bounds = (reaction.lower_bound, reaction.upper_bound)
lp.obj[i] = float(reaction.objective_coefficient)
# create S matrix
lp.matrix = [(int(i), int(j), c) \
for (i, j), c in cobra_model.to_array_based_model().S.todok().iteritems()]
return lp
from glpk import LPX
# set up to maximize the objective function
lp = LPX()
lp.name = 'example'
lp.obj.maximize = True
# append 3 rows, named p, q, r
row_names = ["p", "q", "r"]
lp.rows.add(len(row_names))
for r in lp.rows:
r.name = row_names[r.index]
lp.rows[0].bounds = None, 100.0
lp.rows[1].bounds = None, 600.0
lp.rows[2].bounds = None, 150.0
# append 3 cols, named x0, x1, x2
lp.cols.add(3)
for c in lp.cols:
c.name = 'x%d' % c.index
c.bounds = 0.0, None
# set the objective coefficients and
# non-zero entries of the constraint matrix
lp.obj[:] = [ 5.0, 3.0, 2.0 ]
lp.matrix = [ 1.0, 1.0, 3.0, 10.0, 4.0, 5.0, 1.0, 1.0, 3.0 ]
# report the objective function value and structural variables
def _optimize_glpk(
cobra_model,
new_objective=None,
objective_sense='maximize',
min_norm=0,
the_problem=None,
tolerance_optimality=1e-6,
tolerance_feasibility=1e-6,
tolerance_integer=1e-9,
error_reporting=None,
print_solver_time=False,
lp_method=1,
quadratic_component=None,
reuse_basis=True,
#Not implemented
tolerance_barrier=None,
lp_parallel=None,
copy_problem=None,
relax_b=None,
update_problem_reaction_bounds=True):
"""Uses the GLPK (www.gnu.org/software/glpk/) optimizer via pyglpk
(http://www.tfinley.net/software/pyglpk/release.html) to perform an optimization
on cobra_model for the objective_coefficients in cobra_model._objective_coefficients
based on the objective sense.
cobra_model: A cobra.Model object
new_objective: Reaction, String, or Integer referring to a reaction in
cobra_model.reactions to set as the objective. Currently, only supports single
objective coeffients. Will expand to include mixed objectives.
objective_sense: 'maximize' or 'minimize'
min_norm: not implemented
the_problem: None or a problem object for the specific solver that can be used to hot
start the next solution.
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
error_reporting: None or True to disable or enable printing errors encountered
when trying to find the optimal solution.
print_solver_time: False or True. Indicates if the time to calculate the solution
should be displayed.
quadratic_component: None. GLPK cannot solve quadratic programs at the moment.
reuse_basis: Boolean. If True and the_problem is a model object for the solver,
attempt to hot start the solution. Currently, only True is available for GLPK
update_problem_reaction_bounds: Boolean. Set to True if you're providing the_problem
and you've modified reaction bounds on your cobra_model since creating the_problem. Only
necessary for CPLEX
lp.simplex() with Salmonella model:
cold start: 0.42 seconds
hot start: 0.0013 seconds
"""
from numpy import zeros, array, nan
#TODO: Speed up problem creation
if hasattr(quadratic_component, 'todok'):
raise Exception('GLPK cannot solve quadratic programs please '+\
'try using the gurobi or cplex solvers')
from glpk import LPX
from cobra.flux_analysis.objective import update_objective
from cobra.solvers.legacy import status_dict, variable_kind_dict
status_dict = eval(status_dict['glpk'])
variable_kind_dict = eval(variable_kind_dict['glpk'])
if new_objective and new_objective != 'update problem':
update_objective(cobra_model, new_objective)
#Faster to use these dicts than index lists
index_to_metabolite = dict(
zip(range(len(cobra_model.metabolites)), cobra_model.metabolites))
index_to_reaction = dict(
zip(range(len(cobra_model.reactions)), cobra_model.reactions))
reaction_to_index = dict(
zip(index_to_reaction.values(), index_to_reaction.keys()))
if the_problem == None or the_problem in ['return', 'setup'] or \
not isinstance(the_problem, LPX):
lp = LPX() # Create empty problem instance
lp.name = 'cobra' # Assign symbolic name to problem
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
linear_constraints = []
for r in lp.rows:
the_metabolite = index_to_metabolite[r.index]
r.name = the_metabolite.id
b = float(the_metabolite._bound)
c = the_metabolite._constraint_sense
if c == 'E':
r.bounds = b, b # Set metabolite to steady state levels
elif c == 'L':
r.bounds = None, b
elif c == 'G':
r.bounds = b, None
#Add in the linear constraints
for the_reaction in the_metabolite._reaction:
reaction_index = reaction_to_index[the_reaction]
the_coefficient = the_reaction._metabolites[the_metabolite]
linear_constraints.append(
(r.index, reaction_index, the_coefficient))
#Need to assign lp.matrix after constructing the whole list
lp.matrix = linear_constraints
objective_coefficients = []
for c in lp.cols:
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
the_reaction = index_to_reaction[c.index]
c.kind = variable_kind_dict[the_reaction.variable_kind]
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(
float(the_reaction.objective_coefficient))
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
lp = the_problem
#BUG with changing / unchanging the basis
if new_objective is not None:
objective_coefficients = []
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(
float(the_reaction.objective_coefficient))
c.kind = variable_kind_dict[the_reaction.variable_kind]
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
c.kind = variable_kind_dict[the_reaction.variable_kind]
if objective_sense.lower() == 'maximize':
lp.obj.maximize = True # Set this as a maximization problem
else:
lp.obj.maximize = False
if the_problem == 'setup':
return lp
if print_solver_time:
start_time = time()
the_methods = [1, 2, 3]
if lp_method in the_methods:
the_methods.remove(lp_method)
else:
lp_method = 1
if not isinstance(the_problem, LPX):
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method)
# Solve this LP or MIP with the simplex (depending on if integer variables exist). Takes about 0.35 s without hot start
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
else:
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method,
tm_lim=100) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method,
tm_lim=100)
#If the solver takes more than 0.1 s with a hot start it is likely stuck
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp = optimize_glpk(
cobra_model,
new_objective=new_objective,
objective_sense=objective_sense,
min_norm=min_norm,
the_problem=None,
print_solver_time=print_solver_time,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility)['the_problem']
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp.simplex(tol_bnd=tolerance_optimality,
presolve=True,
tm_lim=5000)
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if print_solver_time:
print 'simplex time: %f' % (time() - start_time)
x = []
y = []
x_dict = {}
y_dict = {}
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status == 'optimal':
objective_value = lp.obj.value
[(x.append(float(c.primal)), x_dict.update({c.name: c.primal}))
for c in lp.cols]
if lp.kind == float:
#return the duals as well as the primals for LPs
[(y.append(float(c.dual)), y_dict.update({c.name: c.dual}))
for c in lp.rows]
else:
#MIPs don't have duals
y = y_dict = None
x = array(x)
else:
x = y = x_dict = y_dict = objective_value = None
if error_reporting:
print 'glpk failed: %s' % lp.status
cobra_model.solution = the_solution = Solution(objective_value,
x=x,
x_dict=x_dict,
y=y,
y_dict=y_dict,
status=status)
solution = {'the_problem': lp, 'the_solution': the_solution}
return solution
def _optimize_glpk(cobra_model, new_objective=None, objective_sense='maximize',
min_norm=0, the_problem=None,
tolerance_optimality=1e-6, tolerance_feasibility=1e-6, tolerance_integer=1e-9,
error_reporting=None, print_solver_time=False,
lp_method=1, quadratic_component=None,
reuse_basis=True,
#Not implemented
tolerance_barrier=None, lp_parallel=None,
copy_problem=None, relax_b=None,update_problem_reaction_bounds=True):
"""Uses the GLPK (www.gnu.org/software/glpk/) optimizer via pyglpk
(http://www.tfinley.net/software/pyglpk/release.html) to perform an optimization
on cobra_model for the objective_coefficients in cobra_model._objective_coefficients
based on the objective sense.
cobra_model: A cobra.Model object
new_objective: Reaction, String, or Integer referring to a reaction in
cobra_model.reactions to set as the objective. Currently, only supports single
objective coeffients. Will expand to include mixed objectives.
objective_sense: 'maximize' or 'minimize'
min_norm: not implemented
the_problem: None or a problem object for the specific solver that can be used to hot
start the next solution.
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
error_reporting: None or True to disable or enable printing errors encountered
when trying to find the optimal solution.
print_solver_time: False or True. Indicates if the time to calculate the solution
should be displayed.
quadratic_component: None. GLPK cannot solve quadratic programs at the moment.
reuse_basis: Boolean. If True and the_problem is a model object for the solver,
attempt to hot start the solution. Currently, only True is available for GLPK
update_problem_reaction_bounds: Boolean. Set to True if you're providing the_problem
and you've modified reaction bounds on your cobra_model since creating the_problem. Only
necessary for CPLEX
lp.simplex() with Salmonella model:
cold start: 0.42 seconds
hot start: 0.0013 seconds
"""
from numpy import zeros, array, nan
#TODO: Speed up problem creation
if hasattr(quadratic_component, 'todok'):
raise Exception('GLPK cannot solve quadratic programs please '+\
'try using the gurobi or cplex solvers')
from glpk import LPX
from cobra.flux_analysis.objective import update_objective
from cobra.solvers.legacy import status_dict, variable_kind_dict
status_dict = eval(status_dict['glpk'])
variable_kind_dict = eval(variable_kind_dict['glpk'])
if new_objective and new_objective != 'update problem':
update_objective(cobra_model, new_objective)
#Faster to use these dicts than index lists
index_to_metabolite = dict(zip(range(len(cobra_model.metabolites)),
cobra_model.metabolites))
index_to_reaction = dict(zip(range(len(cobra_model.reactions)),
cobra_model.reactions))
reaction_to_index = dict(zip(index_to_reaction.values(),
index_to_reaction.keys()))
if the_problem == None or the_problem in ['return', 'setup'] or \
not isinstance(the_problem, LPX):
lp = LPX() # Create empty problem instance
lp.name = 'cobra' # Assign symbolic name to problem
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
linear_constraints = []
for r in lp.rows:
the_metabolite = index_to_metabolite[r.index]
r.name = the_metabolite.id
b = float(the_metabolite._bound)
c = the_metabolite._constraint_sense
if c == 'E':
r.bounds = b, b # Set metabolite to steady state levels
elif c == 'L':
r.bounds = None, b
elif c == 'G':
r.bounds = b, None
#Add in the linear constraints
for the_reaction in the_metabolite._reaction:
reaction_index = reaction_to_index[the_reaction]
the_coefficient = the_reaction._metabolites[the_metabolite]
linear_constraints.append((r.index, reaction_index,
the_coefficient))
#Need to assign lp.matrix after constructing the whole list
lp.matrix = linear_constraints
objective_coefficients = []
for c in lp.cols:
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
the_reaction = index_to_reaction[c.index]
c.kind = variable_kind_dict[the_reaction.variable_kind]
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(float(the_reaction.objective_coefficient))
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
lp = the_problem
#BUG with changing / unchanging the basis
if new_objective is not None:
objective_coefficients = []
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(float(the_reaction.objective_coefficient))
c.kind = variable_kind_dict[the_reaction.variable_kind]
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
c.kind = variable_kind_dict[the_reaction.variable_kind]
if objective_sense.lower() == 'maximize':
lp.obj.maximize = True # Set this as a maximization problem
else:
lp.obj.maximize = False
if the_problem == 'setup':
return lp
if print_solver_time:
start_time = time()
the_methods = [1, 2, 3]
if lp_method in the_methods:
the_methods.remove(lp_method)
else:
lp_method = 1
if not isinstance(the_problem, LPX):
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method)
# Solve this LP or MIP with the simplex (depending on if integer variables exist). Takes about 0.35 s without hot start
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
else:
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method, tm_lim=100) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method, tm_lim=100)
#If the solver takes more than 0.1 s with a hot start it is likely stuck
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp = optimize_glpk(cobra_model, new_objective=new_objective,
objective_sense=objective_sense,
min_norm=min_norm, the_problem=None,
print_solver_time=print_solver_time,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility)['the_problem']
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp.simplex(tol_bnd=tolerance_optimality, presolve=True, tm_lim=5000)
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if print_solver_time:
print 'simplex time: %f'%(time() - start_time)
x = []
y = []
x_dict = {}
y_dict = {}
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status == 'optimal':
objective_value = lp.obj.value
[(x.append(float(c.primal)),
x_dict.update({c.name:c.primal}))
for c in lp.cols]
if lp.kind == float:
#return the duals as well as the primals for LPs
[(y.append(float(c.dual)),
y_dict.update({c.name:c.dual}))
for c in lp.rows]
else:
#MIPs don't have duals
y = y_dict = None
x = array(x)
else:
x = y = x_dict = y_dict = objective_value = None
if error_reporting:
print 'glpk failed: %s'%lp.status
the_solution = Solution(objective_value, x=x, x_dict=x_dict,
y=y, y_dict=y_dict,
status=status)
solution = {'the_problem': lp, 'the_solution': the_solution}
return solution
from glpk import LPX
# set up to maximize the objective function
lp = LPX()
lp.name = 'foobartendr'
lp.obj.maximize = True
# append 3 rows
row_names = ["ingrednt", "bartendr", "delivery"]
lp.rows.add(len(row_names))
for r in lp.rows:
r.name = row_names[r.index]
lp.rows[0].bounds = None, 100.0
lp.rows[1].bounds = None, 600.0
lp.rows[2].bounds = None, 150.0
# append 3 cols, named x0, x1, x2
lp.cols.add(3)
for c in lp.cols:
c.name = 'x%d' % c.index
c.bounds = 0.0, None
# set the objective coefficients and
# non-zero entries of the constraint matrix
lp.obj[:] = [ 5.0, 3.0, 2.0 ]
lp.matrix = [ 1.0, 1.0, 3.0, 10.0, 4.0, 5.0, 1.0, 1.0, 3.0 ]
# report the objective function value and structural variables
def testLpxName(self):
lp = LPX()
with self.assertRaises(ValueError) as cm:
lp.name = 'a' * 256
self.assertIn('name may be at most 255 chars', str(cm.exception))
from glpk import LPX
# set up to maximize the objective function
lp = LPX()
lp.name = 'example'
lp.obj.maximize = True
# append 3 rows, named p, q, r
row_names = ["p", "q", "r"]
lp.rows.add(len(row_names))
for r in lp.rows:
r.name = row_names[r.index]
lp.rows[0].bounds = None, 100.0
lp.rows[1].bounds = None, 600.0
lp.rows[2].bounds = None, 150.0
# append 3 cols, named x0, x1, x2
lp.cols.add(3)
for c in lp.cols:
c.name = 'x%d' % c.index
c.bounds = 0.0, None
# set the objective coefficients and
# non-zero entries of the constraint matrix
lp.obj[:] = [5.0, 3.0, 2.0]
lp.matrix = [1.0, 1.0, 3.0, 10.0, 4.0, 5.0, 1.0, 1.0, 3.0]
# report the objective function value and structural variables
