def ecos_solve_qp(
P, q, G=None, h=None, A=None, b=None, initvals=None, verbose: bool = False
) -> Optional[ndarray]:
"""
Solve a Quadratic Program defined as:
.. math::
\\begin{split}\\begin{array}{ll}
\\mbox{minimize} &
\\frac{1}{2} x^T P x + q^T x \\\\
\\mbox{subject to}
& G x \\leq h \\\\
& A x = h
\\end{array}\\end{split}
using `ECOS <https://github.com/embotech/ecos>`_.
Parameters
----------
P : numpy.array
Primal quadratic cost matrix.
q : numpy.array
Primal quadratic cost vector.
G : numpy.array
Linear inequality constraint matrix.
h : numpy.array
Linear inequality constraint vector.
A : numpy.array, optional
Linear equality constraint matrix.
b : numpy.array, optional
Linear equality constraint vector.
initvals : numpy.array, optional
Warm-start guess vector (not used).
verbose : bool, optional
Set to `True` to print out extra information.
Returns
-------
x : array, shape=(n,)
Solution to the QP, if found, otherwise ``None``.
"""
if initvals is not None:
warn("note that warm-start values ignored by this wrapper")
c_socp, G_socp, h_socp, dims = convert_to_socp(P, q, G, h)
if A is not None:
A_socp = hstack([A, zeros((A.shape[0], 1))])
A_socp = csc_matrix(A_socp)
solution = solve(c_socp, G_socp, h_socp, dims, A_socp, b, verbose=verbose)
else:
solution = solve(c_socp, G_socp, h_socp, dims, verbose=verbose)
flag = solution["info"]["exitFlag"]
if flag != 0:
warn(f"ECOS returned exit flag {flag} ({__exit_flag_meaning__[flag]})")
return None
return solution["x"][:-1]
def runEcos(tSolve, tWait, x_s, m_s, goldSearch=False, tDist=None):
# find linear, SOC, and exponential inequality constraints
# find equality constraints
# initializes minimization function
G, h, q, l, e = socConstraints(tSolve, goldSearch, m_s, tDist=tDist)
A_mat, b = equalityConstraints(tSolve, x_s)
c = np.zeros(11 * tSolve + 1)
if goldSearch:
# optimizes for slack variable, norm of final distance must be
# less than or equal to this slack variable. Returns exit flag
# (whether the solution was optimal or not) and final landing
# distance
c[-1] = 1
solution = ecos.solve(c,
G,
h, {
'l': l,
'q': q,
'e': e
},
A=A_mat,
b=b,
verbose=False,
abstol=1e-4,
feastol=1e-4,
reltol=1e-4)
finDist = linalg.norm(solution['x'][11 * (tSolve - 1) + 1:11 *
(tSolve - 1) + 3])
return solution['info']['exitFlag'], finDist
else:
# optimizes for maximizing final fuel. Returns the solution found
# by ecos
c[11 * (tSolve - 1) + 6] = -1
solution = ecos.solve(c,
G,
h, {
'l': l,
'q': q,
'e': e
},
A=A_mat,
b=b,
verbose=False,
abstol=1e-4,
feastol=1e-4,
reltol=1e-4)
print("The solution was: ", solution['info']['exitFlag'])
return solution['x']
def test_problems():
sol = ecos.solve(c, G, h, dims)
yield check_solution, sol['x'][0], 1
sol = ecos.solve(c, G, h, dims, A, b)
yield check_solution, sol['x'][0], 3
new_dims = {'q':[2], 'l': 0}
sol = ecos.solve(c, G, h, new_dims)
yield check_solution, sol['x'][0], 0.5
def test_problems_with_longs():
new_dims = {'q': [], 'l': long(2)}
sol = ecos.solve(c, G, h, new_dims)
yield check_solution, sol['x'][0], 1
sol = ecos.solve(c, G, h, new_dims, A, b)
yield check_solution, sol['x'][0], 3
new_dims = {'q':[long(2)], 'l': 0}
sol = ecos.solve(c, G, h, new_dims)
yield check_solution, sol['x'][0], 0.5
def test_problems():
myopts = {'feastol': 2e-8, 'reltol': 2e-8, 'abstol': 2e-8, 'verbose':True};
sol = ecos.solve(c, G, h, dims, **myopts)
yield check_solution, sol['x'][0], 4
sol = ecos.solve(c, G, h, dims, A, b, **myopts)
yield check_solution, sol['x'][0], 3
new_dims = {'q':[2], 'l': 0}
sol = ecos.solve(c, G, h, new_dims, **myopts)
yield check_solution, sol['x'][0], 2
def test_problems_with_longs():
new_dims = {'q': [], 'l': long(2)}
myopts = {'feastol': 2e-8, 'reltol': 2e-8, 'abstol': 2e-8};
sol = ecos.solve(c, G, h, new_dims, **myopts)
yield check_solution, sol['x'][0], 4
sol = ecos.solve(c, G, h, new_dims, A, b, **myopts)
yield check_solution, sol['x'][0], 3
new_dims = {'q':[long(2)], 'l': 0}
sol = ecos.solve(c, G, h, new_dims, **myopts)
yield check_solution, sol['x'][0], 2
def solve(self, objective, constraints, cached_data, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
prob_data = self.get_problem_data(objective, constraints, cached_data)
obj_offset = prob_data[1]
results_dict = ecos.solve(*prob_data[0],
verbose=verbose,
**solver_opts)
return self.format_results(results_dict, None, obj_offset)
def solve(self, objective, constraints, cached_data, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
prob_data = self.get_problem_data(objective, constraints, cached_data)
obj_offset = prob_data[1]
# Add arguments for MIP solver.
sym_data = self.get_sym_data(objective, constraints, cached_data)
bool_idx, int_idx = self._noncvx_id_to_idx(sym_data.dims,
sym_data.var_offsets,
sym_data.var_sizes)
results_dict = ecos.solve(*prob_data[0], verbose=verbose,
bool_vars_idx=bool_idx,# int_vars_idx=int_idx,
**solver_opts)
return self.format_results(results_dict, None, obj_offset)
def solve_via_data(self,
data,
warm_start,
verbose,
solver_opts,
solver_cache=None):
import ecos
cones = dims_to_solver_dict(data[ConicSolver.DIMS])
# Default verbose to false for BB wrapper.
if 'mi_verbose' in solver_opts:
mi_verbose = solver_opts['mi_verbose']
del solver_opts['mi_verbose']
else:
mi_verbose = verbose
solution = ecos.solve(data[s.C],
data[s.G],
data[s.H],
cones,
data[s.A],
data[s.B],
verbose=verbose,
mi_verbose=mi_verbose,
bool_vars_idx=data[s.BOOL_IDX],
int_vars_idx=data[s.INT_IDX],
**solver_opts)
return solution
def test_problems_with_longs():
new_dims = {'q': [], 'l': long(2)}
myopts = {
'feastol': 2e-8,
'reltol': 2e-8,
'abstol': 2e-8
}
sol = ecos.solve(c, G, h, new_dims, **myopts)
yield check_solution, sol['x'][0], 4
sol = ecos.solve(c, G, h, new_dims, A, b, **myopts)
yield check_solution, sol['x'][0], 3
new_dims = {'q': [long(2)], 'l': 0}
sol = ecos.solve(c, G, h, new_dims, **myopts)
yield check_solution, sol['x'][0], 2
def test_problems():
myopts = {
'feastol': 2e-8,
'reltol': 2e-8,
'abstol': 2e-8,
'verbose': True
}
sol = ecos.solve(c, G, h, dims, **myopts)
yield check_solution, sol['x'][0], 4
sol = ecos.solve(c, G, h, dims, A, b, **myopts)
yield check_solution, sol['x'][0], 3
new_dims = {'q': [2], 'l': 0}
sol = ecos.solve(c, G, h, new_dims, **myopts)
yield check_solution, sol['x'][0], 2
def test_advanced(self):
"""Test code from the advanced section of the tutorial.
"""
x = Variable()
prob = Problem(Minimize(square(x)), [x == 2])
# Get ECOS arguments.
data = prob.get_problem_data(ECOS)
# Get ECOS_BB arguments.
data = prob.get_problem_data(ECOS_BB)
# Get CVXOPT arguments.
if CVXOPT in installed_solvers():
data = prob.get_problem_data(CVXOPT)
# Get SCS arguments.
data = prob.get_problem_data(SCS)
import ecos
# Get ECOS arguments.
data = prob.get_problem_data(ECOS)
# Call ECOS solver.
solver_output = ecos.solve(data["c"], data["G"], data["h"],
data["dims"], data["A"], data["b"])
# Unpack raw solver output.
prob.unpack_results(ECOS, solver_output)
def test_unpack_results(self):
"""Test unpack results method.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(exp(self.a))).unpack_results("blah", None)
self.assertEqual(str(cm.exception), "Unknown solver.")
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
args = prob.get_problem_data(s.SCS)
results_dict = scs.solve(*args)
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
prob.unpack_results(s.SCS, results_dict)
self.assertAlmostEqual(self.a.value, 0, places=4)
self.assertAlmostEqual(prob.value, 1, places=3)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.ECOS)
results_dict = ecos.solve(*args)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.ECOS, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0,0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.CVXOPT)
results_dict = cvxopt.solvers.conelp(*args)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.CVXOPT, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0,0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
def solve(self, objective, constraints, cached_data,
warm_start, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
warm_start : bool
Not used.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
import ecos
data = self.get_problem_data(objective, constraints, cached_data)
results_dict = ecos.solve(data[s.C], data[s.G], data[s.H],
data[s.DIMS], data[s.A], data[s.B],
verbose=verbose,
**solver_opts)
return self.format_results(results_dict, None,
data[s.OFFSET], cached_data)
def test_advanced(self):
"""Test code from the advanced section of the tutorial.
"""
x = Variable()
prob = Problem(Minimize(square(x)), [x == 2])
# Get ECOS arguments.
data = prob.get_problem_data(ECOS)
# Get ECOS_BB arguments.
data = prob.get_problem_data(ECOS_BB)
# Get CVXOPT arguments.
data = prob.get_problem_data(CVXOPT)
# Get SCS arguments.
data = prob.get_problem_data(SCS)
import ecos
# Get ECOS arguments.
data = prob.get_problem_data(ECOS)
# Call ECOS solver.
solver_output = ecos.solve(data["c"], data["G"], data["h"],
data["dims"], data["A"], data["b"])
# Unpack raw solver output.
prob.unpack_results(ECOS, solver_output)
def solve(self, objective, constraints, cached_data,
warm_start, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
warm_start : bool
Not used.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
data = self.get_problem_data(objective, constraints, cached_data)
results_dict = ecos.solve(data[s.C], data[s.G], data[s.H],
data[s.DIMS], data[s.A], data[s.B],
verbose=verbose,
**solver_opts)
return self.format_results(results_dict, None,
data[s.OFFSET], cached_data)
def test_1():
prob_data = (np.array([-22., -14.5, 13., 0., 13.94907477]),
scipy.sparse.csc_matrix(
[[-1., 0., 0., 0., 0.], [0., -1., 0., 0., 0.],
[0., 0., -1., 0., 0.], [1., 0., 0., 0.,
0.], [0., 1., 0., 0., 0.],
[0., 0., 1., 0., 0.], [0., 0., 0.,
-1., 0.],
[-0.06300143, 0.05999372, -0.04139022, 0., 0.],
[0.32966768, -0.07973959, -0.61737787, 0., 0.],
[0.59441633, 0.77421041, 0.21741083, 0., 0.],
[0., 0., 0., 0., -1.], [0., 0., 0., 0., 1.],
[0., 0., 0., -2., 0.]]),
np.array([
1., 1., 1., 1., 1., 1., -0., -0., -0., -0., 1., 1., -0.
]), {
'bool_ids': [],
'f': 0,
'l': 6,
'q': [4, 3],
's': [],
'int_ids': [],
'ep': 0
}, scipy.sparse.csc_matrix(np.zeros(
(0, 5), dtype=np.float64)), np.array([],
dtype=np.float64))
result = ecos.solve(*prob_data, verbose=False)
assert result['info']['infostring'] == 'Optimal solution found'
def test_unpack_results(self):
"""Test unpack results method.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(exp(self.a))).unpack_results("blah", None)
self.assertEqual(str(cm.exception), "Unknown solver.")
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
args = prob.get_problem_data(s.SCS)
results_dict = scs.solve(*args)
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
prob.unpack_results(s.SCS, results_dict)
self.assertAlmostEqual(self.a.value, 0, places=4)
self.assertAlmostEqual(prob.value, 1, places=3)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.ECOS)
results_dict = ecos.solve(*args)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.ECOS, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0, 0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.CVXOPT)
results_dict = cvxopt.solvers.conelp(*args)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.CVXOPT, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0, 0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
def solve(self, objective, constraints, cached_data, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
prob_data = self.get_problem_data(objective, constraints, cached_data)
obj_offset = prob_data[1]
results = ecos.solve(*prob_data[0], verbose=verbose, **solver_opts)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
if status in s.SOLUTION_PRESENT:
primal_val = results['info']['pcost']
value = primal_val + obj_offset
return (status, value,
results['x'], results['y'], results['z'])
else:
return (status, None, None, None, None)
def test_advanced2(self):
"""Test code from the advanced section of the tutorial.
"""
x = cvx.Variable()
prob = cvx.Problem(cvx.Minimize(cvx.square(x)), [x == 2])
# Get ECOS arguments.
data, chain, inverse = prob.get_problem_data(cvx.ECOS)
# Get ECOS_BB arguments.
data, chain, inverse = prob.get_problem_data(cvx.ECOS_BB)
# Get CVXOPT arguments.
if cvx.CVXOPT in cvx.installed_solvers():
data, chain, inverse = prob.get_problem_data(cvx.CVXOPT)
# Get SCS arguments.
data, chain, inverse = prob.get_problem_data(cvx.SCS)
import ecos
# Get ECOS arguments.
data, chain, inverse = prob.get_problem_data(cvx.ECOS)
# Call ECOS solver.
solution = ecos.solve(data["c"], data["G"], data["h"],
ecos_conif.dims_to_solver_dict(data["dims"]),
data["A"], data["b"])
# Unpack raw solver output.
prob.unpack_results(solution, chain, inverse)
def solve(self, c, G, h, dims, A, b, output):
"""Solves the exponential Cone Program min_{Delta_p}H(T|U,V) where U,V in {X,Y,Z}
Args:
c: numpy.array - objective function weights
G: scipy.sparse.csc_matrix - matrix of exponential and nonnegative inequalities
h: numpy.array - L.H.S. of inequalities
dims: dictionary - cones to be used
keys: string - cone type (exponential or nonegative)
values: int - number of cones
A: scipy.sparse.csc_matrix - Matrix of marginal, q-w coupling, and q-p coupling equations
b: numpy.array - L.H.S. of equalities
output: int - print different outputs based on (int) to console
Returns:
sol_rpq: numpy.array - primal optimal solution
sol_slack: numpy.array - slack of primal optimal solution (G*sol_rpq - h)
sol_lambda: numpy.array - equalities dual optimal solution
sol_mu: numpy.array - inequalities dual optimal solution
sol_info: dictionary - Brief stats of the optimization from ECOS
"""
itic = time.process_time()
self.marg_xyz = None # for cond[]mutinf computation below
if self.verbose != None:
# print(self.verbose)
self.ecos_kwargs["verbose"] = self.verbose
#^ if
solution = ecos.solve(c, G, h, dims, A, b, **self.ecos_kwargs)
if 'x' in solution.keys():
self.sol_rpq = solution['x']
self.sol_slack = solution['s']
self.sol_lambda = solution['y']
self.sol_mu = solution['z']
self.sol_info = solution['info']
itoc = time.process_time()
if output == 2:
print(
"TRIVARIATE_UNQ.solve(): Time to solve the Exponential Program of H(S|W,T)",
itoc - itic, "secs")
return "success", self.sol_rpq, self.sol_slack, self.sol_lambda, self.sol_mu, self.sol_info
else: # "x" not in dict solution
return "TRIVARIATE_UNQ.solve(): x not in dict solution -- No Solution Found!!!"
def solve_via_data(self, data, warm_start, verbose, solver_opts, solver_cache=None):
import ecos
cones = dims_to_solver_dict(data[ConicSolver.DIMS])
solution = ecos.solve(data[s.C], data[s.G], data[s.H],
cones, data[s.A], data[s.B],
verbose=verbose,
**solver_opts)
return solution
def test_advanced(self):
"""Test code from the advanced section of the tutorial.
"""
x = Variable()
prob = Problem(Minimize(square(x)), [x == 2])
# Get ECOS arguments.
c, G, h, dims, A, b = prob.get_problem_data(ECOS)
# Get CVXOPT arguments.
c, G, h, dims, A, b = prob.get_problem_data(CVXOPT)
# Get SCS arguments.
data, dims = prob.get_problem_data(SCS)
import ecos
# Get ECOS arguments.
c, G, h, dims, A, b = prob.get_problem_data(ECOS)
# Call ECOS solver.
solver_output = ecos.solve(c, G, h, dims, A, b)
# Unpack raw solver output.
prob.unpack_results(ECOS, solver_output)
# # Risk return tradeoff curve
# def test_risk_return_tradeoff(self):
# from math import sqrt
# from cvxopt import matrix
# from cvxopt.blas import dot
# from cvxopt.solvers import qp, options
# import scipy
# n = 4
# S = matrix( [[ 4e-2, 6e-3, -4e-3, 0.0 ],
# [ 6e-3, 1e-2, 0.0, 0.0 ],
# [-4e-3, 0.0, 2.5e-3, 0.0 ],
# [ 0.0, 0.0, 0.0, 0.0 ]] )
# pbar = matrix([.12, .10, .07, .03])
# N = 100
# # CVXPY
# Sroot = numpy.asmatrix(scipy.linalg.sqrtm(S))
# x = cp.Variable(n, name='x')
# mu = cp.Parameter(name='mu')
# mu.value = 1 # TODO cp.Parameter("positive")
# objective = cp.Minimize(-pbar*x + mu*quad_over_lin(Sroot*x,1))
# constraints = [sum_entries(x) == 1, x >= 0]
# p = cp.Problem(objective, constraints)
# mus = [ 10**(5.0*t/N-1.0) for t in range(N) ]
# xs = []
# for mu_val in mus:
# mu.value = mu_val
# p.solve()
# xs.append(x.value)
# returns = [ dot(pbar,x) for x in xs ]
# risks = [ sqrt(dot(x, S*x)) for x in xs ]
# # QP solver
def solve(self, c, G, h, dims, A, b, output):
"""Solves the second-order cone program min_{Pi_x}1/2 x^TWx + f^T x
Args:
c: numpy.array - objective function weights
G: scipy.sparse.csc_matrix - matrix of soc and nonnegative inequalities
h: numpy.array - L.H.S. of inequalities
dims: dictionary - cones to be used
keys: string - cone type (soc or nonegative)
values: int - number of cones
A: scipy.sparse.csc_matrix - Matrix of identity equations
b: numpy.array - L.H.S. of equalities
output: int - print different outputs based on (int) to console
Returns:
sol_tx: numpy.array - primal optimal solution
sol_slack: numpy.array - slack of primal optimal solution (G*sol_rpq - h)
sol_lambda: numpy.array - equalities dual optimal solution
sol_mu: numpy.array - inequalities dual optimal solution
sol_info: dictionary - Brief stats of the optimization from ECOS
"""
itic = time.process_time()
if self.verbose != None:
# print(self.verbose)
self.ecos_kwargs["verbose"] = self.verbose
#^ if
solution = ecos.solve(c, G, h, dims, A, b, **self.ecos_kwargs)
if 'x' in solution.keys():
self.sol_tx = solution['x']
self.sol_slack = solution['s']
self.sol_lambda = solution['y']
self.sol_mu = solution['z']
self.sol_info = solution['info']
itoc = time.process_time()
if output == 2:
print(
"TRIVARIATE_QP.solve(): Time to solve the Quadratic Program of Least Squares",
itoc - itic, "secs")
return "success", self.sol_tx, self.sol_slack, self.sol_lambda, self.sol_mu, self.sol_info
else: # "x" not in dict solution
return "TRIVARIATE_QP.solve(): x not in dict solution -- No Solution Found!!!"
def ecos_solver(G, h, A, b, c, n):
# In order to use ecos, we must provide sparse matrices
A = csc_matrix(A)
G = csc_matrix(G)
dims = dict(l=n**2, q=[])
solution = ecos.solve(c, G, h, dims, A, b)
if solution['info']['exitFlag'] == 0:
return True, solution['x']
# TODO status could be unknown here, but we're currently ignoring that
return False, None
def ecos_solver(G, h, A, b, c, n):
# In order to use ecos, we must provide sparse matrices
A = csc_matrix(A)
G = csc_matrix(G)
dims = dict(l=n ** 2, q=[])
solution = ecos.solve(c, G, h, dims, A, b)
if solution['info']['exitFlag'] == 0:
return True, solution['x']
# TODO status could be unknown here, but we're currently ignoring that
return False, None
def solve_func(params):
data = self.prob2socp(params)
sol = ecos.solve(**data)
result = self.socp2prob(sol['x'])
result['info'] = sol['info']
# set the objective value
multiplier = self.__codegen.objective_multiplier
offset = self.__codegen.objective_offset
result['objval'] = multiplier * sol['info']['pcost'] + offset
return result
def solve_func(params, dims):
data = self.prob2socp(params, dims)
sol = ecos.solve(**data)
result = self.socp2prob(sol['x'], dims)
result['info'] = sol['info']
# set the objective value
multiplier = self.__codegen.objective_multiplier
offset = self.__codegen.objective_offset
result['objval'] = multiplier * sol['info']['pcost'] + offset
return result
def NashEquilibriumECOSSolver(M):
"""
https://github.com/embotech/ecos-python
min c*x
s.t. A*x = b
G*x <= h
https://github.com/embotech/ecos/wiki/Usage-from-MATLAB
args:
c,b,h: numpy.array
A, G: Scipy sparse matrix
"""
row, col = M.shape
c = np.zeros(row + 1)
# max z
c[-1] = -1
# x1+x2+...+xn=1
A = np.ones(row + 1)
A[-1] = 0.
A = csr_matrix([A])
b = np.array([1.])
# M.T*x<=z
G1 = np.ones((col, row + 1))
G1[:col, :row] = -1. * M.T
# x>=0
G2 = np.zeros((row, row + 1))
for i in range(row):
G2[i, i] = -1.
# x<=1.
G3 = np.zeros((row, row + 1))
for i in range(row):
G3[i, i] = 1.
G = csr_matrix(np.concatenate((G1, G2, G3)))
h = np.concatenate((np.zeros(2 * row), np.ones(row)))
# specify number of variables
dims = {'l': col + 2 * row, 'q': []}
solution = ecos.solve(c, G, h, dims, A, b, verbose=False)
p1_value = solution['x'][:row]
p2_value = solution['z'][:col] # z is the dual variable of x
# There are at least two bad cases with above constrained optimization,
# where the constraints are not fully satisfied (some numerical issue):
# 1. the sum of vars is larger than 1.
# 2. the value of var may be negative.
abs_p1_value = np.abs(p1_value)
abs_p2_value = np.abs(p2_value)
p1_value = abs_p1_value / np.sum(abs_p1_value)
p2_value = abs_p2_value / np.sum(abs_p2_value)
return (p1_value, p2_value)
def _ecos_solve(self, objective, constr_map, dims,
sorted_vars, var_offsets, x_length,
verbose):
"""Calls the ECOS solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
sorted_vars: list
An ordered list of the problem variables.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._DENSE_INTF,
self._DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Convert c,h,b to 1D arrays.
c, h, b = map(lambda mat: np.asarray(mat)[:, 0], [c.T, h, b])
results = ecos.solve(c, G, h, dims, A, b, verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
if status == s.OPTIMAL:
primal_val = results['info']['pcost']
value = self.objective._primal_to_result(
primal_val - obj_offset)
return (status, value,
results['x'], results['y'], results['z'])
else:
return (status, None, None, None, None)
def solve_via_data(self, data, warm_start: bool, verbose: bool, solver_opts, solver_cache=None):
import ecos
cones = dims_to_solver_dict(data[ConicSolver.DIMS])
if data[s.A] is not None and data[s.A].nnz == 0 and np.prod(data[s.A].shape) > 0:
raise ValueError(
"ECOS cannot handle sparse data with nnz == 0; "
"this is a bug in ECOS, and it indicates that your problem "
"might have redundant constraints.")
solution = ecos.solve(data[s.C], data[s.G], data[s.H],
cones, data[s.A], data[s.B],
verbose=verbose,
**solver_opts)
return solution
def solve_func(params, dims):
data = self.prob2socp(params, dims)
sol = ecos.solve(**data)
result = self.socp2prob(sol["x"], sol["y"], sol["z"], dims)
result["info"] = sol["info"]
# set the objective value
multiplier = self.__codegen.objective_multiplier
offset = self.__codegen.objective_offset
if isinstance(offset, str):
# in this case, offset is likely python *code*
offset = eval(offset)
result["objval"] = multiplier * sol["info"]["pcost"] + offset
return result
def solve_func(params, dims):
data = self.prob2socp(params, dims)
sol = ecos.solve(**data)
result = self.socp2prob(sol['x'], sol['y'], sol['z'], dims)
result['info'] = sol['info']
# set the objective value
multiplier = self.__codegen.objective_multiplier
offset = self.__codegen.objective_offset
if isinstance(offset, str):
# in this case, offset is likely python *code*
offset = eval(offset)
result['objval'] = multiplier * sol['info']['pcost'] + offset
return result
def solve_via_data(data, params):
import ecos
if 'max_iters' in params:
max_iters = params['max_iters']
else:
max_iters = 100000
sol = ecos.solve(data['c'],
data['G'],
data['h'],
data['cones'],
data['A'],
data['b'],
verbose=params['verbose'],
max_iters=max_iters)
return sol
def solver(self, params, dims):
temp = self.prob2socp()
data = temp(params, dims)
sol = ecos.solve(**data)
temp1 = self.socp2prob()
result = temp1(sol['x'], sol['y'], sol['z'], dims)
result['info'] = sol['info']
# set the objective value
multiplier = self.__codegen.objective_multiplier
offset = self.__codegen.objective_offset
if isinstance(offset, str):
# in this case, offset is likely python *code*
offset = eval(offset)
result['objval'] = multiplier * sol['info']['pcost'] + offset
return result
def solve_via_data(data, params):
if not Mosek.is_installed():
warnings.warn(_MOSEK_INSTALL_)
import ecos
if 'max_iters' in params:
max_iters = params['max_iters']
else:
max_iters = 100000
sol = ecos.solve(data['c'],
data['G'],
data['h'],
data['cones'],
data['A'],
data['b'],
verbose=params['verbose'],
max_iters=max_iters)
return sol
def solve(self, objective, constraints, cached_data, warm_start, verbose,
solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
warm_start : bool
Not used.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
import ecos
data = self.get_problem_data(objective, constraints, cached_data)
# Default verbose to false for BB wrapper.
if 'mi_verbose' in solver_opts:
mi_verbose = solver_opts['mi_verbose']
del solver_opts['mi_verbose']
else:
mi_verbose = verbose
results_dict = ecos.solve(data[s.C],
data[s.G],
data[s.H],
data[s.DIMS],
data[s.A],
data[s.B],
verbose=verbose,
mi_verbose=mi_verbose,
bool_vars_idx=data[s.BOOL_IDX],
int_vars_idx=data[s.INT_IDX],
**solver_opts)
return self.format_results(results_dict, data, cached_data)
def solve(self):
# (c) Abdullah Makkeh, Dirk Oliver Theis
# Permission to use and modify under Apache License version 2.0
self.marg_yz = None # for cond[]mutinf computation below
if self.verbose != None:
self.ecos_kwargs["verbose"] = self.verbose
solution = ecos.solve(self.c, self.G,self.h, self.dims, self.A,self.b, **self.ecos_kwargs)
if 'x' in solution.keys():
self.sol_rpq = solution['x']
self.sol_slack = solution['s']
self.sol_lambda = solution['y']
self.sol_mu = solution['z']
self.sol_info = solution['info']
return "success"
else: # "x" not in dict solution
return "x not in dict solution -- No Solution Found!!!"
def _ecos_solve(self, objective, constr_map, dims,
var_offsets, x_length,
verbose, opts):
"""Calls the ECOS solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
opts: dict
List of user-specific options for ECOS
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
prob_data = self._ecos_problem_data(objective, constr_map, dims,
var_offsets, x_length)
obj_offset = prob_data[1]
opts = dict({"VERBOSE": verbose}.items() + opts.items())
results = ecos.solve(*prob_data[0], **opts)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
if status == s.OPTIMAL:
primal_val = results['info']['pcost']
value = self.objective._primal_to_result(
primal_val - obj_offset)
return (status, value,
results['x'], results['y'], results['z'])
else:
return (status, None, None, None, None)
def solve(self, P, q, G, h):
import ecos
n_pairs = P.shape[0]
L, max_eigval = self._decompose(P)
# minimize wrt t,x
c = numpy.empty(n_pairs + 1)
c[1:] = q
c[0] = 0.5 * max_eigval
zerorow = numpy.zeros((1, L.shape[1]))
G_quad = numpy.block([
[-1, zerorow],
[1, zerorow],
[numpy.zeros((L.shape[0], 1)), -2 * L],
])
G_lin = sparse.hstack((sparse.csc_matrix((G.shape[0], 1)), G))
G_all = sparse.vstack((G_lin, sparse.csc_matrix(G_quad)), format="csc")
n_constraints = G.shape[0]
h_all = numpy.empty(G_all.shape[0])
h_all[:n_constraints] = h
h_all[n_constraints:(n_constraints + 2)] = 1
h_all[(n_constraints + 2):] = 0
dims = {
"l": G.shape[0], # scalar, dimension of positive orthant
"q":
[G_quad.shape[0]] # vector with dimensions of second order cones
}
results = ecos.solve(c,
G_all,
h_all,
dims,
verbose=self.verbose,
max_iters=self.max_iter or 1000)
self._check_success(results)
# drop solution for t
x = results["x"][1:]
return x[numpy.newaxis]
def solve(self):
# (c) Abdullah Makkeh, Dirk Oliver Theis
# Permission to use and modify under Apache License version 2.0
self.marg_yz = None # for cond[]mutinf computation below
if self.verbose is not None:
self.ecos_kwargs["verbose"] = self.verbose
solution = ecos.solve(self.c, self.G, self.h,
self.dims, self.A, self.b, **self.ecos_kwargs)
if 'x' in solution.keys():
self.sol_rpq = solution['x']
self.sol_slack = solution['s']
self.sol_lambda = solution['y']
self.sol_mu = solution['z']
self.sol_info = solution['info']
return "success"
else: # "x" not in dict solution
return "x not in dict solution -- No Solution Found!!!"
def prox(self, v):
'''computes prox_{f/rho}(v)'''
# set the RHS of the solver
if self.n == 0:
return np.empty(0)
self.socp_vars['h'][-self.n:] = -v + self.c_offset
if self.solver == "ecos":
sol = ecos.solve(verbose=False, **self.socp_vars)
else:
raise Exception('Unknown solver')
x = np.array(sol['x'])
x = np.reshape(x, (x.shape[0], ))
#self.z = np.array(sol['z'])[:self.m]
# self.objval = sol['info']['pcost']
# self.s = np.array(sol['s'])[:self.m]
return x[:self.n]
def prox(self, v):
'''computes prox_{f/rho}(v)'''
# set the RHS of the solver
if self.n == 0:
return np.empty(0)
self.socp_vars['h'][-self.n:] = -v + self.c_offset
if self.solver == "ecos":
sol = ecos.solve(verbose=False, **self.socp_vars)
else:
raise Exception('Unknown solver')
x = np.array(sol['x'])
x = np.reshape(x, (x.shape[0],))
#self.z = np.array(sol['z'])[:self.m]
# self.objval = sol['info']['pcost']
# self.s = np.array(sol['s'])[:self.m]
return x[:self.n]
def solve(canon, verbose=False, fail_return=True):
if importlib.util.find_spec("ecos"):
import ecos
import scipy # assumed that if you have ecos, you have scipy
else:
print("WARNING: Module 'ecos' not found - can not solve")
return None
G = scipy.sparse.csc_matrix(*canon.G.to_scipy())
c = np.array(canon.c)
h = np.array(canon.h)
if canon.A is not None:
A = scipy.sparse.csc_matrix(*canon.A.to_scipy())
b = np.array(canon.b)
else:
A = None
b = None
return ecos.solve(c, G, h, canon.dims, A, b, verbose=verbose)
def test_advanced(self):
"""Test code from the advanced section of the tutorial.
"""
x = Variable()
prob = Problem(Minimize(square(x)), [x == 2])
# Get ECOS arguments.
c, G, h, dims, A, b = prob.get_problem_data(ECOS)
# Get CVXOPT arguments.
c, G, h, dims, A, b = prob.get_problem_data(CVXOPT)
# Get SCS arguments.
data, dims = prob.get_problem_data(SCS)
import ecos
# Get ECOS arguments.
c, G, h, dims, A, b = prob.get_problem_data(ECOS)
# Call ECOS solver.
solver_output = ecos.solve(c, G, h, dims, A, b)
# Unpack raw solver output.
prob.unpack_results(ECOS, solver_output)
def solve(self, objective, constraints, cached_data,
warm_start, verbose, solver_opts):
"""Returns the result of the call to the solver.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The list of canonicalized cosntraints.
cached_data : dict
A map of solver name to cached problem data.
warm_start : bool
Not used.
verbose : bool
Should the solver print output?
solver_opts : dict
Additional arguments for the solver.
Returns
-------
tuple
(status, optimal value, primal, equality dual, inequality dual)
"""
import ecos
data = self.get_problem_data(objective, constraints, cached_data)
# Default verbose to false for BB wrapper.
if 'mi_verbose' in solver_opts:
mi_verbose = solver_opts['mi_verbose']
del solver_opts['mi_verbose']
else:
mi_verbose = verbose
results_dict = ecos.solve(data[s.C], data[s.G], data[s.H],
data[s.DIMS], data[s.A], data[s.B],
verbose=verbose,
mi_verbose=mi_verbose,
bool_vars_idx=data[s.BOOL_IDX],
int_vars_idx=data[s.INT_IDX],
**solver_opts)
return self.format_results(results_dict, data, cached_data)
def _ecos_solve(self, objective, constr_map, dims, var_offsets, x_length,
verbose, opts):
"""Calls the ECOS solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
opts: dict
List of user-specific options for ECOS
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
prob_data = self._ecos_problem_data(objective, constr_map, dims,
var_offsets, x_length)
obj_offset = prob_data[1]
results = ecos.solve(*prob_data[0], verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
if status == s.OPTIMAL:
primal_val = results['info']['pcost']
value = self.objective._primal_to_result(primal_val - obj_offset)
return (status, value, results['x'], results['y'], results['z'])
else:
return (status, None, None, None, None)
def _ecos_solve(self, objective, constr_map, dims, var_offsets, x_length, verbose, opts):
"""Calls the ECOS solver and returns the result.
Parameters
----------
objective: Expression
The canonicalized objective.
constr_map: dict
A dict of the canonicalized constraints.
dims: dict
A dict with information about the types of constraints.
var_offsets: dict
A dict mapping variable id to offset in the stacked variable x.
x_length: int
The height of x.
verbose: bool
Should the solver show output?
opts: dict
List of user-specific options for ECOS
Returns
-------
tuple
(status, optimal objective, optimal x,
optimal equality constraint dual,
optimal inequality constraint dual)
"""
prob_data = self._ecos_problem_data(objective, constr_map, dims, var_offsets, x_length)
obj_offset = prob_data[1]
results = ecos.solve(*prob_data[0], verbose=verbose, **opts)
status = s.SOLVER_STATUS[s.ECOS][results["info"]["exitFlag"]]
if status in s.SOLUTION_PRESENT:
primal_val = results["info"]["pcost"]
value = self.objective._primal_to_result(primal_val - obj_offset)
return (status, value, results["x"], results["y"], results["z"])
else:
return (status, None, None, None, None)
def test_1():
prob_data = (
np.array([-22. , -14.5 , 13. , 0. , 13.94907477]),
scipy.sparse.csc_matrix([
[-1. , 0. , 0. , 0. , 0. ],
[ 0. , -1. , 0. , 0. , 0. ],
[ 0. , 0. , -1. , 0. , 0. ],
[ 1. , 0. , 0. , 0. , 0. ],
[ 0. , 1. , 0. , 0. , 0. ],
[ 0. , 0. , 1. , 0. , 0. ],
[ 0. , 0. , 0. , -1. , 0. ],
[-0.06300143, 0.05999372, -0.04139022, 0. , 0. ],
[ 0.32966768, -0.07973959, -0.61737787, 0. , 0. ],
[ 0.59441633, 0.77421041, 0.21741083, 0. , 0. ],
[ 0. , 0. , 0. , 0. , -1. ],
[ 0. , 0. , 0. , 0. , 1. ],
[ 0. , 0. , 0. , -2. , 0. ]]),
np.array([ 1., 1., 1., 1., 1., 1., -0., -0., -0., -0., 1., 1., -0.]),
{'bool_ids': [], 'f': 0, 'l': 6, 'q': [4, 3], 's': [], 'int_ids': [], 'ep': 0},
scipy.sparse.csc_matrix(np.zeros((0, 5), dtype=np.float64)),
np.array([], dtype=np.float64)
)
result = ecos.solve(*prob_data, verbose=False)
assert result['info']['infostring'] == 'Optimal solution found'
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective,constr_map,dims = self.canonicalize()
var_offsets,x_length = self.variables(objective,
constr_map[s.EQ] + constr_map[s.INEQ])
c,obj_offset = self.constraints_matrix([objective], var_offsets, x_length,
self.dense_interface, self.dense_interface)
A,b = self.constraints_matrix(constr_map[s.EQ], var_offsets, x_length,
self.interface, self.dense_interface)
G,h = self.constraints_matrix(constr_map[s.INEQ], var_offsets, x_length,
self.interface, self.dense_interface)
# ECHU: get the nonlinear constraints
F = self.nonlinear_constraint_function(constr_map[s.NONLIN], var_offsets,
x_length)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T,F,G,h,A=A,b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
# Target cvxopt solver if SDP or invalid for ECOS.
elif solver == s.CVXOPT or len(dims['s']) > 0 or min(G.size) == 0:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T,G,h,A=A,b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# ECHU: ecos interface has changed and no longer relies on CVXOPT
# as a result, we have to convert cvxopt data structures into
# numpy arrays
#
# ideally, CVXPY would no longer user CVXOPT, except when calling
# conelp
#
cnp, hnp, bnp = map(lambda x: np.fromiter(iter(x),dtype=np.double,count=len(x)), (c, h, b))
Gp,Gi,Gx = G.CCS
m,n1 = G.size
Ap,Ai,Ax = A.CCS
p,n2 = A.size
Gp, Gi, Ap, Ai = map(lambda x: np.fromiter(iter(x),dtype=np.int32,count=len(x)), (Gp,Gi,Ap,Ai))
Gx, Ax = map(lambda x: np.fromiter(iter(x),dtype=np.double,count=len(x)), (Gx, Ax))
Gsp = sp.csc_matrix((Gx,Gi,Gp),shape=(m,n1))
if p == 0:
Asp = None
bnp = None
else:
Asp = sp.csc_matrix((Ax,Ai,Ap),shape=(p,n2))
# ECHU: end conversion
results = ecos.solve(cnp,Gsp,hnp,dims,Asp,bnp,verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.SOLVED:
self.save_values(results['x'], sorted(var_offsets.keys()))
self.save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self.save_values(results['zl'], constr_map[s.INEQ])
else:
self.save_values(results['z'], constr_map[s.INEQ])
return self.objective.value(primal_val - obj_offset[0])
else:
return status
data = np.random.randn(nnz)
Acouple = sp.coo_matrix((data, ij), (m, n))
# add the two
A = A + Acouple
# randomly generate an "x" (free)
x = np.random.randn((n))
# generate a vector which will be used to create the complementary "s" and "y"
tmp = np.random.randn((m))
y = np.maximum(tmp, 0)
s = np.maximum(-tmp, 0)
# now, s and y are complementary primal-dual pair
c = -A.T * y
b = A * x + s
dims = {'l': m, 'q': [], 's': []}
# A = A.tocoo()
# solvers.conelp(cvxopt.matrix(c), cvxopt.spmatrix(A.data, A.row, A.col), cvxopt.matrix(b), dims)
#
import ecos
ecos.solve(c, A, b, dims)
objval = c.T.dot(x)
socp_vars = {'c': c, 'G': A, 'h': b, 'A': None, 'b': None, 'dims': dims}
# print b.T.dot(y)
def properly_solves(lang):
from .. qc_lang import QCML
p = QCML(debug=True)
p.parse(mult)
p.canonicalize()
if lang == "C":
p.codegen(lang)
p.save("test_problem")
c_test_code = """
#include "test_problem.h"
#include "ecos.h"
int main(int argc, char **argv) {
double Adata[6] = {1,2,3,4,5,6};
double Bdata[6] = {1,2,3,4,5,6};
long Ai[6] = {0,0,1,1,2,2};
long Aj[6] = {0,1,0,1,0,1};
long Bj[6] = {0,0,0,1,1,1};
long Bi[6] = {0,1,2,0,1,2};
double c[3] = {1,2,3};
double d[3] = {4,5,6};
qc_matrix A;
qc_matrix B;
A.v = Adata; A.i = Ai; A.j = Aj; A.nnz = 6;
A.m = 3; A.n = 2;
B.v = Bdata; B.i = Bi; B.j = Bj; B.nnz = 6;
B.m = 3; B.n = 2;
test_problem_params p;
p.A = &A;
p.B = &B;
p.c = c;
p.d = d;
qc_socp *data = qc_test_problem2socp(&p, NULL);
// run ecos and solve it
pwork *mywork = ECOS_setup(data->n, data->m, data->p,
data->l, data->nsoc, data->q, 0,
data->Gx, data->Gp, data->Gi,
data->Ax, data->Ap, data->Ai,
data->c, data->h, data->b);
if (mywork)
{
ECOS_solve(mywork);
printf("Objective value at termination of C program is %f\\n", mywork->info->pcost);
ECOS_cleanup(mywork, 0);
}
qc_socp_free(data);
return 0;
}
"""
objval, _ = make_and_execute_ecos_solve("test_problem", c_test_code)
assert objval == solution
else:
p.codegen(lang)
socp_data = p.prob2socp({'A': np.array(A), 'B': np.array(B), 'c': np.array(c), 'd': np.array(d)})
print socp_data
import ecos
sol = ecos.solve(**socp_data)
print sol
assert abs(sol['info']['pcost'] - solution) < 1e-6
def properly_solves(lang):
from .. qc_lang import QCML
p = QCML(debug=True)
p.parse(mult)
p.canonicalize()
if lang == "C":
p.codegen(lang)
p.save("test_problem")
c_test_code = """
#include "test_problem.h"
#include "ecos.h"
int main(int argc, char **argv) {
double Adata[6] = {1,2,3,4,5,6};
double Bdata[6] = {1,2,3,4,5,6};
long Ai[6] = {0,0,1,1,2,2};
long Aj[6] = {0,1,0,1,0,1};
long Bi[6] = {0,0,0,1,1,1};
long Bj[6] = {0,1,2,0,1,2};
double c[3] = {1,2,3};
double d[3] = {4,5,6};
qc_matrix A;
qc_matrix B;
A.v = Adata; A.i = Ai; A.j = Aj; A.nnz = 6;
A.m = 3; A.n = 2;
B.v = Bdata; B.i = Bi; B.j = Bj; B.nnz = 6;
B.m = 2; B.n = 3;
test_problem_params p;
p.A = &A;
p.B = &B;
p.c = c;
p.d = d;
qc_socp *data = qc_test_problem2socp(&p, NULL);
// run ecos and solve it
pwork *mywork = ECOS_setup(data->n, data->m, data->p,
data->l, data->nsoc, data->q,
data->Gx, data->Gp, data->Gi,
data->Ax, data->Ap, data->Ai,
data->c, data->h, data->b);
if (mywork)
{
ECOS_solve(mywork);
printf("Objective value at termination of C program is %f\\n", mywork->info->pcost);
ECOS_cleanup(mywork, 0);
}
qc_socp_free(data);
return 0;
}
"""
with open("test_problem/main.c", "w") as f:
f.write(c_test_code)
os.chdir("test_problem")
print "Running make...."
subprocess.check_output(["make"])
if platform.system() == 'Linux':
cmd = ["cc", "-O3", "main.c",
"-L%s" % ECOS_PATH,
"-I%s/include" % ECOS_PATH, "-I%s/external/SuiteSparse_config" % ECOS_PATH,
"-lecos", "-lm", "-lrt", "test_problem.o", "qcml_utils.o", "-o","main"]
else:
cmd = ["cc", "-O3", "main.c",
"-L%s" % ECOS_PATH,
"-I%s/include" % ECOS_PATH, "-I%s/external/SuiteSparse_config" % ECOS_PATH,
"-lecos", "-lm", "test_problem.o", "qcml_utils.o", "-o","main"]
print ' '.join(cmd)
try:
subprocess.check_output(cmd)
except subprocess.CalledProcessError:
print ""
print "This test fails because it cannot find ECOS,"
print "please set your ECOS_PATH environment variable."
print ""
print " export ECOS_PATH=/PATH/TO/ECOS"
print ""
raise
try:
output = subprocess.check_output(["./main"])
except:
print ""
print "There is a bug in the compiled C code."
print ""
raise
objval = re.findall(r'Objective value at termination of C program is (\d+\.\d*)', output)
os.chdir("..")
shutil.rmtree("%s/test_problem" % os.getcwd())
assert len(objval) == 1
assert float(objval[0]) == solution
else:
p.codegen(lang)
socp_data = p.prob2socp({'A': np.array(A), 'B': np.array(B), 'c': np.array(c), 'd': np.array(d)})
print socp_data
import ecos
sol = ecos.solve(**socp_data)
print sol
assert abs(sol['info']['pcost'] - solution) < 1e-6
for i in range(m):
a = np.random.randn(n)
a = a / np.linalg.norm(a)
bi = 1 + np.random.rand(1)
A[i, :] = a
b[i] = bi
q = QCML()
q.parse('''
dimensions m n
variables x(n) r
parameters A(m,n) b(m)
maximize r
A*x + r <= b
''')
q.canonicalize()
q.dims = {'m': m, 'n': n}
q.codegen("python")
socp_data = q.prob2socp(locals())
# stuffed variable size
n = socp_data['G'].shape[1]
ecos_sol = ecos.solve(**socp_data)
socp_sol = ecos_sol['x']
prob_sol_x = q.socp2prob(ecos_sol['x'])['x']
prob_sol_r = q.socp2prob(ecos_sol['x'])['r']
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
"""Solves a DCP compliant optimization problem.
Saves the values of primal and dual variables in the variable
and constraint objects, respectively.
Args:
solver: The solver to use. Defaults to ECOS.
ignore_dcp: Overrides the default of raising an exception if
the problem is not DCP.
verbose: Overrides the default of hiding solver output.
Returns:
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective, constr_map, dims = self.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_offsets, x_length = self._get_var_offsets(objective, all_ineq)
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._DENSE_INTF,
self._DENSE_INTF)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.NONLIN], var_offsets, x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T, F, G, h, A=A, b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
# Target cvxopt solver if SDP or invalid for ECOS.
elif solver == s.CVXOPT or len(dims['s']) > 0 or min(G.size) == 0:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# ECHU: ecos interface has changed and no longer relies on CVXOPT
# as a result, we have to convert cvxopt data structures into
# numpy arrays
#
# ideally, CVXPY would no longer user CVXOPT, except when calling
# conelp
#
cnp, hnp, bnp = (np.fromiter(iter(x),
dtype=np.double,
count=len(x))
for x in (c, h, b))
Gp, Gi, Gx = G.CCS
m, n1 = G.size
Ap, Ai, Ax = A.CCS
p, n2 = A.size
Gp, Gi, Ap, Ai = (np.fromiter(iter(x),
dtype=np.int32,
count=len(x))
for x in (Gp, Gi, Ap, Ai))
Gx, Ax = (np.fromiter(iter(x),
dtype=np.double,
count=len(x))
for x in (Gx, Ax))
Gsp = sp.csc_matrix((Gx, Gi, Gp), shape=(m, n1))
if p == 0:
Asp = None
bnp = None
else:
Asp = sp.csc_matrix((Ax, Ai, Ap), shape=(p, n2))
# ECHU: end conversion
results = ecos.solve(cnp, Gsp, hnp, dims, Asp, bnp, verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.SOLVED:
self._save_values(results['x'], var_offsets.keys())
self._save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self._save_values(results['zl'], constr_map[s.INEQ])
else:
self._save_values(results['z'], constr_map[s.INEQ])
return self.objective._primal_to_result(primal_val - obj_offset[0])
else:
return status
def _solve(self, solver=s.ECOS, ignore_dcp=False, verbose=False):
"""Solves a DCP compliant optimization problem.
Saves the values of primal and dual variables in the variable
and constraint objects, respectively.
Parameters
----------
solver : str, optional
The solver to use. Defaults to ECOS.
ignore_dcp : bool, optional
Overrides the default of raising an exception if the problem is not
DCP.
verbose : bool, optional
Overrides the default of hiding solver output.
Returns
-------
float
The optimal value for the problem, or a string indicating
why the problem could not be solved.
"""
if not self.is_dcp():
if ignore_dcp:
print ("Problem does not follow DCP rules. "
"Solving a convex relaxation.")
else:
raise Exception("Problem does not follow DCP rules.")
objective, constr_map, dims = self.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_offsets, x_length = self._get_var_offsets(objective, all_ineq)
c, obj_offset = self._constr_matrix([objective], var_offsets, x_length,
self._DENSE_INTF,
self._DENSE_INTF)
# Convert obj_offset to a scalar.
obj_offset = self._DENSE_INTF.scalar_value(obj_offset)
A, b = self._constr_matrix(constr_map[s.EQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
G, h = self._constr_matrix(constr_map[s.INEQ], var_offsets, x_length,
self._SPARSE_INTF, self._DENSE_INTF)
# Save original cvxopt solver options.
old_options = cvxopt.solvers.options
# Silence cvxopt if verbose is False.
cvxopt.solvers.options['show_progress'] = verbose
# Always do one step of iterative refinement after solving KKT system.
cvxopt.solvers.options['refinement'] = 1
# Target cvxopt solver if SDP or invalid for ECOS.
if solver == s.CVXOPT or len(dims['s']) > 0 \
or min(G.shape) == 0 or constr_map[s.NONLIN]:
# Convert c,A,b,G,h to cvxopt matrices.
c, b, h = map(lambda vec:
self._CVXOPT_DENSE_INTF.const_to_matrix(vec,
convert_scalars=True),
[c, b, h])
A, G = map(lambda mat:
self._CVXOPT_SPARSE_INTF.const_to_matrix(mat,
convert_scalars=True),
[A, G])
# Target cvxopt clp if nonlinear constraints exist
if constr_map[s.NONLIN]:
# Get the nonlinear constraints.
F = self._merge_nonlin(constr_map[s.NONLIN], var_offsets,
x_length)
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A, F)
results = cvxopt.solvers.cpl(c.T, F, G, h, A=A, b=b,
dims=dims,kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else:
# Get custom kktsolver.
kktsolver = get_kktsolver(G, dims, A)
# Adjust tolerance to account for regularization.
cvxopt.solvers.options['feastol'] = 2*1e-6
results = cvxopt.solvers.conelp(c.T, G, h, A=A, b=b,
dims=dims, kktsolver=kktsolver)
status = s.SOLVER_STATUS[s.CVXOPT][results['status']]
primal_val = results['primal objective']
else: # If possible, target ECOS.
# Convert c,h,b to 1D arrays.
c, h, b = map(lambda mat: np.asarray(mat)[:, 0], [c.T, h, b])
results = ecos.solve(c, G, h, dims, A, b, verbose=verbose)
status = s.SOLVER_STATUS[s.ECOS][results['info']['exitFlag']]
primal_val = results['info']['pcost']
# Restore original cvxopt solver options.
cvxopt.solvers.options = old_options
if status == s.OPTIMAL:
self._save_values(results['x'], var_offsets.keys())
self._save_values(results['y'], constr_map[s.EQ])
if constr_map[s.NONLIN]:
self._save_values(results['zl'], constr_map[s.INEQ])
else:
self._save_values(results['z'], constr_map[s.INEQ])
self._value = self.objective._primal_to_result(
primal_val - obj_offset)
else:
self._handle_failure(status, var_offsets.keys(),
itertools.chain(constr_map[s.EQ], constr_map[s.INEQ]))
self._status = status
return self.value
# dims = {'l': 2}
import numpy as np
from scipy import sparse
ij = np.array([[0,1],[0,1]])
A = sparse.csc_matrix(([1.,1.], ij), (2,2))
b = np.array([1.,1.])
G = sparse.csc_matrix(([-1.,-1.], ij), (2,2))
h = np.array([0.,0.])
c = np.array([1.,1.])
dims = {'l': 2}
print c
print h
sol = ecos.solve(c,G,h,dims,A,b)
print sol
print sol['x']
# Ai = numpy.matrix([0,1])
# Ap = numpy.matrix([0,1,2])
# b = numpy.matrix([1.,1.])
# c = numpy.matrix([1.,1.])
#
# solution = p.solve(Ax, Ai, Ap, b, c)
# print solution['x']
# print solution['y']
# print solution['status']
#
# print getrefcount(solution['x'])
h = hpy()
b = np.random.randn(m)
q = QCML()
q.parse('''
dimensions m n
variable x(n)
parameters A(m,n) b(m)
minimize norm1(x)
A*x == b
''')
q.canonicalize()
q.dims = {'m': m, 'n': n}
q.codegen('python')
socp_vars = q.prob2socp(locals())
# convert to CSR for fast row slicing to distribute problem
socp_vars['A'] = socp_vars['A'].tocsr()
socp_vars['G'] = socp_vars['G'].tocsr()
# the size of the stuffed x or v
n = socp_vars['A'].shape[1]
ecos_sol = ecos.solve(**socp_vars)
# solution to transformed socp (stuffed)
socp_sol = ecos_sol['x']
# solution to original problem (unstuffed)
prob_sol = q.socp2prob(ecos_sol['x'])['x']
