def GetMinimalSpeedToReachEpsilonNeighbordhoodVector(dt, epsilon, W, dW, dF):
Ndim = W.shape[0]
Nsamples = W.shape[1]
dist_w = np.zeros((Nsamples-1))
for i in range(0,Nsamples-1):
dist_w[i] = np.linalg.norm(W[:,i]-W[:,i+1])
p = Variable(Nsamples-1)
sM = Variable(Nsamples-1)
constraints = []
objfunc = 0.0
for i in range(0,Nsamples-1):
#constraints.append( norm(p*dt*dW0[0:2] + dF +np.dot(dw,np.array((1,0))) ) < epsilon )
constraints.append( norm(p[i]*dt*dW[:,i] + dt*dt/2*dF[:,i] + np.dot(dist_w[i],np.array((1,0,0,0))) ) < epsilon )
constraints.append( sM[i] >= p[i] )
constraints.append( sM[i] >= 0.0)
constraints.append( p[i] >= 0.0 )
objfunc += norm(sM[i])
objective = Minimize(objfunc)
prob = Problem(objective, constraints)
print "solve minimal speed"
result = prob.solve(solver=SCS)
print "done.(",prob.value,"|",np.min(sM.value),")"
if prob.value < inf:
return np.array(sM.value).flatten()
else:
return np.array(sM.value).flatten()
def test_partial_optimize_numeric_fn(self):
x, y = Variable(1), Variable(1)
xval = 4
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(y), [xval + y >= 3])
p1.solve()
# Solve the two-stage problem via partial_optimize
constr = [y >= -100]
p2 = Problem(Minimize(y), [x + y >= 3] + constr)
g = cvxpy.partial_optimize(p2, [y], [x])
x.value = xval
y.value = 42
constr[0].dual_variable.value = 42
result = g.value
self.assertAlmostEqual(result, p1.value)
self.assertAlmostEqual(y.value, 42)
self.assertAlmostEqual(constr[0].dual_value, 42)
# No variables optimized over.
p2 = Problem(Minimize(y), [x + y >= 3])
g = cvxpy.partial_optimize(p2, [], [x, y])
x.value = xval
y.value = 42
p2.constraints[0].dual_variable.value = 42
result = g.value
self.assertAlmostEqual(result, y.value)
self.assertAlmostEqual(y.value, 42)
self.assertAlmostEqual(p2.constraints[0].dual_value, 42)
def test_pnorm(self):
""" Test domain for pnorm.
"""
dom = pnorm(self.a, -0.5).domain
prob = Problem(Minimize(self.a), dom)
prob.solve()
self.assertAlmostEqual(prob.value, 0)
def test_partial_problem(self):
"""Test domain for partial minimization/maximization problems.
"""
for obj in [Minimize((self.a)**-1), Maximize(log(self.a))]:
prob = Problem(obj, [self.x + self.a >= [5, 8]])
# Optimize over nothing.
expr = cvxpy.partial_optimize(prob, dont_opt_vars=[self.x, self.a])
dom = expr.domain
constr = [self.a >= -100, self.x >= 0]
prob = Problem(Minimize(sum_entries(self.x + self.a)), dom + constr)
prob.solve()
self.assertAlmostEqual(prob.value, 13)
assert self.a.value >= 0
assert np.all((self.x + self.a - [5, 8]).value >= -1e-3)
# Optimize over x.
expr = cvxpy.partial_optimize(prob, opt_vars=[self.x])
dom = expr.domain
constr = [self.a >= -100, self.x >= 0]
prob = Problem(Minimize(sum_entries(self.x + self.a)), dom + constr)
prob.solve()
self.assertAlmostEqual(prob.value, 0)
assert self.a.value >= 0
self.assertItemsAlmostEqual(self.x.value, [0, 0])
# Optimize over x and a.
expr = cvxpy.partial_optimize(prob, opt_vars=[self.x, self.a])
dom = expr.domain
constr = [self.a >= -100, self.x >= 0]
prob = Problem(Minimize(sum_entries(self.x + self.a)), dom + constr)
prob.solve()
self.assertAlmostEqual(self.a.value, -100)
self.assertItemsAlmostEqual(self.x.value, [0, 0])
def test_matrix_frac(self):
"""Test domain for matrix_frac.
"""
dom = matrix_frac(self.x, self.A + np.eye(2)).domain
prob = Problem(Minimize(sum_entries(diag(self.A))), dom)
prob.solve(solver=cvxpy.SCS)
self.assertAlmostEquals(prob.value, -2, places=3)
def ForceCanBeCounteractedByAccelerationVector(dt, Fp, u1min, u1max, u2min, u2max, plot=False) :
### question (1) : can we produce an acceleration ddW, such that it counteracts F?
## dynamics projected onto identity element, it becomes obvious that in an infinitesimal neighborhood,
## we can only counteract forces along the x and the theta axes due to non-holonomicity
dt2 = dt*dt/2
## span dt2-hyperball in Ndim
F = dt2*Fp
thetamin = dt2*u2min
thetamax = dt2*u2max
xmin = 0.0
xmax = dt2*u1max
Xlow = np.dot(np.dot(Rz(-pi/2),Rz(thetamin)),np.array((1,0,0)))
Xhigh = np.dot(np.dot(Rz(pi/2),Rz(thetamax)),np.array((1,0,0)))
Ndim = Fp.shape[0]
if Fp.ndim <= 1:
Nsamples = 1
else:
Nsamples = Fp.shape[1]
p = Variable(3,Nsamples)
constraints = []
objfunc = 0.0
for i in range(0,Nsamples):
constraints.append( norm(p[:,i]) <= xmax )
constraints.append( np.matrix(Xlow[0:3])*p[:,i] <= 0 )
constraints.append( np.matrix(Xhigh[0:3])*p[:,i] <= 0 )
if Fp.ndim <= 1:
objfunc += norm(p[:,i]-F[0:3])
else:
objfunc += norm(p[:,i]-F[0:3,i])
#objfunc.append(norm(p[:,i]-F[:,i]))
objective = Minimize(objfunc)
prob = Problem(objective, constraints)
result = prob.solve(solver=SCS, eps=1e-7)
#nearest_ddq = np.array(p.value)
nearest_ddq = np.array(p.value/dt2)
codimension = Ndim-nearest_ddq.shape[0]
#print Ndim, nearest_ddq.shape
#print codimension
zero_rows = np.zeros((codimension,Nsamples))
if nearest_ddq.shape[0] < Ndim:
nearest_ddq = np.vstack((nearest_ddq,zero_rows))
if plot:
PlotReachableSetForceDistance(dt, u1min, u1max, u2min, u2max, -F, dt2*nearest_ddq)
return nearest_ddq
def l1_solution(A, b, lam=0.5):
N = A.shape[0]
x = Variable(N)
objective = Minimize(sum_entries(square(A * x - b)) + lam * norm(x, 1))
constraints = []
prob = Problem(objective, constraints)
prob.solve()
xhat = x.value
return xhat
def test_partial_optimize_numeric_fn(self):
x,y = Variable(1), Variable(1)
xval = 4
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(y), [xval+y>=3])
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=3])
g = partial_optimize(p2, [y], [x])
result = g(x).numeric([xval])
self.assertAlmostEqual(result, p1.value)
def test_indicator(self):
"""Test indicator transform.
"""
cons = [self.a >= 0, self.x == 2]
obj = cvxpy.Minimize(self.a - sum_entries(self.x))
expr = cvxpy.indicator(cons)
assert expr.is_convex()
assert expr.is_positive()
prob = Problem(Minimize(expr) + obj)
result = prob.solve()
self.assertAlmostEqual(-4, result)
self.assertAlmostEqual(0, self.a.value)
self.assertItemsAlmostEqual([2, 2], self.x.value)
self.assertAlmostEqual(0, expr.value)
self.a.value = -1
self.assertAlmostEqual(np.infty, expr.value)
def test_yield_constr_cost_min(self):
# Create problem data.
n = 10
c = numpy.random.randn(n)
P, q, r = numpy.eye(n), numpy.random.randn(n), numpy.random.randn()
mu, Sigma = numpy.zeros(n), 0.1*numpy.eye(n)
omega = NormalRandomVariable(mu, Sigma)
m, eta = 100, 0.95
# Create and solve optimization problem.
x = Variable(n)
yield_constr = prob(quad_form(x+omega,P)
+ (x+omega).T*q + r >= 0, m) <= 1-eta
p = Problem(Minimize(x.T*c), [yield_constr])
p.solve()
self.assert_feas(p)
def test_partial_problem(self):
"""Test grad for partial minimization/maximization problems.
"""
for obj in [Minimize((self.a)**-1), Maximize(entr(self.a))]:
prob = Problem(obj, [self.x + self.a >= [5, 8]])
# Optimize over nothing.
expr = cvxpy.partial_optimize(prob, dont_opt_vars=[self.x, self.a])
self.a.value = None
self.x.value = None
grad = expr.grad
self.assertAlmostEqual(grad[self.a], None)
self.assertAlmostEqual(grad[self.x], None)
# Outside domain.
self.a.value = 1.0
self.x.value = [5, 5]
grad = expr.grad
self.assertAlmostEqual(grad[self.a], None)
self.assertAlmostEqual(grad[self.x], None)
self.a.value = 1
self.x.value = [10, 10]
grad = expr.grad
self.assertAlmostEqual(grad[self.a], obj.args[0].grad[self.a])
self.assertItemsAlmostEqual(grad[self.x].todense(), [0, 0, 0, 0])
# Optimize over x.
expr = cvxpy.partial_optimize(prob, opt_vars=[self.x])
self.a.value = 1
grad = expr.grad
self.assertAlmostEqual(grad[self.a], obj.args[0].grad[self.a] + 0)
# Optimize over a.
fix_prob = Problem(obj, [self.x + self.a >= [5, 8], self.x == 0])
fix_prob.solve()
dual_val = fix_prob.constraints[0].dual_variable.value
expr = cvxpy.partial_optimize(prob, opt_vars=[self.a])
self.x.value = [0, 0]
grad = expr.grad
self.assertItemsAlmostEqual(grad[self.x].todense(), dual_val)
# Optimize over x and a.
expr = cvxpy.partial_optimize(prob, opt_vars=[self.x, self.a])
grad = expr.grad
self.assertAlmostEqual(grad, {})
def mcFrobSolveLeftFactor_cvx(V, M_Omega, mask, **kwargs):
"""
mcFrobSolveLeftFactor_cvx(V, M_Omega, mask, **kwargs)
A solver for the left factor, U, in the problem
min FrobNorm( P_Omega(U * V.T - M) )
where U is an m-by-r matrix, V an n-by-r matrix.
M_Omega is the set of observed entries in matrix form, while
mask is a Boolean array with 1/True-valued entries corresponding
to those indices that were observed.
This function is computed using the CVXPY package (and
thus is likely to be slower than a straight iterative
least squares solver).
"""
# Options
returnObjectiveValue = kwargs.get('returnObjectiveValue', False)
solver = kwargs.get('solver', SCS)
verbose = kwargs.get('verbose', False)
if isinstance(verbose, int):
if verbose > 1:
verbose = True
else:
verbose = False
# Parameters
m = mask.shape[0]
if V.shape[0] < V.shape[1]:
# make sure V_T is "short and fat"
V = V.T
r = V.shape[1]
Omega_i, Omega_j = matIndicesFromMask(mask)
# Problem
U = Variable(m, r)
obj = Minimize(cvxnorm(cvxvec((U @ V.T)[Omega_i, Omega_j]) - M_Omega))
prob = Problem(obj)
prob.solve(solver=solver, verbose=verbose)
if returnObjectiveValue:
return (U.value, prob.value)
else:
return U.value
def test_simple_problem(self):
# Create problem data.
n = numpy.random.randint(1,10)
eta = 0.95
num_samples = 10
c = numpy.random.rand(n,1)
mu = numpy.zeros(n)
Sigma = numpy.eye(n)
a = NormalRandomVariable(mu, Sigma)
b = numpy.random.randn()
# Create and solve optimization problem.
x = Variable(n)
p = Problem(Maximize(x.T*c), [prob(max_entries(x.T*a-b) >= 0, num_samples) <= 1-eta])
p.solve()
self.assert_feas(p)
def sparse_system(self, solver):
m = 100
n = 80
numpy.random.seed(1)
density = 0.4
A = sp.rand(m, n, density)
b = numpy.random.randn(m)
p = Problem(Minimize(sum_squares(A*self.xs - b)), [self.xs == 0])
s = self.solve_QP(p, solver)
self.assertAlmostEqual(b.T.dot(b), p.value, places=4)
def define_schedule_problem():
"""
Define the optimization problem
:return:
"""
demand_schedule = create_demand_schedule()
variables = create_variables(plant, demand_schedule)
objective = create_objective(variables, demand_schedule)
constraints = create_constraints(variables, plant, demand_schedule)
problem = Problem(objective, constraints)
return problem
def test_card():
"""Test card variable."""
x = Card(5, k=3, M=1)
p = Problem(Maximize(sum(x)), [x <= 1, x >= 0])
result = p.solve(**solve_args)
assert result[0] == approx(3)
for v in np.nditer(x.value):
assert v * (1 - v) == approx(0)
assert x.value.sum() == approx(3)
# Should be equivalent to x == choose.
x = Variable((5, 4))
c = Choose((5, 4), k=4)
b = Boolean((5, 4))
p = cp.Problem(Minimize(sum(1 - x) + sum(x)), [x == c, x == b])
result = p.solve(**solve_args)
assert result[0] == approx(20)
for v in np.nditer(x.value):
assert v * (1 - v) == approx(0)
def test_log_normcdf(self) -> None:
self.assertEqual(cp.log_normcdf(self.x).sign, s.NONPOS)
self.assertEqual(cp.log_normcdf(self.x).curvature, s.CONCAVE)
for x in range(-4, 5):
self.assertAlmostEqual(
np.log(scipy.stats.norm.cdf(x)),
cp.log_normcdf(x).value,
places=None,
delta=1e-2,
)
y = Variable((2, 2))
obj = Minimize(cp.sum(-cp.log_normcdf(y)))
prob = Problem(obj, [y == 2])
result = prob.solve()
self.assertAlmostEqual(-result,
4 * np.log(scipy.stats.norm.cdf(2)),
places=None,
delta=1e-2)
def test_rho_init(self):
p_list = [Problem(Minimize(norm(self.x)))]
rho_list = assign_rho(p_list)
self.assertDictEqual(rho_list[0], {self.x.id: 1.0})
rho_list = assign_rho(p_list, default=0.5)
self.assertDictEqual(rho_list[0], {self.x.id: 0.5})
rho_list = assign_rho(p_list, rho_init={self.x.id: 1.5})
self.assertDictEqual(rho_list[0], {self.x.id: 1.5})
p_list.append(
Problem(Minimize(0.5 * sum_squares(self.y)), [norm(self.x) <= 10]))
rho_list = assign_rho(p_list)
self.assertDictEqual(rho_list[0], {self.x.id: 1.0})
self.assertDictEqual(rho_list[1], {self.x.id: 1.0, self.y.id: 1.0})
rho_list = assign_rho(p_list, rho_init={self.x.id: 2.0}, default=0.5)
self.assertDictEqual(rho_list[0], {self.x.id: 2.0})
self.assertDictEqual(rho_list[1], {self.x.id: 2.0, self.y.id: 0.5})
def test_partial_optimize_min_1norm(self) -> None:
# Minimize the 1-norm in the usual way
dims = 3
x, t = Variable(dims), Variable(dims)
p1 = Problem(Minimize(cp.sum(t)), [-t <= x, x <= t])
# Minimize the 1-norm via partial_optimize
g = partial_optimize(p1, [t], [x])
p2 = Problem(Minimize(g))
p2.solve()
p1.solve()
self.assertAlmostEqual(p1.value, p2.value)
def test_partial_optimize_params(self):
"""Test partial optimize with parameters.
"""
x, y = Variable(1), Variable(1)
gamma = Parameter()
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(x+y), [x+y >= gamma, y >= 4, x >= 5])
gamma.value = 3
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y >= gamma, y >= 4])
g = cvxpy.partial_optimize(p2, [y], [x])
p3 = Problem(Minimize(x+g), [x >= 5])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
def test_simple_problem(self):
# Create problem data.
n = numpy.random.randint(1, 10)
eta = 0.95
num_samples = 10
c = numpy.random.rand(n, 1)
mu = numpy.zeros(n)
Sigma = numpy.eye(n)
a = NormalRandomVariable(mu, Sigma)
b = numpy.random.randn()
# Create and solve optimization problem.
x = Variable(n)
p = Problem(
Maximize(x.T * c),
[prob(max_entries(x.T * a - b) >= 0, num_samples) <= 1 - eta])
p.solve()
self.assert_feas(p)
def clean_angles(Om, print_out):
from cvxpy import Semidef, Variable, Mnimize, Problem
E = len(Om)
X = Semidef(E)
Noise = Variable(E, E)
constraints = [X + Noise == Om] # include weighting matrix?
[constraints.append(X[i, i] == 1.0) for i in range(E)]
obj = Minimize(trace(X) + norm(Noise))
prob = Problem(obj, constraints)
#total_cost = prob.solve(solver='SCS',verbose=True, eps=1e-10)
#total_cost = prob.solve(solver='CVXOPT',verbose=True,
# abstol=1e-10, reltol=1e-8, feastol=1e-10,
# kktsolver="robust")
total_cost = prob.solve(solver='CVXOPT',
verbose=print_out,
kktsolver="robust")
if X.value is not None:
return X.value, Noise.value
def test_partial_optimize_numeric_fn(self):
x, y = Variable(), Variable()
xval = 4
# Solve the (simple) two-stage problem by "combining" the two stages
# (i.e., by solving a single linear program)
p1 = Problem(Minimize(y), [xval + y >= 3])
p1.solve()
# Solve the two-stage problem via partial_optimize
constr = [y >= -100]
p2 = Problem(Minimize(y), [x + y >= 3] + constr)
g = partial_optimize(p2, [y], [x])
x.value = xval
y.value = 42
constr[0].dual_variables[0].value = 42
result = g.value
self.assertAlmostEqual(result, p1.value)
self.assertAlmostEqual(y.value, 42)
self.assertAlmostEqual(constr[0].dual_value, 42)
# No variables optimized over.
p2 = Problem(Minimize(y), [x + y >= 3])
g = partial_optimize(p2, [], [x, y])
x.value = xval
y.value = 42
p2.constraints[0].dual_variables[0].value = 42
result = g.value
self.assertAlmostEqual(result, y.value)
self.assertAlmostEqual(y.value, 42)
self.assertAlmostEqual(p2.constraints[0].dual_value, 42)
def mcFrobSolveRightFactor_cvx(U, M_Omega, mask, **kwargs):
"""
A solver for the right factor, V, in the problem
min FrobNorm( P_Omega(U * V.T - M) )
where U is an m-by-r matrix, V an n-by-r matrix.
M_Omega is the set of observed entries in matrix form, while
mask is a Boolean array with 1/True-valued entries corresponding
to those indices that were observed.
This function is computed using the CVXPY package (and
thus is likely to be slower than a straight iterative
least squares solver).
"""
# Options
returnObjectiveValue = kwargs.get('returnObjectiveValue', False)
solver = kwargs.get('solver', SCS)
verbose = kwargs.get('verbose', False)
if isinstance(verbose, int):
if verbose > 1:
verbose = True
else:
verbose = False
# Parameters
n = mask.shape[1]
r = U.shape[1]
Omega_i, Omega_j = matIndicesFromMask(mask)
# Problem
V_T = Variable(r, n)
obj = Minimize(cvxnorm(cvxvec((U @ V_T)[Omega_i, Omega_j]) - M_Omega))
prob = Problem(obj)
prob.solve(solver=solver, verbose=verbose)
V = V_T.value.T
if returnObjectiveValue:
return (V, prob.value)
else:
return V
def test_value_at_risk(self):
# Create problem data.
n = numpy.random.randint(1,10)
pbar = numpy.random.randn(n)
Sigma = numpy.eye(n)
p = NormalRandomVariable(pbar,Sigma)
o = numpy.ones((n,1))
beta = 0.05
num_samples = 50
# Create and solve optimization problem.
x = Variable(n)
p1 = Problem(Minimize(-x.T*pbar), [prob(-x.T*p >= 0, num_samples) <= beta, x.T*o == 1, x >= -0.1])
p1.solve()
# Create and solve analytic form of optimization problem (as a check).
p2 = Problem(Minimize(-x.T*pbar),
[x.T*pbar >= scipy.stats.norm.ppf(1-beta) * norm2(sqrtm(Sigma) * x), x.T*o == 1, x >= -0.1])
p2.solve()
tol = 0.1
if numpy.abs(p1.value - p2.value) < tol:
self.assertAlmostEqual(1,1)
else:
self.assertAlmostEqual(1,0)
def test_quad_over_lin(self):
"""Test quad_over_lin atom.
"""
P = np.array([[10, 1j], [-1j, 10]])
X = Variable((2, 2), complex=True)
b = 1
y = Variable(complex=False)
value = cvx.quad_over_lin(P, b).value
expr = cvx.quad_over_lin(X, y)
prob = Problem(cvx.Minimize(expr), [X == P, y == b])
result = prob.solve(solver=cvx.SCS,
eps=1e-6,
max_iters=7500,
verbose=True)
self.assertAlmostEqual(result, value, places=3)
expr = cvx.quad_over_lin(X - P, y)
prob = Problem(cvx.Minimize(expr), [y == b])
result = prob.solve(solver=cvx.SCS,
eps=1e-6,
max_iters=7500,
verbose=True)
self.assertAlmostEqual(result, 0, places=3)
self.assertItemsAlmostEqual(X.value, P, places=3)
def test_multistage(self):
# Create problem data.
b = 10
s = 25
r = 5
d_probs = [0.3, 0.7]
d_vals = [55, 141]
d = RandomVariableFactory().create_categorical_rv(d_vals, d_probs)
u = 150
# Create optimization variables.
x = Variable()
y1, y2 = Variable(), Variable()
y3, y4 = Variable(), Variable()
# Create third stage problem.
p3 = Problem(Minimize(-s * y3 - r * y4),
[y3 + y4 <= x, 0 <= y3, y3 <= d, y4 >= 0])
Q2 = partial_optimize(p3, [y3, y4])
# Create second stage problem.
p2 = Problem(
Minimize(-s * y1 - r * y2 + expectation(Q2, want_de=True)),
[y1 + y2 <= x, 0 <= y1, y1 <= d, y2 >= 0])
Q1 = partial_optimize(p2, [y1, y2])
# Create and solve first stage problem.
p1 = Problem(Minimize(b * x + expectation(Q1, want_de=True)),
[0 <= x, x <= u])
p1.solve()
self.assert_feas(p1)
def test_socp(self):
"""Test SOCP problems.
"""
for solver in self.solvers:
# Basic.
p = Problem(Minimize(self.b), [pnorm(self.x, p=2) <= self.b])
pmod = Problem(Minimize(self.b), [SOC(self.b, self.x)])
self.assertTrue(ConeMatrixStuffing().accepts(pmod))
p_new = ConeMatrixStuffing().apply(pmod)
if not solver.accepts(p_new[0]):
return
result = p.solve(solver.name())
sltn = solver.solve(p_new[0], False, False, {})
self.assertAlmostEqual(sltn.opt_val, result)
inv_sltn = ConeMatrixStuffing().invert(sltn, p_new[1])
self.assertAlmostEqual(inv_sltn.opt_val, result)
for var in p.variables():
self.assertItemsAlmostEqual(inv_sltn.primal_vars[var.id],
var.value)
# More complex.
p = Problem(Minimize(self.b), [
pnorm(self.x / 2 + self.y[:2], p=2) <= self.b + 5, self.x >= 1,
self.y == 5
])
pmod = Problem(Minimize(self.b), [
SOC(self.b + 5, self.x / 2 + self.y[:2]), self.x >= 1, self.y
== 5
])
self.assertTrue(ConeMatrixStuffing().accepts(pmod))
result = p.solve(solver.name())
p_new = ConeMatrixStuffing().apply(pmod)
sltn = solver.solve(p_new[0], False, False, {})
self.assertAlmostEqual(sltn.opt_val, result, places=2)
inv_sltn = ConeMatrixStuffing().invert(sltn, p_new[1])
self.assertAlmostEqual(inv_sltn.opt_val, result, places=2)
for var in p.variables():
self.assertItemsAlmostEqual(inv_sltn.primal_vars[var.id],
var.value,
places=2)
def smooth_ridge(self, solver):
numpy.random.seed(1)
n = 500
k = 50
eta = 1
A = numpy.ones((k, n))
b = numpy.ones((k, 1))
obj = sum_squares(A * self.xsr -
b) + eta * sum_squares(self.xsr[:-1] - self.xsr[1:])
p = Problem(Minimize(obj), [])
s = self.solve_QP(p, solver)
self.assertAlmostEqual(0, s.opt_val)
def test_robust_svm(self):
# Create problem data.
m = 100 # num train points
m_pos = math.floor(m / 2)
m_neg = m - m_pos
n = 2 # num dimensions
mu_pos = 2 * numpy.ones(n)
mu_neg = -2 * numpy.ones(n)
sigma = 1
X = numpy.matrix(
numpy.vstack((mu_pos + sigma * numpy.random.randn(m_pos, n),
mu_neg + sigma * numpy.random.randn(m_neg, n))))
y = numpy.hstack((numpy.ones(m_pos), -1 * numpy.ones(m_neg)))
C = 1 # regularization trade-off parameter
ns = 50
eta = 0.1
# Create and solve optimization problem.
w, b, xi = Variable(n), Variable(), NonNegative(m)
constr = []
Sigma = 0.1 * numpy.eye(n)
for i in range(m):
mu = numpy.array(X[i])[0]
x = NormalRandomVariable(mu, Sigma)
chance = prob(-y[i] * (w.T * x + b) >= (xi[i] - 1), ns)
constr += [chance <= eta]
p = Problem(Minimize(norm(w, 2) + C * sum_entries(xi)), constr)
p.solve(verbose=True)
w_new = w.value
b_new = b.value
# Create and solve the canonical SVM problem.
constr = []
for i in range(m):
constr += [y[i] * (X[i] * w + b) >= (1 - xi[i])]
p2 = Problem(Minimize(norm(w, 2) + C * sum_entries(xi)), constr)
p2.solve()
w_old = w.value
b_old = b.value
self.assert_feas(p)
def test_power(self) -> None:
"""Test domain for power.
"""
opts = {'eps': 1e-8, 'max_iters': 100000}
dom = cp.sqrt(self.a).domain
Problem(Minimize(self.a), dom).solve(solver=cp.SCS, **opts)
self.assertAlmostEqual(self.a.value, 0)
dom = cp.square(self.a).domain
Problem(Minimize(self.a), dom + [self.a >= -100]).solve(solver=cp.SCS,
**opts)
self.assertAlmostEqual(self.a.value, -100)
dom = ((self.a)**-1).domain
Problem(Minimize(self.a), dom + [self.a >= -100]).solve(solver=cp.SCS,
**opts)
self.assertAlmostEqual(self.a.value, 0)
dom = ((self.a)**3).domain
Problem(Minimize(self.a), dom + [self.a >= -100]).solve(solver=cp.SCS,
**opts)
self.assertAlmostEqual(self.a.value, 0)
def calc_Input_Koopman(Kol,Yf,Yp,Up,flag=1,lambda_val=0.0):
solver_instance = cvxpy.SCS;
Ki = None;
if flag==1: # moore penrose inverse, plain ol' least squares input-Koopman
#Yp_inv = np.dot(np.transpose(Yp_final), np.linalg.inv( np.dot(Yp_final,np.transpose(Yp_final)) ) );
Yfprime = Yf-np.dot(Kol,Yp)
Up_inv = np.linalg.pinv(Up);
Ki = np.dot(Yfprime,Up_inv);
if flag ==2: # cvx optimization approach - L2 + L1 lasso
norm1_term = 0.0;
all_col_handles = [None]*Up.shape[0]
for i in range(0,Up.shape[0]):
#print(Yf.shape[0])
all_col_handles[i] = Variable(shape=(Yf.shape[0],1)) ;#Variable(shape=(Yf.shape[0],1) );
# if norm1_term < cvxpy.norm(all_col_handles[i],p=1):
# norm1_term = cvxpy.norm(all_col_handles[i],p=1);
#norm1_term = cvxpy.max(cvxpy.hstack( [norm1_term,cvxpy.norm(all_col_handles[i],p=1) ]) );
operator = cvxpy.hstack(all_col_handles);
norm1_term =cvxpy.norm( operator,p=1);
#operator = all_col_handles[0];
#for i in range(1,Yf.shape[0]):
# operator = cvxpy.hstack([operator,all_col_handles[i]]);
#operator.
#print("[INFO]: CVXPY Koopman operator variable: " +repr(operator.shape));
#print(repr(operator));
#print("[INFO]: Yf.shape in calc_Koopman: " + repr(Yf.shape));
#print("[INFO]: Yp.shape in calc_Koopman: " + repr(Yp.shape));
Yfprime = Yf-np.dot(Kol,Yp)
norm2_fit_term = cvxpy.norm(cvxpy.norm(Yfprime-operator*Up,p=2,axis=0),p=2);
objective = Minimize(norm2_fit_term + lambda_val*norm1_term)
constraints = [];
prob = Problem(objective,constraints);
result = prob.solve(verbose=True,solver=solver_instance,max_iters=np.int(1e7))#,reltol=1e-10,abstol=1e-10);
print("[INFO]: Finished executing cvx solver, printing CVXPY problem status")
print(prob.status);
Ki = operator.value;
return Ki;
def smooth_ridge(self, solver):
np.random.seed(1)
n = 200
k = 50
eta = 1
A = np.ones((k, n))
b = np.ones((k))
obj = sum_squares(A*self.xsr - b) + \
eta*sum_squares(self.xsr[:-1]-self.xsr[1:])
p = Problem(Minimize(obj), [])
self.solve_QP(p, solver)
self.assertAlmostEqual(0, p.value, places=4)
def test_nonneg_constraints_backend(self):
x = Variable(shape=(2,), name='x')
objective = Maximize(-4 * x[0] - 5 * x[1])
constr_expr = hstack([3 - (2 * x[0] + x[1]),
3 - (x[0] + 2 * x[1]),
x[0],
x[1]])
constraints = [NonNeg(constr_expr)]
prob = Problem(objective, constraints)
self.assertFalse(ConeMatrixStuffing().accepts(prob))
self.assertTrue(FlipObjective().accepts(prob))
p_min = FlipObjective().apply(prob)
self.assertTrue(ConeMatrixStuffing().accepts(p_min[0]))
def calculate_charging_schedule(normalized_demand, maximum_charging_rate, power_req, plug_in_time,
plug_out_time, previous_schedule):
# Define variables for new charging rates during each time slot
# new_schedule = V(T)
length = int(np.ceil(power_req/maximum_charging_rate))
A = plug_out_time - length - plug_in_time + 1
rate = np.zeros(shape=(A, T))
for i in range(A):
for t in range(A, A+length):
rate[i][t] = maximum_charging_rate
rate_new = np.transpose(rate)
new_schedule = V(T)
# probability = np.empty(A)
# probability.fill(1/A)
# prob = np.transpose(probability)
# prod = rate_new.dot(prob)
# print(normalized_demand)
# print(prod)
# Define Objective functio
objective = MIN( SS((normalized_demand - new_schedule) + (new_schedule - previous_schedule) ) )
# Define constraints list
constraints = []
# Solve the problem
prob = PB(objective, constraints)
prob.solve()
# Solution
result = (new_schedule.value).tolist()
return result
def test_news_vendor(self):
# Create problem data.
c, s, r, b = 10, 25, 5, 150
d_probs = [0.5, 0.5]
d_vals = [55, 139]
d = CategoricalRandomVariable(d_vals, d_probs)
# Create optimization variables.
x = NonNegative()
y, z = NonNegative(), NonNegative()
# Create second stage problem.
obj = -s * y - r * z
constrs = [y + z <= x,
z <= d] # Putting these constrs in breaks the test:
# y<=d, z<=d
p2 = Problem(Minimize(obj), constrs)
Q = partial_optimize(p2, [y, z], [x])
# Create and solve first stage problem
p1 = Problem(Minimize(c * x + expectation(Q, want_de=True)), [x <= b])
p1.solve()
# Solve problem the old way (i.e., deterministic equivalent) as a check.
x = Variable()
y1 = Variable()
y2 = Variable()
z1 = Variable()
z2 = Variable()
p3 = Problem(
Minimize(c * x + 0.5 * (-r * y1 - s * z1) + 0.5 *
(-r * y2 - s * z2)), [
0 <= x, x <= b, 0 <= y1, 0 <= z1, 0 <= y2, 0 <= z2,
y1 + z1 <= x, y2 + z2 <= x
]) # Putting these constrs in breaks the test:
# y1 <= 55, y2 <= 139, z1 <= 55, z2 <= 139
p3.solve()
self.assertAlmostEqual(p1.value, p3.value, 4)
def markowitz_optimizer_2(mu, sigma, m, alpha, lam=1):
"""
Implementation of a long only mean-variance optimizer based
on Markowitz's Portfolio
Construction method:
https://en.wikipedia.org/wiki/Modern_portfolio_theory
This function relies on cvxpy.
Argument Definitions:
:param mu: 1xn numpy array of expected asset returns
:param sigma: nxn covariance matrix between asset return time series
:param m: first m
:param alpha: percentage of portfolio weight to place in the first m assets
note that 1-alpha percent of the portfolio weight will be placed
in (m+1)st through nth asset
:param lam: optional risk tolerance parameter
Argument Constraints:
sigma -- positive semidefinite symmetric matrix
m -- m < n
alpha -- a float between 0 and 1
lam -- any non-negative float
"""
# define variable of weights to be solved for by optimizer
x = Variable(len(sigma))
# define Markowitz mean/variance objective function
objective = Minimize(quad_form(x, sigma) - lam * mu * x)
constraints = [
sum_entries(x[0:m]) == alpha,
sum_entries(x[m::]) == (1 - alpha), x >= 0
] # define long only constraint
p = Problem(objective, constraints) # create optimization problem
L = p.solve() # solve problem
return np.array(x.value).flatten() # return optimal weights
def test_geo_mean(self):
"""Test domain for geo_mean
"""
dom = geo_mean(self.x).domain
prob = Problem(Minimize(sum_entries(self.x)), dom)
prob.solve()
self.assertAlmostEqual(prob.value, 0)
# No special case for only one weight.
dom = geo_mean(self.x, [0, 2]).domain
dom.append(self.x >= -1)
prob = Problem(Minimize(sum_entries(self.x)), dom)
prob.solve()
self.assertItemsAlmostEqual(self.x.value, [-1, 0])
dom = geo_mean(self.z, [0, 1, 1]).domain
dom.append(self.z >= -1)
prob = Problem(Minimize(sum_entries(self.z)), dom)
prob.solve()
self.assertItemsAlmostEqual(self.z.value, [-1, 0, 0])
def compute_node_be_curvature(g, n=None, solver=None, solver_options={}, verbose=False):
if n is not None:
if g.degree[n] > 0:
dgamma2 = construct_dgamma2(g, n, verbose)
gammax = construct_gammax(g, n)
dim_b1 = gammax.shape[0]
dim_b2 = dgamma2.shape[0]
dim_s2 = dgamma2.shape[0] - gammax.shape[0]
if verbose:
print('dim dgamma2 {0}; dim gammax {1}'.format(dim_b2, dim_b1))
gammax_ext = np.block([
[gammax, np.zeros((dim_b1, dim_s2))],
[np.zeros((dim_b1, dim_s2)).T, np.zeros((dim_s2, dim_s2))],
])
a = Parameter((dim_b2, dim_b2), value=dgamma2)
b = Parameter((dim_b2, dim_b2), value=gammax_ext)
kappa = Variable()
constraints = [(a - kappa * b >> 0)]
objective = Maximize(kappa)
prob = Problem(objective, constraints)
if verbose:
print(prob.status)
prob.solve(solver=solver, **solver_options)
if verbose:
print(prob.status)
return prob.value
else:
return 0
else:
r = {n: compute_node_be_curvature(g, n, solver=solver, solver_options=solver_options, verbose=verbose) for n in g.nodes()}
return r
def test_gurobi_time_limit_no_solution(self) -> None:
"""Make sure that if Gurobi terminates due to a time limit before finding a solution:
1) no error is raised,
2) solver stats are returned.
The test is skipped if something changes on Gurobi's side so that:
- a solution is found despite a time limit of zero,
- a different termination criteria is hit first.
"""
from cvxpy import GUROBI
if GUROBI in INSTALLED_SOLVERS:
import gurobipy
objective = Minimize(self.x[0])
constraints = [self.x[0] >= 1]
prob = Problem(objective, constraints)
try:
prob.solve(solver=GUROBI, TimeLimit=0.0)
except Exception as e:
self.fail(
"An exception %s is raised instead of returning a result."
% e)
extra_stats = None
solver_stats = getattr(prob, "solver_stats", None)
if solver_stats:
extra_stats = getattr(solver_stats, "extra_stats", None)
self.assertTrue(extra_stats,
"Solver stats have not been returned.")
nb_solutions = getattr(extra_stats, "SolCount", None)
if nb_solutions:
self.skipTest(
"Gurobi has found a solution, the test is not relevant anymore."
)
solver_status = getattr(extra_stats, "Status", None)
if solver_status != gurobipy.StatusConstClass.TIME_LIMIT:
self.skipTest(
"Gurobi terminated for a different reason than reaching time limit, "
"the test is not relevant anymore.")
else:
with self.assertRaises(Exception) as cm:
prob = Problem(Minimize(norm(self.x, 1)), [self.x == 0])
prob.solve(solver=GUROBI, TimeLimit=0)
self.assertEqual(str(cm.exception),
"The solver %s is not installed." % GUROBI)
def equivalent_forms_1(self, solver):
m = 100
n = 80
r = 70
np.random.seed(1)
A = np.random.randn(m, n)
b = np.random.randn(m)
G = np.random.randn(r, n)
h = np.random.randn(r)
obj1 = .1 * sum((A * self.xef - b)**2)
cons = [G * self.xef == h]
p1 = Problem(Minimize(obj1), cons)
self.solve_QP(p1, solver)
self.assertAlmostEqual(p1.value, 68.1119420108, places=4)
def equivalent_forms_1(self, solver):
m = 100
n = 80
r = 70
numpy.random.seed(1)
A = numpy.random.randn(m, n)
b = numpy.random.randn(m, 1)
G = numpy.random.randn(r, n)
h = numpy.random.randn(r, 1)
obj1 = sum((A * self.xef - b)**2)
cons = [G * self.xef == h]
p1 = Problem(Minimize(obj1), cons)
s = self.solve_QP(p1, solver)
self.assertAlmostEqual(s.opt_val, 681.119420108)
def convert_to_cvxpy(sdp):
"""Convert an SDP relaxation to a CVXPY problem.
:param sdp: The SDP relaxation to convert.
:type sdp: :class:`ncpol2sdpa.sdp`.
:returns: :class:`cvxpy.Problem`.
"""
from cvxpy import Minimize, Problem, Variable
row_offsets = [0]
cumulative_sum = 0
for block_size in sdp.block_struct:
cumulative_sum += block_size**2
row_offsets.append(cumulative_sum)
x = Variable(sdp.n_vars)
# The moment matrices are the first blocks of identical size
constraints = []
for idx, bs in enumerate(sdp.block_struct):
nonzero_set = set()
F = [lil_matrix((bs, bs)) for _ in range(sdp.n_vars + 1)]
for ri, row in enumerate(
sdp.F.rows[row_offsets[idx]:row_offsets[idx + 1]],
row_offsets[idx]):
block_index, i, j = convert_row_to_sdpa_index(
sdp.block_struct, row_offsets, ri)
for col_index, k in enumerate(row):
value = sdp.F.data[ri][col_index]
F[k][i, j] = value
F[k][j, i] = value
nonzero_set.add(k)
if bs > 1:
sum_ = sum(F[k] * x[k - 1] for k in nonzero_set if k > 0)
if not isinstance(sum_, (int, float)):
if F[0].getnnz() > 0:
sum_ += F[0]
constraints.append(sum_ >> 0)
else:
sum_ = sum(F[k][0, 0] * x[k - 1] for k in nonzero_set if k > 0)
if not isinstance(sum_, (int, float)):
sum_ += F[0][0, 0]
constraints.append(sum_ >= 0)
obj = sum(ci * xi for ci, xi in zip(sdp.obj_facvar, x) if ci != 0)
problem = Problem(Minimize(obj), constraints)
return problem
def test_partial_optimize_min_1norm(self):
# Minimize the 1-norm in the usual way
dims = 3
x, t = Variable(dims), Variable(dims)
p1 = Problem(Minimize(sum_entries(t)), [-t<=x, x<=t])
# Minimize the 1-norm via partial_optimize
g = partial_optimize(p1, [t], [x])
p2 = Problem(Minimize(g))
p2.solve()
p1.solve()
self.assertAlmostEqual(p1.value, p2.value)
def test_partial_optimize_simple_problem(self):
x, y = Variable(1), Variable(1)
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(x+y), [x+y>=3, y>=4, x>=5])
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=3, y>=4])
g = partial_optimize(p2, [y], [x])
p3 = Problem(Minimize(x+g), [x>=5])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
def test_quad_form(self):
"""Test quad_form atom.
"""
# Create a random positive definite Hermitian matrix for all tests.
np.random.seed(42)
P = np.random.randn(3, 3) - 1j * np.random.randn(3, 3)
P = np.conj(P.T).dot(P)
# Solve a problem with real variable
b = np.arange(3)
x = Variable(3, complex=False)
value = cvx.quad_form(b, P).value
prob = Problem(cvx.Minimize(cvx.quad_form(x, P)), [x == b])
result = prob.solve()
self.assertAlmostEqual(result, value)
# Solve a problem with complex variable
b = np.arange(3) + 3j * (np.arange(3) + 10)
x = Variable(3, complex=True)
value = cvx.quad_form(b, P).value
prob = Problem(cvx.Minimize(cvx.quad_form(x, P)), [x == b])
result = prob.solve()
normalization = max(abs(result), abs(value))
self.assertAlmostEqual(result / normalization,
value / normalization,
places=5)
# Solve a problem with an imaginary variable
b = 3j * (np.arange(3) + 10)
x = Variable(3, imag=True)
value = cvx.quad_form(b, P).value
expr = cvx.quad_form(x, P)
prob = Problem(cvx.Minimize(expr), [x == b])
result = prob.solve()
normalization = max(abs(result), abs(value))
self.assertAlmostEqual(result / normalization, value / normalization)
def test_ols(self):
# Solve the following consensus problem using ADMM:
# Minimize sum(f_i(x)), where f_i(x) = square(norm(x - a_i))
# Generate a_i's.
np.random.seed(0)
a = np.random.randn(3,10)
# Construct separate problems.
x = Variable(3)
funcs = [square(norm(x - a_i)) for a_i in a.T]
p_list = [Problem(Minimize(f_i)) for f_i in funcs]
probs = Problems(p_list)
probs.pretty_vars()
# Solve via consensus.
probs.solve(method = "consensus", rho_init = 5, max_iter = 50)
print("Objective:", probs.value)
print("Solution:", x.value)
def test_partial_optimize_eval_1norm(self):
# Evaluate the 1-norm in the usual way (i.e., in epigraph form).
dims = 3
x, t = Variable(dims), Variable(dims)
xval = [-5]*dims
p1 = Problem(Minimize(sum_entries(t)), [-t<=xval, xval<=t])
p1.solve()
# Minimize the 1-norm via partial_optimize.
p2 = Problem(Minimize(sum_entries(t)), [-t<=x, x<=t])
g = partial_optimize(p2, [t], [x])
p3 = Problem(Minimize(g(xval)), [])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
def test_robust_svm(self):
# Create problem data.
m = 100 # num train points
m_pos = math.floor(m/2)
m_neg = m - m_pos
n = 2 # num dimensions
mu_pos = 2*numpy.ones(n)
mu_neg = -2*numpy.ones(n)
sigma = 1
X = numpy.matrix(numpy.vstack((mu_pos + sigma*numpy.random.randn(m_pos,n),
mu_neg + sigma*numpy.random.randn(m_neg,n))))
y = numpy.hstack((numpy.ones(m_pos), -1*numpy.ones(m_neg)))
C = 1 # regularization trade-off parameter
ns = 50
eta = 0.1
# Create and solve optimization problem.
w, b, xi = Variable(n), Variable(), NonNegative(m)
constr = []
Sigma = 0.1*numpy.eye(n)
for i in range(m):
mu = numpy.array(X[i])[0]
x = NormalRandomVariable(mu, Sigma)
chance = prob(-y[i]*(w.T*x+b) >= (xi[i]-1), ns)
constr += [chance <= eta]
p = Problem(Minimize(norm(w,2) + C*sum_entries(xi)),
constr)
p.solve(verbose=True)
w_new = w.value
b_new = b.value
# Create and solve the canonical SVM problem.
constr = []
for i in range(m):
constr += [y[i]*(X[i]*w+b) >= (1-xi[i])]
p2 = Problem(Minimize(norm(w,2) + C*sum_entries(xi)), constr)
p2.solve()
w_old = w.value
b_old = b.value
self.assert_feas(p)
def test_partial_optimize_params(self):
"""Test partial optimize with parameters.
"""
x, y = Variable(1), Variable(1)
gamma = Parameter()
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(x+y), [x+y>=gamma, y>=4, x>=5])
gamma.value = 3
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=gamma, y>=4])
g = partial_optimize(p2, [y], [x])
p3 = Problem(Minimize(x+g), [x>=5])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
def main():
argparser = argparse.ArgumentParser(description="Solves for the optimal set of queries to attempt in order to "
"maximize coverage during a symbolic execution.")
argparser.add_argument('explorationgraph', help="The serialized exploration graph on which to solve the best "
"scheduling strategy.")
argparser.add_argument('-d', '--debug', help="Enables debugging output.", action="store_true")
argparser.add_argument('-v', '--verbose', help="Enables verbose output. Debugging output includes verbose output.",
action='store_true')
args = argparser.parse_args()
debuglogging = args.debug
verboselogging = args.verbose
if debuglogging:
loglevel = logging.DEBUG
elif verboselogging:
loglevel = logging.INFO
else:
loglevel = logging.WARNING
FORMAT = '%(asctime)s - %(levelname)s : %(message)s'
logging.basicConfig(stream=sys.stderr, level=loglevel, format=FORMAT, datefmt='%m/%d/%Y %I:%M:%S %p')
graph = pickle.load(open(args.explorationgraph, 'rb'))
root = graph.root_constraint
exploration_timeout = 0.1
maximize_code = True
maximize_branch = False
assert(maximize_code != maximize_branch)
ilp_constraints = []
# Create constraint variables
path_constraints = {} # {Constraint.id : ilp_constraint_id}
for path_constraint in all_path_constraints(root):
path_constraints[path_constraint.id] = len(path_constraints)
ilp_path_constraints = Int(len(path_constraints))
for ilp_path_constraint in ilp_path_constraints:
ilp_constraints.append(ilp_path_constraint <= 1)
ilp_constraints.append(ilp_path_constraint >= 0)
# Create branch coverage variables
if maximize_branch:
branch_coverage = {} # {(filename, arc_origin, arc_dest) : ilp_branch_id}
for path_constraint in all_path_constraints(root):
for filename, arcs in path_constraint.branches_covered.items():
for arc in arcs:
arc_origin, arc_dest = arc
if (filename, arc_origin, arc_dest) not in branch_coverage:
branch_coverage[(filename, arc_origin, arc_dest)] = len(branch_coverage)
ilp_branches = Int(len(branch_coverage))
for ilp_branch in ilp_branches:
ilp_constraints.append(ilp_branch <= 1)
ilp_constraints.append(ilp_branch >= 0)
# Create code coverage variables
if maximize_code:
code_coverage = {} # {(filename, line): ilp_code_id}
for path_constraint in all_path_constraints(root):
for filename, lines in path_constraint.lines_covered.items():
for line in lines:
if (filename, line) not in code_coverage:
code_coverage[(filename, line)] = len(code_coverage)
ilp_code_lines = Int(len(code_coverage))
for ilp_code_line in ilp_code_lines:
ilp_constraints.append(ilp_code_line <= 1)
ilp_constraints.append(ilp_code_line >= 0)
# Calculate response times
response_times = {} # {Constraint.id : response_time}
for path_constraint in all_path_constraints(root):
if path_constraint.parent is not None and path_constraint.parent.inputs == path_constraint.inputs:
response_times[path_constraint.id] = 0.
else:
response_times[path_constraint.id] = path_constraint.solving_time
# Constraint 1: Total solve time
total_solve_time = 0
for path_constraint_id, ilp_path_constraint_id in path_constraints.items():
total_solve_time += ilp_path_constraints[ilp_path_constraint_id]*response_times[path_constraint_id]
ilp_constraints.append(total_solve_time <= exploration_timeout)
# Constraint 2: Seed input
ilp_constraints.append(ilp_path_constraints[0] == 1)
# Constraint 3: Branch discovery
for path_constraint in all_path_constraints(root):
parent = path_constraint.parent
if parent is not None:
# The constraint is only in the schedule if its parent is in the schedule
ilp_constraints.append(ilp_path_constraints[path_constraints[path_constraint.id]] <= ilp_path_constraints[path_constraints[parent.id]])
if extract_model(parent) == extract_model(path_constraint):
ilp_constraints.append(ilp_path_constraints[path_constraints[path_constraint.id]] == ilp_path_constraints[path_constraints[parent.id]])
# Constraint 4: Coverage
## A path constraint is "covering" a branch if the input that discovers the path constraint covers the branch.
if maximize_branch:
for branch, ilp_branch_var in branch_coverage.items():
covering_path_constraints = 0
for path_constraint in all_path_constraints(root):
filename, arc_origin, arc_dest = branch
if (arc_origin, arc_dest) in path_constraint.branches_covered.get(filename, set()):
covering_path_constraints += ilp_path_constraints[path_constraints[path_constraint.id]]
assert(type(covering_path_constraints) != int)
ilp_constraints.append(ilp_branches[ilp_branch_var] <= covering_path_constraints)
if maximize_code:
for code_line, ilp_code_line_var in code_coverage.items():
covering_path_constraints = 0
for path_constraint in all_path_constraints(root):
filename, line = code_line
if line in path_constraint.lines_covered.get(filename, set()):
covering_path_constraints += ilp_path_constraints[path_constraints[path_constraint.id]]
assert(type(covering_path_constraints) != int)
ilp_constraints.append(ilp_code_lines[ilp_code_line_var] <= covering_path_constraints)
if maximize_branch:
objective = Maximize(sum_entries(ilp_branches)) # Maximize branch coverage
if maximize_code:
objective = Maximize(sum_entries(ilp_code_lines)) # Maximize code coverage
problem = Problem(objective, ilp_constraints)
problem.solve()
# Correctness assertions
## All constraints are 0 or 1 indicator variables
for ilp_path_constraint_var in path_constraints.values():
assert(0 <= round(ilp_path_constraints[ilp_path_constraint_var].value) <= 1)
## All branch coverage variables are 0 or 1
if maximize_branch:
for ilp_branch_var in branch_coverage.values():
assert(0 <= round(ilp_branches[ilp_branch_var].value) <= 1)
## All code coverage variables are 0 or 1
if maximize_code:
for ilp_code_line_var in code_coverage.values():
assert(0 <= round(ilp_code_lines[ilp_code_line_var].value) <= 1)
## Initial values are in the schedule and they have a response time of 0
assert(round(ilp_path_constraints[path_constraints[0]].value) == 1)
assert(response_times[path_constraints[0]] == 0)
## Constraints are discovered if used
for path_constraint_id, ilp_path_constraint_var in path_constraints.items():
if round(ilp_path_constraints[ilp_path_constraint_var].value) == 1:
for path_constraint in all_path_constraints(root):
if path_constraint.id == path_constraint_id and path_constraint.parent is not None:
assert(round(ilp_path_constraints[path_constraints[path_constraint.parent.id]].value) == 1)
## If input is used in constraint, then all constraints from that input are used as well
for path_constraint_id, ilp_path_constraint_var in path_constraints.items():
if round(ilp_path_constraints[ilp_path_constraint_var].value) == 1:
path_constraint_input = None
for path_constraint in all_path_constraints(root):
if path_constraint_id == path_constraint.id:
path_constraint_input = extract_model(path_constraint)
assert(path_constraint_input is not None or path_constraint_id == 0)
for path_constraint in all_path_constraints(root):
if extract_model(path_constraint) == path_constraint_input:
assert(round(ilp_path_constraints[path_constraints[path_constraint.id]].value) == 1)
## Branch coverage comes from discovered constraints
if maximize_branch:
for branch, ilp_branch_var in branch_coverage.items():
if round(ilp_branches[ilp_branch_var].value) == 1:
filename, arc_origin, arc_dest = branch
assert(any((arc_origin, arc_dest) in path_constraint.branches_covered.get(filename, set()) for path_constraint
in all_path_constraints(root) if round(ilp_path_constraints[path_constraints[path_constraint.id]].value) == 1))
## Code coverage comes from discovered constraints
if maximize_code:
for code_line, ilp_code_line_var in code_coverage.items():
if round(ilp_code_lines[ilp_code_line_var].value) == 1:
filename, line = code_line
assert(any(line in path_constraint.lines_covered.get(filename, set()) for path_constraint
in all_path_constraints(root) if round(ilp_path_constraints[path_constraints[path_constraint.id]].value) == 1))
optimal_constraint_ids = set() # {Constraint.id}
optimal_inputs = {} # {inputs : solving_time}
optimal_branches = {} # {(source_file: str) : {(origin_line: int, dest_line: int)}}
optimal_lines = {} # {(source_file: str) : {line: int}}
for path_constraint_id, var_index in path_constraints.items():
if bool(round(ilp_path_constraints[var_index].value)):
optimal_constraint_ids.add(path_constraint_id)
for path_constraint in all_path_constraints(root):
if path_constraint.id in optimal_constraint_ids and not extract_model(path_constraint) is None:
optimal_inputs[extract_model(path_constraint)] = path_constraint.solving_time
for file, branches in path_constraint.branches_covered.items():
if file in optimal_branches:
optimal_branches[file] |= branches
else:
optimal_branches[file] = set(branches)
for file, lines in path_constraint.lines_covered.items():
if file in optimal_lines:
optimal_lines[file] |= lines
else:
optimal_lines[file] = set(lines)
print("Solver CPU: {} seconds".format(sum(optimal_inputs.values())))
print("Path coverage: {} paths".format(len(optimal_inputs)))
print("Line coverage: {} lines".format(sum(len(lines) for file, lines in optimal_lines.items())))
print("Branch coverage: {} branches".format(sum(len(branches) for file, branches in optimal_branches.items())))
def test_nonnegative_variable(self):
x = NonNegative()
p = Problem(Minimize(5+x),[x>=3])
p.solve()
self.assertAlmostEqual(p.value,8)
self.assertAlmostEqual(x.value,3)
rohs = rohs[idx[0]] A3 = vstack([A,identity(m)*sqrt(rohs)]) b3 = vstack([ones((n,1)),sqrt(rohs)*0.5*ones((m,1))]) p_ls_reg = np.linalg.lstsq(A3, b3)[0] val_ls_reg = np.max(np.abs(log(A*matrix(p_ls_reg)))) print p_ls_reg print val_ls_reg #solution 4 chebyshev approximation from cvxpy import Minimize, normInf, Variable, Problem, inv_pos x=Variable (m,1) objective = Minimize(normInf(matrix(A)*x-ones((n,1)))) constraints =[x>=0,x<=1] pro = Problem(objective, constraints) result = pro.solve() print x.value val_ls_chev = np.max(np.abs(log(A*matrix(x.value)))) print val_ls_chev #solution 5 cvxpy from cvxpy import max y=Variable (m,1) Am = matrix(A) qq = [max(Am[i,:]*y,inv_pos(Am[i,:]*y)) for i in range(n)] objective1 = Minimize(max(*qq)) constraints1 =[y>=0,y<=1] pro1 = Problem(objective1, constraints1) result1 = pro1.solve()
def test_partial_optimize_eval_1norm(self):
# Evaluate the 1-norm in the usual way (i.e., in epigraph form).
dims = 3
x, t = Variable(dims), Variable(dims)
xval = [-5]*dims
p1 = Problem(Minimize(sum_entries(t)), [-t<=xval, xval<=t])
p1.solve()
# Minimize the 1-norm via partial_optimize.
p2 = Problem(Minimize(sum_entries(t)), [-t<=x, x<=t])
g = partial_optimize(p2, [t], [x])
p3 = Problem(Minimize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
# Try leaving out args.
# Minimize the 1-norm via partial_optimize.
g = partial_optimize(p2, opt_vars=[t])
p3 = Problem(Minimize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
# Minimize the 1-norm via partial_optimize.
g = partial_optimize(p2, dont_opt_vars=[x])
p3 = Problem(Minimize(g), [x == xval])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
with self.assertRaises(Exception) as cm:
g = partial_optimize(p2)
self.assertEqual(str(cm.exception),
"partial_optimize called with neither opt_vars nor dont_opt_vars.")
with self.assertRaises(Exception) as cm:
g = partial_optimize(p2, [], [x])
self.assertEqual(str(cm.exception),
("If opt_vars and new_opt_vars are both specified, "
"they must contain all variables in the problem.")
)
from cvxpy import Minimize, Variable, Problem, max, abs, sum import numpy as np n = 3 N = 30 A = np.matrix([[-1, 0.4, 0.8], [1, 0, 0], [0, 1, 0]]) b = np.matrix([1, 0, 0.3]).T x0 = zeros((n, 1)) xdes = np.matrix([7, 2, -6]).T x = Variable(n, N + 1) u = Variable(1, N) objective = Minimize(sum(max(abs(u), 2 * abs(u) - 1))) constraints1 = [x[:, 1 : N + 1] == A * x[:, 0:N] + b * u] constraints2 = [x[:, 0] == x0] constraints3 = [x[:, N] == xdes] constraints = constraints1 + constraints2 + constraints3 prob1 = Problem(objective, constraints) prob1.solve() print u.value step(range(30), u.value.T)
def create_schedule(n_days, inventory_start,
n_totes_washed_start, pars=None,
do_plot=True, verbose=True):
"""
Demo an optimal supply chain scheduling with variable
labor costs, and the concept of totes that hold a number of
products. Totes need to be cleaned on a regular basis.
:param pars: parameters from create_default_params
:param do_plot: True if you want a plot created (default)
:return: None
"""
if pars is None:
pars = create_default_params()
days = np.arange(n_days)
print 'creating demand'
demand = create_demand(days)
labor_costs = get_labor_costs(days, pars)
# define variables which keep track of
# production, inventory and number of totes washed per day
print 'defining variables'
production = Variable(n_days)
sales = Variable(n_days)
inventory = Variable(n_days)
n_totes_washed = Variable(n_days)
print 'calculating costs and profit'
# calculate when the totes that were washed become dirty again
shift_matrix = mu.time_shift_matrix(n_days,
pars['days_until_cleaning'])
n_totes_become_dirty = (shift_matrix*n_totes_washed)[:n_days]
# calculate the number of clean totes on any day
cum_matrix = mu.cumulative_matrix(n_days)
n_washed_totes_available = n_totes_washed_start \
+ cum_matrix*(n_totes_washed - n_totes_become_dirty)
print 'calculating total cost'
# Minimize total cost which is
# sum of labor costs, storage costs and washing costs
total_cost = production.T*labor_costs + \
pars['storage_cost'] * sum(inventory) + \
pars['washing_tote_cost'] * sum(n_totes_washed)
total_profit = pars['sales_price']*sum(sales)-total_cost
print 'defining objective'
objective = Maximize(total_profit)
# Subject to these constraints
constraints = make_constraints(production, sales, inventory, pars,
n_washed_totes_available,
n_totes_washed, demand, inventory_start)
# define the problem and solve it
problem = Problem(objective, constraints)
solver = 'cvxpy'
print 'solving with: %s' % solver
start = time()
problem.solve(verbose=verbose)
finish = time()
run_time = finish - start
print 'Solve time: %s seconds' % run_time
print "Status: %s" % problem.status
if problem.status == 'infeasible':
print "Problem is infeasible, no solution found"
return
n_items_sold = sum(sales.value)
total_cost = problem.value
total_washing_cost = pars['washing_tote_cost']*sum(n_totes_washed.value)
total_labor_cost = (production.T*labor_costs).value
total_storage_cost = sum(inventory.value)*pars['storage_cost']
total_cost_per_item = problem.value/n_items_sold
print "Total cost: %s" % total_cost
print "Total labor cost: %s" % total_labor_cost
print "Total washing cost: %s" % total_washing_cost
print "Total storage cost: %s" % total_storage_cost
print "Total cost/item: %s" % total_cost_per_item
print "Total profit: %s" % total_profit.value
if do_plot:
plot_variables(days, production, inventory, sales, demand,
n_washed_totes_available)
plt.clf()
from cvxpy import Variable, Problem, Minimize, log
import cvxopt
cvxopt.solvers.options['show_progress'] = False
# create problem data
m, n = 5, 10
A = cvxopt.normal(m,n)
tmp = cvxopt.uniform(n,1)
b = A*tmp
x = Variable(n)
p = Problem(
Minimize(-sum(log(x))),
[A*x == b]
)
status = p.solve()
cvxpy_x = x.value
def acent(A, b):
m, n = A.size
def F(x=None, z=None):
if x is None: return 0, cvxopt.matrix(1.0, (n,1))
if min(x) <= 0.0: return None
f = -sum(cvxopt.log(x))
Df = -(x**-1).T
if z is None: return f, Df
H = cvxopt.spdiag(z[0] * x**-2)
return f, Df, H
sol = cvxopt.solvers.cp(F, A=A, b=b)
def WaypointsToWeights(waypts):
## fit a polynomial from a set of basis functions to estimate a N-dim curve
Ndim = waypts.shape[0]
Nsamples = waypts.shape[1]
#######################################################################
## discretization of trajectory
#######################################################################
M = 500 ## points on precomputed functions
K = 500 ## number of precomputed basis functions
plotFunctionalSpace = True
#######################################################################
if M < Nsamples:
print "ERROR: more waypoints than discretization, abord"
sys.exit(0)
constraints = []
print np.around(waypts,2)
##### FUNC SPACE CONSTRAINTS
T = np.linspace(0.0,1.0,M)
F = Fpoly(T,K)
dF = dFpoly(T,K)
#F = Fchebyshev(T,K)
#dF = dFchebyshev(T,K)
print np.around(F,decimals=2)
Weights = Variable(K,Ndim)
if plotFunctionalSpace:
plt.title('Basis Functions')
Kp = min(10,K)
print T.shape,F.shape
for i in range(0,Kp):
plt.subplot(Kp, 1, i)
plot(T,F[i,:],'-r',markersize=5)
plt.ylabel(i)
plt.show()
#print np.around(F,decimals=2)
#sys.exit(0)
dw = 1.0/float(Nsamples-1)
ctr=0
Twpt = np.zeros((Nsamples,1))
for i in range(0,Nsamples):
tidx = find_nearest_idx(T,i*dw)
Twpt[ctr]=tidx
ctr=ctr+1
Ftmp = np.reshape(F[:,tidx],(K,1))
constraints.append(norm(waypts[:,i] - Weights.T*Ftmp) <= 0.01)
#constraints.append(waypts[:,i] == Weights.T*Ftmp)
## add smoothing condition
for t in T[1:]:
tidx = find_nearest_idx(T,t)
Ftmp0 = np.reshape(F[:,tidx-1],(K,1))
Ftmp1 = np.reshape(F[:,tidx],(K,1))
constraints.append(norm(Weights.T*Ftmp0 - Weights.T*Ftmp1) <= 0.01)
if plotFunctionalSpace:
plt.title('Waypoints')
plt.subplot(3, 1, 1)
plot(Twpt,waypts[0,:].flatten(),'ok',markersize=10)
plt.ylabel('X')
plt.subplot(3, 1, 2)
plot(Twpt,waypts[1,:].flatten(),'ok',linewidth=3,markersize=10)
plt.ylabel('Y')
plt.subplot(3, 1, 3)
plot(Twpt,waypts[2,:].flatten(),'ok',linewidth=3,markersize=10)
plt.ylabel('Z')
plt.show()
objective = Minimize(norm(Weights,1))
prob = Problem(objective, constraints)
#ECOS, ECOS_BB, CVXOPT, SCS
#result = prob.solve(solver=SCS, use_indirect=True, eps=1e-2, verbose=True)
#prob.solve(verbose=True, abstol_inacc=1e-2,reltol_inacc=1e-2,max_iters= 300, reltol=1e-2)
result = prob.solve(solver=SCS, verbose=True)
if plotFunctionalSpace:
Y = np.zeros((M,Ndim))
ctr=0
for t in T:
tidx = find_nearest_idx(T,t)
Ftmp = np.reshape(F[:,tidx],(K,1))
WF = Weights.T.value*Ftmp
Y[ctr,0] = WF[0]
Y[ctr,1] = WF[1]
Y[ctr,2] = WF[2]
ctr=ctr+1
plt.title('Waypoints')
plt.subplot(3, 1, 1)
plot(Twpt,waypts[0,:].flatten(),'ok',markersize=10)
plot(Y[:,0].flatten(),'or',markersize=3)
plt.ylabel('X')
plt.subplot(3, 1, 2)
plot(Twpt,waypts[1,:].flatten(),'ok',linewidth=3,markersize=10)
plot(Y[:,1].flatten(),'or',linewidth=3,markersize=3)
plt.ylabel('Y')
plt.subplot(3, 1, 3)
plot(Twpt,waypts[2,:].flatten(),'ok',linewidth=3,markersize=10)
plot(Y[:,2].flatten(),'or',linewidth=3,markersize=3)
plt.ylabel('Z')
plt.show()
if not (prob.status == OPTIMAL):
print "ERROR: infeasible cvx program"
sys.exit(0)
return [Weights.value,T,F,dF]
#qp example from cvxopt import matrix, solvers from cvxopt.solvers import qp from cvxpy import Variable Q = matrix([[1.0,-1/2], [-1/2,2]]) f = matrix([-1.0,0]) A = matrix([[1.0,2],[1,-4],[5,76]]) b = matrix([-2.0,-3,1]) sol = qp(Q,f,A.T,b,None,None) print sol['x'] from cvxpy import Minimize, Problem,norm2 #cholesky L = matrix(np.linalg.cholesky(Q)) x = Variable(2,1) objective = Minimize(norm2(L*x)+f.T*x) constraints = [A.T*x <= b] pro1 = Problem(objective, constraints) print pro1.solve() print x.value #purtube version of QP
def cvxpy_solve_qp(P, q, G=None, h=None, A=None, b=None, initvals=None,
solver=None):
"""
Solve a Quadratic Program defined as:
minimize
(1/2) * x.T * P * x + q.T * x
subject to
G * x <= h
A * x == b
calling a given solver using the CVXPY <http://www.cvxpy.org/> modelling
language.
Parameters
----------
P : array, shape=(n, n)
Primal quadratic cost matrix.
q : array, shape=(n,)
Primal quadratic cost vector.
G : array, shape=(m, n)
Linear inequality constraint matrix.
h : array, shape=(m,)
Linear inequality constraint vector.
A : array, shape=(meq, n), optional
Linear equality constraint matrix.
b : array, shape=(meq,), optional
Linear equality constraint vector.
initvals : array, shape=(n,), optional
Warm-start guess vector (not used).
solver : string, optional
Solver name in ``cvxpy.installed_solvers()``.
Returns
-------
x : array, shape=(n,)
Solution to the QP, if found, otherwise ``None``.
"""
if initvals is not None:
print("CVXPY: note that warm-start values are ignored by wrapper")
n = q.shape[0]
x = Variable(n)
P = Constant(P) # see http://www.cvxpy.org/en/latest/faq/
objective = Minimize(0.5 * quad_form(x, P) + q * x)
constraints = []
if G is not None:
constraints.append(G * x <= h)
if A is not None:
constraints.append(A * x == b)
prob = Problem(objective, constraints)
prob.solve(solver=solver)
x_opt = array(x.value).reshape((n,))
return x_opt
