def __init__(self, obstacle, resolution=200):
self.w_t, self.w_j = (cvx.Parameter(nonneg=True) for _ in range(2))
self.w_t.value = W_T
self.w_j.value = W_J
self.resolution = resolution
self.alpha = cvx.Variable(resolution + 1)
self.beta = cvx.Variable(resolution + 1)
delta_s = (S_F - S_0) / resolution
self.delta_s = delta_s
self.J_t = 2 * sum(
delta_s * inv_pos(sqrt(self.beta)[:-1] + sqrt(self.beta)[1:]))
self.J_s = sum(
((self.alpha[1:] - self.alpha[:-1]) / delta_s)**2 * delta_s)
self.dynamic_model = [
(self.beta[1:] - self.beta[:-1]) / delta_s == 2 * self.alpha[-1]
]
t_corner = obstacle.bottom_left_corner[1] + obstacle.height
s_corner = obstacle.bottom_left_corner[0]
index_s = int(math.ceil((s_corner - S_0) / delta_s))
self.obstacle_constraint = (2 * sum(delta_s * inv_pos(
sqrt(self.beta)[:(index_s - 1)] + sqrt(self.beta)[1:index_s])) >=
t_corner)
self.friction_circle_constraints = [
self.beta <= (V_MAX**2), self.alpha <= A_MAX
]
self.initial_condition = [
self.beta[0] == (V_0**2), self.alpha[0] == A_0
]
def c():
x = cp.Variable()
y = cp.Variable()
obj = cp.Minimize(0)
constraints = [x >= 0, y >= 0, 1/x + 1/y <=1]
problem = cp.Problem(obj, constraints)
print(f"c before: {problem.is_dcp()}")
x = cp.Variable(nonneg=True)
y = cp.Variable(nonneg=True)
obj = cp.Minimize(0)
constraints = [cp.inv_pos(x) + cp.inv_pos(y) <=1, x >= 0, y >= 0]
problem = cp.Problem(obj, constraints)
print(f"c after: {problem.is_dcp()}")
problem.solve()
def updateEi2(self,sigmai,ei_):
sigmai=np.array(sigmai)
ei_=np.array(ei_)
ei=cvx.Variable(I)
si=cvx.Variable(I)
constraints=[0<=si]
slacost=cvx.sum_entries(cvx.mul_elemwise(self.lamb,cvx.inv_pos(self.mu-cvx.mul_elemwise(self.lamb,cvx.inv_pos(self.S-si)))))
watcost=np.array(self.omegawat)*si
for i in range(I):
constraints+=[ei[i]==self.gamma[i]*si[i]]
objective = cvx.Minimize(-np.transpose(sigmai)*ei+self.omegadc*(slacost+watcost)+rho/2*cvx.sum_squares(ei-np.array(ei_)))
prob = cvx.Problem(objective, constraints)
result = prob.solve(solver=slv)
#print ei.value.A1
#print result
self.e=ei.value.A1
mins=self.minServer()
maxe=np.zeros(I)
for i in range(I):
maxe[i]=(self.S[i]-mins[i])*self.gamma[i]
if self.e[i]<0:
self.e[i]==0
else:
if self.e[i]>maxe[i]:
self.e[i]=maxe[i]
print('\nWarning: reducing si lower than minimum active server!!!!')
#print("ei:",self.e)
self.setSwitchSever(self.e)
def DFFweights(A, B):
"""
This function minimizes (total variance(B/mean(A*x)) where A.shape (m x n), X.shape (n x k), and B.shape (m x k)
where m = image flattened in row-major order, n = number of EigenFlats, and k = observations.
A is the array of EigenFlats, X is the coefficients for each EigenFlat, B is the observation to correct.
"""
k = B.shape[1]
m = B.shape[0]
n = A.shape[1]
# Preallocate the empty arrays
coeff = np.arange(0, n * k, 1, dtype='f8').reshape(n, k) * 0
b = cp.Parameter(m, nonneg=True)
x = cp.Variable(n, nonneg=True)
totalVariance = cp.tv((b * cp.inv_pos(cp.sum(A * x))))
objective = cp.Minimize(totalVariance)
prob = cp.Problem(objective)
# Loop through all spectra and find optimal solutions with the warm start
for ind in range(0, k):
b.value = B[:, ind]
loss = prob.solve()
coeff[:, ind] = x.value
return coeff
def SFCLS_unmix(A, b, lam=1e-6):
A = A
m = A.shape[0]
n = A.shape[1]
x = cp.Variable(n)
c = cp.Parameter(n)
objective = cp.Minimize(
cp.sum_squares(A * x - b) + lam * cp.inv_pos(c * x))
constraints = [x >= 0, cp.sum(x) == 1]
prob = cp.Problem(objective, constraints)
# iterate over n convex programs
temp_loss = np.zeros(n)
for i in range(n):
c_new = np.zeros(n)
c_new[i] = 1
c.value = c_new
temp_loss[i] = prob.solve()
# choose index with minimum loss
i_min = temp_loss.argmin()
c_new = np.zeros(n)
c_new[i_min] = 1
c.value = c_new
loss = prob.solve()
return x.value, loss
def constr(self, x, phi, log_cash):
def to_constant(x):
"""return violation if constant, constraint if variable"""
return -x.value if x.is_constant() else x >= 0
expr1 = cvx.log(sum(a - a*b*cvx.inv_pos(x[g] + b)
for g, a, b in izip(self.goods, self.a, self.b)))
return [to_constant(expr1 - np.log(a) + cvx.log(x[g] + b) + phi[g] - log_cash)
for g, a, b in izip(self.goods, self.a, self.b)]
def convertToHyperrectangle(self, t):
"""
Find a minimum-volume hyperrectangle that outer bounds the ellipsoid
{x : x^T*P*x <= t}
Parameters
----------
t : float
Right hand side of the inequality ellipsoid definition, which
scales the ellipsoid.
Returns
-------
H : Hyperrectangle
Smallest hyperrectangle that contains the ellipsoid.
"""
S = self.S
m = S.shape[0]
# Find upper bound
u = cvx.Variable(m)
y = cvx.Variable(m)
cost = cvx.Minimize(sum(u))
constraints = [cvx.inv_pos(4*y[i])*S[i,i]+y[i]*t<=u[i] for i in range(m)]
constraints += [y >= 0]
problem = cvx.Problem(cost, constraints)
problem.solve(**global_vars.SOLVER_OPTIONS)
u = np.array(u.value.T).flatten()
# Find lower bound
l = cvx.Variable(m)
cost = cvx.Maximize(sum(l))
constraints = [-cvx.inv_pos(4*y[i])*S[i,i]-y[i]*t>=l[i] for i in range(m)]
constraints += [y >= 0]
problem = cvx.Problem(cost, constraints)
problem.solve(**global_vars.SOLVER_OPTIONS)
l = np.array(l.value.T).flatten()
# Make the hyperrectangle
H = Hyperrectangle(l,u)
return H
def optimize(path, params):
"""
main function to optimize trajectory
solves convex optimization
"""
theta = path['theta']
dtheta = path['dtheta']
S = path['S']
S_prime = path['S_prime']
S_dprime = path['S_dprime']
num_wpts = theta.size
# opt vars
A = cv.Variable((num_wpts - 1))
B = cv.Variable((num_wpts))
U = cv.Variable((2, num_wpts - 1))
cost = 0
constr = []
# no constr on A[0], U[:,0], defined on mid points
# TODO: constr could be vectorized?
constr += [B[0] == 0]
for j in range(num_wpts - 1):
cost += 2 * dtheta * cv.inv_pos(
cv.power(B[j], 0.5) + cv.power(B[j + 1], 0.5))
R, M, C, d = dynamics_cvx(S_prime[:, j], S_dprime[:, j], params)
constr += [R * U[:, j] == M * A[j] + C * ((B[j] + B[j + 1]) / 2) + d]
constr += [B[j] >= 0]
constr += [cv.norm(U[:, j], 2) <= params['Fmax']]
constr += [U[0, j] <= params['Flongmax']]
constr += [B[j + 1] - B[j] == 2 * A[j] * dtheta]
# problem_define_time = time.time()
problem = cv.Problem(cv.Minimize(cost), constr)
# problem_define_done = time.time()
solution = problem.solve(solver=cv.MOSEK, verbose=False)
# problem_solve_done = time.time()
B, A, U = B.value, A.value, U.value
B = abs(B)
vopt, topt = simulate(B, A, U, path, params)
# cvx_simulate_done_time = time.time()
# print('Problem defn time: ' + str(problem_define_done - problem_define_time) + ', problem solve time: ' + str(problem_solve_done - problem_define_done) + ', cvx sim time: ' + str(cvx_simulate_done_time - problem_solve_done))
return B, A, U, vopt, topt
def _get_f_error(self, idx):
# get relevant coefficients for desired index set
coeffs = self._coeffs[idx].cpu().numpy()
coeffs[coeffs < 0.0] = 0.0
# define variables and parameters
num_var = coeffs.shape[0]
x_arg = cp.Variable(num_var)
alpha = cp.Parameter(num_var, nonneg=True)
alpha.value = coeffs
# construct symbolic error vector for theoretical error per filter
k_constant = 3
expr = cp.vstack([
cp.multiply(cp.inv_pos(x_arg), alpha / k_constant),
cp.multiply(cp.inv_pos(cp.sqrt(x_arg)),
cp.sqrt(6 * alpha / k_constant)),
])
f_error = cp.norm(expr, axis=0) + cp.multiply(cp.inv_pos(x_arg),
alpha / k_constant)
f_error = 1 / 2 * f_error
# return argument and symbolic error function to argument
return x_arg, f_error
def gstar(self, x, dh):
# This corresponds to Step 3 of Algprithm 1 DSLEA and corresponds to the primal problem with linearized
# concave part. See detailed comments for computation in function dh.
#
# Instead of numpy, we use expressions from cvxpy, which are equivalent
var_in_inverse = cp.diag(cp.inv_pos(self.var_in))
# vec_exp = cp.exp(cp.matmul(cp.matmul(cp.transpose(self.kWeightsTop), var_in_inverse), (x-self.mean_in))
# + cp.transpose(self.kBiasTop))
# return cp.log(cp.sum(vec_exp)) - self.mean_out / self.var_out - cp.transpose(x)@dh
return cp.log_sum_exp(
cp.matmul(
cp.matmul(cp.transpose(self.kWeightsTop), var_in_inverse),
(x - self.mean_in)) + self.kBiasTop
) - self.mean_out / self.var_out - cp.transpose(x) @ dh
def optimize(path, params, plot_results, print_updates):
""" main function to solve convex optimization
"""
theta = path['theta']
dtheta = path['dtheta']
S = path['S']
S_prime = path['S_prime']
S_dprime = path['S_dprime']
num_wpts = theta.size
# opt vars
A = cv.Variable((num_wpts - 1))
B = cv.Variable((num_wpts))
U = cv.Variable((2, num_wpts - 1))
cost = 0
constr = []
# no constr on A[0], U[:,0], defined on mid points
constr += [B[0] == 0]
for j in range(num_wpts - 1):
cost += 2 * dtheta * cv.inv_pos(
cv.power(B[j], 0.5) + cv.power(B[j + 1], 0.5))
R, M, C, d = dynamics_cvx(S_prime[:, j], S_dprime[:, j], params)
constr += [R * U[:, j] == M * A[j] + C * ((B[j] + B[j + 1]) / 2) + d]
constr += [B[j] >= 0]
constr += [cv.norm(U[:, j], 2) <= params['Fmax']]
constr += [U[0, j] <= params['Flongmax']]
constr += [B[j + 1] - B[j] == 2 * A[j] * dtheta]
problem = cv.Problem(cv.Minimize(cost), constr)
solution = problem.solve(solver=cv.ECOS, verbose=False)
B, A, U = B.value, A.value, U.value
B = abs(B)
vopt, topt = simulate(B,
A,
U,
path,
params,
plot_results=plot_results,
print_updates=print_updates)
return B, A, U, vopt, topt
def txprocdurtrans_time_model(self, s_id, datasize, comp_list, num_itres):
#datasize: MB, bw: Mbps, proc: Mbps
tx_t = (8*datasize)*cp.inv_pos(BWREGCONST*self.s_bw[s_id, 0]) # sec
numitfuncs = len(comp_list)
quadoverlin_vector = expr((numitfuncs, 1))
for i, comp in enumerate(comp_list):
quadoverlin = comp*cp.quad_over_lin(self.s_n[s_id, i], self.s_proc.get((s_id, 0)) )
quadoverlin_vector.set_((i, 0), quadoverlin)
#
quadoverlin_ = (quadoverlin_vector.agg_to_row()).get((0,0))
# proc_t = num_itres* (8*datasize)*(quadoverlin_) # sec
proc_t = (8*datasize)*(quadoverlin_) # sec
stage_t = 0 #self.s_dur.get((s_id, 0))
#trans_t = cp.max(tx_t, proc_t)
trans_t = tx_t + proc_t #+ stage_t
return [tx_t, proc_t, stage_t, trans_t]
def adaptive_stim_4(model,
metrics,
ntrials_per_phase,
n_amps=38,
n_trials_max_global=25,
use_decoder=False):
probs_smoothen_recons = model.probs_smoothen_recons
ntrials_cumsum = metrics.ntrials_cumsum
probs_variance = model.probs_variance
# Solve a convex problem!
n_elecs = probs_smoothen_recons.shape[0]
var_elec_amp_cell = probs_variance # probs_smoothen_recons * (1 - probs_smoothen_recons)
if use_decoder:
# use decoder
print('Using decoder')
decoder = model.decoder
dec_energy = np.sum(decoder**2, 0)
var_elec_amp_cell = var_elec_amp_cell * dec_energy
var_elecs_amp = np.nansum(var_elec_amp_cell, 2)
var_elecs_amp = np.ndarray.flatten(var_elecs_amp)
print('scaled up the variance')
var_elecs_amp *= np.ndarray.flatten(ntrials_cumsum)
print(
'Added extra statement : var_elecs_amp = np.minimum(var_elecs_amp, 0.00000000001)'
)
var_elecs_amp = np.minimum(var_elecs_amp, 0.000000001)
T = cp.Variable(n_elecs * n_amps)
objective = cp.Minimize(
cp.sum(var_elecs_amp *
cp.inv_pos(T + np.ndarray.flatten(ntrials_cumsum))))
constraints = [cp.sum(T) <= ntrials_per_phase * n_elecs * n_amps, 0 <= T]
prob = cp.Problem(objective, constraints)
result = prob.solve()
trial_elec_amps = (T.value).astype(np.int)
trial_elec_amps = np.reshape(trial_elec_amps, [n_elecs, n_amps])
trial_elec_amps[np.isnan(trial_elec_amps)] = 0
return trial_elec_amps
def sumcvxp(graph, testset, priorities, debug=None):
"""
Generates and solves the Cohen et al. SUM objective convex program
for the provided list of tests and dictionary of edge priorities.
:param graph: topology, a NetworkX graph object
:param testset: a list of probing tests, each a list of probing paths
:param priorities: a dictionary mapping edges to their priorities.
We assume that priorities are scaled such that sum(priorities.values()) == 1.
:return: list q of length m=len(testset), where, for each timestep, q[i] is the probability that test[i] should be probed
"""
m = len(testset)
# produce a dictionary tests_for_edge that maps edges to a list of indices corresponding to tests in the testset list that contain that edge
# as a dictionary, keys are unordered and iteration through it needs to be made predictable (later in code)
# the test indices are iterated in ascending order, and so each edge's list is ordered
edges_in_tests = edgeset_per_test(testset, graph.is_directed())
tests_for_edge = dict()
for i in range(m):
for edge in edges_in_tests[i]:
tests_for_edge.setdefault(edge, list()).append(i)
Q = cp.Variable(m)
constraints = [Q >= 0, cp.sum(Q) == 1]
# below, the inline interation through keys of tests_for_edge is done through a sorted list of those keys so that the constraint is formulated in a deterministic way
objective = cp.Minimize(
cp.sum([
priorities[e] *
cp.inv_pos(cp.sum([Q[i] for i in tests_for_edge[e]]))
for e in sorted(tests_for_edge)
]))
prob = cp.Problem(objective, constraints)
prob.solve()
if debug is not None:
debug['constraints'] = constraints
debug['objective'] = objective
debug['Q'] = Q
return list(Q.value)
def e():
x = cp.Variable()
y = cp.Variable()
obj = cp.Minimize(0)
constraints = [
x * y >= 1,
x >= 0,
y >= 0
]
problem = cp.Problem(obj, constraints)
print(f"e before: {problem.is_dcp()}")
x = cp.Variable()
y = cp.Variable()
obj = cp.Minimize(0)
constraints = [
cp.inv_pos(y) - x <= 1,
x >= 0,
]
problem = cp.Problem(obj, constraints)
print(f"e after: {problem.is_dcp()}")
problem.solve()
def adaptive_stim(model,
metrics,
ntrials_per_phase,
n_amps=38,
n_trials_max_global=25):
probs_est = model.probs_est
probs_smoothen_recons = model.probs_smoothen_recons
ntrials_cumsum = metrics.ntrials_cumsum
# Solve a convex problem!
var_elec_cell = np.nansum(probs_est * (1 - probs_est), 1)
var_elecs = np.nansum(var_elec_cell, 1)
T = cp.Variable(512)
objective = cp.Minimize(
cp.sum(var_elecs * cp.inv_pos(T + np.sum(ntrials_cumsum, 1) / n_amps)))
constraints = [cp.sum(T) <= ntrials_per_phase * 512, 0 <= T]
prob = cp.Problem(objective, constraints)
result = prob.solve(verbose=False)
n_trials_per_elec = (T.value)
print('# Trials per electrode computed')
# Convert # stimulations per electrode to elec_amp
diff = np.abs(probs_est - probs_smoothen_recons)**2
diff = np.sum(diff, 2) # collapse across cells
diff = diff / np.expand_dims(np.sum(diff, 1), 1) # normalize
trial_elec_amps = np.zeros((512, n_amps))
for ielec in range(512):
if n_trials_per_elec[ielec] > 0:
trial_elec_amps[ielec, :] = np.round(
n_amps * diff[ielec, :n_amps] * n_trials_per_elec[ielec])
trial_elec_amps = np.maximum(trial_elec_amps, 0)
# replace nans with 0
trial_elec_amps[np.isnan(trial_elec_amps)] = 0
return trial_elec_amps
2.50760010e+03, 2.07638980e+03, 5.81797641e+03, 1.08570667e+04,
5.12726392e+03, 1.00000000e+00, 6.58929541e+03, 7.09769073e+03,
3.34303516e+03, 2.66082789e+03, 2.77756166e+03, 1.77592755e+03,
3.07584351e+03, 2.35098041e+03, 7.04177079e+03, 3.03844715e+03,
3.51614270e+03, 2.06672946e+03, 1.39886981e+03, 1.17892981e+03,
1.16711613e+03, 2.99732387e+03, 1.50369037e+03, 2.52066711e+03,
1.05911714e+04, 3.21540906e+03, 2.98497302e+03, 7.70131934e+03,
4.41149255e+03, 9.79452597e+03, 7.03271168e+03, 6.58929541e+03,
1.00000000e+00, 7.13570746e+03, 9.24697217e+03, 1.40667535e+03,
1.18594623e+03, 1.38497012e+03, 3.06499432e+03, 1.16380303e+04,
5.08549064e+03, 6.19199273e+03, 6.66881592e+03, 9.94092682e+02,
9.64287628e+02, 6.75036224e+02, 9.87007515e+02, 8.14448081e+02,
1.40279779e+03, 1.00999878e+03, 6.06632482e+03, 3.18211285e+03,
1.77704749e+03, 4.73147520e+03, 1.05468057e+04, 2.66577881e+03,
1.25102759e+03, 7.09769073e+03, 7.13570746e+03, 1.00000000e+00
])
Iij = Iij / 1000
print(min(Iij), max(Iij))
# Rij = np.array([1,2,3,4,5])
# Iij = np.array([0.34, 0.1, 0.955, 0.3, 0.1])
dim = 676
c = cvx.Variable(dim)
constr = []
for i in range(dim):
constr.append(c[i] >= Rij[i])
prob = cvx.Problem(cvx.Maximize(cvx.norm(cvx.multiply(Iij, cvx.inv_pos(c)))),
constr)
prob.solve(method="dccp", solver="MOSEK", verbose=True)
print(c.value)
# sliceArray = PTl[np.asmatrix([1,3,5]).T, [1,3,5]]
# pl.figure(figsize=(6, 6))
# fig = pl.figure()
# ax = fig.gca(projection='3d')
# ax.plot(xs=p.value[0,:].A1,ys=p.value[1,:].A1,zs=p.value[2,:].A1)
# legend(loc='upper center', bbox_to_anchor=(0.5, 1.05), prop={'size': 18})
# print(dir(ct))
# raise Exception('exit')
import veh_speed_sched_data as ct
lowDiag = np.tril(np.ones((ct.n, ct.n)))
u = cv.Variable(ct.n)
obj = cv.Minimize(
cv.sum_entries(
cv.mul_elemwise(ct.d,
ct.a * cv.inv_pos(u) + ct.b + ct.c * u)))
cst = [
ct.tau_min <= lowDiag * cv.mul_elemwise(ct.d, u),
lowDiag * cv.mul_elemwise(ct.d, u) <= ct.tau_max, 1 / ct.smin >= u,
u >= 1 / ct.smax
]
prb = cv.Problem(obj, cst)
prb.solve()
print(prb.status)
print('fuel', prb.value)
dAccu = lowDiag * ct.d
pl.step(np.vstack((0, dAccu)), np.vstack((0, 1 / u.value)))
de = 1 / 10
dehigh = 5 * de
m = np.real(np.max(
np.linalg.eigvals(G))) # Compute the maximum eigenvalue of the graph
bar = de / m
ba = 2 * bar
bs = 30 * ba / 100
alpha1 = 1 / (1 / (1 - dehigh) - 1 / (1 - de))
alpha2 = 1 / (1 / bs - 1 / ba)
# Geometric program
print(alpha1)
print(alpha2)
B = cp.Variable(shape=(N))
D = cp.Variable(N)
v = cp.Variable(N)
lamb = cp.Variable()
p = cp.Variable()
obj = cp.Minimize(alpha1 * cp.sum(cp.inv_pos(D)) +
alpha2 * cp.sum(cp.inv_pos(B)))
constraints = []
constraints.append((cp.diag(B) * G + cp.diag(D)) * v <= v)
constraints.append(v >= np.zeros(N))
prob = cp.Problem(obj, constraints)
print(prob.solve(gp=True))
E = np.load('./cvxpy/E.npy')
T = np.load('./cvxpy/T.npy')
A = np.load('./cvxpy/A.npy')
m, n = X_c.shape
I_n = np.ones(n)[:, np.newaxis]
I_m = np.ones(m)[:, np.newaxis]
C = np.array([25,50,25,25])[:,np.newaxis]
Y_c = np.dot(X_c, R_c)
# Matrix variable with shape X_c.shape.
X = cp.Variable(X_c.shape, boolean=True)
F1 = cp.multiply(X.T @ P, cp.inv_pos(U))
F2 = cp.multiply(X.T @ M, cp.inv_pos(E))
F3 = cp.multiply(X.T @ S, cp.inv_pos(T))
F = 1 / n * (cp.sum(F1) + cp.sum(F2) + cp.sum(F3))
V = cp.diag(Y_c @ A @ R_c.T @ X.T) @ Q
# objective = cp.Minimize((C.T @ cp.max(R_c.T @ X.T @ B, axis=1)) - 3000 * F) can successfully run
# add expression V into objective（as below） will cause "Segmentation fault (core dumped)"
objective = cp.Minimize((C.T @ cp.max(R_c.T @ X.T @ B, axis=1)) + 20 * V - 3000 * F)
constraints = [X.T @ P <= U, X.T @ M <= E, X.T @ S <= T, X @ I_n == I_m]
start = datetime.now()
prob = cp.Problem(objective, constraints)
prob.solve(solver=cp.GUROBI)
print("status:", prob.status)
import numpy as np
import cvxpy as cp
n = 3
u = 2
gamma = 2
G = (np.ones((n, n)) - np.identity(n)) / 2
d = cp.Variable(n)
k = cp.Variable(n)
A = cp.Variable((n, n))
constraints = [
d >= 0,
k >= 0,
A == cp.diag(d) + cp.diag(k) @ G,
gamma * cp.sum(cp.inv_pos(d)) + cp.sum(cp.inv_pos(k)) <= u,
]
obj = cp.Minimize(cp.norm(A))
problem = cp.Problem(obj, constraints)
problem.solve()
print('status: ', problem.status)
print('optimal value: ', problem.value)
print("D: ")
print(np.diag(d.value))
print("K: ")
print(np.diag(k.value))
'cars': 20, # number of cars
'timeRange': [18, 32], # time range to run simulation
'actRate': 1. / 4, # step time in hours
'chargeRate': 1. / 12, # level 1 full charge rate
'lambda': 1e-2, # dual function weight
'priceRise':
0., # amount (as a decimal percent) which the price rises when all cars are being charged
'beta': 1.0, # exponentiate price by beta [CURRENTLY UNUSED]
'mu_stCharge': 0.4, # mean on starting charge level
'std_stCharge': 0.1, # standard deviation on starting charge level
'mu_arr': 19, # mean on arrival time
'std_arr': 2, # standard deviation on arrival time
'mu_dep': 31, # mean on departure time
'std_dep': 1, # standard deviation on departure time
'terminalFunc': (
lambda x: -cp.inv_pos(x)
), # terminal reward function in terms of CVXPY atoms ### MUST BE SOCP-compatible for GUROBI
'terminalFuncCalc': (lambda x: -1. / x),
}
def meanField(params=None, gmm=None, plotAgainstBase=False):
if params is None:
params = DEFAULT_PARAMS
if gmm is None:
gmm = makeModel(timeRange=params['timeRange'])
eGMM = energyGMM(gmm, time_range=params['timeRange'])
tau_1 = cvx.Variable(N) #tau_2 = cvx.Variable(N) tau_2 = np.zeros(N) print tau_2, b print b.shape, tau_2.shape #inv_alpha_1 = cvx.Variable(1) inv_alpha_1 = 0.5 # specify objective function #obj = cvx.Minimize(-cvx.sum_entries(cvx.log(tau_1)) - cvx.log_det(A - cvx.diag(tau_1))) #obj = cvx.Minimize(-cvx.sum_entries(cvx.log(tau_1)) - cvx.log_det(A - cvx.diag(tau_1))) # original #obj = cvx.Minimize( 0.5*N*(inv_alpha_1-1)*log_2_pi - 0.5*inv_alpha_1*(N*cvx.log(1/inv_alpha_1) + cvx.sum_entries(cvx.log(tau_1))) + 0.5*cvx.sum_entries(cvx.square(tau_2)/tau_1) + inv_alpha_1*cvx.sum_entries(log_normcdf(tau_2*cvx.sqrt(1/(inv_alpha_1*tau_1)))) +0.5*N*(1-inv_alpha_1)*cvx.log(1-inv_alpha_1) -0.5*(1-inv_alpha_1)*cvx.log_det(A-cvx.diag(tau_1)) + 0.5*cvx.matrix_frac(b-tau_2, A-cvx.diag(tau_1)) ) # modifications #obj = cvx.Minimize( 0.5*N*(inv_alpha_1-1)*log_2_pi - 0.5*inv_alpha_1*(-N*cvx.log(inv_alpha_1) + cvx.sum_entries(cvx.log(tau_1))) + 0.5*cvx.matrix_frac(tau_2, cvx.diag(tau_1)) + inv_alpha_1*cvx.sum_entries(log_normcdf(tau_2.T*cvx.inv_pos(cvx.sqrt(inv_alpha_1*tau_1)))) +0.5*N*(1-inv_alpha_1)*cvx.log(1-inv_alpha_1) -0.5*(1-inv_alpha_1)*cvx.log_det(A-cvx.diag(tau_1)) + 0.5*cvx.matrix_frac(b-tau_2, A-cvx.diag(tau_1)) ) obj = cvx.Minimize( 0.5*N*(inv_alpha_1-1)*log_2_pi - 0.5*inv_alpha_1*(-N*cvx.log(inv_alpha_1) + cvx.sum_entries(cvx.log(tau_1))) + 0.5*cvx.matrix_frac(tau_2, cvx.diag(tau_1)) + cvx.sum_entries(inv_alpha_1*log_normcdf(cvx.inv_pos(cvx.sqrt(inv_alpha_1*tau_1)))) )# +0.5*N*(1-inv_alpha_1)*cvx.log(1-inv_alpha_1) -0.5*(1-inv_alpha_1)*cvx.log_det(A-cvx.diag(tau_1)) + 0.5*cvx.matrix_frac(b-tau_2, A-cvx.diag(tau_1)) ) #def upper_bound_logpartition(tau, inv_alpha_1): # tau_1, tau_2 = tau[:D+N], tau[D+N:] # tau_1_N, tau_2_N = tau_1[D:], tau_2[D:] # first D values correspond to w # alpha_1 = 1.0 / inv_alpha_1 # inv_alpha_2 = 1 - inv_alpha_1 # if np.any(tau_1 <= 0): # integral_1 = INF2 # else: # integral_1 = inv_alpha_1 * (-0.5 * ((D+N)*np.log(alpha_1) + np.sum(np.log(tau_1)) ) \ # + np.sum(norm.logcdf(np.sqrt(alpha_1)*tau_2_N/np.sqrt(tau_1_N)))) \ # + 0.5 * np.sum(np.power(tau_2, 2) / tau_1) # mat = A - np.diag(tau_1) # sign, logdet = np.linalg.slogdet(mat)
import cvxpy as cp
# Create two scalar optimization variables.
x = cp.Variable()
y = cp.Variable()
# Create two constraints.
constraints = [cp.inv_pos(x) + cp.inv_pos(y) <= 1]
#constraints = [x + y >= 0]
# Form objective.
obj = cp.Minimize((x - y + 2)**2)
# Form and solve problem.
prob = cp.Problem(obj, constraints)
prob.solve() # Returns the optimal value.
print("status:", prob.status)
print("optimal value", prob.value)
print("optimal var", x.value, y.value)
def solve_problem_func(env, alpha_parameter):
# ----------parameters----------
I = env["I"]
M = env["M"]
h_ul = env["h_ul"]
bandwidth_max = env["bandwidth_max"]
tx_power_m_max = env["tx_power_m_max"]
comp_bs = env["comp_bs"]
comp_m = env["comp_m"]
task = env["task"]
data = env["data"]
M_list = env["M_list"]
time_scale = env["time_scale"]
rate_m_itr = bandwidth_max * np.log2(1 + tx_power_m_max * h_ul)
average_rate = bandwidth_max * np.log2(1 + tx_power_m_max * h_ul) / M
alpha_v = alpha_parameter
# ----------itration variable parameter----------
# this part is defined to use the iteration variable in the subproblem
# ----------variables----------
# define the variables
# bandwidth allocation factor w
omega = cp.Variable([M, I])
# offloading factor alpha
alpha = cp.Variable([M, I])
# bs sever allocation factor beta
beta = cp.Variable([M, I])
eta = cp.Variable([M, I])
mu = cp.Variable([M, I])
# max delay T
T = cp.Variable()
# additional variables
t1 = cp.Variable()
t2 = cp.Variable()
t3 = cp.Variable()
# ----------problem formulation----------
# --------objective function--------
objective_func = T
objective1 = cp.Minimize(objective_func)
# --------constraints--------
# offloading constraints
c1 = [alpha >= 0, alpha <= 1]
# bandwidth allocation constraints
c4_5 = [cp.sum(omega) <= 1, omega >= (1e-7)]
# bs server allocation constraints
c2_3 = [cp.sum(beta) <= 1, beta >= (1e-7)]
c6 = [cp.multiply(1 - alpha, task) / comp_m * time_scale <= t1]
c7b = [
-cp.log(t3) - cp.log(beta) + np.log2(alpha_v) +
cp.multiply(1 / alpha_v / np.log(2),
(alpha - alpha_v)) + np.log2(task / comp_bs * time_scale)
<= 0
]
c8b = [
-cp.log(t2) - cp.log(omega) + np.log2(alpha_v) + cp.multiply(
1 / alpha_v / np.log(2),
(alpha - alpha_v)) + np.log2(data / rate_m_itr * time_scale) <= 0
]
#c8 = [cp.multiply(eta,task/comp_bs)*time_scale<=t3]
#c7 = [cp.multiply ( mu, data / rate_m_itr)*time_scale<=t2]
R1a2 = []
for i in range(0, M):
for j in range(0, I):
R1a2 = R1a2 + [
cp.norm(cp.vstack([2 * (alpha[i, j]), eta[i, j] - beta[i, j]]),
2) <= eta[i, j] + beta[i, j]
]
#assert R1a2[0].is_dqcp()
R1a3 = [alpha <= 1e7 * beta + (1e-7) * eta - 1, alpha <= eta]
R2a3 = [alpha <= 1e7 * omega + (1e-7) * mu - 1, alpha <= mu]
R2a4 = [eta <= 1e7, mu <= 1e7]
# local computing constraints R1
#R1 = [cp.ceil(cp.multiply(alpha, task)/comp_m) <= T]
R1 = [cp.ceil(cp.multiply(1 - alpha, task) / comp_m) - T <= 0]
#R1 = [cp.ceil(alpha) - 10 <= 0]
#assert R1[0].is_dqcp ()
# offloading constraints R2
R2a = cp.ceil(
cp.multiply(cp.multiply(alpha, task / comp_bs), cp.inv_pos(beta)))
R2b = cp.ceil(
cp.multiply(
cp.multiply(
alpha,
data / bandwidth_max * np.log2(1 + tx_power_m_max * h_ul)),
cp.inv_pos(omega)))
R2 = [R2a + R2b <= T]
R2a1 = cp.ceil((cp.multiply(eta, task / comp_bs)))
objective2 = cp.Minimize(
1 / 2 * cp.max(cp.ceil(cp.multiply(alpha, task) / comp_m)))
objective2 = cp.Minimize(
cp.max(cp.ceil(cp.multiply(1 - alpha, task / beta / comp_bs))))
obj3_part1 = 1 / 2 * cp.max(cp.ceil(cp.multiply(1 - alpha, task / comp_m)))
obj3_part1 = 1 / 2 * cp.ceil(cp.max(cp.multiply(1 - alpha, task / comp_m)))
obj3_part2 = 1 / 2 * cp.max(
cp.ceil(cp.multiply(eta, task / comp_bs)) +
cp.ceil(cp.multiply(mu, data / rate_m_itr)))
obj3_part2 = 1 / 2 * cp.ceil(cp.max(cp.multiply(
eta, task / comp_bs))) + 1 / 2 * cp.ceil(
cp.max(cp.multiply(mu, data / rate_m_itr)))
obj3_part3 = cp.abs(obj3_part1 - obj3_part2)
objective3 = cp.Minimize(obj3_part1 + obj3_part2 + obj3_part3)
#assert obj3_part1.is_dqcp ()
#assert obj3_part1.is_dcp()
#assert (cp.max(cp.ceil(cp.multiply(eta,task/comp_bs)))).is_dqcp()
#assert (cp.max(cp.ceil(cp.multiply(eta,task/comp_bs)))).is_dcp()
#assert (cp.ceil(cp.multiply(mu,data/rate_m_itr))).is_dqcp
#assert (cp.ceil(alpha)+cp.ceil(beta)).is_dqcp()
#assert obj3_part2.is_dqcp ()
#assert obj3_part3.is_dqcp ()
#assert objective3.is_dqcp ()
t = cp.Variable([M, I])
objective2 = cp.Minimize(cp.max(cp.ceil(cp.multiply(t, task / comp_bs))))
c4 = [(1 - alpha) / beta <= t]
objective6 = cp.Minimize(1 / 2 *
cp.ceil(t1 + t2 + t3 + cp.abs(t1 - t2 - t3)) +
3 / 2)
rho = 1
upsilon = 1
varsigma = 1e-27
obj7_func1 = 1 / 2 * cp.ceil(t1 + t2 + t3 + cp.abs(t1 - t2 - t3)) + 3 / 2
obj7_func1 = 1 / 2 * (t1 + t2 + t3 + cp.abs(t1 - t2 - t3))
obj7_func2 = cp.sum(
cp.multiply(1 - alpha, varsigma * task * np.square(comp_m))) + cp.sum(
tx_power_m_max * cp.multiply(mu, data / rate_m_itr))
objective7 = cp.Minimize(rho * obj7_func1 + upsilon * obj7_func2)
try:
# ----------probalem solve and results----------
# problem6 = cp.Problem(objective6, c1+c2_3+c4_5+c6+c7+c8+R1a3+R2a3+R2a4)
problem6 = cp.Problem(objective6, c1 + c2_3 + c4_5 + c6 + c7b + c8b)
problem6.solve(qcp=True, verbose=True, solver=cp.ECOS)
print()
print("problem1 solve: ", problem6.value)
print("alpha.value", alpha.value)
print("beta.value", beta.value)
print("omega.value", omega.value)
np.ceil(data / rate_m_itr * M * time_scale)
# ----------data collection and depict-----------
plt.clf()
plt.subplot(441)
plt.title("user_rate in M/s")
# plt.bar(x=M_list, height=(average_rate/1e6).reshape(M), width=1)
plt.plot(M_list,
omega.value * rate_m_itr / 1e6,
'-*',
color='b',
label="optimized rate")
plt.plot(M_list,
average_rate / 1e6,
'-o',
color='r',
label="average bandwidth allocation rate")
plt.legend()
plt.subplot(442)
plt.title("data transmitting delay")
plt.plot(
M_list,
data / average_rate * time_scale,
'-*',
color='b',
label=
"full date transmitting delay with average bandwidth allocation")
plt.plot(M_list, (alpha.value * data) / (omega.value * rate_m_itr) *
time_scale,
'-o',
color='r',
label="optimized transmitting delay")
# plt.bar(x=M_list, height=np.ceil(data / average_rate*time_scale).reshape(M), width=1)
plt.legend(fontsize='xx-small')
plt.subplot(443)
plt.title("local_computing_delay")
bar_width = 0.3
plt.bar(x=M_list,
height=np.ceil(time_scale * task / comp_m).reshape(M),
width=bar_width,
label='full local computing delay')
plt.bar(x=M_list + bar_width,
height=np.ceil(time_scale * (1 - alpha.value) * task /
comp_m).reshape(M),
width=bar_width,
label='remain local computing delay')
plt.plot(M_list,
problem6.value * np.ones(M),
'o',
color='m',
label="optimized delay")
plt.legend(fontsize='xx-small') # 显示图例，即label
plt.xticks(x=M_list +
bar_width / 2) # 显示x坐标轴的标签,即tick_label,调整位置，使其落在两个直方图中间位置
plt.subplot(444)
plt.title("offloading_computing_delay")
bar_width = 0.3 # 设置柱状图的宽度
plt.bar(x=M_list,
height=(np.ceil(task / (comp_bs / M)) * time_scale).reshape(M),
width=bar_width,
label='average full offloading computing delay')
plt.bar(x=M_list + bar_width,
height=(np.ceil(task * alpha.value / (beta.value * comp_bs) *
time_scale)).reshape(M),
width=bar_width,
label='optimized offloading computing delay')
# 绘制并列柱状图
plt.legend() # 显示图例，即label
plt.xticks(x=M_list +
bar_width / 2) # 显示x坐标轴的标签,即tick_label,调整位置，使其落在两个直方图中间位置
plt.subplot(445)
plt.title("optimized local computing_delay gain")
plt.plot(M_list, (problem6.value -
np.ceil(task / comp_m * time_scale)).reshape(M),
'x',
color='r')
plt.plot(M_list,
problem6.value * np.ones(M),
'o',
color='m',
label="optimized delay")
plt.plot(M_list,
t1.value * np.ones(M),
'v',
color='g',
label="local computing delay t1")
plt.plot(M_list,
t3.value * np.ones(M),
'^',
color='k',
label="offloading computing delay t3")
plt.plot(M_list,
t2.value * np.ones(M),
'*',
color='b',
label="transmitting delay t2")
plt.legend(fontsize='xx-small')
plt.subplot(446)
plt.title("optimized alpha beta")
plt.plot(M_list, alpha.value, '-v', label='alpha')
plt.plot(M_list, beta.value, '-x', label='beta')
plt.plot(M_list, omega.value, '^', label='omega')
plt.legend()
plt.subplot(447)
plt.title("optimized omega")
plt.plot(M_list, omega.value, '-^')
plt.subplot(448)
plt.title("optimized beta")
plt.plot(M_list, beta.value, '-^')
'''
plt.subplot(449)
plt.title("optimized eta")
plt.plot(M_list, eta.value,'-^')
plt.subplot(4,4,10)
plt.title("optimized mu")
plt.plot(M_list, mu.value,'-^')
plt.subplot(4,4,11)
plt.title("recalculated omega")
plt.plot(M_list, alpha.value/eta.value,'-^')
plt.subplot(4,4,12)
plt.title("recalculated beta")
plt.plot(M_list, alpha.value/mu.value,'-^')
'''
print("func1.value", obj7_func1.value)
print(
"local computing energy",
cp.sum(cp.multiply(1 - alpha,
varsigma * task * np.square(comp_m))).value)
print(
"offloading energy",
cp.sum(tx_power_m_max * cp.multiply(mu, data / rate_m_itr)).value)
print("func2.value", obj7_func2.value)
problem_result = {
"problem6.value": problem6.value,
"alpha.value": alpha.value
}
return problem_result
except SolverError:
problem6.value = 0
problem_result = {
"problem6.value": problem6.value,
"alpha.value": alpha_v
}
return problem_result
pass
obj = cvx.Minimize(0)
constraints = [cvx.abs(Tpow*a - cvx.mul_elemwise(y, Tpow*cvx.vstack(1, b)))
<= mid * Tpow*cvx.vstack(1, b)]
prob = cvx.Problem(obj, constraints)
sol = prob.solve(solver=cvx.CVXOPT)
if prob.status == cvx.OPTIMAL:
print('gamma = {}', format(mid))
u = mid
a_opt = a
b_opt = b
objval_opt = mid
else:
l = mid
y_fit = cvx.mul_elemwise(Tpow*a_opt.value,
cvx.inv_pos(Tpow*cvx.vstack(1, b_opt.value)))
plt.figure(0)
plt.plot(t.A1, y.A1, label='y')
plt.plot(t.A1, y_fit.value.A1,'g-o', label='fit')
plt.xlabel('t')
plt.ylabel('y')
plt.title('A5.2: Fit vs. Exponential Function')
plt.legend(loc='lower right', frameon=False);
plt.figure(1)
plt.plot(t.A1,y_fit.value.A1-y.A1)
plt.xlabel('t')
plt.ylabel('error')
plt.title('A5.2: Fitting Error Plot')
print('a: {}'.format(a_opt.T.value))
print('b: {}'.format(b_opt.T.value))
print('optimal objective value: {}'.format(mid))
def test_noop_inv_pos_constr(self):
x = cp.Variable()
constr = [cp.inv_pos(cp.ceil(x)) >= -5]
problem = cp.Problem(cp.Minimize(0), constr)
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.status, s.OPTIMAL)
import numpy as np
import cvxpy as cp
from satisfy_some_constraints_data import m, n, k, A, b, c
epsilon = 1e-5
u = cp.Variable()
v = cp.Variable()
x = cp.Variable((A.shape[1], ))
f_x = A @ x - b
constraints = [
cp.sum(cp.pos(f_x + u)) <= (m - k) * u,
cp.inv_pos(v) <= u,
]
obj = cp.Minimize(c @ x)
p1 = cp.Problem(obj, constraints)
p1.solve()
if p1.status == 'optimal':
lambda_value = 1 / u.value
print(f'lambda: {lambda_value:.4f}')
print(f'objective value: {p1.value:.4f}')
f_values = np.matmul(A, x.value) - b
satisfied = f_values <= epsilon
satisfied_count = satisfied.sum()
print(f"satisfied count: {satisfied_count}")
#part b
smallest_indexes = np.argsort(f_values)[:k]
constraints = [A[smallest_indexes, :] @ x <= b[smallest_indexes]]
p2 = cp.Problem(obj, constraints)
p2.solve()
print(f'Improved objective value: {p2.value:.4f}')
prox("NORM_2", lambda: cp.norm(X, "fro")),
prox("NORM_2", lambda: cp.norm2(x)),
prox("NORM_NUCLEAR", lambda: cp.norm(X, "nuc")),
#prox("QUAD_OVER_LIN", lambda: cp.quad_over_lin(p, q1)),
prox("SECOND_ORDER_CONE", None, C_soc_scaled),
prox("SECOND_ORDER_CONE", None, C_soc_scaled_translated),
prox("SECOND_ORDER_CONE", None, C_soc_translated),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm(X, "fro") <= t]),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm2(x) <= t]),
prox("SEMIDEFINITE", None, lambda: [X >> 0]),
prox("SUM_DEADZONE", f_dead_zone),
prox("SUM_EXP", lambda: cp.sum_entries(cp.exp(x))),
prox("SUM_HINGE", f_hinge),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_INV_POS", lambda: cp.sum_entries(cp.inv_pos(x))),
prox("SUM_KL_DIV", lambda: cp.sum_entries(cp.kl_div(p1,q1))),
prox("SUM_LARGEST", lambda: cp.sum_largest(x, 4)),
prox("SUM_LOGISTIC", lambda: cp.sum_entries(cp.logistic(x))),
prox("SUM_NEG_ENTR", lambda: cp.sum_entries(-cp.entr(x))),
prox("SUM_NEG_LOG", lambda: cp.sum_entries(-cp.log(x))),
prox("SUM_QUANTILE", f_quantile),
prox("SUM_QUANTILE", f_quantile_elemwise),
prox("SUM_SQUARE", f_least_squares_matrix),
prox("SUM_SQUARE", lambda: f_least_squares(20)),
prox("SUM_SQUARE", lambda: f_least_squares(5)),
prox("SUM_SQUARE", f_quad_form),
prox("TOTAL_VARIATION_1D", lambda: cp.tv(x)),
prox("ZERO", None, C_linear_equality),
prox("ZERO", None, C_linear_equality_matrix_lhs),
prox("ZERO", None, C_linear_equality_matrix_rhs),
def solveOracle(SP, startingFund, c, c_0):
result_M = []
result_M.append(startingFund)
result_P = []
result_R = []
compNum = len(SP[0])
ini_P_value = 1.0 / (compNum + 1)
ini_P = [ini_P_value] * compNum
result_P.append(ini_P)
# calculate the return at the begining of the 2nd time period
# ignore transaction cost for now
R_1 = np.dot(np.divide(ini_P, SP[0]), np.subtract(SP[1], SP[0]))
result_R.append(R_1)
M_1 = startingFund * (1 + R_1)
result_M.append(M_1)
for i in xrange(1, (len(SP) - 1)):
P_pre = result_P[-1] #vector
M_pre = result_M[-2]
M = result_M[-1]
S_pre = SP[i - 1] #vector
S = SP[i]
S_next = SP[i + 1]
# Variables:
P = cvx.Variable(compNum)
# Constraints:
constraints = [0 <= P, P <= 1, sum(P) <= 1]
# Form Objective:
'''
print 'P:',P
print 'M_p:', M_pre
print 'P_p:',P_pre
print 'M:',M
print 'S_pre:', S_pre
print 'S:', S
print '1/S:', cvx.inv_pos(S)
'''
term1 = cvx.mul_elemwise(np.subtract(S_next, S),
cvx.mul_elemwise(cvx.inv_pos(S), P))
absTerm = cvx.abs(
cvx.mul_elemwise(cvx.inv_pos(S), P) -
cvx.mul_elemwise(cvx.mul_elemwise(M_pre, P_pre),
cvx.inv_pos(cvx.mul_elemwise(M, S_pre))))
term2 = cvx.mul_elemwise(S, cvx.mul_elemwise(c, absTerm))
obj = cvx.Maximize(sum(term1 - term2) - c_0)
# Form and solve problem:
prob = cvx.Problem(obj, constraints)
prob.solve()
'''print prob.status'''
result_P.append(P.value)
R = prob.value
result_R.append(R)
M_next = M * (1 + R)
result_M.append(M_next)
#print result_M
#print len(result_M)
#print result_P
return_accum = [0] * len(result_R)
for i in xrange(len(result_R)):
for j in xrange(i + 1):
return_accum[i] += result_R[j]
#print return_accum
#print result_R
#print result_M
return result_R
prox("NORM_1", lambda: cp.norm1(x)),
prox("NORM_2", lambda: cp.norm(X, "fro")),
prox("NORM_2", lambda: cp.norm2(x)),
prox("NORM_NUCLEAR", lambda: cp.norm(X, "nuc")),
prox("SECOND_ORDER_CONE", None, C_soc_scaled),
prox("SECOND_ORDER_CONE", None, C_soc_scaled_translated),
prox("SECOND_ORDER_CONE", None, C_soc_translated),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm(X, "fro") <= t]),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm2(x) <= t]),
prox("SEMIDEFINITE", None, lambda: [X >> 0]),
prox("SUM_DEADZONE", f_dead_zone),
prox("SUM_EXP", lambda: cp.sum_entries(cp.exp(x))),
prox("SUM_HINGE", f_hinge),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_INV_POS", lambda: cp.sum_entries(cp.inv_pos(x))),
prox("SUM_KL_DIV", lambda: cp.sum_entries(cp.kl_div(p1,q1))),
prox("SUM_LARGEST", lambda: cp.sum_largest(x, 4)),
prox("SUM_LOGISTIC", lambda: cp.sum_entries(cp.logistic(x))),
prox("SUM_NEG_ENTR", lambda: cp.sum_entries(-cp.entr(x))),
prox("SUM_NEG_LOG", lambda: cp.sum_entries(-cp.log(x))),
prox("SUM_QUANTILE", f_quantile),
prox("SUM_QUANTILE", f_quantile_elemwise),
prox("SUM_SQUARE", f_least_squares_matrix),
prox("SUM_SQUARE", lambda: f_least_squares(20)),
prox("SUM_SQUARE", lambda: f_least_squares(5)),
prox("SUM_SQUARE", f_quad_form),
prox("TOTAL_VARIATION_1D", lambda: cp.tv(x)),
prox("ZERO", None, C_linear_equality),
prox("ZERO", None, C_linear_equality_matrix_lhs),
prox("ZERO", None, C_linear_equality_matrix_rhs),
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() print y.value val_ls_cvx = np.max(np.abs(log(A*matrix(y.value)))) print val_ls_cvx #solution 6 cvxpy equvelent z=Variable (m,1) u = Variable(1) qq = [(max(Am[i,:]*z,inv_pos(Am[i,:]*z))<=u) for i in range(n)] objective2 = Minimize(u) pp =[z>=0,z<=1]
def get_allocation(self, unflattened_throughputs, scale_factors,
unflattened_priority_weights, times_since_start,
num_steps_remaining, cluster_spec):
throughputs, index = super().flatten(unflattened_throughputs,
cluster_spec)
if throughputs is None:
self._isolated_throughputs_prev_iteration = {}
self._num_steps_remaining_prev_iteration = {}
return None
(m, n) = throughputs.shape
(job_ids, worker_types) = index
# Row i of scale_factors_array is the scale_factor of job i
# repeated len(worker_types) times.
scale_factors_array = self.scale_factors_array(scale_factors, job_ids,
m, n)
# TODO: Do something with these priority_weights.
priority_weights = np.array(
[1. / unflattened_priority_weights[job_id] for job_id in job_ids])
# Create allocation variable, and isolated allocation.
x = cp.Variable(throughputs.shape)
isolated_throughputs = self._isolated_policy.get_throughputs(
throughputs, index, scale_factors, cluster_spec)
expected_time_fractions = []
for i in range(len(job_ids)):
if job_ids[i] not in self._cumulative_isolated_time:
self._cumulative_isolated_time[job_ids[i]] = 0
if job_ids[i] in self._num_steps_remaining_prev_iteration:
self._cumulative_isolated_time[job_ids[i]] += (
self._num_steps_remaining_prev_iteration[job_ids[i]] -
num_steps_remaining[job_ids[i]]) / \
self._isolated_throughputs_prev_iteration[job_ids[i]]
allocation_throughput = cp.sum(cp.multiply(throughputs[i], x[i]))
expected_time_isolated = self._cumulative_isolated_time[job_ids[i]] + \
(num_steps_remaining[job_ids[i]] / isolated_throughputs[i])
expected_time_allocation = times_since_start[job_ids[i]] + \
(num_steps_remaining[job_ids[i]] * cp.inv_pos(allocation_throughput))
expected_time_fraction = expected_time_allocation / expected_time_isolated
expected_time_fractions.append(expected_time_fraction)
if len(expected_time_fractions) == 1:
objective = cp.Minimize(expected_time_fractions[0])
else:
objective = cp.Minimize(cp.maximum(*expected_time_fractions))
# Make sure that the allocation can fit in the cluster.
constraints = self.get_base_constraints(x, scale_factors_array)
cvxprob = cp.Problem(objective, constraints)
result = cvxprob.solve(solver=self._solver)
if cvxprob.status != "optimal":
print('WARNING: Allocation returned by policy not optimal!')
self._num_steps_remaining_prev_iteration = copy.copy(
num_steps_remaining)
self._isolated_throughputs_prev_iteration = {}
for i in range(m):
self._isolated_throughputs_prev_iteration[job_ids[i]] = \
isolated_throughputs[i]
if x.value is None:
return self._isolated_policy.get_allocation(
unflattened_throughputs, scale_factors, cluster_spec)
return super().unflatten(x.value.clip(min=0.0).clip(max=1.0), index)
def get_allocation(self, unflattened_throughputs, scale_factors,
unflattened_priority_weights, times_since_start,
num_steps_remaining, cluster_spec):
all_throughputs, index = \
self.flatten(d=unflattened_throughputs,
cluster_spec=cluster_spec,
priority_weights=unflattened_priority_weights)
if all_throughputs is None or len(all_throughputs) == 0:
self._isolated_throughputs_prev_iteration = {}
self._num_steps_remaining_prev_iteration = {}
return None
(m, n) = all_throughputs[0].shape
(job_ids, single_job_ids, worker_types, relevant_combinations) = index
x = cp.Variable((m, n))
# Row i of scale_factors_array is the scale_factor of job
# combination i repeated len(worker_types) times.
scale_factors_array = self.scale_factors_array(scale_factors, job_ids,
m, n)
throughputs_no_packed_jobs = np.zeros((len(single_job_ids), n))
for i, single_job_id in enumerate(single_job_ids):
for j, worker_type in enumerate(worker_types):
throughputs_no_packed_jobs[i, j] = \
unflattened_throughputs[single_job_id][worker_type]
isolated_throughputs = self._isolated_policy.get_throughputs(
throughputs_no_packed_jobs, (single_job_ids, worker_types),
scale_factors, cluster_spec)
single_throughputs = np.zeros((len(single_job_ids), n))
expected_time_fractions = []
for i in range(len(all_throughputs)):
if single_job_ids[i] not in self._cumulative_isolated_time:
self._cumulative_isolated_time[single_job_ids[i]] = 0
if single_job_ids[i] in self._num_steps_remaining_prev_iteration:
self._cumulative_isolated_time[single_job_ids[i]] += (
self._num_steps_remaining_prev_iteration[single_job_ids[i]] -
num_steps_remaining[single_job_ids[i]]) / \
self._isolated_throughputs_prev_iteration[single_job_ids[i]]
indexes = relevant_combinations[single_job_ids[i]]
isolated_throughput = isolated_throughputs[i]
allocation_throughput = cp.sum(
cp.multiply(all_throughputs[i][indexes], x[indexes]))
expected_time_isolated = self._cumulative_isolated_time[single_job_ids[i]] + \
(num_steps_remaining[single_job_ids[i]] / isolated_throughput)
expected_time_allocation = times_since_start[single_job_ids[i]] + \
(num_steps_remaining[single_job_ids[i]] * cp.inv_pos(allocation_throughput))
expected_time_fraction = expected_time_allocation / expected_time_isolated
expected_time_fractions.append(expected_time_fraction)
if len(expected_time_fractions) == 1:
objective = cp.Minimize(expected_time_fractions[0])
else:
objective = cp.Minimize(cp.maximum(*expected_time_fractions))
# Make sure the allocation can fit in the cluster.
constraints = self.get_base_constraints(x, single_job_ids,
scale_factors_array,
relevant_combinations)
# Explicitly constrain all allocation values with an effective scale
# factor of 0 to be 0.
# NOTE: This is not strictly necessary because these allocation values
# do not affect the optimal allocation for nonzero scale factor
# combinations.
for i in range(m):
for j in range(n):
if scale_factors_array[i, j] == 0:
constraints.append(x[i, j] == 0)
cvxprob = cp.Problem(objective, constraints)
result = cvxprob.solve(solver=self._solver)
if cvxprob.status != "optimal":
print('WARNING: Allocation returned by policy not optimal!')
self._num_steps_remaining_prev_iteration = copy.copy(
num_steps_remaining)
self._isolated_throughputs_prev_iteration = {}
for i in range(len(all_throughputs)):
self._isolated_throughputs_prev_iteration[single_job_ids[i]] = \
isolated_throughputs[i]
return self.unflatten(x.value.clip(min=0.0).clip(max=1.0), index)
def test_infeasible_inv_pos_constr(self):
x = cp.Variable(nonneg=True)
constr = [cp.inv_pos(cp.ceil(x)) <= -5]
problem = cp.Problem(cp.Minimize(0), constr)
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.status, s.INFEASIBLE)
Rij.transpose()) / 2. # R1+R2 combined radii (min distance) matrix
Iij = (Iij + Iij.transpose()) / 2. # Intensity matrix
Iij[Iij < 1] = 1
Iij[20, 15] = 100000
Rij[Rij < 1e-6] = 1e-6
Iij = Iij / 1000
c = cvx.Variable(dim * dim)
constr = []
# for i in range(dim):
# for j in range(i, dim):
# constr.append(c[i, j] >= Rij[i, j])
for i in range(dim * dim):
constr.append(c[i] >= Rij.flatten()[i])
prob = cvx.Problem(
cvx.Maximize(cvx.norm(cvx.multiply(Iij.flatten(), cvx.inv_pos(c)), 1)),
constr)
#prob = cvx.Problem(cvx.Minimize(cvx.max(cvx.max(cvx.abs(cvx.multiply(cvx.inv_pos(cvx.multiply(1./Iij.flatten(), c)), 1/100))))), constr)
prob.solve(method="dccp", solver=cvx.MOSEK, verbose=True)
rij_opt = np.reshape(c.value, (dim, dim))
r = rij[0, 1] / rij_opt[0, 1]
for i, j in product(range(dim), range(dim)):
if i >= j: continue
print("d[%d,%d]: %1.2f(true) %1.2f(sol.)" %
(i, j, rij[i, j], rij_opt[i, j] * r))
df['opt. distance'] = df.index.size * [0]
for i1 in range(dim):
for i2 in range(dim):
val_ls_reg = np.max(np.abs(log(A * matrix(p_ls_reg)))) print p_ls_reg print val_ls_reg ########################################################################################### # solution 4 # chebshev approximation p_chev = cp.Variable(m) objective = cp.Minimize(cp.norm(A * p_chev - ones((n, 1)), "inf")) constraints = [p_chev <= 1, p_chev >= 0] p4 = cp.Problem(objective, constraints) result = p4.solve() f_4 = np.max(np.abs(log(A * matrix(p_chev.value)))) print p_chev.value print f_4 ########################################################################################### # solution 5 # cvxpy u = cp.Variable(1) p_cp = cp.Variable(m) objective = cp.Minimize(u) constraints = [cp.max(matrix(A[i, :]) * p_cp, cp.inv_pos(matrix(A[i, :]) * p_cp)) <= u for i in range(n)] constraints.extend([p_cp <= 1, p_cp >= 0]) p5 = cp.Problem(objective, constraints) result = p5.solve() f_5 = np.max(np.abs(log(A * matrix(p_cp.value)))) print p_cp.value print f_5
#fixing data
d = np.asarray(d)
smin = np.asarray(smin)
smax = np.asarray(smax)
tau_min = np.asarray(tau_min)
tau_max = np.asarray(tau_max)
d = d[:, 0]
smin = smin[:, 0]
smax = smax[:, 0]
tau_min = tau_min[:, 0]
tau_max = tau_max[:, 0]
k = cp.Variable(n)
h = cp.cumsum(k)
phi = a * cp.multiply(cp.inv_pos(k), d**2) + c * k + cp.multiply(b, d)
obj = cp.Minimize(cp.sum(phi))
constraints = [
cp.multiply(smin, k) <= d,
cp.multiply(smax, k) >= d,
tau_min <= h,
tau_max >= h,
]
problem = cp.Problem(obj, constraints)
problem.solve()
print(f"status: {problem.status}")
if problem.status == 'optimal':
print(f"Total fuel: {problem.value}")
s = d / k.value
plt.step(np.arange(n), s)
plt.show()