def find_ideal_pt_for_person_in_ball(center, radius, idealpt_and_radius, constraint="l1"):
X = cvxpy.Variable(5) # 1 point for each item
fun = 0
y = idealpt_and_radius[0]
w = idealpt_and_radius[1]
sumsq = math.sqrt(sum([math.pow(w[i], 2) for i in range(5)]))
w = [w[i] / sumsq for i in range(5)]
for slider in range(5):
fun += w[slider] * cvxpy.abs(X[slider] - y[slider])
obj = cvxpy.Minimize(fun)
constraints = [X >= 0, X[0] + X[1] + X[2] - X[3] + 162 == X[4]]
if constraint == "l1":
constraints += [cvxpy.sum_entries(
cvxpy.abs(X[0:4] - center[0:4])) <= radius]
else:
constraints += [cvxpy.sum_entries(
cvxpy.square(X[0:4] - center[0:4])) <= radius**2]
prob = cvxpy.Problem(obj, constraints)
result = prob.solve()
items = [X.value[i, 0] for i in range(5)]
if constraint == "l1":
credits = [abs(items[i] - center[i]) / radius for i in range(4)]
else:
credits = [(items[i] - center[i])**2 / radius**2 for i in range(4)]
deficit = calculate_deficit(items)
items.append(deficit)
return items, credits
def test_signed_curvature(self):
# Convex argument.
expr = cvx.abs(1 + cvx.exp(cvx.Variable()) )
self.assertEqual(expr.curvature, s.CONVEX)
expr = cvx.abs( -cvx.entr(cvx.Variable()) )
self.assertEqual(expr.curvature, s.UNKNOWN)
expr = cvx.abs( -cvx.log(cvx.Variable()) )
self.assertEqual(expr.curvature, s.UNKNOWN)
# Concave argument.
expr = cvx.abs( cvx.log(cvx.Variable()) )
self.assertEqual(expr.curvature, s.UNKNOWN)
expr = cvx.abs( -cvx.square(cvx.Variable()) )
self.assertEqual(expr.curvature, s.CONVEX)
expr = cvx.abs( cvx.entr(cvx.Variable()) )
self.assertEqual(expr.curvature, s.UNKNOWN)
# Affine argument.
expr = cvx.abs( cvx.NonNegative() )
self.assertEqual(expr.curvature, s.CONVEX)
expr = cvx.abs( -cvx.NonNegative() )
self.assertEqual(expr.curvature, s.CONVEX)
expr = cvx.abs( cvx.Variable() )
self.assertEqual(expr.curvature, s.CONVEX)
def linear_mpc_control(xref, xbar, x0, dref):
"""
linear mpc control
xref: reference point
xbar: operational point
x0: initial state
dref: reference steer angle
"""
x = cvxpy.Variable((NX, T + 1))
u = cvxpy.Variable((NU, T))
cost = 0.0
constraints = []
for t in range(T):
cost += cvxpy.quad_form(u[:, t], R)
if t != 0:
cost += cvxpy.quad_form(xref[:, t] - x[:, t], Q)
A, B, C = get_linear_model_matrix(
xbar[2, t], xbar[3, t], dref[0, t])
constraints += [x[:, t + 1] == A * x[:, t] + B * u[:, t] + C]
if t < (T - 1):
cost += cvxpy.quad_form(u[:, t + 1] - u[:, t], Rd)
constraints += [cvxpy.abs(u[1, t + 1] - u[1, t]) <=
MAX_DSTEER * DT]
cost += cvxpy.quad_form(xref[:, T] - x[:, T], Qf)
constraints += [x[:, 0] == x0]
constraints += [x[2, :] <= MAX_SPEED]
constraints += [x[2, :] >= MIN_SPEED]
constraints += [cvxpy.abs(u[0, :]) <= MAX_ACCEL]
constraints += [cvxpy.abs(u[1, :]) <= MAX_STEER]
prob = cvxpy.Problem(cvxpy.Minimize(cost), constraints)
prob.solve(solver=cvxpy.ECOS, verbose=False)
if prob.status == cvxpy.OPTIMAL or prob.status == cvxpy.OPTIMAL_INACCURATE:
ox = get_nparray_from_matrix(x.value[0, :])
oy = get_nparray_from_matrix(x.value[1, :])
ov = get_nparray_from_matrix(x.value[2, :])
oyaw = get_nparray_from_matrix(x.value[3, :])
oa = get_nparray_from_matrix(u.value[0, :])
odelta = get_nparray_from_matrix(u.value[1, :])
else:
print("Error: Cannot solve mpc..")
oa, odelta, ox, oy, oyaw, ov = None, None, None, None, None, None
return oa, odelta, ox, oy, oyaw, ov
def transition_to_action(s0,s1, dynamics, max_dtheta, max_ddx, max_iter=30,
max_line_searches=10):
"""recovers a control signal u that can cause a transition from s0 to s1.
specifically, minimize || f(s0,u) - s1 ||^2 as a Sequential
Quadratic Program.
"""
# the current step size along the search direction recovered by the QP
step = 1.
# initial guess
s0 = array(s0)
s1 = array(s1)
u0 = array((0,0))
def cost(u):
"|| f(s0,u) - s1 ||^2"
return sum((dynamics(s0,u)['val'] - s1)**2)
# the value of the initial guess
best_cost = cost(u0)
for it in xrange(max_iter):
f = dynamics(s0, u0, derivs={'du'})
# linearize || f(s0,u) - s1 ||^2 about u0 and solve as a QP
u = CX.Variable(len(u0), name='u')
objective = CX.square(CX.norm( array(f['val']) + vstack(f['du'])*(u-u0) - s1 ))
p = CX.Problem(CX.Minimize(objective),
[CX.abs(u[0]) <= max_ddx,
CX.abs(u[1]) <= max_dtheta])
r = p.solve()
unew = array(u.value.flat)
# line search along unew-u0 from u0
line_search_success = False
for line_searches in xrange(max_line_searches):
new_cost = cost(u0 + step*(unew-u0))
if new_cost < best_cost:
# accept the step
best_cost = new_cost
u0 = u0 + step*(unew-u0)
# grow the step for the next iteration
step *= 1.2
line_search_success = True
else:
# shrink the step size and try again
step *= 0.5
if not line_search_success:
# convergence is when line search fails.
return u0
print 'Warning: failed to converge'
return u0
def distance_from_separating_hyperplane(self,tple): no_of_weights=self.dimensions no_of_tuple=self.dimensions weights=cvxpy.Variable(no_of_weights,1) tuple=numpy.array(tple) print "weights:",weights print "tuple:",tuple bias=self.bias svm_function = 0.0 for i in xrange(no_of_weights): svm_function += cvxpy.abs(weights[i,0]) objective=cvxpy.Minimize(cvxpy.abs(svm_function)*0.5) print "============================================" print "Objective Function" print "============================================" print objective constraint=0.0 constraints=[] for i,k in zip(xrange(no_of_weights),xrange(no_of_tuple)): constraint += weights[i,0]*tuple[k] constraint += bias print "constraint:",constraint constraints.append(cvxpy.abs(constraint) >= 1) print "============================================" print "Constraints" print "============================================" print constraints problem=cvxpy.Problem(objective,constraints) print "=====================================" print "Installed Solvers:" print "=====================================" print cvxpy.installed_solvers() print "Is Problem DCCP:",dccp.is_dccp(problem) print "=====================================" print "CVXPY args:" print "=====================================" result=problem.solve(solver=cvxpy.SCS,verbose=True,method='dccp') print "=====================================" print "Problem value:" print "=====================================" print problem.value print "=====================================" print "Result:" print "=====================================" print result return (result,tuple)
def setUp(self):
"""
Use cvxopt to get ground truth values
"""
from cvxopt import lapack,solvers,matrix,spdiag,log,div,normal,setseed
from cvxopt.modeling import variable,op,max,sum
solvers.options['show_progress'] = 0
setseed()
m,n = 100,30
A = normal(m,n)
b = normal(m,1)
b /= (1.1*max(abs(b)))
self.m,self.n,self.A,self.b = m,n,A,b
# l1 approximation
# minimize || A*x + b ||_1
x = variable(n)
op(sum(abs(A*x+b))).solve()
self.x1 = x.value
# l2 approximation
# minimize || A*x + b ||_2
bprime = -matrix(b)
Aprime = matrix(A)
lapack.gels(Aprime,bprime)
self.x2 = bprime[:n]
# Deadzone approximation
# minimize sum(max(abs(A*x+b)-0.5, 0.0))
x = variable(n)
dzop = op(sum(max(abs(A*x+b)-0.5, 0.0)))
dzop.solve()
self.obj_dz = sum(np.max([np.abs(A*x.value+b)-0.5,np.zeros((m,1))],axis=0))
# Log barrier
# minimize -sum (log ( 1.0 - (A*x+b)**2))
def F(x=None, z=None):
if x is None: return 0, matrix(0.0,(n,1))
y = A*x+b
if max(abs(y)) >= 1.0: return None
f = -sum(log(1.0 - y**2))
gradf = 2.0 * A.T * div(y, 1-y**2)
if z is None: return f, gradf.T
H = A.T * spdiag(2.0*z[0]*div(1.0+y**2,(1.0-y**2)**2))*A
return f,gradf.T,H
self.cxlb = solvers.cp(F)['x']
def solve_problem(weights, alpha_vector):
constaints = [sum(weights) == 0.0, sum(cvx.abs(weights)) <= 1.0]
obj = optimal_holdings_strict_factor._get_obj(weights, alpha_vector)
prob = cvx.Problem(obj, constaints)
prob.solve(max_iters=500)
return np.asarray(weights.value).flatten()
def TRCPA_v2(M,n,tf,q,lam):
Avars = []
for i in range(tf-1):
Avars.append(cvx.Variable(n,n))
Ltop = cvx.Variable(n,q)
Lbottom = np.zeros((n*(tf-1),q))
L = cvx.vstack(Ltop,Lbottom)
S = cvx.Variable(n*tf,q)
print("Check 1")
objective = cvx.Minimize(cvx.norm(L,"nuc") + lam*np.ones((1,n*tf))*cvx.abs(S)*np.ones((q,1)))
identity = np.eye(n)
print("Check 2")
constraints = [np.dot(identity,M[0:n,:])==Ltop+S[0:n,:]]
for i in range(tf-1):
constraints.append(-1*Avars[i]*M[(i*n):(i+1)*n,:] + np.dot(identity,M[((i+1)*n):(i+2)*n,:])==L[((i+1)*n):(i+2)*n,:]+S[((i+1)*n):(i+2)*n,:])
print("Check 3")
print(constraints)
prob = cvx.Problem(objective,constraints)
print("Check 4")
result = prob.solve(verbose = True)
print("Check 5")
Ltop_final = Ltop.value
Avars_final = []
for x in Avars:
Avars_final.append(x.value)
S_final = S.value
return (Avars_final,Ltop_final,Lbottom,S_final)
def _constraints(self, X, S, error_tolerance):
"""
Parameters
----------
X : np.array
Data matrix with missing values
S : cvxpy.Variable
Representation of solution variable
"""
missing_values = np.isnan(X)
self._check_missing_value_mask(missing_values)
# copy the array before modifying it
X = X.copy()
# zero out the NaN values
X[missing_values] = 0
ok_mask = ~missing_values
masked_X = cvxpy.mul_elemwise(ok_mask, X)
masked_S = cvxpy.mul_elemwise(ok_mask, S)
abs_diff = cvxpy.abs(masked_S - masked_X)
close_to_data = abs_diff <= error_tolerance
constraints = [close_to_data]
if self.require_symmetric_solution:
constraints.append(S == S.T)
if self.min_value is not None:
constraints.append(S >= self.min_value)
if self.max_value is not None:
constraints.append(S <= self.max_value)
return constraints
def _constraints(self, X, missing_mask, S, error_tolerance):
"""
Parameters
----------
X : np.array
Data matrix with missing values filled in
missing_mask : np.array
Boolean array indicating where missing values were
S : cvxpy.Variable
Representation of solution variable
"""
ok_mask = ~missing_mask
masked_X = cvxpy.mul_elemwise(ok_mask, X)
masked_S = cvxpy.mul_elemwise(ok_mask, S)
abs_diff = cvxpy.abs(masked_S - masked_X)
close_to_data = abs_diff <= error_tolerance
constraints = [close_to_data]
if self.require_symmetric_solution:
constraints.append(S == S.T)
if self.min_value is not None:
constraints.append(S >= self.min_value)
if self.max_value is not None:
constraints.append(S <= self.max_value)
return constraints
def cbp_taylor(y, F, Delta, penalty=0.1, order=1):
"""
1st order taylor approximation
"""
# generate derivative matrices
dF = list()
current = F
for i in range(order):
dF.append( deriv(current,t) )
current = dF[-1]
# Construct the problem.
Fp = cvxopt.matrix(F)
dFp = cvxopt.matrix(dF[0])
yp = cvxopt.matrix(y)
gamma = cp.Parameter(sign="positive", name='gamma')
gamma.value = penalty
x = cp.Variable(F.shape[1],name='x')
d = cp.Variable(F.shape[1],name='d')
objective = cp.Minimize(sum(cp.square(yp - Fp*x - dFp*d)) + gamma*cp.norm(x, 1))
constraints = [0 <= x, cp.abs(d) <= 0.5*Delta*x]
p = cp.Problem(objective, constraints)
# solve
result = p.solve()
# reconstruct
yhat = F.dot(np.array(x.value)) + dF[0].dot(np.array(d.value))
return np.array(x.value), yhat, np.array(d.value), p.value
def optimize_pos_basic(self, df):
w_target = df['pos']/df['pos'].abs().sum()
w_target = w_target.values
nassets=df.shape[0]
w = cvxpy.Variable(nassets)
obj = cvxpy.Minimize(cvxpy.norm(w-w_target))
constraints = [cvxpy.sum_entries(cvxpy.abs(w)) == 1.0]
constraints += [cvxpy.abs(cvxpy.sum_entries(w)) <= 0.1]
constraints += [cvxpy.abs(w) <= 1.0/nassets]
#constraints += [w >= 0]
prob = cvxpy.Problem(obj, constraints)
prob.solve(verbose=False, method='dccp')
return np.reshape(w.value, [nassets])
def get_constr_error(constr):
if isinstance(constr, cvx.constraints.EqConstraint):
error = cvx.abs(constr.args[0] - constr.args[1])
elif isinstance(constr, cvx.constraints.LeqConstraint):
error = cvx.pos(constr.args[0] - constr.args[1])
elif isinstance(constr, cvx.constraints.PSDConstraint):
mat = constr.args[0] - constr.args[1]
error = cvx.neg(cvx.lambda_min(mat + mat.T)/2)
return cvx.sum_entries(error)
def runndCVXPy(A, b, clambda):
n_vars = A.shape[1]
x = cvxpy.Variable(n_vars)
obj = cvxpy.Minimize(
clambda * cvxpy.sum_entries(cvxpy.abs(x)) +
0.5 * cvxpy.sum_entries(cvxpy.square(A * x - b)))
prob = cvxpy.Problem(obj, [])
prob.solve(verbose=False)
return x.value
def F(x=None, z=None):
if x is None: return 0, matrix(0.0,(n,1))
y = A*x+b
if max(abs(y)) >= 1.0: return None
f = -sum(log(1.0 - y**2))
gradf = 2.0 * A.T * div(y, 1-y**2)
if z is None: return f, gradf.T
H = A.T * spdiag(2.0*z[0]*div(1.0+y**2,(1.0-y**2)**2))*A
return f,gradf.T,H
def create(**kwargs):
m = kwargs["m"]
n = kwargs["n"]
k = 10
A = [problem_util.normalized_data_matrix(m,n,1) for i in range(k)]
B = problem_util.normalized_data_matrix(k,n,1)
c = np.random.rand(k)
x = cp.Variable(n)
t = cp.Variable(k)
f = cp.max_entries(t+cp.abs(B*x-c))
C = []
for i in range(k):
C.append(cp.pnorm(A[i]*x, 2) <= t[i])
t_eval = lambda: np.array([cp.pnorm(A[i]*x, 2).value for i in range(k)])
f_eval = lambda: cp.max_entries(t_eval() + cp.abs(B*x-c)).value
return cp.Problem(cp.Minimize(f), C), f_eval
def test_problem_penalty(self):
"""
Compare cvxpy solutions to cvxopt ground truth
"""
from cvxpy import (matrix,variable,program,minimize,
sum,abs,norm2,log,square,zeros,max,
hstack,vstack)
m, n = self.m, self.n
A = matrix(self.A)
b = matrix(self.b)
# set tolerance to 5 significant digits
tol_exp = 5
# l1 approximation
x = variable(n)
p = program(minimize(sum(abs(A*x + b))))
p.solve(True)
np.testing.assert_array_almost_equal(x.value,self.x1,tol_exp)
# l2 approximation
x = variable(n)
p = program(minimize(norm2(A*x + b)))
p.solve(True)
np.testing.assert_array_almost_equal(x.value,self.x2,tol_exp)
# Deadzone approximation - implementation is currently ugly (need max along axis)
x = variable(n)
Axbm = abs(A*x+b)-0.5
Axbm_deadzone = vstack([max(hstack((Axbm[i,0],0.0))) for i in range(m)])
p = program(minimize(sum(Axbm_deadzone)))
p.solve(True)
obj_dz_cvxpy = np.sum(np.max([np.abs(A*x.value+b)-0.5,np.zeros((m,1))],axis=0))
np.testing.assert_array_almost_equal(obj_dz_cvxpy,self.obj_dz,tol_exp)
# Log barrier
x = variable(n)
p = program(minimize(-sum(log(1.0-square(A*x + b)))))
p.solve(True)
np.testing.assert_array_almost_equal(x.value,self.cxlb,tol_exp)
def constraints(self):
cons = []
capacity_limit = [cp.abs(self.flow) <= self.capacity]
ptdf_constraint = [sum(gv.ptdf_matrix[self.uid,s.uid] * -1 * s.accumulation for s in \
gv.sources + gv.nodes if s.uid != gv.slack) == self.flow]
cons.extend(ptdf_constraint)
cons.extend(capacity_limit)
#ptdf_constraint = [cp.abs(sum(gv.ptdf_matrix[self.uid,s.uid] * -1 * s.accumulation for s in \
#gv.sources + gv.nodes if s.uid != gv.slack)) <= self.capacity]
#cons.extend(ptdf_constraint)
return cons
def solveMarkowitzConstraint(c, A, Q, qc, v, x0, bxl, bxu, bcl, bcu):
"""
Solves a convex program with a quadratic constraint and linear abs penalty
maximize c'*x - v'*abs{x - x0}
subject to bcl <= A*x <= bcu
bxl <= x <= bxu
sqrt(x'*Q*x) <= qc
"""
x = cvx.Variable(len(c))
constraints = [A*x <= bcu, bcl <= A*x, bxl <= x, x <= bxu, cvx.quad_form(x, Q) <= qc*qc]
objective = x.T*c - cvx.abs(x - x0).T*v
ccu.maximize(objective=objective, constraints=constraints)
return x.value
def setup_optim(users, xs, L, Ux, constraints, uo, lambda_=1e-2):
"""Compute all terms needed to define the optimization problem"""
(n, d), nx = users.shape, xs.shape[0]
weight = np.dot(np.ones(nx), np.dot(xs, xs.T))
laps = []
for m, xm in enumerate(xs):
k = np.matrix(np.kron(np.eye(n), xm[:, np.newaxis]))
vm = k.T*Ux
laps.append(cvx.quad_form(vm, L[m]))
weighted_laplacian = sum((w*l for w, l in zip(weight, laps)))
visible_users = sorted(set(range(n)) - set(uo))
visible_l1_norm = np.abs(users[visible_users, :]).sum()
regul = lambda_*(cvx.sum_entries(cvx.abs(Ux)) - visible_l1_norm)
obj = cvx.Minimize(weighted_laplacian + regul)
return cvx.Problem(obj, constraints)
def create_fused_lasso(W, g):
reg = 0
inds = W.nonzero()
rows = np.asarray(inds[0]).T.squeeze()
cols = np.asarray(inds[1]).T.squeeze()
if rows.size == 0 or len(rows.shape) == 0:
return reg
for i in range(rows.shape[0]):
row = rows[i]
col = cols[i]
if row == col:
continue
Wij = W[row,col]
'''
if i >= j or Lij == 0:
continue
'''
reg = reg + Wij*cvx.abs(g[row]-g[col])
return reg
def PROGRAM( roadnet, surplus, objectives ) :
""" construct the program """
# optvars
assist = dict()
cost = dict()
DELTA = .00001 # cvxpy isn't quite robust to non-full dimensional optimization
for _,__,road in roadnet.edges_iter( keys=True ) :
assist[road] = cvxpy.variable( name='z_{%s}' % road )
cost[road] = cvxpy.variable( name='c_{%s}' % road )
#print assist
#print cost
objfunc = sum( cost.values() )
OBJECTIVE = cvxpy.minimize( objfunc )
CONSTRAINTS = []
# the flow conservation constraints
for u in roadnet.nodes_iter() :
INFLOWS = []
for _,__,road in roadnet.in_edges( u, keys=True ) :
INFLOWS.append( assist[road] + surplus[road] )
OUTFLOWS = []
for _,__,road in roadnet.out_edges( u, keys=True ) :
OUTFLOWS.append( assist[road] )
#conserve_u = cvxpy.eq( sum(OUTFLOWS), sum(INFLOWS) )
error_u = sum(OUTFLOWS) - sum(INFLOWS)
conserve_u = cvxpy.leq( cvxpy.abs( error_u ), DELTA )
CONSTRAINTS.append( conserve_u )
# the cost-form constraints
for road in cost :
for f, line in objectives[road].iter_items() :
# is this plus or minus alpha?
LB = cvxpy.geq( cost[road], line.offset + line.slope * assist[road] )
CONSTRAINTS.append( LB )
prog = cvxpy.program( OBJECTIVE, CONSTRAINTS )
return prog, assist
def calculate_full_elicitation_euclideanpoint(data):
X = cvxpy.Variable(5) #1 point for each mechanism
fun = 0
for d in data:
y = [d['question_data']['slider' + str(slider) + '_loc'] for slider in range(5)]
w = [d['question_data']['slider' + str(slider) + '_weight'] for slider in range(5)]
sumsq = math.sqrt(sum([math.pow(w[i],2) for i in range(5)]))
w = [w[i] / sumsq for i in range(5)]
for slider in range(5):
fun += w[slider]*cvxpy.abs(X[slider] - y[slider])
obj = cvxpy.Minimize(fun)
constraints = [X >= 0, X[0] + X[1] + X[2] - X[3] + INITIALDEFICITADDITIVE == X[4]]
prob = cvxpy.Problem(obj, constraints)
result = prob.solve()
items = [X.value[i,0] for i in range(5)]
print 'Optimal full elicitation:', items
deficit = items[0] + items[1] + items[2] - items[3] + INITIALDEFICITADDITIVE
items.append(deficit)
return items
def mixing_sp(y_fit,ref1,ref2):
"""mix two reference spectra to match the given ones
Parameters
----------
y_fit : ndarray, shape m * n
an array containing the signals with m datapoints and n experiments
ref1 : ndarray, shape m
an array containing the first reference signal
ref2 : ndarray, shape m
an array containing the second reference signal
Returns
-------
out : ndarray, shape n
the fractions of ref1 in the mix
Notes
-----
Performs the calculation by minimizing the sum of the least absolute value of the objective function:
obj = sum(abs(y_fit-(ref1*F1 + ref2*(1-F1))))
Uses cvxpy to perform this calculation
"""
try:
import cvxpy
except ImportError:
print('ERROR: Install cvxpy>=1.0 to use this function.')
ref1 = ref1.reshape(1,-1)
ref2 = ref2.reshape(1,-1)
F1 = cvxpy.Variable(shape=(y_fit.shape[1],1))
objective = cvxpy.Minimize(cvxpy.sum(cvxpy.abs(F1*ref1 + (1-F1)*ref2 - y_fit.T)))
constraints = [0 <= F1, F1 <= 1]
prob = cvxpy.Problem(objective, constraints)
prob.solve()
return np.asarray(F1.value).reshape(-1)
def to_cvxpy(self, weight_var, weight_var_series, init_weights):
# 在原权重中分别找出多头与空头权重序列
long_w = init_weights[init_weights >= 0]
short_w = init_weights[init_weights < 0]
# 为使shape一致，需要使用fillna，以0值填充
common_index = long_w.index.union(short_w.index).unique()
# 与其值无关
# long_w = long_w.reindex(common_index).fillna(0)
# short_w = short_w.reindex(common_index).fillna(0)
# 找到涉及到变量的位置
ix = get_ix(weight_var_series, common_index)
# 如果没有相应位置序列，则返回空限制(即无限制)
if len(ix) == 0:
return []
# 限定其和的绝对值不超过容忍阀值
return [
cvx.abs(cvx.sum(weight_var[ix])) <= self.tolerance,
]
def lr_recover_l1(invecs, intensities, nonneg=True, **kwargs):
"""Computes the low-rank matrix reconstruction using l1-minimisation
.. math::
\min_Z \sum_i \vert \langle a_i| Z | a_i \rangle - y_i \vert \\
\mathrm{s.t.} Z \ge 0
where :math:`a_i` are the input vectors and :math:`y_i` are the measured
intensities.
For the arguments not listed see :func:`recover`
:param bool nonneg: Enfornce the constraint Z >= 0 (default True)
:param kwargs: Additional arguemnts passed to `cvx.Problem.solve`
:returns: array of shape (dim, dim); Low-rank matrix approximation for
given measurements
"""
dim = invecs.shape[1]
# we have to manually convert convex programm to real form since cvxpy
# does not support complex programms
z, mat_cons = _semidef_complex_as_real(dim) if nonneg else \
_hermitian_as_real(dim)
invecs_real = np.concatenate((invecs.real, invecs.imag), axis=1)
obj = cvx.Minimize(
sum(
cvx.abs(cvx.quad_form(a, z) - y)
for a, y in zip(invecs_real, intensities)))
prob = cvx.Problem(obj, mat_cons)
prob.solve(**kwargs)
if prob.status not in ['optimal', 'optimal_inaccurate']:
raise RuntimeError("Optimization did not converge: " + prob.status)
return z.value[:dim, :dim] + 1.j * z.value[dim:, :dim]
def objective(matrices_list):
error_terms: Vector = []
is_data_real: bool = data_type in [np.float32, np.float64]
for k1, k2, m in product(range(signal_length), repeat=3):
other_index = (k2 - k1) % signal_length
k1_plus_m = (k1 + m) % signal_length
current_term = tri_spectrum[k1, k1_plus_m, (k2 + m) % signal_length]
current_term -= matrices_list[other_index][k1, k1_plus_m]
current_term -= matrices_list[m][k1, k2]
if is_data_real:
next_index: int = (k1 + k2 + m) % signal_length
current_term -= matrices_list[next_index][
- k2 % signal_length, (-k2 - m) % signal_length]
error_terms.append(current_term)
if use_cp:
fit_score = cp.sum([cp.abs(term) ** 2 for term in error_terms])
else:
fit_score = np.sum([np.abs(term) ** 2 for term in error_terms])
return fit_score
def multiple_regress_l1(x, y, reg_param):
"""
Function to return the fitted coefficients and intercept for
a matrix of covariates and a matrix of targets with complete l1 regularization
Arguments:
- x: matrix of size (n x d_x)
- y: matrix of size (n x d_y)
- reg_param: float
"""
n, d_x = x.shape
n, d_y = y.shape
W = cvx.Variable((d_y, d_x))
b = cvx.Variable((1, d_y))
obj = cvx.sum_squares(y - x @ W.T - np.ones((711, 1)) @ b)
reg_obj = obj + reg_param * cvx.sum(cvx.abs(W))
problem = cvx.Problem(cvx.Minimize(reg_obj))
problem.solve()
if problem.status == cvx.OPTIMAL:
return (W.value, b.value)
else:
raise Exception("Solver not converged")
def get_constraints(self, X_v, U_v, X_last_p, U_last_p):
"""
Get model specific constraints.
:param X_v: cvx variable for current states
:param U_v: cvx variable for current inputs
:param X_last_p: cvx parameter for last states
:param U_last_p: cvx parameter for last inputs
:return: A list of cvx constraints
"""
# Boundary conditions:
constraints = [
X_v[:, 0] == self.x_init, X_v[:, -1] == self.x_final,
U_v[:, 0] == 0, U_v[:, -1] == 0
]
# Input conditions:
constraints += [
0 <= U_v[0, :],
U_v[0, :] <= self.v_max,
cvx.abs(U_v[1, :]) <= self.w_max,
]
# State conditions:
constraints += [
X_v[0:2, :] <= self.upper_bound - self.robot_radius,
X_v[0:2, :] >= self.lower_bound + self.robot_radius,
]
# linearized obstacles
for j, obst in enumerate(self.obstacles):
p = obst[0]
r = obst[1] + self.robot_radius
lhs = [(X_last_p[0:2, k] - p) / (cvx.norm(
(X_last_p[0:2, k] - p)) + 1e-6) * (X_v[0:2, k] - p)
for k in range(K)]
constraints += [r - cvx.vstack(lhs) <= self.s_prime[j]]
return constraints
def build(self, structures, exact=False): """ Update :mod:`cvxpy` optimization based on structure data. Extract dose matrix, target doses, and objective weights from structures. Use doses and weights to add minimization terms to :attr:`SolverCVXPY.problem.objective`. Use dose constraints to extend :attr:`SolverCVXPY.problem.constraints`. (When constraints include slack variables, a penalty on each slack variable is added to the objective.) Arguments: structures: Iterable collection of :class:`Structure` objects. Returns: :obj:`str`: String documenting how data in ``structures`` were parsed to form an optimization problem. """ self.clear() if isinstance(structures, Anatomy): structures = structures.list A, dose, weight_abs, weight_lin = \ self._Solver__gather_matrix_and_coefficients(structures) self.problem.objective = cvxpy.Minimize( weight_abs.T * cvxpy.abs(A * self.__x - dose) + weight_lin.T * (A * self.__x - dose)) for s in structures: self.__add_constraints(s, exact=exact) return self._Solver__construction_report(structures)
def optimizeRelationships(relPred,relNodes,gtNodeNeighbors,penalty=490):
#if 'cvxpy' not in sys.modules:
import cvxpy
useRel = cvxpy.Variable(relPred.size(0),boolean=True)
obj =0
huh=0
for i in range(relPred.size(0)):
obj += relPred[i].item()*useRel[i]
huh +=useRel[i]
constraint = [0]*len(gtNodeNeighbors)
for i in range(len(gtNodeNeighbors)):
relI=0
for a,b in relNodes:
j=None
if a==i:
j=b
elif b==i:
j=a
if j is not None:
constraint[i] += useRel[relI]
relI+=1
constraint[i] -= gtNodeNeighbors[i]
#obj -= cvxpy.power(penalty,(cvxpy.abs(constraint[i]))) #this causes it to not miss on the same node more than once
constraint[i] = cvxpy.abs(constraint[i])
obj -= penalty*constraint[i]
cs=[]
for i in range(len(gtNodeNeighbors)):
cs.append(constraint[i]<=1)
problem = cvxpy.Problem(cvxpy.Maximize(obj),cs)
#problem.solve(solver=cvxpy.GLPK_MI)
problem.solve(solver=cvxpy.ECOS_BB)
assert(useRel.value is not None)
return useRel.value
def test_quad_form(self) -> None:
"""Test gradient for quad_form.
"""
# Issue 1260
n = 10
np.random.seed(1)
P = np.random.randn(n, n)
P = P.T @ P
q = np.random.randn(n)
# define the optimization problem with the 2nd constraint as a quad_form constraint
x = cp.Variable(n)
prob = cp.Problem(
cp.Maximize(q.T @ x - (1 / 2) * cp.quad_form(x, P)),
[
cp.norm(x, 1) <= 1.0,
cp.quad_form(x, P) <= 10, # quad form constraint
cp.abs(x) <= 0.01
])
prob.solve(solver=cp.SCS)
# access quad_form.expr.grad without error
prob.constraints[1].expr.grad
def run_opt(self):
""" Run optimization for the worst case risk over possible covariance matrices """
sigma_opt = cp.Variable((self.n, self.n),
PSD=True) # positive semi-definite
delta = cp.Variable(
(self.n, self.n), symmetric=True
) # difference between the input covar and the testing ones
risk = cp.quad_form(self.w, sigma_opt)
# elementwise delta constrained and must be zero on diagonals
constraints_ls = [
sigma_opt == self.sigma + delta,
cp.diag(delta) == 0,
cp.abs(delta) <= 0.2
]
prob = cp.Problem(cp.Maximize(risk), constraints_ls)
prob.solve()
return {
'actual_std': cp.sqrt(cp.quad_form(self.w, self.sigma)).value,
'worst_case_std': cp.sqrt(risk).value,
'delta': delta.value
}
def nucmin_estimator(A, y, eta=None, **kwargs):
"""@todo: Docstring for nucmin_estimator.
:param A: @todo
:param y: @todo
:param **kwargs: @todo
:returns: @todo
"""
x_sharp = cvx.Variable(A.shape[1], A.shape[2])
objective = cvx.Minimize(cvx.normNuc(x_sharp))
if eta is None:
constraints = [_expval(A, x_sharp) == y]
else:
constraints = [cvx.abs(_expval(A, x_sharp) - y) < eta]
problem = cvx.Problem(objective, constraints)
problem.solve(**kwargs)
if problem.status not in ['optimal']:
raise ValueError("Optimization did not converge: " + problem.status)
return np.array(x_sharp.value)
def _init_constraints(self, parameters, init_model_constraints):
# Upper constraints from initial model
l1_w = init_model_constraints["w_l1"]
init_loss = init_model_constraints["loss"]
C = parameters["C"]
epsilon = parameters["epsilon"]
# New Variables
self.w = cvx.Variable(shape=(self.d), name="w")
self.b = cvx.Variable(name="b")
self.slack = cvx.Variable(shape=(self.n), nonneg=True, name="slack")
# New Constraints
distance_from_plane = cvx.abs(self.y - (self.X * self.w + self.b))
self.loss = cvx.sum(self.slack)
self.weight_norm = cvx.norm(self.w, 1)
self.add_constraint(distance_from_plane <= epsilon + self.slack)
self.add_constraint(self.weight_norm <= l1_w)
self.add_constraint(C * self.loss <= C * init_loss)
self.feature_relevance = cvx.Variable(nonneg=True, name="Feature Relevance")
def __init__(self,
problemType,
di=None,
kwargs=None,
X=None,
Y=None,
initLoss=None,
initL1=None,
parameters=None,
presetModel=None):
super().__init__(problemType,
di=di,
kwargs=kwargs,
X=X,
Y=Y,
initLoss=initLoss,
initL1=initL1,
parameters=parameters,
presetModel=presetModel)
self._constraints.extend([cvx.abs(self.omega[self.di]) <= self.xp])
self._objective = cvx.Minimize(self.xp)
def mixing_sp(y_fit, ref1, ref2):
"""mix two reference spectra to match the given ones
Parameters
----------
y_fit : ndarray, shape m * n
an array containing the signals with m datapoints and n experiments
ref1 : ndarray, shape m
an array containing the first reference signal
ref2 : ndarray, shape m
an array containing the second reference signal
Returns
-------
out : ndarray, shape n
the fractions of ref1 in the mix
Notes
-----
Performs the calculation by minimizing the sum of the least absolute value of the objective function:
obj = sum(abs(y_fit-(ref1*F1 + ref2*(1-F1))))
Uses cvxpy to perform this calculation
"""
F1 = cvxpy.Variable(y_fit.shape[1], 1)
objective = cvxpy.Minimize(
cvxpy.sum_entries(
cvxpy.abs((F1 * ref1.reshape(1, -1) +
(1 - F1) * ref2.reshape(1, -1)) - np.transpose(y_fit))))
constraints = [0 <= F1, F1 <= 1]
prob = cvxpy.Problem(objective, constraints)
prob.solve()
return np.asarray(F1.value).reshape(-1)
def fit_MIP(self, x, y):
n_points = x.shape[0]
n_feat = x.shape[1]
w = cp.Variable(shape=n_feat)
# Additional variables representing the actual predictions.
yhat = cp.Variable(shape=n_points, boolean=True)
bigM = 1e3
constraints = [
(yhat-1) * bigM <= x @ w,
yhat * bigM >= x @ w,
]
fairness = 0
for key, Ip in self.I_train.items():
Np = np.sum(Ip)
if Np >= 0:
# tmp = 2 * (cp.sum(x @ w) / n_points -
# cp.sum(cp.multiply(Ip, (x @ w))) / Np)
tmp = 2 * (cp.sum(yhat) / n_points -
cp.sum(cp.multiply(Ip, yhat)) / Np)
fairness += cp.abs(tmp)
loglike = -self.log_likelihood(x, y, w) / n_points
fair_reg = self.alpha * fairness
w_reg = self.gamma * cp.sum_squares(w)
obj_fct = loglike + fair_reg + w_reg
prob = cp.Problem(cp.Minimize(obj_fct), constraints)
prob.solve()
# prob.solve(verbose=False, solver=cp.SCS)
# prob.solve(verbose=True, solver=cp.ECOS, feastol=1e-5, abstol=1e-5)
print("Value of log likelihood: %.3f" % loglike.value)
print("Value of fairness regularization: %.3f" % fairness.value)
self.w = w.value
def minSet(test, gap): # A = eigentable
m = test.shape[1]
# https://www.cvxpy.org/examples/applications/sparse_solution.html#iterative-log-heuristic
delta = 1e-8 # threshold for 0
NUM_RUNS = 30
nnzs_log = np.array(()) # (cardinality of p) for each run
W = cp.Parameter(shape=m, nonneg=True)
p = cp.Variable(shape=m, nonneg=True)
W.value = np.ones(m)
# Initial weights
obj = cp.Minimize(W.T * cp.abs(p))
constraints = [cp.sum(p) == 1, test * p <= 1 - gap]
prob = cp.Problem(obj, constraints)
for k in range(1, NUM_RUNS + 1):
# The ECOS solver has known numerical issues with this problem
# so force a different solver.
prob.solve(solver=cp.GLPK)
# Check for error.
if prob.status != cp.OPTIMAL:
raise Exception("Solver did not converge!")
# Display new number of nonzeros in the solution vector.
nnz = (np.absolute(p.value) > delta).sum()
nnzs_log = np.append(nnzs_log, nnz)
# print('Iteration {}: Found a feasible p in R^{}'
# ' with {} nonzeros...'.format(k, n, nnz))
# Adjust the weights elementwise and re-iterate
W.value = np.ones(m) / (delta * np.ones(m) + np.absolute(p.value))
return (p.value, nnz)
def remove_dc_from_spad(noisy_spad,
bin_edges,
bin_weight,
lam=1e-2,
eps_rel=1e-5):
"""
Works in numpy.
:param noisy_spad: Length C array with the raw spad histogram to denoise.
:param bin_edges: Length C+1 array with the bin widths in meters of the original bins.
:param bin_weight: Length C nonnegative array controlling relative strength of L1 regularization on each bin.
:param lam: float value controlling strength of overall L1 regularization on the signal
:param eps: float value controlling precision of solver
"""
assert len(noisy_spad.shape) == 1
C = noisy_spad.shape[0]
assert bin_edges.shape == (C + 1, )
bin_widths = bin_edges[1:] - bin_edges[:-1]
spad_equalized = noisy_spad / bin_widths
x = cp.Variable((C, ), "signal")
z = cp.Variable((1, ), "noise")
print("lam", lam)
print("eps_rel", eps_rel)
# print("spad_equalized", spad_equalized)
orig_sum = np.sum(spad_equalized)
spad_normalized = spad_equalized / orig_sum
obj = cp.Minimize(
cp.sum_squares(spad_normalized - (x + z)) +
lam * cp.sum(bin_weight * cp.abs(x)))
constr = [
x >= 0,
# z >= 0
]
prob = cp.Problem(obj, constr)
prob.solve(solver=cp.OSQP, eps_rel=eps_rel)
print("z.value", z.value)
denoised_spad = np.clip(x.value * bin_widths, a_min=0., a_max=None)
return denoised_spad
def solve_cvx(p0, v0, pk, vk, K):
'''Solve convex optimization problem for trajectory and thruster direction'''
# create problem variables
f_k = cp.Variable((K, 2))
v_k = cp.Variable((K + 1, 2))
p_k = cp.Variable((K + 1, 2))
# create problem constrains
constraints = [
p_k[0, :] == p0, v_k[0, :] == v0, p_k[-1, :] == pk, v_k[-1, :] == vk
]
e2 = np.zeros(2)
e2[1] = 1.0
for i in range(K):
constraints.append(v_k[i + 1, :] == v_k[i, :] + (h / m) * f_k[i, :] -
h * g * e2)
constraints.append(p_k[i + 1, :] == p_k[i, :] + (h / 2) *
(v_k[i, :] + v_k[i + 1, :]))
constraints.append(p_k[i, 1] >= alpha * cp.abs(p_k[i, 0]))
constraints.append(cp.norm(f_k[i, :]) <= Fmax)
# form objective
# minimum fuel descent
# obj = cp.Minimize(gamma * h * cp.sum(cp.norm(f_k, axis=1)))
# minimum time descent
obj = cp.Minimize(0)
# form and solve the problem
prob = cp.Problem(obj, constraints)
prob.solve()
# print result
# print("status:", prob.status)
# print("optimal value", prob.value)
# print("")
return p_k.T.value, f_k.T.value, prob
def _calculate_objective(self, mu_l, mu_r, tau, l_cs_value, r_cs_value,
beta_value, weights, sum_components=True):
weights_w1 = np.diag(weights)
# Note: Not using cvx.sum and cvx.abs as in following caused
# an error at * weights_w1:
# ValueError: operands could not be broadcast together with shapes
# (288,1300) (1300,1300)
# term_f1 = sum((0.5 * abs(
# self._power_signals_d - l_cs_value.dot(r_cs_value))
# + (tau - 0.5)
# * (self._power_signals_d - l_cs_value.dot(r_cs_value)))
# * weights_w1)
term_f1 = (cvx.sum((0.5 * cvx.abs(
self._power_signals_d - l_cs_value.dot(r_cs_value))
+ (tau - 0.5) * (self._power_signals_d - l_cs_value.dot(
r_cs_value))) * weights_w1)).value
weights_w2 = np.eye(self._rank_k)
term_f2 = mu_l * norm((l_cs_value[:-2, :] - 2 * l_cs_value[1:-1, :] +
l_cs_value[2:, :]).dot(weights_w2), 'fro')
term_f3 = mu_r * norm(r_cs_value[:, :-2] - 2 * r_cs_value[:, 1:-1] +
r_cs_value[:, 2:], 'fro')
if r_cs_value.shape[1] < 365 + 2:
term_f4 = 0
else:
# Note: it was cvx.norm. Check if this modification makes a
# difference:
# term_f4 = (mu_r * norm(
# r_cs_value[1:, :-365] - r_cs_value[1:, 365:], 'fro'))
term_f4 = ((mu_r * cvx.norm(
r_cs_value[1:, :-365] - r_cs_value[1:, 365:], 'fro'))).value
components = [term_f1, term_f2, term_f3, term_f4]
objective = sum(components)
if sum_components:
return objective
else:
return components
def calc_objective(self, sum_components=True):
W1 = np.diag(self.weights)
f1 = (cvx.sum(
(0.5 * cvx.abs(self.D - self.L_cs.value.dot(self.R_cs.value)) +
(self.tau - 0.5) *
(self.D - self.L_cs.value.dot(self.R_cs.value))) * W1)).value
W2 = np.eye(self.k)
f2 = self.mu_L * norm(
((self.L_cs[:-2, :]).value - 2 * (self.L_cs[1:-1, :]).value +
(self.L_cs[2:, :]).value).dot(W2), 'fro')
f3 = self.mu_R * norm(
(self.R_cs[:, :-2]).value - 2 * (self.R_cs[:, 1:-1]).value +
(self.R_cs[:, 2:]).value, 'fro')
if self.R_cs.shape[1] < 365 + 2:
f4 = 0
else:
f4 = (self.mu_R * cvx.norm(
self.R_cs[1:, :-365] - self.R_cs[1:, 365:], 'fro')).value
components = [f1, f2, f3, f4]
objective = sum(components)
if sum_components:
return objective
else:
return components
def relax(self):
return [cvx.abs(self) <= self.M]
def objective_state(self):
return sum(
cvxpy.abs(link.state.flow - link.v_flow) +
cvxpy.abs(link.state.density - link.v_dens)
for link in self.get_links()
)
def opt_actor(l1, l2, l3, max_a, K, A=None, B=None, strict=True):
W1 = l1.weight.data.clone().cpu().numpy()
W2 = l2.weight.data.clone().cpu().numpy()
W3 = l3.weight.data.clone().cpu().numpy()
b1 = l1.bias.data.clone().unsqueeze(-1).cpu().numpy()
b2 = l2.bias.data.clone().unsqueeze(-1).cpu().numpy()
b3 = l3.bias.data.clone().unsqueeze(-1).cpu().numpy()
W1p = W1.copy()
b1p = b1.copy()
idx1 = (b1p < 0).nonzero()
idx1 = (idx1[0], np.vstack((idx1[1], idx1[1] + 1)))
b1p[b1p < 0] = 0
W1p[idx1] = 0
W2W1p = W2 @ W1p
W2b1pb2 = W2 @ b1p + b2
W2W1p_p = W2W1p.copy()
W2b1pb2_p = W2b1pb2.copy()
idx2 = (W2b1pb2_p < 0).nonzero()
idx2 = (idx2[0], np.vstack((idx2[1] + i for i in range(W2W1p_p.shape[1]))))
W2b1pb2_p[W2b1pb2_p < 0] = 0
W2W1p_p[idx2] = 0
K = torch.Tensor(K).numpy()
Wopt = cp.Variable(W3.shape)
bopt = cp.Variable(b3.shape)
iterations = 0
if strict:
cost = 0
constraints = []
constraints.append(max_a * (Wopt @ W2W1p_p) + K == 0)
constraints.append(Wopt @ (W2b1pb2_p) + bopt == 0)
cost += cp.norm(Wopt - W3)
cost += 0.5 * cp.norm(bopt - b3)
obj = cp.Minimize(cost)
prob = cp.Problem(obj, constraints)
prob.solve()
else:
eps = 0.0001
nu_k = 1
done = False
while not done:
iterations += 1
cost = 0
constraints = []
constraints.append(cp.abs(Wopt @ (W2b1pb2_p) + bopt) <= eps)
cost += cp.norm(Wopt - W3)
cost += nu_k * cp.norm(max_a * (Wopt @ W2W1p_p) + K)
obj = cp.Minimize(cost)
prob = cp.Problem(obj, constraints)
prob.solve()
done = np.all(
np.linalg.eig(A + B @ (max_a * Wopt.value @ W2W1p_p +
Wopt.value @ (W2b1pb2_p) + bopt.value))
[0] < 0)
nu_k *= nu_k * 1.1
# print('Optimization complete for Actor.')
# print(f'CVX Problem Status: {prob.status}')
# print(f'CVX Objective Value: {prob.value}')
# print(f'--------------------------------------------')
# print(f"Last layer diff: {np.linalg.norm(Wopt.value - W3)}")
# print(f"LQR Fit: {np.linalg.norm(max_a*Wopt.value@W2W1p_p + K) + np.linalg.norm(Wopt.value @ (W2b1pb2_p) + bopt.value)}")
# print(f"Max Closed Loop Eval: {np.max(np.linalg.eig(A + B @ (max_a*Wopt.value @ W2W1p_p + Wopt.value @ (W2b1pb2_p) + bopt.value))[0])}")
# print(f'--------------------------------------------')
l3.weight.data = torch.from_numpy(Wopt.value).to(device).float()
l3.bias.data = torch.from_numpy(bopt.value).squeeze(-1).to(device).float()
return None
def solve(playery,
playerVelY,
lowerPipes,
prev_flaps,
prev_path,
est_y=0,
std_y=100):
pipeVelX = -4 # speed in x
playerAccY = 1 # players downward accleration
playerFlapAcc = -14 # players speed on flapping
# unpack path variables
y = path[:, 0]
vy = path[:, 1]
c = [] # init constraint list
c += [y <= GROUND, y >= SKY] # constraints for sky and ground
c += [y[0] == playery, vy[0] == playerVelY] # initial conditions
obj = 0
x = PLAYERX
xs = [x] # init x list
for t in range(N - 1): # look ahead
dt = t // 15 + 1 # let time get coarser further in the look ahead
x -= dt * pipeVelX # update x
xs += [x] # add to list
c += [vy[t + 1] == vy[t] + playerAccY * dt + playerFlapAcc * flap[t]
] # add y velocity constraint, f=ma
c += [y[t + 1] == y[t] + vy[t + 1] * dt] # add y constraint, dy/dt = a
pipe_c, dist = getPipeConstraintsDistance(
x, y[t + 1], lowerPipes) # add pipe constraints
c += pipe_c
obj += dist
# New code for terminal constraint
# Pipe Region:
if lowerPipes[-1]['x'] < 181 and 181 < lowerPipes[-1]['x'] + 52:
c += [
y[t + 1] >= (lowerPipes[-1]['y'] - 100) + cvx.square(vy[t + 1]) / 2
]
else:
pass
# Btwn-Pipe Region
if lowerPipes[-1]['x'] > 181:
n = abs((lowerPipes[-1]['x'] - 181) / 4)
c += [
y[t + 1] >=
(lowerPipes[-1]['y'] - 100) - n * (n - 1) / 2 - vy[t + 1] * n
]
pass
# Add c1 and check if terminal set within gpr stddev is feasible
c1 = c + [y[t + 1] >= est_y - std_y] + [y[t + 1] <= est_y + std_y]
objective = cvx.Minimize(cvx.sum(cvx.abs(vy)) + 100 * obj)
if std_y < 50:
prob = cvx.Problem(objective, c1) # if low std, use the strategy
else:
prob = cvx.Problem(
objective,
c) # if high standard deviation, do not solve with the strategy
try: # try solving problem with c1, otherwise try using c
prob.solve(verbose=False, solver="GUROBI")
new_path = list(zip(xs, y.value)) # store the path
new_flaps = np.round(flap.value).astype(bool) # store the solution
return new_flaps, new_path # return the one-step flap, and the entire path
except:
try:
prob = cvx.Problem(objective, c)
prob.solve(verbose=False, solver="GUROBI")
new_path = list(zip(xs, y.value)) # store the path
new_flaps = np.round(flap.value).astype(bool) # store the solution
return new_flaps, new_path # return the one-step flap, and the entire path
except:
new_flaps = prev_flaps[
1:] # if we didn't get a solution this round, use the inputs and flaps from the last solve iter
new_path = [((x - 4), y) for (x, y) in prev_path[1:]]
if len(prev_flaps) < 12:
#print('returning false')
return [False], [(0, 0), (0, 0)]
else:
#print('is this what is causing the error')
return new_flaps, new_path
for j in range(i + 1, n):
constr.append(
cvx.norm(cvx.vec(c[i, :] - c[j, :]), 2) >= r[i] + r[j])
# prob = Problem(
# Minimize(
# cvx.max(
# cvx.max(cvx.abs(c), axis=1) + r # max dim = c_max + r
# )
# ),
# constr
# )
prob = Problem(
Minimize(
cvx.max(cvx.abs(c[:, 0]) + r) + cvx.max(cvx.abs(c[:, 1]) + r)),
constr)
print(prob.is_dcp(), prob.is_dcp())
print(dccp.is_dccp(prob))
prob.solve(method='dccp',
solver='ECOS',
ep=1e-2,
max_slack=1e-2,
verbose=True)
l = cvx.max(cvx.max(cvx.abs(c), axis=1) + r).value * 2
pi = np.pi
ratio = pi * cvx.sum(cvx.square(r)).value / cvx.square(l).value
print("ratio =", ratio)
def reachable(T, s0, sT, cost, dynamics, max_dtheta, max_theta, max_ddx,
max_line_search=30, show_results=lambda *a:None):
"""Find control signals u_1...u_T, u_t=(ddx_t,dtheta_t) and the
ensuing states s_1...s_T that
minimize L(s_0,...,s_{T-1})
subject to s_t = f(s_{t-1}, u_t)
| dtheta_t | < max_dtheta
| ddx_t | < max_ddx
One of sT or cost must be None. if sT is set, then
L = || s_{t-1} - sT ||
otherwise, it is
L = sum_{t=0}^{T-1} cost(s_t)
Solves this as a Sequential Quadratic program by approximating L by
a quadratic and f by an affine function.
"""
s0 = array(s0)
if sT is not None:
sT = array(sT)
assert (cost is None) != (sT is None), 'only one of cost or sT may be specified'
# initial iterates and objective terms
Sv = [s0] * T
Uv = [None] + [zeros(2)]*T
L = None
if cost:
L = [cost(s0)['val']] * T
last_obj = None # last objective value attained
step = 1. # last line search step size
iters = 0
n_line_searches = 0
while True:
show_results(Sv, L, '%d, %d line searches so far. step size %g'%(iters,
n_line_searches,
step))
iters += 1
# variables, objective, and constraints of the quadratic problem
S = [None] * T
U = [None] * T
S[0] = CX.Parameter(5, name='s0')
S[0].value = s0
constraints = []
if cost:
objective = zeros(1)
# define the QP
for t in xrange(1,T):
# f(u_t, s_{t-1}) and its derivatives
f = dynamics(Sv[t-1], Uv[t], {'du','ds'})
dfds = vstack(f['ds'])
dfdu = vstack(f['du'])
# define u_t and s_t
U[t] = CX.Variable(2, name='u%d'%t)
S[t] = CX.Variable(5, name='s%d'%t)
# constraints:
# s_t = linearized f(s_t-1, u_t) about previous iterate
# and bounds on s_t and u_t
constraints += [
S[t] == f['val'] + dfds*(S[t-1]-Sv[t-1]) + dfdu*(U[t]-Uv[t]),
CX.abs(U[t][0]) <= max_ddx,
CX.abs(U[t][1]) <= max_dtheta,
CX.abs(S[t][4]) <= max_theta ]
if cost:
# accumulate objective
c = cost(Sv[t], derivs={'ds','ds2'})
c['ds2'] = make_psd(c['ds2'])
objective += c['val'] + (S[t]-Sv[t]).T*c['ds'] + 0.5*CX.quad_form(S[t]-Sv[t],
c['ds2'])
if sT is not None:
# objective is || s_t - sT ||
objective = CX.square(CX.norm(S[T-1] - sT))
# solve for S and U
p = CX.Problem(CX.Minimize(objective), constraints)
r = p.solve(solver=CX.CVXOPT, verbose=False)
assert isfinite(r)
# line search on U, from Uv along U-Uv
line_search_failed = True
while n_line_searches < max_line_search:
n_line_searches += 1
# compute and apply the controls along the step
Us = []
Svs = [s0]
for u,u0 in zip(U[1:],Uv[1:]):
# a step along the search direction
us = u0 + step * (ravel(u.value)-u0)
# make it feasible
us[0] = clip(us[0], -max_ddx, max_ddx)
us[1] = clip(us[1], -max_dtheta, max_dtheta)
Us.append(us)
# apply controls
Svs.append( sim.apply_control(Svs[-1], us)['val'] )
# objective value based on the last state
if cost:
L = [ cost(s)['val'] for s in Svs ]
obj = sum(L)
else:
obj = sum((Svs[-1]-sT)**2)
if last_obj is None or obj < last_obj:
step *= 1.1 # lengthen the step for the next round
line_search_failed = False # converged
break
else:
step *= 0.7 # shorten the step and try again
if line_search_failed: # converged
break # throw away this iterate
else:
# accept the iterate
Sv = Svs
Uv = [None] + Us
last_obj = obj
return Sv,Uv
def _control(self, reference_state, predicted_state, reference_steer):
"""
Solve the MPC control problem.
:param reference_state: np.array of reference states
:param predicted_state: np.array of predicted states obtained using propogated controls
:param reference_steer: np.array of reference steering
:return:
"""
# intialize problem
x = cvxpy.Variable((self.num_state, self.config['horizon'] + 1))
u = cvxpy.Variable((self.num_input, self.config['horizon']))
cost = constants.Constant(0.0)
constraints = []
# iterate over the horizon
for t in range(self.config['horizon']):
cost += cvxpy.quad_form(u[:, t], self.config['R'])
if t != 0:
cost += cvxpy.quad_form(reference_state[:, t] - x[:, t],
self.config['Q'])
matrix_a, matrix_b, matrix_c = self._linearized_model_matrix(
predicted_state[2, t], predicted_state[3, t],
reference_steer[0, t])
constraints += [
x[:,
t + 1] == matrix_a * x[:, t] + matrix_b * u[:, t] + matrix_c
]
if t < (self.config['horizon'] - 1):
cost += cvxpy.quad_form(u[:, t + 1] - u[:, t],
self.config['Rd'])
constraints += [
cvxpy.abs(u[1, t + 1] - u[1, t]) <=
self.vehicle.config['max_steer_speed'] * self.delta_t
]
# set the cost
cost += cvxpy.quad_form(
reference_state[:, self.config['horizon']] -
x[:, self.config['horizon']], self.config['Qf'])
# set the constraints
constraints += [x[:, 0] == self.vehicle.get_state()]
constraints += [x[2, :] <= self.vehicle.config['max_vel']]
constraints += [x[2, :] >= self.vehicle.config['min_vel']]
constraints += [u[0, :] <= self.vehicle.config['max_accel']]
constraints += [u[0, :] >= self.vehicle.config['min_accel']]
constraints += [u[1, :] <= self.vehicle.config['max_steer']]
constraints += [u[1, :] >= self.vehicle.config['min_steer']]
# solve the problem
prob = cvxpy.Problem(cvxpy.Minimize(cost), constraints)
prob.solve(solver=cvxpy.OSQP, verbose=False, warm_start=True)
# keep track of optimality
solved = False
if prob.status == cvxpy.OPTIMAL or \
prob.status == cvxpy.OPTIMAL_INACCURATE:
solved = True
# return solution
horizon_x = np.array(x.value[0, :]).flatten()
horizon_y = np.array(x.value[1, :]).flatten()
horizon_vel = np.array(x.value[2, :]).flatten()
horizon_yaw = np.array(x.value[3, :]).flatten()
horizon_accel = np.array(u.value[0, :]).flatten()
horizon_steer = np.array(u.value[1, :]).flatten()
return horizon_x, horizon_y, horizon_vel, horizon_yaw, horizon_accel, horizon_steer, solved
def solve_group_SDP(
Sigma,
groups=None,
verbose=False,
objective="abs",
norm_type=2,
num_iter=10,
tol=1e-2,
**kwargs,
):
""" Solves the group SDP problem: extends the
formulation from Barber and Candes 2015/
Candes et al 2018 (MX Knockoffs). Note this will be
much faster with equal-sized groups and objective="abs."
:param Sigma: true covariance (correlation) matrix,
p by p numpy array.
:param groups: numpy array of length p with
integer values between 1 and m.
:param verbose: if True, print progress of solver
:param objective: How to optimize the S matrix for
group knockoffs. (For ungrouped knockoffs, using the
objective = 'abs' is strongly recommended.)
There are several options:
- 'abs': minimize sum(abs(Sigma - S))
between groups and the group knockoffs.
- 'pnorm': minimize Lp-th matrix norm.
Equivalent to abs when p = 1.
- 'norm': minimize different type of matrix norm
(see norm_type below).
:param norm_type: Means different things depending on objective.
- When objective == 'pnorm', i.e. objective is Lp-th matrix norm,
which p to use. Can be any float >= 1.
- When objective == 'norm', can be 'fro', 'nuc', np.inf, or 1
(i.e. which other norm to use).
Defaults to 2.
:param num_iter: We do a line search and scale S at the end to make
absolutely sure there are no numerical errors. Defaults to 10.
:param tol: Minimum eigenvalue of S must be greater than this.
"""
# By default we lower the convergence epsilon a bit for drastic speedup.
if "eps" not in kwargs:
kwargs["eps"] = 5e-3
# Default groups
p = Sigma.shape[0]
if groups is None:
groups = np.arange(1, p + 1, 1)
# Test corr matrix
TestIfCorrMatrix(Sigma)
# Check to make sure the objective is valid
objective = str(objective).lower()
if objective not in OBJECTIVE_OPTIONS:
raise ValueError(
f"Objective ({objective}) must be one of {OBJECTIVE_OPTIONS}")
# Warn user if they're using a weird norm...
if objective == "norm" and norm_type == 2:
warnings.warn(
"Using norm objective and norm_type = 2 can lead to strange behavior: consider using Frobenius norm"
)
# Find minimum tolerance, possibly warn user if lower than they specified
maxtol = np.linalg.eigh(Sigma)[0].min() / 1.1
if tol > maxtol and verbose:
warnings.warn(
f"Reducing SDP tol from {tol} to {maxtol}, otherwise SDP would be infeasible"
)
tol = min(maxtol, tol)
# Figure out sizes of groups
m = groups.max()
group_sizes = utilities.calc_group_sizes(groups)
# Possibly solve non-grouped SDP
if m == p:
return solve_SDP(
Sigma=Sigma,
verbose=verbose,
num_iter=num_iter,
tol=tol,
)
# Sort the covariance matrix according to the groups
inds, inv_inds = utilities.permute_matrix_by_groups(groups)
sortedSigma = Sigma[inds][:, inds]
# Create blocks of semidefinite matrix S,
# as well as the whole matrix S
variables = []
constraints = []
S_rows = []
shift = 0
for j in range(m):
# Create block variable
gj = int(group_sizes[j])
Sj = cp.Variable((gj, gj), symmetric=True)
constraints += [Sj >> 0]
variables.append(Sj)
# Create row of S
if shift == 0 and shift + gj < p:
rowj = cp.hstack([Sj, cp.Constant(np.zeros((gj, p - gj)))])
elif shift + gj < p:
rowj = cp.hstack([
cp.Constant(np.zeros((gj, shift))),
Sj,
cp.Constant(np.zeros((gj, p - gj - shift))),
])
elif shift + gj == p and shift > 0:
rowj = cp.hstack([cp.Constant(np.zeros((gj, shift))), Sj])
elif gj == p and shift == 0:
rowj = cp.hstack([Sj])
else:
raise ValueError(
f"shift ({shift}) and gj ({gj}) add up to more than p ({p})")
S_rows.append(rowj)
# Incremenet shift
shift += gj
# Construct S and Grahm Matrix
S = cp.vstack(S_rows)
sortedSigma = cp.Constant(sortedSigma)
constraints += [2 * sortedSigma - S >> 0]
# Construct optimization objective
if objective == "abs":
objective = cp.Minimize(cp.sum(cp.abs(sortedSigma - S)))
elif objective == "pnorm":
objective = cp.Minimize(cp.pnorm(sortedSigma - S, norm_type))
elif objective == "norm":
objective = cp.Minimize(cp.norm(sortedSigma - S, norm_type))
# Note we already checked objective is one of these values earlier
# Construct, solve the problem.
problem = cp.Problem(objective, constraints)
problem.solve(verbose=verbose, **kwargs)
if verbose:
print("Finished solving SDP!")
# Unsort and get numpy
S = S.value
if S is None:
raise ValueError(
"SDP formulation is infeasible. Try decreasing the tol parameter.")
S = S[inv_inds][:, inv_inds]
# Clip 0 and 1 values
for i in range(p):
S[i, i] = max(tol, min(1 - tol, S[i, i]))
# Scale to make this PSD using binary search
S, gamma = scale_until_PSD(Sigma, S, tol, num_iter)
if verbose:
mineig = np.linalg.eigh(2 * Sigma - S)[0].min()
print(
f"After SDP, mineig is {mineig} after {num_iter} line search iters. Gamma is {gamma}"
)
# Return unsorted S value
return S
def area_direct_blockwise_int(tar_image: np.ndarray, src_img: np.ndarray,
ksizex: int, ksizey: int, verbose: bool,
eps: int, attack_norm: AreaNormEnumType):
"""
L1/L2 attack variant against Area scaling.
Divides the image into several larger blocks where optimization problem is solved to get attack image.
Is faster than 'area_direct' (which solves each block)...
"""
src_img_new = np.zeros(src_img.shape)
use_l2: bool = (attack_norm == AreaNormEnumType.L2) # otherwise, use L1
# we need to divide the target image into blocks
def get_step(tar_image_sh):
for divi in range(20, 2, -1):
if tar_image_sh % divi == 0:
return int(tar_image_sh / divi)
stepx = get_step(tar_image_sh=tar_image.shape[0])
stepy = get_step(tar_image_sh=tar_image.shape[1])
for r in range(0, tar_image.shape[0], stepx):
for c in range(0, tar_image.shape[1], stepy):
if verbose is True and c == 0:
print("Iteration: {}, {}".format(r, c))
target_value = tar_image[r:(r + stepx), c:(c + stepy)]
# define optimization problem
novelpixels = cp.Variable((ksizex * stepx, ksizey * stepy))
# get region in source image
startx = r * ksizex
endx = ((r + stepx) * ksizex)
starty = c * ksizey
endy = ((c + stepy) * ksizey)
# objective function
obj_vec = novelpixels - src_img[startx:endx,
starty:endy] # .reshape(-1)
if use_l2:
obj = (1 / 2) * cp.sum_squares(obj_vec)
else:
obj = cp.sum(cp.abs(obj_vec))
# constraint 1:
constrs = []
for rb, rtarind in zip(range(0, endx - startx, ksizex),
range(stepx)):
for cb, ctarind in zip(range(0, endy - starty, ksizey),
range(stepy)):
# we use zip to obtain the index in src-img (rb, cd) first and
# index in target-image (rtarind, ctarind) as 2nd object.
# print(rb, cb, rtarind, ctarind)
temp_constr = cp.abs(cp.sum(novelpixels[rb:(rb + ksizex), cb:(cb + ksizey)]) - \
(target_value[rtarind, ctarind] * ksizex * ksizey)) <= eps
constrs.append(temp_constr)
constr2 = novelpixels <= 255
constr3 = novelpixels >= 0
prob = cp.Problem(cp.Minimize(obj), [*constrs, constr2, constr3])
# solve it, we first try default solver, and then if not possible (rarely the case), we try another.
# check the docu: https://www.cvxpy.org/tutorial/intro/index.html#infeasible-and-unbounded-problems
try:
prob.solve()
except:
if verbose is True:
print("QSQP failed at {}, {}".format(r, c))
try:
prob.solve(solver=cp.ECOS)
except:
print(
"Could not solve with QSPS and ECOS at {}, {}".format(
r, c))
raise Exception("Could not solve at {}, {}".format(r, c))
if prob.status != cp.OPTIMAL and prob.status != cp.OPTIMAL_INACCURATE:
print("Could only solve at {}, {} with status: {}".format(
r, c, prob.status))
raise Exception(
"Only solveable with infeasible/unbounded/optimal_inaccurate solution"
)
assert prob is not None and novelpixels.value is not None # actually not needed, just to ensure..
# print(np.round(novelpixels.value.reshape((ksizex, ksizey))))
src_img_new[startx:endx, starty:endy] = np.round(novelpixels.value)
return src_img_new
def area_direct_int(tar_image: np.ndarray, src_img: np.ndarray, ksizex: int,
ksizey: int, verbose: bool, eps: int,
attack_norm: AreaNormEnumType):
src_img_new = np.zeros(src_img.shape)
use_l2: bool = (attack_norm == AreaNormEnumType.L2) # otherwise, use L1
for r in range(tar_image.shape[0]):
for c in range(tar_image.shape[1]):
if verbose is True and r % 20 == 0 and c == 0:
print("Iteration: {}, {}".format(r, c))
target_value = tar_image[r, c]
# define optimization problem
novelpixels = cp.Variable(ksizex * ksizey)
# ident = np.identity(ksizex*ksizey)
startx = r * ksizex
endx = ((r + 1) * ksizex)
starty = c * ksizey
endy = ((c + 1) * ksizey)
obj_vec = novelpixels - src_img[startx:endx,
starty:endy].reshape(-1)
if use_l2:
obj = (1 / 2) * cp.quad_form(obj_vec,
np.identity(ksizex * ksizey))
else:
obj = cp.sum(cp.abs(obj_vec))
# constr1 = cp.sum(novelpixels) == (target_value * ksizex*ksizey)
constr1 = cp.abs(
cp.sum(novelpixels) - (target_value * ksizex * ksizey)) <= eps
constr2 = novelpixels <= 255
constr3 = novelpixels >= 0
prob = cp.Problem(cp.Minimize(obj), [constr1, constr2, constr3])
try:
prob.solve()
except:
if verbose is True:
print("QSQP failed at {}, {}".format(r, c))
try:
prob.solve(solver=cp.ECOS)
except:
print(
"Could not solve with QSPS and ECOS at {}, {}".format(
r, c))
raise Exception("Could not solve at {}, {}".format(r, c))
if prob.status != cp.OPTIMAL and prob.status != cp.OPTIMAL_INACCURATE:
print("Could only solve at {}, {} with status: {}".format(
r, c, prob.status))
raise Exception(
"Only solveable with infeasible/unbounded/optimal_inaccurate solution"
)
assert prob is not None and novelpixels.value is not None # actually not needed, just to ensure..
# print(np.round(novelpixels.value.reshape((ksizex, ksizey))))
src_img_new[startx:endx, starty:endy] = np.round(
novelpixels.value.reshape((ksizex, ksizey)))
return src_img_new
n_srt) + length_setion
point_y_e[i] = length - length_setion - length_setion * (i // n_srt)
radius_p = 2 * length / np.sqrt(n * np.pi)
r = [radius_p for i in range(n)]
radius = 1.5
c = cvx.Variable((n, 2))
constr = []
for i in range(n - 1):
for j in range(i + 1, n):
constr.append(
cvx.norm(cvx.vec(c[i, :] - c[j, :]), 2) >= r[i] + r[j])
prob = cvx.Problem(cvx.Minimize(cvx.max(cvx.max(cvx.abs(c), axis=1) + r)),
constr)
prob.solve(method='dccp', solver='ECOS', ep=1e-2, max_slack=1e-2)
point_e = np.column_stack((point_x_e, point_y_e))
point_t = np.column_stack((point_x_t, point_y_t))
point_c = np.column_stack((point_x_c, point_y_c))
z_t = np.zeros((n, 1))
z_e = np.zeros((n, 1))
z_c = np.zeros((n, 1))
firing_position_x_t = np.zeros((n, nsteps))
firing_position_y_t = np.zeros((n, nsteps))
firing_position_x_e = np.zeros((n, nsteps))
firing_position_y_e = np.zeros((n, nsteps))
def total_variation_plus_seasonal_quantile_filter(signal,
use_ixs=None,
tau=0.995,
c1=1e3,
c2=1e2,
c3=1e2,
solver='ECOS',
residual_weights=None,
tv_weights=None):
'''
This performs total variation filtering with the addition of a seasonal baseline fit. This introduces a new
signal to the model that is smooth and periodic on a yearly time frame. This does a better job of describing real,
multi-year solar PV power data sets, and therefore does an improved job of estimating the discretely changing
signal.
:param signal: A 1d numpy array (must support boolean indexing) containing the signal of interest
:param c1: The regularization parameter to control the total variation in the final output signal
:param c2: The regularization parameter to control the smoothness of the seasonal signal
:return: A 1d numpy array containing the filtered signal
'''
n = len(signal)
if residual_weights is None:
residual_weights = np.ones_like(signal)
if tv_weights is None:
tv_weights = np.ones(len(signal) - 1)
if use_ixs is None:
use_ixs = np.ones(n, dtype=np.bool)
# selected_days = np.arange(n)[index_set]
# np.random.shuffle(selected_days)
# ix = 2 * n // 3
# train = selected_days[:ix]
# validate = selected_days[ix:]
# train.sort()
# validate.sort()
s_hat = cvx.Variable(n)
s_seas = cvx.Variable(max(n, 366))
s_error = cvx.Variable(n)
s_linear = cvx.Variable(n)
c1 = cvx.Parameter(value=c1, nonneg=True)
c2 = cvx.Parameter(value=c2, nonneg=True)
c3 = cvx.Parameter(value=c3, nonneg=True)
tau = cvx.Parameter(value=tau)
# w = len(signal) / np.sum(index_set)
beta = cvx.Variable()
objective = cvx.Minimize(
# (365 * 3 / len(signal)) * w * cvx.sum(0.5 * cvx.abs(s_error) + (tau - 0.5) * s_error)
2 * cvx.sum(0.5 * cvx.abs(cvx.multiply(residual_weights, s_error)) +
(tau - 0.5) * cvx.multiply(residual_weights, s_error)) +
c1 * cvx.norm1(cvx.multiply(tv_weights, cvx.diff(s_hat, k=1))) +
c2 * cvx.norm(cvx.diff(s_seas, k=2)) + c3 * beta**2)
constraints = [
signal[use_ixs] == s_hat[use_ixs] + s_seas[:n][use_ixs] +
s_error[use_ixs],
cvx.sum(s_seas[:365]) == 0
]
if True:
constraints.append(s_seas[365:] - s_seas[:-365] == beta)
constraints.extend([beta <= 0.01, beta >= -0.1])
problem = cvx.Problem(objective=objective, constraints=constraints)
problem.solve(solver='MOSEK')
return s_hat.value, s_seas.value[:n]
def linear_mpc_control(xref, xbar, x0, dref):
"""
linear mpc control
xref: reference point
xbar: operational point
x0: initial state
dref: reference steer angle
"""
x = cvxpy.Variable((NX, T + 1))
u = cvxpy.Variable((NU, T))
x_obs = cvxpy.Variable((NX, T + 1))
cost = 0.0
constraints = []
x_g = np.array([[75, 75], [65, 65], [1, 1], [0.5, 0.5]])
#x_g = np.stack(x,y)
print(x_g)
print(type(xref))
for t in range(T):
cost += cvxpy.quad_form(u[:, t], R)
if t != 0:
cost += cvxpy.quad_form(x_g[:, t] - x[:, t], Q)
A, B, C = get_linear_model_matrix(xbar[2, t], xbar[3, t], dref[0, t])
constraints += [x[:, t + 1] == A * x[:, t] + B * u[:, t] + C]
if t < (T - 1):
cost += cvxpy.quad_form(u[:, t + 1] - u[:, t], Rd)
constraints += [
cvxpy.abs(u[1, t + 1] - u[1, t]) <= MAX_DSTEER * DT
]
cost += cvxpy.quad_form(x_g[:, T] - x[:, T], Qf)
constraints += [x[:, 0] == x0]
constraints += [x[2, :] <= MAX_SPEED]
constraints += [x[2, :] >= MIN_SPEED]
constraints += [cvxpy.abs(u[0, :]) <= MAX_ACCEL]
constraints += [cvxpy.abs(u[1, :]) <= MAX_STEER]
prob = cvxpy.Problem(cvxpy.Minimize(cost), constraints)
prob.solve(solver=cvxpy.ECOS, verbose=False)
print(xref)
if prob.status == cvxpy.OPTIMAL or prob.status == cvxpy.OPTIMAL_INACCURATE:
ox = get_nparray_from_matrix(x.value[0, :])
oy = get_nparray_from_matrix(x.value[1, :])
ov = get_nparray_from_matrix(x.value[2, :])
oyaw = get_nparray_from_matrix(x.value[3, :])
oa = get_nparray_from_matrix(u.value[0, :])
odelta = get_nparray_from_matrix(u.value[1, :])
else:
print("Error: Cannot solve mpc..")
oa, odelta, ox, oy, oyaw, ov = None, None, None, None, None, None
return oa, odelta, ox, oy, oyaw, ov
import cvxpy as cp
k = 2000
t = [-3.0+6.0*(i)/(k-1) for i in range(k) ] #range start from zero
y = np.exp(t)
T_powers = np.matrix(np.hstack((np.ones((k,1)),np.matrix(t).T,np.power(np.matrix(t).T,2))))
u = np.exp(3)
l = 0
bisection_tol = 1e-3
gamma1 = cp.Parameter(sign='positive')
a = cp.Variable(3)
b = cp.Variable(2)
objective = 0
#constraints = [cp.abs(T_powers[i]*a-y[i]*(T_powers[i]*cp.vstack(1,b)))<=gamma1*(T_powers[i]*cp.vstack(1,b)) for i in range(100)]
#constraints = [T_powers*a-np.diag(y)*(T_powers*cp.vstack(1,b))<=gamma1*(T_powers*cp.vstack(1,b)),
# T_powers*a-np.diag(y)*(T_powers*cp.vstack(1,b))>=-gamma1*(T_powers*cp.vstack(1,b))]
constraints = [cp.abs(T_powers*a-np.diag(y)*(T_powers*cp.vstack(1,b)))<=gamma1*(T_powers*cp.vstack(1,b))]
objective = cp.Minimize(np.ones((1,3))*a)
p = cp.Problem(objective,constraints)
gamma1.value = (l+u)/2.0
a_opt = 0
b_opt = 0
gamma1.value = (u+l)/2
while (u-l)>=bisection_tol:
print p.is_dcp()
# p.solve(solver=cp.CVXOPT)
p.solve()
# p.solve(verbose=True)
if p.status is 'optimal':
u = gamma1.value
a_opt = a.value
b_opt = b.value
def compute_compensation(self):
"""
Compute CoP and normalized leg stiffness compensation.
"""
Delta_com = self.pendulum.com.p - self.ref_com
Delta_comd = self.pendulum.com.pd - self.ref_comd
measured_comd = self.pendulum.com.pd
lambda_d = self.ref_lambda
nu_d = self.ref_vrp
omega_d = self.ref_omega
r_d_contact = self.ref_cop_contact
xi_d = self.ref_dcm
height = dot(self.contact.normal, self.pendulum.com.p - self.contact.p)
lambda_max = max_force / (mass * height)
lambda_min = min_force / (mass * height)
omega_max = sqrt(lambda_max)
omega_min = sqrt(lambda_min)
Delta_lambda = cvxpy.Variable(1)
Delta_nu = cvxpy.Variable(3)
Delta_omega = cvxpy.Variable(1)
Delta_r = cvxpy.Variable(2)
u = cvxpy.Variable(3)
Delta_xi = Delta_com + Delta_comd / omega_d \
- measured_comd / (omega_d ** 2) * Delta_omega
Delta_omegad = 2 * omega_d * Delta_omega - Delta_lambda
Delta_r_world = contact.R[:3, :2] * Delta_r
r_contact = r_d_contact + Delta_r
lambda_ = lambda_d + Delta_lambda
omega = omega_d + Delta_omega
Delta_xid = (
Delta_lambda * (xi_d - nu_d)
+ lambda_d * (Delta_xi - Delta_nu) +
- Delta_omega * lambda_d * (xi_d - nu_d) / omega_d) / omega_d
xi_z = self.ref_dcm[2] + Delta_xi[2] + 1.5 * sim.dt * Delta_xid[2]
costs = []
sq_costs = [
(1., u[0]),
(1., u[1]),
(1e-3, u[2])]
for weight, expr in sq_costs:
costs.append((weight, cvxpy.sum_squares(expr)))
cost = sum(weight * expr for (weight, expr) in costs)
prob = cvxpy.Problem(
objective=cvxpy.Minimize(cost),
constraints=[
Delta_xid == lambda_d / omega_d * ((1 - k_p) * Delta_xi + u),
Delta_omegad == omega_d * (1 - k_p) * Delta_omega,
Delta_nu == Delta_r_world
+ gravity * Delta_lambda / lambda_d ** 2,
cvxpy.abs(r_contact) <= self.r_contact_max,
lambda_ <= lambda_max,
lambda_ >= lambda_min,
xi_z <= max_dcm_height,
xi_z >= min_dcm_height,
omega <= omega_max,
omega >= omega_min])
prob.solve()
Delta_lambda_opt = Delta_lambda.value
Delta_r_opt = array(Delta_r.value).reshape((2,))
self.omega = omega_d + Delta_omega.value
self.dcm = self.pendulum.com.p \
+ self.pendulum.com.pd / self.omega
return (Delta_r_opt, Delta_lambda_opt)
def portfolio_optimization_cvx(r,
cov=None,
Xf=None,
F=None,
D=None,
wb=None,
w0=None,
c_=None,
lambda_=None,
sigma=None,
delta_=None,
wmin=None,
wmax=None,
A=None,
bmin=None,
bmax=None,
B=None,
beq=None,
fmin=None,
fmax=None,
cpct=None,
**kwargs):
"""
组合优化器
目标函数：
--------
maximize x'r - c'|w-w0| - lambda x'Vx
subject to
w = wb + x
x'Vx <= sigma^2
||w-w0|| <= delta * 2
wmin <= w <= wmax
fmin <= Xf'x <= fmax
w'(wb>0) >= cpct
bmin <= A'x <= bmax
B'x == beq
其中 , w 是绝对权重 , x 是主动权重 , 股票协方差 V 由结构化因子模型确定.
如果传入cov, V=cov; 否则，V=V = Xf'(F)Xf + D^2
Parameter:
-----------
r: numpy.array(n,)
股票预期收益
cov: numpy.array(n,n)
股票协方差矩阵
Xf: numpy.array(n,m)
风险因子取值
F: numpy.array(m,m)
风险因子收益率协方差矩阵
D: numpy.array(n,)
股票残差风险矩阵
w0: numpy.array(n,)
组合初始权重,None表示首次建仓,初始权重为0
wb: numpy.array(n,)
基准指数权重
c_: float or numpy.array(n,)
换手惩罚参数
lambda_:float
风险惩罚参数
sigma_: float
跟踪误差约束,0.05
delta_: float
换手约束参数,单边
wmin: float or numpy.array(n,)
绝对权重最小值
wmax: float or numpy.array(n,)
绝对权重最大值
fmin: float/list/tuple/numpy.array(m,)
因子暴露最小值
fmax: float/list/tuple/numpy.array(m,)
因子暴露最大值
cpct: float
from 0 to 1, 成分股内股票权重占比
A: numpy.array(n,p)
其他线性约束矩阵
kwargs: dict
传入cvxpy.problem.solve()中的参数。
指定优化器
"""
n = len(r) # 资产数量
x = cvx.Variable(n)
# 设定目标函数
obj = x @ r
if wb is None:
wb = np.zeros(n, dtype='float')
if w0 is None:
w0 = np.zeros(n, dtype='float')
w = wb + x
if isinstance(c_, float):
obj = obj - cvx.sum(c_ * cvx.abs(w - w0))
elif isinstance(c_, np.ndarray):
obj = obj - c_ @ cvx.abs(w - w0)
if cov is not None:
risk = cvx.quad_form(x, cov)
else:
risk = cvx.quad_form(x, Xf.T @ F @ Xf) + cvx.quad_form(
x, np.diag(D**2))
if lambda_:
obj = obj - lambda_ * risk
# 限制条件
constraints = []
if wmin is not None:
constraints.append(wmin <= w)
if wmax is not None:
constraints.append(w <= wmax)
if A is not None:
ineq = A.T @ x
if bmin is not None:
constraints.append(ineq >= bmin)
if bmax is not None:
constraints.append(ineq <= bmax)
if B is not None:
eq = B.T @ x
constraints.append(beq == eq)
if cpct is not None and wb is not None:
is_member = np.where(wb != 0.0)[0]
constraints.append(cvx.sum(w[is_member]) >= cpct)
# 优化
prob = cvx.Problem(cvx.Maximize(obj), constraints)
prob.solve(**kwargs)
if prob.status == 'optimal':
result = {
'abswt': x.value + wb,
'relwt': x.value,
'er': x.value @ r,
'sigmal': risk.value
}
else:
result = {}
return result
def solveMarkowitzObjective(c, A, Q, v, x0, bxl, bxu, bcl, bcu):
"""
Solves a convex program with a quadratic constraint and linear abs penalty
maximize c'*x - (1/2) x'*Q*x - v'*abs{x - x0}
subject to bcl <= A*x <= bcu
bxl <= x <= bxu
"""
x = cvx.Variable(len(c))
constraints = [A*x <= bcu, bcl <= A*x, bxl <= x, x <= bxu]
objective = x.T*c -0.5 * cvx.quad_form(x, Q) - cvx.abs(x - x0).T*v
ccu.maximize(objective=objective, constraints=constraints, verbose=True)
return x.value