def optimal_kernel_combinations(
kernel_values: List[torch.Tensor]) -> torch.Tensor:
# use quadratic program to get optimal kernel
num_kernel = len(kernel_values)
kernel_values_numpy = array(
[float(k.detach().cpu().data.item()) for k in kernel_values])
if np.all(kernel_values_numpy <= 0):
beta = solve_qp(
P=-np.eye(num_kernel),
q=np.zeros(num_kernel),
A=kernel_values_numpy,
b=np.array([-1.]),
G=-np.eye(num_kernel),
h=np.zeros(num_kernel),
)
else:
beta = solve_qp(
P=np.eye(num_kernel),
q=np.zeros(num_kernel),
A=kernel_values_numpy,
b=np.array([1.]),
G=-np.eye(num_kernel),
h=np.zeros(num_kernel),
)
beta = beta / beta.sum(axis=0) * num_kernel # normalize
return sum([k * b for (k, b) in zip(kernel_values, beta)])
def main():
#### Order 2 Polynomial, No Velocity Constraints ####
P2 = np.array([[1, 1], [1, 4 / 3]])
A2 = np.array([1, 1])
b2 = np.array([1])
G2 = np.zeros((2, 2))
h2 = np.zeros((2, ))
q2 = np.zeros((2, ))
p2_star = solve_qp(P2, q2, G2, h2, A2, b2)
print("QP for polynomial of degree 2, no velocity constraints")
print("Optimal value of cost function: {}".format(
p2_star.T @ P2 @ p2_star))
print("QP Solver for N=2, No Velocity Constraints: {} \n".format(p2_star))
#### Order 3 Polynomial, No Velocity Constraints ####
P3 = np.array([[1, 1, 1], [1, 4 / 3, 5 / 4], [1, 5 / 4, 9 / 5]])
A3 = np.array([1, 1, 1])
b3 = np.array([1])
G3 = np.zeros((3, 3))
h3 = np.zeros((3, ))
q3 = np.zeros((3, ))
p3_star = solve_qp(P3, q3, G3, h3, A3, b3)
print("QP for polynomial of degree 3, no velocity constraints")
print("Optimal value of cost function: {}".format(
p3_star.T @ P3 @ p3_star))
print("QP Solver for N=3, No Velocity Constraints: {} \n".format(p3_star))
#### Order 2 Polynomial, Velocity Constraints ####
P2v = np.array([[1, 1], [1, 4 / 3]])
A2v = np.array([[1, 2], [1, 1]])
b2v = np.array([-2, 1]).T
G2v = np.zeros((2, 2))
h2v = np.zeros((2, ))
q2v = np.zeros((2, ))
p2v_star = solve_qp(P2v, q2v, G2v, h2v, A2v, b2v)
print("QP for polynomial of degree 2, velocity constraints")
print("Optimal value of cost function: {}".format(
p2v_star.T @ P2v @ p2v_star))
print("QP Solver for N=2, Velocity Constraints: {} \n".format(p2v_star))
#### Order 3 Polynomial, Velocity Constraints ####
P3v = np.array([[1, 1, 1], [1, 4 / 3, 5 / 4], [1, 5 / 4, 9 / 5]])
A3v = np.array([[1, 2, 3], [1, 1, 1]])
b3v = np.array([-2, 1]).T
G3v = np.zeros((3, 3))
h3v = np.zeros((3, ))
q3v = np.zeros((3, ))
p3v_star = solve_qp(P3v, q3v, G3v, h3v, A3v, b3v)
print("QP for polynomial of degree 3, velocity constraints")
print("Optimal value of cost function: {}".format(
p3v_star.T @ P3v @ p3v_star))
print("QP Solver for N=3, Velocity Constraints: {} \n".format(p3v_star))
def solve_PGIRL(
estimated_gradients,
verbose=False,
solver='quadprog',
seed=1234,
):
num_episodes, num_parameters, num_objectives = estimated_gradients.shape[:]
mean_gradients = np.mean(estimated_gradients, axis=0)
ns = scipy.linalg.null_space(mean_gradients)
P = np.dot(mean_gradients.T, mean_gradients)
if ns.shape[1] > 0:
if (ns >= 0).all() or (ns <= 0).all():
print("Jacobian has a null space:", ns[:, 0] / np.sum(ns[:, 0]))
weights = ns[:, 0] / np.sum(ns[:, 0])
loss = np.dot(np.dot(weights.T, P), weights)
return weights, loss
else:
weights = solve_polyhedra(ns)
print("Null space:", ns)
if weights is not None and (weights != 0).any():
print("Linear programming sol:", weights)
weights = np.dot(ns, weights.T)
weights = weights / np.sum(weights)
loss = np.dot(np.dot(weights.T, P), weights)
print("Weights from non positive null space:", weights)
return weights, loss
else:
print("Linear prog did not find positive weights")
q = np.zeros(num_objectives)
A = np.ones((num_objectives, num_objectives))
b = np.ones(num_objectives)
G = np.diag(np.diag(A))
h = np.zeros(num_objectives)
normalized_P = P / np.linalg.norm(P)
try:
weights = solve_qp(P, q, -G, h, A=A, b=b, solver=solver)
except ValueError:
try:
weights = solve_qp(normalized_P, q, -G, h, A=A, b=b, solver=solver)
except:
#normalize matrix
print("Error in Girl")
print(P)
print(normalized_P)
u, s, v = np.linalg.svd(P)
print("Singular Values:", s)
ns = scipy.linalg.null_space(mean_gradients)
print("Null space:", ns)
weights, loss = solve_girl_approx(P, seed=seed)
loss = np.dot(np.dot(weights.T, P), weights)
if verbose:
print('loss:', loss)
print(weights)
return weights, loss
def check_same_solutions(tol=0.05):
sol0 = solve_qp(P, q, G, h, solver=sparse_solvers[0])
for solver in sparse_solvers:
sol = solve_qp(P, q, G, h, solver=solver)
relvar = norm(sol - sol0) / norm(sol0)
assert relvar < tol, "%s's solution offset by %.1f%%" % (
solver, 100. * relvar)
for solver in dense_solvers:
sol = solve_qp(P_array, q, G_array, h, solver=solver)
relvar = norm(sol - sol0) / norm(sol0)
assert relvar < tol, "%s's solution offset by %.1f%%" % (
solver, 100. * relvar)
def check_same_solutions(tol=0.05):
sol0 = solve_qp(P, q, G, h, solver=sparse_solvers[0])
for solver in sparse_solvers:
sol = solve_qp(P, q, G, h, solver=solver)
relvar = norm(sol - sol0) / norm(sol0)
assert relvar < tol, "%s's solution offset by %.1f%%" % (solver,
100. * relvar)
for solver in dense_solvers:
sol = solve_qp(P_array, q, G_array, h, solver=solver)
relvar = norm(sol - sol0) / norm(sol0)
assert relvar < tol, "%s's solution offset by %.1f%%" % (solver,
100. * relvar)
def test_qpsolvers() -> None:
"""Tests qpsolvers and numpy conflicts."""
# pylint: disable=C0415
import numpy as np
from qpsolvers import solve_qp
M = np.array([[1.0, 2.0, 0.0], [-8.0, 3.0, 2.0], [0.0, 1.0, 1.0]])
P = np.dot(M.T, M) # this is a positive definite matrix
q = np.dot(np.array([3.0, 2.0, 3.0]), M).reshape((3,))
G = np.array([[1.0, 2.0, 1.0], [2.0, 0.0, 1.0], [-1.0, 2.0, -1.0]])
h = np.array([3.0, 2.0, -2.0]).reshape((3,))
A = np.array([1.0, 1.0, 1.0])
b = np.array([1.0])
solve_qp(P, q, G, h, A, b)
def move(n, robot_def, vel_ctrl, vd):
global jobid
try:
w = 0.2
Kq = .01 * np.eye(n) #small value to make sure positive definite
KR = np.eye(3) #gains for position and orientation error
q_cur = vel_ctrl.joint_position()
J = robotjacobian(robot_def, q_cur) #calculate current Jacobian
Jp = J[3:, :]
JR = J[:3, :]
H = np.dot(np.transpose(Jp),
Jp) + Kq + w * np.dot(np.transpose(JR), JR)
H = (H + np.transpose(H)) / 2
robot_pose = fwdkin(robot_def, q_cur.reshape((n, 1)))
R_cur = robot_pose.R
ER = np.dot(R_cur, np.transpose(R_ee.R_ee(0)))
k, theta = R2rot(ER)
k = np.array(k, dtype=float)
s = np.sin(theta / 2) * k #eR2
wd = -np.dot(KR, s)
f = -np.dot(np.transpose(Jp), vd) - w * np.dot(np.transpose(JR), wd)
qdot = 0.5 * normalize_dq(solve_qp(H, f))
vel_ctrl.set_velocity_command(qdot)
jobid = top.after(10, lambda: move(n, robot_def, vel_ctrl, vd))
except:
traceback.print_exc()
return
def project(self, x):
proj_mat = self.metric_aug * 2
q = -2 * np.dot(self.metric_aug, x)
x_hat = solve_qp(proj_mat, q, self.constraints_mat,
self.cons_rhs + 1e-5)
return x_hat
def runOptimiser(K, u, preOptw, initialValue, maxWeight=10000):
"""
Args:
K (double 2d array): Similarity/distance matrix
u (double array): Mean similarity of each prototype
preOptw (double): Weight vector
initialValue (double): Initialize run
maxWeight (double): Upper bound on weight
Returns:
Prototypes, weights and objective values
"""
d = u.shape[0]
lb = np.zeros((d, 1))
ub = maxWeight * np.ones((d, 1))
x0 = np.append(preOptw, initialValue / K[d - 1, d - 1])
G = np.vstack((np.identity(d), -1 * np.identity(d)))
h = np.vstack((ub, -1 * lb))
# Solve a QP defined as follows:
# minimize
# (1/2) * x.T * P * x + q.T * x
# subject to
# G * x <= h
# A * x == b
sol = solve_qp(K, -u, G, h, A=None, b=None, solver='cvxopt', initvals=x0)
# compute objective function value
x = sol.reshape(sol.shape[0], 1)
P = K
q = -u.reshape(u.shape[0], 1)
obj_value = 1 / 2 * np.matmul(np.matmul(x.T, P), x) + np.matmul(q.T, x)
return (sol, obj_value[0, 0])
def opt(k):
global w
v = []
b = []
for i in range(data_qnum):
df_data = data_ls[i]
v.append(
feature_map(k, data_ls[i], y_hat_ls[i]) -
feature_map(k, data_ls[i]))
[data_Row, data_Col] = df_data.shape
docs_num = data_Row
r = np.arange(1, docs_num + 1)
bq = 1 - NDCG(k, df_data, r)
b.append(bq)
v_matrix = np.asarray(v) #q*n
K = np.dot(v_matrix, v_matrix.T)
b_matrix = np.asarray(b) #1*q
G = -1 * np.eye(data_qnum)
h = np.zeros(data_qnum)
A = np.ones(data_qnum)
b = np.array([10])
# print(K.shape, b_matrix.shape, G.shape, h.shape, A.shape, b.shape)
try:
alpha = solve_qp(K, b_matrix, G, h, A, b)
except ValueError:
print("ValueError")
return 0
w = np.dot(alpha, v_matrix)
def optimize(t, sigma, pi):
nonlocal last_solution
nr_of_assets = len(sigma)
# only optimize if we have a re-balance trigger (early exit)
if last_solution is not None and last_solution.sum() > 0.99:
# so we had at least one valid solution in the past
# we can early exit if we do not have any signal or or no signal for any currently hold asset
if len(t.shape) > 1 and t.shape[1] == nr_of_assets:
if t[:, last_solution >= 0.01].sum().any() < 1:
return keep_solution
else:
if t.sum().any() < 1:
return keep_solution
# make sure covariance matrix is positive definite
simga = cov_nearest(sigma)
# we perform optimization except when all expected returns are < 0
# then we early exit with an un-invest command
if len(pi[:, pi[0] < 0]) == pi.shape[1]:
return uninvest
else:
try:
sol = solve_qp(risk_aversion * sigma, -pi.T, G=G, h=h, A=A, b=b, solver=solver)
if sol is None:
_log.error("no solution found")
return uninvest
else:
return sol
except Exception as e:
_log.error(traceback.format_exc())
return uninvest
def servo_cb(self, goal):
if goal.stamped_pose.header.frame_id == '':
goal.stamped_pose.header.frame_id = self.base_frame
transformed = self.tf_listener.transformPose(self.base_frame,
goal.stamped_pose)
wTep = transforms.pose_msg_to_trans(transformed.pose)
Y = 0.005
Q = Y * np.eye(7)
arrived = False
rate = rospy.Rate(200)
while not arrived and self.state.errors == 0:
msg = JointVelocity()
v, arrived = rp.p_servo(self.configuration.T, wTep,
goal.scaling if goal.scaling else 0.6)
Aeq = self.configuration.Je
beq = v.reshape((6, ))
c = -self.configuration.Jm.reshape((7, ))
dq = qp.solve_qp(Q, c, None, None, Aeq, beq)
self.joint_velocity_cb(JointVelocity(joints=dq.tolist()))
rate.sleep()
return self.pose_servo_server.set_succeeded(
ServoToPoseResult(result=0 if self.state.errors == 0 else 1))
def qplcp(P, q, G, h, A, b):
P = 0.5 * (P + P.T) # make sure P is symmetric
q = -q.flatten()
h = h.flatten()
b = b.flatten()
return solve_qp(P, q, -G, -h, A, b)
def qp(P):
C = differentiate(P)
P_new = np.zeros((MaxStep - 1, N, N, N))
for k in range(len(P)):
for i in range(N):
for j in range(N):
connected_roads = []
q = []
for l in range(N):
if G[i, l, 0] != -1 and (MaxStep - 1 - k >=
shortestPaths()[l, j]):
connected_roads.append(l)
q.append(C[k, i, j, l] - P[k, i, j, l])
q = np.asarray(q)
n = len(connected_roads)
M = np.identity(n)
A = np.ones(n)
b = np.array([1])
I = -np.identity(n)
h = np.zeros(n)
#print(len(q))
raw_sol = []
if len(q) != 0:
raw_sol = solve_qp(M, q, I, h, A, b)
sol = []
for t in range(N):
if t in connected_roads:
sol.append(raw_sol[connected_roads.index(t)])
else:
sol.append(0)
P_new[k, i, j] = sol
return P_new
def quad_solver(self, ref_act, Xf, deltaW):
## set constraints
self.M = np.zeros((self.Nc * 4, self.Nc), dtype=np.double)
self.gamma = np.zeros((self.Nc * 4, 1), dtype=np.double)
for i in range(0, self.Nc):
for j in range(0, self.Np):
if i == j:
self.M[i, j] = 1
self.gamma[i, ] = self.rate_constraint
self.M[i + self.Nc, j] = -1
self.gamma[i + self.Nc, ] = self.rate_constraint
if i >= j:
self.M[i + 2 * self.Nc, j] = 1
self.M[i + 3 * self.Nc, j] = -1
self.gamma[i + 2 *
self.Nc, ] = self.amplitude_constraint - self.u0
self.gamma[i + 3 *
self.Nc, ] = self.amplitude_constraint + self.u0
E = 2 * (self.PhiT_phi + self.rw * np.eye(self.Nc))
Xf = np.reshape(Xf, (6, ))
deltaW = np.reshape(deltaW, (self.Nc, ))
Fconstraint = -2 * (np.matmul(self.PhiT_Rs, ref_act) - np.matmul(
self.PhiT_F, Xf) - np.matmul(self.PhiT_Omega, deltaW))
self.gamma = np.reshape(self.gamma, (self.Nc * 4, ))
Fconstraint = np.reshape(Fconstraint, (self.Nc, ))
x = solve_qp(E, Fconstraint, self.M, self.gamma)
return x[0]
def svm_qp(x, y, is_bias=1, is_wconstrained=1):
"""svm_qp(x,y,is_bias=1,is_wconstrained=1) returns the weights, bias and margin if the given pattern set X with labels Y is linearly separable, and 0s otherwise. x is the input matrix with dimension N (number of neurons) by P (number of patterns). y is the desired output vector of dimension P. y vector should consist of -1 and 1 only"""
import qpsolvers
R = x.shape[1]
G = -(x * y).T
if is_bias:
N = x.shape[0] + 1
G = np.append(G.T, -y)
G = G.reshape(N, R)
G = G.T
P = np.identity(N)
P[-1, -1] = 1e-12 # regularization
#for j in range(N):
#P[j,j] += 1e-16
#P += 1e-10
else:
N = x.shape[0]
P = np.identity(N)
if is_wconstrained:
if is_bias:
G = np.append(G, -np.identity(N)[:N - 1, :])
G = G.reshape(R + N - 1, N)
h = np.array([-1.] * R + [0] * (N - 1))
else:
G = np.append(G, -np.identity(N))
G = G.reshape(R + N, N)
h = np.array([-1.] * R + [0] * N)
else:
h = np.array([-1.] * R)
w = qpsolvers.solve_qp(P, np.zeros(N), G, h)
if is_bias:
return w[:-1], w[-1], 2 / pylab.norm(w[:-1])
else:
return w, 2 / pylab.norm(w)
def getRowLNSM(v, mInp, idx=-1):
nObj = mInp.shape[0]
ar = np.zeros(nObj)
for i, inp in enumerate(mInp):
ar[i] = utils.getTanimotoScore(v, inp)
if idx >= 0:
ar[idx] = -10
args = np.argsort(ar)[::-1][:const.KNN]
P = np.ndarray((const.KNN, const.KNN))
for i in range(const.KNN):
for j in range(i, const.KNN):
P[i][j] = np.dot(v - mInp[args[i]], v - mInp[args[j]])
P[j][i] = P[i][j]
I = np.diag(np.ones(const.KNN))
P = P + I
q = np.zeros(const.KNN)
gg = np.ndarray(const.KNN)
gg.fill(-1)
G = np.diag(gg)
h = np.zeros(const.KNN)
b = np.ones(1)
A = np.ones(const.KNN)
re = solve_qp(P, q, G, h, A, b)
out = np.zeros(nObj)
for i in range(const.KNN):
out[args[i]] = re[i]
return out
def __find_optimal_solution(self, S, D):
lo_bounds = []
up_bounds = []
bounds = []
for i in range(D):
lb, ub = self.__get_bounds(self.x[i])
lo_bounds.append(lb)
up_bounds.append(ub)
bounds.append((lb, ub))
bounds = tuple(bounds)
S_d = S[:D]
P = self.A[:, S_d].transpose()[:, S_d].transpose()
q = self.gradient[S_d]
G = np.zeros((D,))
A = np.zeros((D,))
h = np.zeros((D,))
b = np.zeros((D,))
solution_quadprog = solve_qp(P=P, q=q,
G=G, A=A, h=h, b=b,
lb=np.array(lo_bounds),
ub=np.array(up_bounds))
solution_minimize = minimize(fun=objective_function, x0=np.array([1] * D), args=(D, S, self.A, self.gradient),
bounds=bounds)
return solution_quadprog
def weight_descriptors(descs0, descs1, descs2, descs3, method='std'):
"""
Arguments:
- descs0,1,2,3: (D, )
Returns:
- w0, w1, w2, w3, weights
"""
H = np.vstack([descs0, descs1, -descs2, -descs3]).T
H = H.T.dot(H)
c = np.zeros(H.shape[0])
# constraint
Ae = np.array([[1, 1, 0, 0], [0, 0, 1, 1]])
be = np.array([1, 1])
Ai = np.eye(4)
bi = np.zeros(4)
x0 = np.array([1, 0, 1, 0])
def tofloat(*args):
return [x.astype(np.float) for x in args]
[H, c, Ae, be, Ai, bi, x0] = tofloat(H, c, Ae, be, Ai, bi, x0)
if method == 'std':
import qpsolvers
Ai = -Ai
bi = -bi
x = qpsolvers.solve_qp(H, c, Ai, bi, Ae, be)
else:
x, status = quadprog(H, c, x0, Ae, be, Ai, bi)
# diff = descs0 * x[0] + descs1 * x[1] - descs2 * x[2] - descs3 * x[3]
return x
def solve_svm(n, x, d, kernel, tol):
# Define matrices for quadprog
P = np.array(
[d[i] * d[j] * kernel(x[i], x[j]) for i in range(n)
for j in range(n)]).reshape(n, n) + 1e-9 * np.eye(n)
q = -np.ones(n)
G = -np.eye(n)
h = np.zeros(n)
A = np.array(d)
b = np.zeros(1)
# Run the solver
a = qp.solve_qp(P, q, G, h, A, b)
# Remove all small alphas
a[a < tol] = 0
# Find the support vectors
isv = np.nonzero(a)[0]
asv = [a[i] for i in isv]
xsv = [x[i] for i in isv]
dsv = [d[i] for i in isv]
# Compute the separator
theta = dsv[0] - sum(
[asv[i] * dsv[i] * kernel(xsv[i], xsv[0]) for i in range(len(isv))])
sep = lambda z: sum(
[asv[i] * dsv[i] * kernel(xsv[i], z) for i in range(len(isv))]) + theta
# Return separator and support vectors
return sep, xsv, dsv
def solve_qp(self, X, y):
"""
Solves a quadratic programming problem. In QP formulation (dual):
m variables, 2m+1 constraints (1 equation, 2m inequations).
:param X: array of size [n_samples, n_features] holding the training samples
:param y: array of size [n_samples] holding the class labels
"""
m = len(y) # m = n_samples
self.K = self.kernel(X) # gram matrix
P = np.vstack((
np.hstack((self.K, -self.K)), # alphas_p, alphas_n
np.hstack((-self.K, self.K)))) # alphas_n, alphas_p
q = np.hstack((-y, y)) + self.epsilon
lb = np.zeros(2 * m) # lower bounds
ub = np.ones(2 * m) * self.C # upper bounds
A = np.hstack((np.ones(m), -np.ones(m))) # equality matrix
b = np.zeros(1) # equality vector
alphas = solve_qp(P,
q,
A=A,
b=b,
lb=lb,
ub=ub,
solver='cvxopt',
sym_proj=True,
verbose=self.verbose)
self.alphas_p = alphas[:m]
self.alphas_n = alphas[m:]
def test(self):
P, q, G, h, A, b = self.get_problem()
print(solver)
x = solve_qp(P, q, G, h, A, b, solver=solver)
self.assertIsNotNone(x)
self.assertTrue((dot(G, x) <= h).all())
self.assertTrue(allclose(dot(A, x), b))
def quadratic_solver(mu, d_beta, d_ri, epsilon): #xk = (lambda, mu, beta)
beta = pd.Series(d_beta)
ri = pd.Series(d_ri)
indx = ri.index
beta = beta.values
ri = ri.values
mu = np.array([mu])
i = len(ri)
L = mu[0] + np.multiply(beta, ri)
xk = np.concatenate((L, mu, beta))
P = 2 * np.eye(2 * i + 1)
q = -2 * xk
G = np.diag(np.concatenate((-np.ones(i), np.zeros(1 + i))))
h = -np.concatenate((np.ones(i) * epsilon, np.zeros(i + 1)))
A = np.concatenate((np.eye(i), -1 * np.ones((i, 1)), -ri * np.eye(i)),
axis=1)
b = np.zeros(i)
x_r = solve_qp(P, q, G, h, A, b)
lambda_r = pd.Series(x_r[:i], index=indx).to_dict()
mu_r = x_r[i]
beta_r = pd.Series(x_r[-i:], index=indx).to_dict()
return lambda_r, mu_r, beta_r
def x_star(self):
if not hasattr(self, 'x_opt'):
self.x_opt = solve_qp(P=self.f.Q,
q=self.f.q,
lb=np.zeros_like(self.f.q),
ub=self.ub,
solver='quadprog')
return self.x_opt
def solve_qp2(P, q, G, h, lb, ub):
Gl = -np.eye(np.shape(P)[0])
hl = -lb
Gu = np.eye(np.shape(P)[0])
hu = ub
G = np.vstack((G, Gl, Gu))
h = np.hstack((h, hl, hu))
return solve_qp(P, q, G, h)
def test_qp():
M = np.array([[1., 2., 0.], [-8., 3., 2.], [0., 1., 1.]])
P = np.dot(M.T, M) # quick way to build a symmetric matrix
q = np.dot(np.array([3., 2., 3.]), M).reshape((3, ))
G = np.array([[1., 2., 1.], [2., 0., 1.], [-1., 2., -1.]])
h = np.array([3., 2., -2.]).reshape((3, ))
sol = solve_qp(P, q, G, h)
print('QP solution:', sol)
def lcs_ind_qps(wr, wmin, wmax, alpha):
N = 200
T = len(wr)
vmin = 0
vs = np.linspace(0, 1, N)
bets = np.zeros((T + 1, len(vs), 2))
log_wealth = np.log(0.5) * np.ones(len(vs))
neg_log_alpha = np.log(1 / alpha)
psi = -0.77258872224 # 2 - 4 * ln(2)
for i, v in enumerate(vs):
from qpsolvers import solve_qp
G = -np.array([[ww - 1, ww * rr - v] for ww in (0, wmax)
for rr in (0, 1)] + [(0, 1)])
h = -np.array([-0.5 for ww in (0, wmax) for rr in (0, 1)] + [0])
A = np.zeros((2, 2))
b = np.zeros(2)
A0 = np.zeros((2, 2))
A1 = np.zeros((2, 2))
A2 = np.zeros((2, 2))
b0 = np.zeros(2)
b1 = np.zeros(2)
z = np.zeros(2)
z2 = np.zeros((2, 2))
z2[1, 1] = 1
z3 = np.zeros(2)
z3[1] = -1
z4 = np.zeros((2, 2))
reg = 1e-6 * np.eye(2)
cur_bet = np.zeros(2)
local_capital = np.log(0.5)
for t, (wi, ri) in enumerate(wr):
local_capital += np.log1p(cur_bet[0] * (wi - 1) + cur_bet[1] *
(wi * ri - v))
if local_capital > neg_log_alpha:
break
z[:] = [wi - 1, wi * ri]
z4 *= 0
z4[:, 1] -= z
z4[1, :] -= z
A0 = t / (t + 1.0) * A0 + np.outer(z, z) / (t + 1.0)
A1 = t / (t + 1.0) * A1 + z4 / (t + 1.0)
A2 = t / (t + 1.0) * A2 + z2 / (t + 1.0)
b0 = t / (t + 1.0) * b0 + z / (t + 1.0)
b1 = t / (t + 1.0) * b1 + z3 / (t + 1.0)
A[...] = 2 * (-psi * (A0 + v * (A1 + v * A2)) + reg)
b[...] = -(b0 + v * b1)
cur_bet[:] = solve_qp(A, b, G, h, solver='quadprog')
bets[t, i, :] = cur_bet
these_bets = np.zeros((N, 2))
for t, (wi, ri) in enumerate(wr):
multi_update_wealth(log_wealth, these_bets, vs, wi, ri)
newvmin = update_lb_2d(log_wealth, vs, neg_log_alpha)
vmin = max(vmin, newvmin)
yield vmin
these_bets[...] = bets[t, :, :]
def testQP():
A = np.array([[1., 2., 0.], [-8., 3., 2.], [0., 1., 1.]])
b = np.array([3., 2., 3.])
G = np.array([[1., 2., 1.], [2., 0., 1.], [-1., 2., -1.]])
h = np.array([3., 2., -2.])
P = np.dot(A.T, A)
q = -np.dot(A.T, b)
return qpsolvers.solve_qp(P=P, q=q, G=G, h=h)
def get_spline_expansion(self, f_eval, xgrid=None):
"""
Returns the coefficient of the spline expansion for f_eval
"""
out = super().get_spline_expansion(f_eval, xgrid)
proj = solve_qp(self.metric * 2, -2 * np.dot(self.metric, out),
self.constraints_mat, self.cons_rhs)
return proj
def cost_function(t_input):
global p_x_final
global p_y_final
global p_z_final
t = [0.2]
sum = 0.2
for i in range(len(t_input)):
sum += t_input[i]
t.append(sum)
#print(t)
Q_1 = form_Q(1, t)
Q_2 = form_Q(2, t)
Q_3 = form_Q(3, t)
Q = block_diag(Q_1, Q_2,
Q_3) #converts to block diagonal form in given order
Q = Q + (0.0001 * np.identity(n * m))
A = comp_A(t)
b_x = [x[0], 0, 0, x[m], 0, 0, x[1], x[2]]
b_x.extend(np.zeros(shape=(3 * (m - 1))))
b_y = [y[0], 0, 0, y[m], 0, 0, y[1], y[2]]
b_y.extend(np.zeros(shape=(3 * (m - 1))))
b_z = [z[0], 0, 0, z[m], 0, 0, z[1], z[2]]
b_z.extend(np.zeros(shape=(3 * (m - 1))))
q = np.zeros(shape=(n * m, 1)).reshape((n * m, ))
G = np.zeros(shape=((4 * m) + 2, n * m))
h = np.zeros(shape=((4 * m) + 2, 1)).reshape(((4 * m) + 2, ))
p_x = solve_qp(Q, q, G, h, A, b_x)
p_y = solve_qp(Q, q, G, h, A, b_y)
p_z = solve_qp(Q, q, G, h, A, b_z)
p_x_final = np.copy(p_x)
p_y_final = np.copy(p_y)
p_z_final = np.copy(p_z)
K = 10000000
J_x = (0.00001 * (np.matmul(np.matmul(np.transpose(p_x), Q), p_x))) + (
0.00001 * (np.matmul(np.matmul(np.transpose(p_y), Q), p_y))
) + (0.00001 *
(np.matmul(np.matmul(np.transpose(p_z), Q), p_z))) + (K *
(t[-1] - t[0]))
return J_x / 100000
def _solve_optimization(self, agent, avoid_collision, p_mat, q_mat, g_mat, h_mat):
"""To find acceleration input by solvin the qp problem.
If no solution is found whithin constraints, will try to lower relaxation.
1/2 x.T * p * x + q.T * x s.t. g*x <= h
Args:
agent (:obj:`Agent`): Current agent
avoid_collisiont (:obj:`bool`): If solving for collision or not
p_mat (:obj:`np.Array`)
q_mat (:obj:`np.Array`)
g_mat (:obj:`np.Array`)
h_mat (:obj:`np.Array`)
Returns:
:obj:`np.Array`: Acceleration input
"""
cur_relaxation = self.relaxation_max_bound # To locally increase relaxation bound
find_solution = True
accel_input = None
relax_vals = None
while find_solution:
try:
accel_input = solve_qp(p_mat, q_mat, G=g_mat, h=h_mat, solver='quadprog')
relax_vals = accel_input[3*self.steps_in_horizon:]
accel_input = accel_input[0:3*self.steps_in_horizon]
accel_input = accel_input.reshape(3*self.steps_in_horizon, 1)
find_solution = False
# No solution whithin constraints
except ValueError:
cur_relaxation -= self.relaxation_inc
# Relax until 2*min is reached
if cur_relaxation > self.relaxation_min_bound*2 and avoid_collision:
print "No solution, relaxing constraints: %.2f" % cur_relaxation
# Update constraint in h matrix
n_collision = len(agent.close_agents.keys())
for i in range(n_collision):
h_mat[(-1 - i*3), 0] = -cur_relaxation
# Max relaxation reached
else:
self.in_collision = True
find_solution = False
if self.verbose:
print "ERROR: No solution in constraints, Check max space"
return accel_input, relax_vals
if __name__ == "__main__":
if get_ipython() is None:
print "Usage: ipython -i %s" % basename(__file__)
exit()
dense_instr = {
solver: "u = solve_qp(P, q, G, h, solver='%s')" % solver
for solver in dense_solvers}
sparse_instr = {
solver: "u = solve_qp(P_csc, q, G_csc, h, solver='%s')" % solver
for solver in sparse_solvers}
print "\nTesting all QP solvers on a dense quadratic program..."""
sol0 = solve_qp(P, q, G, h, solver=dense_solvers[0])
for solver in dense_solvers:
sol = solve_qp(P, q, G, h, solver=solver)
delta = norm(sol - sol0)
assert delta < 1e-4, "%s's solution offset by %.1e" % (solver, delta)
for solver in sparse_solvers:
sol = solve_qp(P_csc, q, G_csc, h, solver=solver)
delta = norm(sol - sol0)
assert delta < 1e-4, "%s's solution offset by %.1e" % (solver, delta)
print "\nDense solvers",
print "\n-------------"
for solver, instr in dense_instr.iteritems():
print "%s: " % solver,
get_ipython().magic(u'timeit %s' % instr)
# You should have received a copy of the GNU Lesser General Public License # along with qpsolvers. If not, see <http://www.gnu.org/licenses/>. from numpy import array, dot from qpsolvers import solve_qp from time import time M = array([[1., 2., 0.], [-8., 3., 2.], [0., 1., 1.]]) P = dot(M.T, M) # quick way to build a symmetric matrix q = dot(array([3., 2., 3.]), M).reshape((3,)) G = array([[1., 2., 1.], [2., 0., 1.], [-1., 2., -1.]]) h = array([3., 2., -2.]).reshape((3,)) t_start = time() solver = "quadprog" # see qpsolvers.available_solvers x_sol = solve_qp(P, q, G, h, solver=solver) t_end = time() print "" print " min. 1/2 x^T P x + q^T x" print " s.t. G * x <= h" print "" print "P =", P print "q =", q print "G =", G print "h =", h print "" print "Solution: x =", x_sol print "Solve time:", 1000. * (t_end - t_start), "[ms]" print "Solver:", solver
def solve_random_qp(n, solver):
M, b = random.random((n, n)), random.random(n)
P, q = dot(M.T, M), dot(b, M).reshape((n,))
G = toeplitz([1., 0., 0.] + [0.] * (n - 3), [1., 2., 3.] + [0.] * (n - 3))
h = ones(n)
return solve_qp(P, q, G, h, solver=solver)
