def test_sum_squares(self):
"""Test sum squares prox fn.
"""
# No modifiers.
tmp = Variable(10)
fn = sum_squares(tmp)
rho = 1
v = np.arange(10) * 1.0
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, v * rho / (2 + rho))
rho = 2
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, v * rho / (2 + rho))
# With modifiers.
mod_fn = sum_squares(tmp, alpha=2, beta=-1,
c=np.ones(10) * 1.0, b=np.ones(10) * 1.0, gamma=1)
rho = 2
v = np.arange(10) * 1.0
x = mod_fn.prox(rho, v.copy())
# vhat = mod_fn.beta*(v - mod_fn.c/rho)*rho/(rho+2*mod_fn.gamma) - mod_fn.b
# rho_hat = rho/(mod_fn.alpha*np.sqrt(np.abs(mod_fn.beta)))
# xhat = fn.prox(rho_hat, vhat)
x_var = cvx.Variable(10)
cost = 2 * cvx.sum_squares(-x_var - np.ones(10)) + \
np.ones(10).T * x_var + cvx.sum_squares(x_var) + \
(rho / 2) * cvx.sum_squares(x_var - v)
prob = cvx.Problem(cvx.Minimize(cost))
prob.solve()
self.assertItemsAlmostEqual(x, x_var.value, places=3)
def create(m, n):
mu = 1
rho = 1
sigma = 0.1
A = problem_util.normalized_data_matrix(m, n, mu)
x0 = sp.rand(n, 1, rho)
x0.data = np.random.randn(x0.nnz)
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma*np.random.randn(m))
A[b>0,:] += 0.7*np.tile([x0], (np.sum(b>0),1))
A[b<0,:] -= 0.7*np.tile([x0], (np.sum(b<0),1))
P = la.block_diag(np.random.randn(n-1,n-1), 0)
lam = 1
x = cp.Variable(A.shape[1])
# Straightforward formulation w/ no constraints
# TODO(mwytock): Fix compiler so this works
z0 = 1 - sp.diags([b],[0])*A*x + cp.norm1(P.T*x)
f_eval = lambda: (lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z0, 0))).value
# Explicit epigraph constraint
t = cp.Variable(1)
z = 1 - sp.diags([b],[0])*A*x + t
f = lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
C = [cp.norm1(P.T*x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def create(**kwargs):
# m>k
k = kwargs['k'] #class
m = kwargs['m'] #instance
n = kwargs['n'] #dim
p = 5 #p-largest
q = 10
X = problem_util.normalized_data_matrix(m,n,1)
Y = np.random.randint(0, k-1, (q,m))
Theta = cp.Variable(n,k)
t = cp.Variable(q)
texp = cp.Variable(m)
f = cp.sum_largest(t, p)+cp.sum_entries(texp) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X*Theta, axis=1) <= texp)
for i in range(q):
Yi = one_hot(Y[i], k)
C.append(-cp.sum_entries(cp.mul_elemwise(X.T.dot(Yi), Theta)) == t[i])
t_eval = lambda: np.array([
-cp.sum_entries(cp.mul_elemwise(X.T.dot(one_hot(Y[i], k)), Theta)).value for i in range(q)])
f_eval = lambda: cp.sum_largest(t_eval(), p).value \
+ cp.sum_entries(cp.log_sum_exp(X*Theta, axis=1)).value \
+ cp.sum_squares(Theta).value
return cp.Problem(cp.Minimize(f), C), f_val
def create(m, n):
# Generate random points uniform over hypersphere
A = np.random.randn(m, n)
A /= np.sqrt(np.sum(A**2, axis=1))[:,np.newaxis]
A *= (np.random.rand(m)**(1./n))[:,np.newaxis]
# Shift points and add some outliers
# NOTE(mwytock): causes problems for operator splitting, should fix
#x0 = np.random.randn(n)
x0 = np.zeros(n)
A += x0
k = max(m/50, 1)
idx = np.random.randint(0, m, k)
A[idx, :] += np.random.randn(k, n)
lam = 1
x = cp.Variable(n)
rho = cp.Variable(1)
# Straightforward expression
#z = np.sum(A**2, axis=1) - 2*A*x + cp.sum_squares(x) # z_i = ||a_i - x||^2
#f = cp.sum_entries(cp.max_elemwise(z - rho, 0)) + lam*cp.max_elemwise(0, rho)
# Explicit epigraph form
t = cp.Variable(1)
z = np.sum(A**2, axis=1) - 2*A*x + t # z_i = ||a_i - x||^2
z0 = np.sum(A**2, axis=1) - 2*A*x + cp.sum_squares(x)
f_eval = lambda: ((1./n)*cp.sum_entries(cp.max_elemwise(z0 - rho, 0)) + cp.max_elemwise(0, rho)).value
f = (1./n)*cp.sum_entries(cp.max_elemwise(z-rho, 0)) + lam*cp.sum_entries(cp.max_elemwise(rho, 0))
C = [cp.sum_squares(x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def blockCompressedSenseL1(block, rho, alpha, basis_premultiplied, mixing_matrix):
""" Run L1 compressed sensing given alpha and a basis."""
# Get block size.
block_len = block.shape[0] * block.shape[1]
# Unravel this image into a single column vector.
img_vector = np.asmatrix(block.ravel()).T
# Determine m (samples)
img_measured = mixing_matrix * img_vector
# Construct the problem.
coefficients = cvx.Variable(block_len)
coefficients_premultiplied = basis_premultiplied * coefficients
L2 = cvx.sum_squares(coefficients_premultiplied - img_measured)
REG = cvx.sum_squares(coefficients)
L1 = cvx.norm(coefficients, 1)
objective = cvx.Minimize(L2 + rho * REG + alpha * L1)
constraints = []
problem = cvx.Problem(objective, constraints)
# Solve.
problem.solve(verbose=False, solver="SCS")
# Print problem status.
print "Problem status: " + str(problem.status)
sys.stdout.flush()
return coefficients.value
def run_spsolve(Ax_expr, x_var):
b0 = Ax_expr.value
b0 += sigma*np.random.randn(*b0.shape)
obj = cvx.sum_squares(Ax_expr - b0) + lam*cvx.sum_squares(x_var)
prob = cvx.Problem(cvx.Minimize(obj))
t0 = time.time()
prob.solve(solver=cvx.LS)
print "solve_time: %.2f secs" % (time.time() - t0)
print "objective: %.3e" % obj.value
def create(**kwargs):
n = kwargs["n"]
x = cp.Variable(n)
u = np.random.rand(n)
f = cp.sum_squares(x-u)+cp.sum_entries(cp.max_elemwise(x, 0))
return cp.Problem(cp.Minimize(f))
def create(m, n):
# Generate data
X = np.hstack([np.random.randn(m,n), np.ones((m,1))])
theta0 = np.random.randn(n+1)
y = np.sign(X.dot(theta0) + 0.1*np.random.randn(m))
X[y>0,:] += np.tile([theta0], (np.sum(y>0),1))
X[y<0,:] -= np.tile([theta0], (np.sum(y<0),1))
# Generate uncertainty envelope
P = la.block_diag(np.random.randn(n,n), 0)
lam = 1e-8
theta = cp.Variable(n+1)
# TODO(mwytock): write this as:
# f = (lam/2*cp.sum_squares(theta) +
# problem_util.hinge(1 - y[:,np.newaxis]*X*theta+cp.norm1(P.T*theta)))
# already in prox form
t1 = cp.Variable(m)
t2 = cp.Variable(1)
z = cp.Variable(n+1)
f = lam/2*cp.sum_squares(theta) + problem_util.hinge(1-t1)
C = [t1 == y[:,np.newaxis]*X*theta - t2,
cp.norm1(z) <= t2,
P.T*theta == z]
return cp.Problem(cp.Minimize(f), C)
def create(**kwargs):
A, b = problem_util.create_classification(**kwargs)
lam = 1
x = cp.Variable(A.shape[1])
f = ep.hinge_loss(x, A, b) + lam*cp.sum_squares(x)
return cp.Problem(cp.Minimize(f))
def test_least_squares_plot_cost_ests(self, A, b, P, q, r, x, num_replications_list, alpha, fn):
# Estimate the true objective value
stoch_objf = cvx.sum_squares(A*x-b)
fhatmeans, fhatvars, fhatucbs, fhatlcbs = [], [], [], []
for num_replications in num_replications_list:
print "Averaging [%d] times the obj. vals. at a candidate point of SAAs with 1 Monte Carlo sample to the stochastic least squares objective." % num_replications
(fhatmean, fhatvar, fhatucb, fhatlcb) = self.unconstr_diag.est_cost(stoch_objf, num_replications, alpha)
fhatmeans.append(fhatmean)
fhatvars.append(fhatvar)
fhatucbs.append(fhatucb)
fhatlcbs.append(fhatlcb)
# Compute the true objective value
print "Evaluating the true stochastic least squares objective value at a candidate point."
fstar = (cvx.quad_form(x,P) - 2*x.T*q + r).value
fstars = np.tile( fstar, len(num_replications_list) )
# Make plots
print "Plotting results to [" + fn + "] (on a linear/log scale)."
fig, ax = plt.subplots()
plt.rc("text", usetex=True)
ax.plot( num_replications_list, fhatmeans, "-", label=r"$\hat{f}_{0,N}(x)$", color="blue", lw=self.linewidth )
ax.fill_between( num_replications_list, fhatucbs, fhatlcbs, facecolor="lightskyblue", alpha=0.5 )
ax.plot( num_replications_list, fstars, "-", label=r"$f_0(x)$", color="crimson", lw=self.linewidth )
ax.legend(loc="upper right", fontsize=self.fontsize)
ax.set_xlabel(r"\# samples $N$", fontsize=self.fontsize)
ax.set_xscale("log")
for label in (ax.get_xticklabels() + ax.get_yticklabels()):
label.set_fontsize(self.fontsize_axis)
fig.savefig(fn, bbox_inches="tight")
print "All done."
# Return
return (fhatmeans, fhatvars, fstars)
def lasso(A, b, gam):
import cvxpy as cp
import numpy as np
import cvxopt
#from multiprocessing import Pool
# Problem data.
gamma = cp.Parameter(sign="positive")
# Construct the problem.
x = cp.Variable(A.shape[1])
objective = cp.Minimize(cp.sum_squares(A * x - b) + gamma * cp.norm(x, 1))
p = cp.Problem(objective)
# Assign a value to gamma and find the optimal x.
def get_x(gamma_value):
gamma.value = gamma_value
result = p.solve()
return x.value
#gammas = np.logspace(-1, 2, num=100)
# Serial computation.
#x_values = [get_x(value) for value in gammas]
# Parallel computation.
#pool = Pool(processes=4)
#par_x = pool.map(get_x, gammas)
#for v1, v2 in zip(x_values, par_x):
#if np.linalg.norm(v1 - v2) > 1e-5:
#print "error"
return get_x(gam)
def f_least_squares_matrix():
m = 20
k = 3
A = np.random.randn(m, n)
B = np.random.randn(m, k)
X = cp.Variable(n, k)
return cp.sum_squares(A*X - B)
def disc_one(x,y,ncuts,k=1,segs=None,lnorm=1,tune=50,constant=True,eps=0.01,cvx_solver=2):
# possible solvers to choose from: typically CVXOPT works better for simulations thus far.
solvers = [cvx.SCS,cvx.ECOS,cvx.CVXOPT] # 0 is SCS, 1 is ECOS, 2 CVXOPT
n = x.size
# Create D-matrix: specify n and k
if segs==None:
segs = np.linspace(min(x)-eps,max(x)+eps,ncuts)
D = utils.form_Dk(n=ncuts,k=k)
# Create O-matrix: specify x and number of desired cuts
O = utils.Omatrix(x,ncuts,constant=constant,eps=eps,segs=segs)
# Solve convex problem.
theta = cvx.Variable(ncuts)
obj = cvx.Minimize(0.5 * cvx.sum_squares(y - O*theta)
+ tune * cvx.norm(D*theta, lnorm) )
prob = cvx.Problem(obj)
# Use CVXOPT as the solver
prob.solve(solver=solvers[cvx_solver],verbose=False)
print 'Solver status: ', prob.status
# Check for error.
if prob.status != cvx.OPTIMAL:
raise Exception("Solver did not converge!")
if constant==True: return [segs, np.array(theta.value),x,y,segs,constant,eps]
if constant==False: return [x, O.dot(np.array(theta.value)),x,y,segs,constant,eps]
def lars_one(x,y,k=1,tune=50,eps=0.01,cvx_solver=0):
# possible solvers to choose from: typically CVXOPT works better for simulations thus far.
solvers = [cvx.SCS,cvx.CVXOPT] # 0 is SCS, 1 CVXOPT
default_iter = [160000,3200][cvx_solver] # defaults are 2500 and 100
# Create T: the knots
T = knots(x=x,k=k)
D = utils.form_Dk(n=x.size,k=k)
# Create G-matrix (truncated power basis): specify n and k
G = tpb(x=x,t=T,k=k)
# Solve convex problem.
theta = cvx.Variable(x.size)
obj = cvx.Minimize(0.5 * cvx.sum_squares(y - G*theta)
+ tune * cvx.norm(D*theta, 1) )
prob = cvx.Problem(obj)
prob.solve(solver=solvers[cvx_solver],verbose=False,max_iters = default_iter)
# Check for error.
# This while loop only works for SCS. CVXOPT terminates after 1 iteration.
counter = 0
while prob.status != cvx.OPTIMAL:
maxit = 2*default_iter
prob.solve(solver=solvers[cvx_solver],verbose=False,max_iters=maxit)
default_iter = maxit
counter = counter +1
if counter>4:
raise Exception("Solver did not converge with %s iterations! (N=%s,d=%s,k=%s)" % (default_iter,n,ncuts,k) )
output = {'theta.hat':np.array(theta.value),'fitted': G.dot(np.array(theta.value)),'x':x,'y':y,'eps':eps}
return output
def solveCardinalityObjective(prices,error):
"""
Solves the problem
for i=1:n
max: x[i]
subject to: ||Rx - y||_2 <= error, x>=0, sum(x)==1
which is a lower bound approximation to the problem with objective:
card(x)
R is a number of time periods by number of assets matrix of returns
for each asset in the index.
y is the time series for the index returns
(The index is assumed to be one share of each asset in the index)
error is the treshold for the tracking error.
"""
numAssets = prices.shape[1]
x = cvx.Variable(numAssets)
returns = si.pricesToReturns(prices)
indexReturns = si.pricesToReturnsForIndex(prices)
TrackingErrorSquared = cvx.sum_squares(returns*x -indexReturns)
obj = cvx.Maximize(x[0])
constraints = [x>=0,sum(x)==1,TrackingErrorSquared <=error**2]
prob = cvx.Problem(obj,constraints)
optimalVal = 0
optimalSol = np.array([])
for i in range(numAssets):
prob.obj = cvx.Maximize(x[i])
prob.solve(warm_start=True)
value = prob.value
if value > optimalVal:
optimalVal = value
optimalSol = x.value
return optimalVal, np.array(optimalSol).reshape(-1,)
def test_problem(self):
"""Test problem object.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8), (4, 2)) * 1.
prox_fns = [norm1(X), sum_squares(X, b=B)]
prob = Problem(prox_fns)
# prob.partition(quad_funcs = [prox_fns[0], prox_fns[1]])
prob.set_automatic_frequency_split(False)
prob.set_absorb(False)
prob.set_implementation(Impl['halide'])
prob.set_solver('admm')
prob.solve()
true_X = norm1(X).prox(2, B.copy())
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="pc")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs", eps_rel=1e-6,
rho_0=1.0, rho_scale=np.sqrt(2.0) * 2.0, rho_max=2**16,
max_iters=20, max_inner_iters=500, verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# CG
prob = Problem(prox_fns)
prob.set_lin_solver("cg")
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs", eps_rel=1e-6,
rho_0=1.0, rho_scale=np.sqrt(2.0) * 2.0, rho_max=2**16,
max_iters=20, max_inner_iters=500, verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Quad funcs.
prob = Problem(prox_fns)
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Absorbing lin ops.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X, b=B)]
prob = Problem(prox_fns)
prob.set_absorb(True)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
cvx_X = cvx.Variable(4, 2)
cost = cvx.sum_squares(-2 * cvx_X - B) + cvx.norm(5 * cvx.mul_elemwise(B, cvx_X), 1)
cvx_prob = cvx.Problem(cvx.Minimize(cost))
cvx_prob.solve(solver=cvx.SCS)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
prob.set_absorb(False)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
# Constant offsets.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X - B)]
prob = Problem(prox_fns)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
def create(**kwargs):
A, B = problem_util.create_regression(**kwargs)
lambda_max = np.abs(A.T.dot(B)).max()
lam = 0.5*lambda_max
X = cp.Variable(A.shape[1], B.shape[1] if len(B.shape) > 1 else 1)
f = cp.sum_squares(A*X - B) + lam*cp.norm1(X)
return cp.Problem(cp.Minimize(f))
def create(m, n, density=0.1):
np.random.seed(0)
mu = np.exp(0.01*np.random.randn(n))-1 # returns
D = np.random.rand(n)/10; # idiosyncratic risk
F = sp.rand(n,m,density) # factor model
F.data = np.random.randn(len(F.data))/10
gamma = 1
B = 1
x = cp.Variable(n)
f = mu.T*x - gamma*(cp.sum_squares(F.T.dot(x)) +
cp.sum_squares(cp.mul_elemwise(D, x)))
C = [cp.sum_entries(x) == B,
x >= 0]
return cp.Problem(cp.Maximize(f), C)
def least_squares():
np.random.seed(0)
m = 10
n = 5
A = np.random.randn(m,n)
b = np.random.randn(m)
x = cvx.Variable(n)
return cvx.Problem(cvx.Minimize(cvx.sum_squares(A*x - b)))
def create(n, lam):
# get data
A = np.rot90(scipy.misc.imread(IMAGE), -1)[400:1400,600:1600]
Y = scipy.misc.imresize(A, (n,n))
# set up problem
X = [cp.Variable(n,n) for i in range(3)]
f = sum([cp.sum_squares(X[i] - Y[:,:,i]) for i in range(3)]) + lam * cp.tv(*X)
return cp.Problem(cp.Minimize(f))
def test_half_quadratic_splitting(self):
"""Test half quadratic splitting.
"""
X = Variable((10,5))
B = np.reshape(np.arange(50), (10,5))
prox_fns = [sum_squares(X, b=B)]
sltn = hqs.solve(prox_fns, [], eps_rel=1e-4, max_iters = 100, max_inner_iters = 50)
self.assertItemsAlmostEqual(X.value, B, places=2)
self.assertAlmostEqual(sltn, 0)
prox_fns = [norm1(X, b=B, beta=2)]
sltn = hqs.solve(prox_fns, [], eps_rel=1e-4, max_iters = 100, max_inner_iters = 50)
self.assertItemsAlmostEqual(X.value, B/2., places=2)
self.assertAlmostEqual(sltn, 0)
prox_fns = [norm1(X), sum_squares(X, b=B)]
sltn = hqs.solve(prox_fns, [], eps_rel=1e-7,
rho_0 = 1.0, rho_scale = np.sqrt(2.0) * 2.0, rho_max = 2**16,
max_iters = 20, max_inner_iters = 500)
cvx_X = cvx.Variable(10, 5)
cost = cvx.sum_squares(cvx_X - B) + cvx.norm(cvx_X, 1)
prob = cvx.Problem(cvx.Minimize(cost))
prob.solve()
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
self.assertAlmostEqual(sltn, prob.value, places=3)
psi_fns, omega_fns = hqs.partition(prox_fns)
sltn = hqs.solve(psi_fns, omega_fns, eps_rel=1e-7,
rho_0 = 1.0, rho_scale = np.sqrt(2.0) * 2.0, rho_max = 2**16,
max_iters = 20, max_inner_iters = 500)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
self.assertAlmostEqual(sltn, prob.value, places=3)
# With linear operators.
kernel = np.array([1,2,3])
kernel_mat = np.matrix("2 1 3; 3 2 1; 1 3 2")
L = np.linalg.norm(kernel_mat)
x = Variable(3)
b = np.array([-41,413,2])
prox_fns = [nonneg(x), sum_squares(conv(kernel, x), b=b)]
hqs.solve(prox_fns, [], eps_rel=1e-9, rho_0 = 4, rho_scale = np.sqrt(2.0)*1.0,
rho_max = 2**16, max_iters = 30, max_inner_iters = 500)
cvx_X = cvx.Variable(3)
cost = cvx.norm(kernel_mat*cvx_X - b)
prob = cvx.Problem(cvx.Minimize(cost), [cvx_X >= 0])
prob.solve()
self.assertItemsAlmostEqual(x.value, cvx_X.value, places=0)
psi_fns, omega_fns = hqs.partition(prox_fns)
hqs.solve(psi_fns, omega_fns, eps_rel=1e-9, rho_0 = 4, rho_scale = np.sqrt(2.0)*1.0,
rho_max = 2**16, max_iters = 30, max_inner_iters = 500)
self.assertItemsAlmostEqual(x.value, cvx_X.value, places=0)
def trainLinearRegressor(featuresMat, targetDeltas):
nSamples, nFeats = featuresMat.shape
nOutputs = targetDeltas.shape[1]
b = cvxpy.Variable(nOutputs)
R = cvxpy.Variable(nOutputs, nFeats)
residuals = featuresMat * R.T + cvxpy.kron(cvxpy.Constant(np.ones((nSamples))), b) - targetDeltas
func = cvxpy.sum_squares(residuals)
prob = cvxpy.Problem(cvxpy.Minimize(func))
prob.solve(verbose=False)
return R.value, b.value
def lasso_dense(n):
m = 2*n
A = np.random.randn(m, n)
A /= np.sqrt(np.sum(A**2, 0))
b = A*sp.rand(n, 1, 0.1) + 1e-2*np.random.randn(m,1)
lam = 0.2*np.max(np.abs(A.T.dot(b)))
x = cvx.Variable(n)
f = cvx.sum_squares(A*x - b) + lam*cvx.norm1(x)
return cvx.Problem(cvx.Minimize(f))
def create(m, n, d):
Xp = problem_util.normalized_data_matrix(m, d, 1)
Xn = problem_util.normalized_data_matrix(n, d, 1)
lam = 1
theta = cp.Variable(d)
f = ep.infinite_push(theta, Xp, Xn) + lam*cp.sum_squares(theta)
f_eval = lambda: f.value
return cp.Problem(cp.Minimize(f)), f_eval
def test_norm1(self):
"""Test L1 norm prox fn.
"""
# No modifiers.
tmp = Variable(10)
fn = norm1(tmp)
rho = 1
v = np.arange(10) * 1.0 - 5.0
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 1.0 / rho, 0))
rho = 2
x = fn.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, np.sign(v) * np.maximum(np.abs(v) - 1.0 / rho, 0))
# With modifiers.
mod_fn = norm1(tmp, alpha=0.1, beta=5,
c=np.ones(10) * 1.0, b=np.ones(10) * -1.0, gamma=4)
rho = 2
v = np.arange(10) * 1.0
x = mod_fn.prox(rho, v.copy())
# vhat = mod_fn.beta*(v - mod_fn.c/rho)*rho/(rho+2*mod_fn.gamma) - mod_fn.b
# rho_hat = rho/(mod_fn.alpha*mod_fn.beta**2)
# xhat = fn.prox(rho_hat, vhat)
x_var = cvx.Variable(10)
cost = 0.1 * cvx.norm1(5 * x_var + np.ones(10)) + np.ones(10).T * x_var + \
4 * cvx.sum_squares(x_var) + (rho / 2) * cvx.sum_squares(x_var - v)
prob = cvx.Problem(cvx.Minimize(cost))
prob.solve()
self.assertItemsAlmostEqual(x, x_var.value, places=3)
# With weights.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = weighted_norm1(tmp, -v + 1)
rho = 2
x = fn.prox(rho, v)
self.assertItemsAlmostEqual(x, np.sign(v) *
np.maximum(np.abs(v) - np.abs(-v + 1) / rho, 0))
def run_tensorflow(Ax_expr, x_var):
import tensorflow as tf
from cvxflow.conjugate_gradient import conjugate_gradient_solve
from cvxflow import cvxpy_expr
b0 = Ax_expr.value
b0 += sigma*np.random.randn(*b0.shape)
obj = cvx.sum_squares(Ax_expr - b0) + lam*cvx.sum_squares(x_var)
t0 = time.time()
expr = Ax_expr.canonicalize()[0]
def A(x):
return cvxpy_expr.tensor(expr, {x_var.id: x})
def AT(y):
return cvxpy_expr.adjoint_tensor(expr, y)[x_var.id]
def M(x):
return lam*x + AT(A(x))
b = tf.constant(b0.reshape(-1,1), dtype=tf.float32)
x_init = tf.zeros((n,1))
x, iters, r_norm_sq = conjugate_gradient_solve(M, AT(b), x_init)
init = tf.initialize_all_variables()
print "init_time: %.2f secs" % (time.time() - t0)
t0 = time.time()
with tf.Session(config=tf.ConfigProto(device_count={"GPU": 0})) as sess:
sess.run(init)
x0, iters0, r_norm_sq0 = sess.run([x, iters, r_norm_sq])
print "cpu_solve_time: %.2f secs" % (time.time() - t0)
t0 = time.time()
with tf.Session() as sess:
sess.run(init)
x0, iters0, r_norm_sq0 = sess.run([x, iters, r_norm_sq])
print "gpu_solve_time: %.2f secs" % (time.time() - t0)
x_var.value = x0
print "objective: %.3e" % obj.value
print "cg_iterations:", iters0
def __init__(self, returns, indexReturns,regularizer,i):
#initiate a problem with data
numAssets = returns.shape[1]
self.x = cvx.Variable(numAssets)
self.index = i
self.t=cvx.Variable()
baseConstraints = [self.x>=0,self.t>=0,sum(self.x)==1]
#should have a check to see if i is in the range of num of assets
constraints = baseConstraints+ [cvx.log(self.x[i])+cvx.log(self.t)>= cvx.log(regularizer)]
TrackingErrorSquared = cvx.sum_squares(returns*self.x -indexReturns )
obj = cvx.Minimize( TrackingErrorSquared+self.t)
cvx.Problem.__init__(self,obj,constraints)
def lasso_conv(n):
sigma = n/10
c = np.exp(-np.arange(-n/2., n/2.)**2./(2*sigma**2))/np.sqrt(2*sigma**2*np.pi)
c[c < 1e-4] = 0
x0 = np.array(sp.rand(n, 1, 0.1).todense()).ravel()
b = np.convolve(c, x0) + 1e-2*np.random.randn(2*n-1)
lam = 0.2*np.max(np.abs(np.convolve(b, c, "valid")))
print lam
x = cvx.Variable(n)
f = cvx.sum_squares(cvx.conv(c, x) - b) + lam*cvx.norm1(x)
return cvx.Problem(cvx.Minimize(f))
def foo_prox(a, b, x0, phi0, rho):
n = len(a)
x = cvx.Variable(n)
phi = cvx.Variable(n)
logb = np.log(b)
logcash = cvx.log_sum_exp(phi + logb)
ag_exp = cvx.log(x.T*a) - logcash
t = cvx.Variable()
constr = [x >= 0, ag_exp >= t]
for j in range(n):
expr = t >= np.log(a[j]) - phi[j]
constr += [expr]
obj = cvx.sum_squares(x-x0) + cvx.sum_squares(phi-phi0)
obj = obj*rho/2.0
prob = cvx.Problem(cvx.Minimize(obj), constr)
prob.solve(verbose=False, solver='ECOS')
return np.array(x.value).flatten(), np.array(phi.value).flatten()
A = np.array(train_data['A'])
B = np.array(train_data['B'])
_, num_samples = np.shape(A)
print "num_samples:", num_samples
u = cvx.Variable(num_samples)
v = cvx.Variable(num_samples)
constraints = [cvx.sum_entries(u) == 1,
cvx.sum_entries(v) == 1,
u >= 0,
v >= 0]
obj = cvx.Minimize(cvx.sum_squares(A * u - B * v))
prob = cvx.Problem(obj, constraints)
prob.solve()
print "status: ", prob.status
print "optimal value " , prob.value
#print "optimal var", u.value, v.value
w = A * u.value - B * v.value
r = np.transpose(A * u.value + B * v.value) / 2.0 * w
print w
print r
def _create_obj(self):
print("Creating optimization objective...")
self._obj = cp.Minimize(cp.sum_squares(self._W * self._x - self._tau))
def cvx_solve(row, regions, debug=False):
if row.isna().sum() > 0:
raise ValueError("Cannot call this method on data with NaNs")
n_regions = len(regions)
D = row[[KEYS["E"]["D"] % r for r in regions]].values
D_W = [
el ** 0.5
for el in row[[KEYS["E"]["D"] % r + "_W" for r in regions]].values
]
NG = row[[KEYS["E"]["NG"] % r for r in regions]].values
NG_W = [
el ** 0.5
for el in row[[KEYS["E"]["NG"] % r + "_W" for r in regions]].values
]
TI = row[[KEYS["E"]["TI"] % r for r in regions]].values
TI_W = [
el ** 0.5
for el in row[[KEYS["E"]["TI"] % r + "_W" for r in regions]].values
]
delta_D = cp.Variable(n_regions, name="delta_D")
delta_NG = cp.Variable(n_regions, name="delta_NG")
delta_TI = cp.Variable(n_regions, name="delta_TI")
obj = (
cp.sum_squares(cp.multiply(D_W, delta_D))
+ cp.sum_squares(cp.multiply(NG_W, delta_NG))
+ cp.sum_squares(cp.multiply(TI_W, delta_TI))
)
ID = {}
ID_W = {}
for i, ri in enumerate(regions):
for j, rj in enumerate(regions):
if KEYS["E"]["ID"] % (ri, rj) in row.index:
ID[(ri, rj)] = row[KEYS["E"]["ID"] % (ri, rj)]
ID_W[(ri, rj)] = row[KEYS["E"]["ID"] % (ri, rj) + "_W"]
delta_ID = {k: cp.Variable(name=f"{k}") for k in ID}
constraints = [
D + delta_D >= 1.0,
NG + delta_NG >= 1.0,
D + delta_D + TI + delta_TI - NG - delta_NG == 0.0,
]
if with_ng_src:
NG_SRC = {}
NG_SRC_W = {}
for i, src in enumerate(SRC):
for j, r in enumerate(regions):
if KEYS["E"][f"SRC_{src}"] % r in row.index:
NG_SRC[(src, r)] = row[KEYS["E"][f"SRC_{src}"] % r]
NG_SRC_W[(src, r)] = row[KEYS["E"][f"SRC_{src}"] % r + "_W"]
delta_NG_SRC = {k: cp.Variable(name=f"{k}") for k in NG_SRC}
for k in NG_SRC:
constraints += [NG_SRC[k] + delta_NG_SRC[k] >= 1.0]
obj += NG_SRC_W[k] * delta_NG_SRC[k] ** 2
# Add the antisymmetry constraints twice is less efficient but not a huge deal.
for ri, rj in ID: # then (rj, ri) must also be in ID
constraints += [
ID[(ri, rj)]
+ delta_ID[(ri, rj)]
+ ID[(rj, ri)]
+ delta_ID[(rj, ri)]
== 0.0
]
obj += ID_W[(ri, rj)] * delta_ID[(ri, rj)] ** 2
for i, ri in enumerate(regions):
if with_ng_src:
constraints += [
NG[i]
+ delta_NG[i]
- cp.sum(
[
NG_SRC[(src, ri)] + delta_NG_SRC[(src, ri)]
for src in SRC
if (src, ri) in NG_SRC
]
)
== 0.0
]
constraints += [
TI[i]
+ delta_TI[i]
- cp.sum(
[
ID[(ri, rj)] + delta_ID[(ri, rj)]
for rj in regions
if (ri, rj) in ID
]
)
== 0.0
]
objective = cp.Minimize(obj)
prob = cp.Problem(objective, constraints)
prob.solve()
if with_ng_src:
r = pd.concat(
[
pd.Series(
NG + delta_NG.value,
index=[KEYS["E"]["NG"] % r for r in regions],
),
pd.Series(
D + delta_D.value,
index=[KEYS["E"]["D"] % r for r in regions],
),
pd.Series(
TI + delta_TI.value,
index=[KEYS["E"]["TI"] % r for r in regions],
),
pd.Series(
{KEYS["E"]["ID"] % k: ID[k] + delta_ID[k].value for k in ID}
),
pd.Series(
{
KEYS["E"][f"SRC_{s}"] % r: NG_SRC[(s, r)]
+ delta_NG_SRC[(s, r)].value
for (s, r) in NG_SRC
}
),
pd.Series({"CleaningObjective": prob.value})
]
)
else:
r = pd.concat(
[
pd.Series(
NG + delta_NG.value,
index=[KEYS["E"]["NG"] % r for r in regions],
),
pd.Series(
D + delta_D.value,
index=[KEYS["E"]["D"] % r for r in regions],
),
pd.Series(
TI + delta_TI.value,
index=[KEYS["E"]["TI"] % r for r in regions],
),
pd.Series(
{KEYS["E"]["ID"] % k: ID[k] + delta_ID[k].value for k in ID}
),
pd.Series({"CleaningObjective": prob.value})
]
)
if not debug:
return r
if with_ng_src:
deltas = pd.concat(
[
pd.Series(
delta_NG.value, index=[KEYS["E"]["NG"] % r for r in regions]
),
pd.Series(
delta_D.value, index=[KEYS["E"]["D"] % r for r in regions]
),
pd.Series(
delta_TI.value, index=[KEYS["E"]["TI"] % r for r in regions]
),
pd.Series({KEYS["E"]["ID"] % k: delta_ID[k].value for k in ID}),
pd.Series(
{
KEYS["E"][f"SRC_{s}"] % r: delta_NG_SRC[(s, r)].value
for (s, r) in NG_SRC
}
),
]
)
else:
deltas = pd.concat(
[
pd.Series(
delta_NG.value, index=[KEYS["E"]["NG"] % r for r in regions]
),
pd.Series(
delta_D.value, index=[KEYS["E"]["D"] % r for r in regions]
),
pd.Series(
delta_TI.value, index=[KEYS["E"]["TI"] % r for r in regions]
),
pd.Series({KEYS["E"]["ID"] % k: delta_ID[k].value for k in ID}),
]
)
return pd.concat([r, deltas.rename(lambda x: x + "_Delta")])
import numpy as np
import cvxpy as cp
import matplotlib.pyplot as plt
from nonlin_meas_data import m, n, sigma, alpha, beta, A, y
np.set_printoptions(precision=3)
EPSILON = 1e-8
#Verifying that the data is sorted
for i in range(m - 1):
assert y[i] < y[i + 1] + EPSILON
z = cp.Variable(m)
x = cp.Variable(n)
next_diff_z = z[1:] - z[:-1]
next_diff_y = y[1:] - y[:-1]
constraints = [
next_diff_z <= next_diff_y / alpha,
next_diff_z >= next_diff_y / beta,
]
obj = cp.Minimize(cp.sum_squares(A @ x - z))
problem = cp.Problem(obj, constraints)
problem.solve()
print(f"problem status: {problem.status}")
if problem.status == 'optimal':
print(f"x = {x.value}")
plt.plot(y, z.value)
plt.show()
FontPath = '/System/Library/Fonts/ヒラギノ角ゴシック W4.ttc'
elif sys.platform.startswith('linux'):
FontPath = '/usr/share/fonts/truetype/takao-gothic/TakaoPGothic.ttf'
jpfont = FontProperties(fname=FontPath)
#%% 収益率データの読み込み
R = pd.read_csv('asset_return_data.csv', index_col=0)
T = R.shape[0]
N = R.shape[1]
Mu = R.mean().values
Sigma = R.cov().values * ((T - 1.0) / T)
Return_Dev = (R - Mu).values / np.sqrt(T)
#%% 空売り制約の下での分散最小化問題の設定
Weight = cvx.Variable(N)
Deviation = cvx.Variable(T)
Target_Return = cvx.Parameter(sign='positive')
Risk_Variance = cvx.sum_squares(Deviation)
Opt_Portfolio = cvx.Problem(cvx.Minimize(Risk_Variance), [
Return_Dev * Weight == Deviation, Weight.T * Mu == Target_Return,
cvx.sum_entries(Weight) == 1.0, Weight >= 0.0
])
#%% 空売り制約の下での最小分散フロンティアの計算
V_Target = np.linspace(Mu.min(), Mu.max(), num=250)
V_Risk = np.zeros(V_Target.shape)
for idx, Target_Return.value in enumerate(V_Target):
Opt_Portfolio.solve()
V_Risk[idx] = np.sqrt(Risk_Variance.value)
#%% 最小分散フロンティアのグラフの作成
fig1 = plt.figure(1, facecolor='w')
plt.plot(V_Risk, V_Target, 'k-')
plt.plot(np.sqrt(np.diagonal(Sigma)), Mu, 'kx')
plt.legend([u'最小分散フロンティア', u'個別資産'], loc='best', frameon=False, prop=jpfont)
def approxBalATE(X, T, Y, tol_vals, objective):
# weight the control and treated units so that they match the whole population
n_ctrl = np.sum(1 - T) # number of controls
n_trt = np.sum(T)
n_cov = X.shape[1] # number of covariates
tol = cp.Parameter()
# weight the control units to match the population
w_c = cp.Variable(n_ctrl)
if objective == "l1":
obj_c = cp.Minimize(cp.norm((w_c - 1 / n_ctrl), 1))
elif objective == "l2":
obj_c = cp.Minimize(cp.sum_squares(w_c - 1 / n_ctrl))
elif objective == "entropy":
obj_c = cp.Minimize(-cp.sum(cp.entr(w_c)))
else:
print("invalid objective")
# return -1
constraints_c = [cp.sum(w_c) == 1]
constraints_c += [0 <= w_c]
for i in range(n_cov):
constraints_c += [X[T==0][:,i]*w_c - \
np.mean(X[:,i]) <= \
tol * X[:,i].std()]
constraints_c += [np.mean(X[:,i]) -\
X[T==0][:,i]*w_c <=\
tol * X[:,i].std()]
prob_c = cp.Problem(obj_c, constraints_c)
w_c_vals = []
for tol_val in tol_vals:
tol.value = tol_val
try:
result_c = prob_c.solve()
if w_c.value is None:
w_c.value = -1. * np.ones(n_ctrl)
w_c_vals.append(w_c.value)
except SolverError:
w_c_vals.append(-1. * np.ones(n_ctrl))
# weight the treated units to match the population
w_t = cp.Variable(n_trt)
if objective == "l1":
obj_t = cp.Minimize(cp.norm((w_t - 1 / n_trt), 1))
elif objective == "l2":
obj_t = cp.Minimize(cp.sum_squares(w_t - 1 / n_trt))
elif objective == "entropy":
obj_t = cp.Minimize(-cp.sum(cp.entr(w_t)))
else:
print("invalid objective")
# return -1
constraints_t = [cp.sum(w_t) == 1]
constraints_t += [0 <= w_t]
for i in range(n_cov):
constraints_t += [X[T==1][:,i]*w_t - \
np.mean(X[:,i]) <= \
tol * X[:,i].std()]
constraints_t += [np.mean(X[:,i]) -\
X[T==1][:,i]*w_t <= \
tol * X[:,i].std()]
prob_t = cp.Problem(obj_t, constraints_t)
w_t_vals = []
for tol_val in tol_vals:
tol.value = tol_val
try:
result_t = prob_t.solve()
if w_t.value is None:
w_t.value = -1. * np.ones(n_trt)
w_t_vals.append(w_t.value)
except SolverError:
w_t_vals.append(-1. * np.ones(n_trt))
return w_c_vals, w_t_vals
split_plane = ck.prompt('Which Plane to split weight', type=int)
while split_plane < 1 or split_plane > N:
print('please enter a number between 1-', N)
split_plane = ck.prompt('Which Plane to split weight', type=int)
continue
Split(W[split_plane - 1].value)
# =============================================================================
# =============================================================================
# # #USING CVXPY LEAST SQUARES TO SOLVE THE PROBLEM
# =============================================================================
# =============================================================================
W = cp.Variable((N, 1), complex=True)
objective = cp.Minimize(cp.sum_squares(ALPHA * W + A))
prob = cp.Problem(objective)
prob.solve()
print("Residule Squares")
print("-----------------")
print("Maximum Residual Error =", "%.2f" % error(W))
prnt(W)
print("Expected residual Array")
print(np.round(abs(np.add(np.matmul(ALPHA, W.value), A)), 2))
Call_Split(W)
# =============================================================================
# =============================================================================
# # # SOLVING USING MIN-MAX
# =============================================================================
def to_cvxpy(self, current_weights):
self._make_variable(current_weights)
self._target_weights = self._target_weights.reindex(
self._new_index).fillna(0)
err = cvx.sum_squares(self._new_weights - self._target_weights.values)
return cvx.Minimize(err)
def deviation_risk_parity(w, cov_matrix):
n = cov_matrix.shape[0]
rp = (w * (cov_matrix @ w)) / cp.quad_form(w, cov_matrix)
return cp.sum_squares(rp - 1 / n).value
import cvxpy as cvx
import qcqp
n = 10
m = 8
l = 2
tau = 10
eta = 1
np.random.seed(1)
H = np.random.randn(m, n)
G = np.random.randn(l, n)
w = cvx.Variable(n)
obj = cvx.Minimize(cvx.sum_squares(w))
cons = [cvx.square(H * w) >= tau, cvx.square(G * w) <= eta]
prob = cvx.Problem(obj, cons)
# SDP-based lower bound
lb = prob.solve(method='sdp-relax', solver=cvx.MOSEK)
print('Lower bound: %.3f' % lb)
# Upper bounds
ub_cd = prob.solve(method='coord-descent', solver=cvx.MOSEK, num_samples=10)
ub_admm = prob.solve(method='qcqp-admm', solver=cvx.MOSEK, num_samples=10)
ub_dccp = prob.solve(method='qcqp-dccp',
solver=cvx.MOSEK,
num_samples=10,
tau=1)
print('Lower bound: %.3f' % lb)
def __init__(self,
d,
dataset_name=None,
X=None,
use_slab=False,
constrain_max_loss=False,
use_l2=False,
x_pos_tuple=None,
x_neg_tuple=None,
model_type='svm'):
self.use_slab = use_slab
self.constrain_max_loss = constrain_max_loss
self.use_l2 = use_l2
self.dataset = dataset_name
# creating variables with shape of "d"
# need to deal with some binary feature attibutes
if dataset_name == "adult":
# ---- adult -----
# attributes 0-3 are continuous and represent: "age", "capital-gain", "capital-loss", "hours-per-week"
# attributes 4-11 are binary representing the work class.
# attributes 12-26: education background
# attributes 27-32: martial status
# attributes 33-46: occupation
# attributes 47-51: relationship
# 52-56: race
# bool_inds = np.array([0]*d)
# bool_inds[4:] = bool_inds[4:] + 1
# print("the bolean indices are:",tuple(bool_inds))
# self.cvx_x_pos = cvx.Variable(d, boolean = tuple([bool_inds]))
self.cvx_x_pos_real = cvx.Variable(4)
self.cvx_x_neg_real = cvx.Variable(4)
self.cvx_x_pos_binary = cvx.Bool(d - 4)
self.cvx_x_neg_binary = cvx.Bool(d - 4)
# used for the binary constraints
arr = np.array([0] * (d - 4))
arr[0:8] = 1
self.cvx_work_class = cvx.Parameter(d - 4, value=arr)
arr = np.array([0] * (d - 4))
arr[8:23] = 1
self.cvx_education = cvx.Parameter(d - 4, value=arr)
arr = np.array([0] * (d - 4))
arr[23:29] = 1
self.cvx_martial = cvx.Parameter(d - 4, value=arr)
arr = np.array([0] * (d - 4))
arr[29:43] = 1
self.cvx_occupation = cvx.Parameter(d - 4, value=arr)
arr = np.array([0] * (d - 4))
arr[43:48] = 1
self.cvx_relationship = cvx.Parameter(d - 4, value=arr)
arr = np.array([0] * (d - 4))
arr[48:53] = 1
self.cvx_race = cvx.Parameter(d - 4, value=arr)
else:
self.cvx_x_pos = cvx.Variable(d)
self.cvx_x_neg = cvx.Variable(d)
self.cvx_g = cvx.Parameter(d)
self.cvx_theta = cvx.Parameter(d)
self.cvx_bias = cvx.Parameter(1)
self.cvx_epsilon_pos = cvx.Parameter(1)
self.cvx_epsilon_neg = cvx.Parameter(1)
self.cvx_centroid_pos = cvx.Parameter(d)
self.cvx_centroid_neg = cvx.Parameter(d)
if use_l2:
self.cvx_sphere_radius_pos = cvx.Parameter(1)
self.cvx_sphere_radius_neg = cvx.Parameter(1)
if use_slab:
self.cvx_centroid_vec = cvx.Parameter(d)
self.cvx_slab_radius_pos = cvx.Parameter(1)
self.cvx_slab_radius_neg = cvx.Parameter(1)
if constrain_max_loss:
self.cvx_max_loss_pos = cvx.Parameter(1)
self.cvx_max_loss_neg = cvx.Parameter(1)
self.cvx_err = cvx.Variable(d)
self.objective = cvx.Minimize(cvx.pnorm(self.cvx_err, 2))
# version 0.4 is below
if dataset_name == 'adult':
self.constraints = [
self.cvx_g - self.cvx_epsilon_pos * cvx.vstack(self.cvx_x_pos_real,self.cvx_x_pos_binary) +\
self.cvx_epsilon_neg * cvx.vstack(self.cvx_x_neg_real,self.cvx_x_neg_binary) == self.cvx_err,
cvx_dot(self.cvx_theta, cvx.vstack(self.cvx_x_pos_real,self.cvx_x_pos_binary)) + self.cvx_bias < 1, # margin constraint, ideally should be 1
-(cvx_dot(self.cvx_theta, cvx.vstack(self.cvx_x_neg_real,self.cvx_x_neg_binary)) + self.cvx_bias) < 1 , # ideally should be 1
]
else:
if model_type == 'svm':
self.constraints = [
self.cvx_g - self.cvx_epsilon_pos * self.cvx_x_pos +
self.cvx_epsilon_neg * self.cvx_x_neg == self.cvx_err,
cvx_dot(self.cvx_theta, self.cvx_x_pos) + self.cvx_bias <
1, # margin constraint, ideally should be 1
-(cvx_dot(self.cvx_theta, self.cvx_x_neg) + self.cvx_bias)
< 1, # ideally should be 1
]
# cvx 1.0 version
# if model_type == 'svm':
# self.constraints = [
# self.cvx_g - self.cvx_epsilon_pos * self.cvx_x_pos + self.cvx_epsilon_neg * self.cvx_x_neg == self.cvx_err,
# cvx_dot(self.cvx_theta, self.cvx_x_pos) + self.cvx_bias <= 1, # margin constraint, ideally should be 1
# -(cvx_dot(self.cvx_theta, self.cvx_x_neg) + self.cvx_bias) <= 1 , # ideally should be 1
# ]
elif model_type == 'lr': # lr is not convex, cannot support it now
pos_margin = cvx_dot(self.cvx_x_pos,
self.cvx_theta) + self.cvx_bias
neg_margin = -cvx_dot(self.cvx_x_neg,
self.cvx_theta) + self.cvx_bias
pos_grad = -sigmoid(-pos_margin) * self.cvx_x_pos
neg_grad = sigmoid(-neg_margin) * self.cvx_x_neg
self.constraints = [
self.cvx_g - self.cvx_epsilon_pos * pos_grad +
self.cvx_epsilon_neg * neg_grad == self.cvx_err
]
else:
print("Please use common linear classifier!")
raise NotImplementedError
if use_slab:
self.constraints.append(
cvx_dot(self.cvx_centroid_vec, self.cvx_x_pos -
self.cvx_centroid_pos) < self.cvx_slab_radius_pos)
self.constraints.append(
-cvx_dot(self.cvx_centroid_vec, self.cvx_x_pos -
self.cvx_centroid_pos) < self.cvx_slab_radius_pos)
self.constraints.append(
cvx_dot(self.cvx_centroid_vec, self.cvx_x_neg -
self.cvx_centroid_neg) < self.cvx_slab_radius_neg)
self.constraints.append(
-cvx_dot(self.cvx_centroid_vec, self.cvx_x_neg -
self.cvx_centroid_neg) < self.cvx_slab_radius_neg)
if dataset_name in ['mnist_17', 'enron', 'imdb']:
self.constraints.append(self.cvx_x_pos >= 0)
self.constraints.append(self.cvx_x_neg >= 0)
# additional constraints on synthetic dataset
if x_pos_tuple:
assert x_neg_tuple != None
self.x_pos_min, self.x_pos_max = x_pos_tuple
self.x_neg_min, self.x_neg_max = x_neg_tuple
if dataset_name == 'adult':
self.constraints.append(self.cvx_x_pos_real >= self.x_pos_min)
self.constraints.append(self.cvx_x_pos_real <= self.x_pos_max)
self.constraints.append(self.cvx_x_neg_real >= self.x_neg_min)
self.constraints.append(self.cvx_x_neg_real <= self.x_neg_max)
else:
self.constraints.append(self.cvx_x_pos >= self.x_pos_min)
self.constraints.append(self.cvx_x_pos <= self.x_pos_max)
self.constraints.append(self.cvx_x_neg >= self.x_neg_min)
self.constraints.append(self.cvx_x_neg <= self.x_neg_max)
if constrain_max_loss:
self.constraints.append(1 -
(cvx_dot(self.cvx_theta, self.cvx_x_pos) +
self.cvx_bias) < self.cvx_max_loss_pos)
self.constraints.append(1 +
(cvx_dot(self.cvx_theta, self.cvx_x_neg) +
self.cvx_bias) < self.cvx_max_loss_neg)
if dataset_name in ['mnist_17']:
self.constraints.append(self.cvx_x_pos <= 1)
self.constraints.append(self.cvx_x_neg <= 1)
if dataset_name == 'adult':
# binary featutre constraints: beacuse of one-hot encoding
self.constraints.append(
cvx_dot(self.cvx_work_class, self.cvx_x_pos_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_work_class, self.cvx_x_neg_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_education, self.cvx_x_pos_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_education, self.cvx_x_neg_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_martial, self.cvx_x_pos_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_martial, self.cvx_x_neg_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_occupation, self.cvx_x_pos_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_occupation, self.cvx_x_neg_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_relationship, self.cvx_x_pos_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_relationship, self.cvx_x_neg_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_race, self.cvx_x_pos_binary) == 1)
self.constraints.append(
cvx_dot(self.cvx_race, self.cvx_x_neg_binary) == 1)
# If we pass in X, do the LP/integer constraint
if (X is not None) and (dataset_name in ['enron', 'imdb']):
if sparse.issparse(X):
X_max = np.max(X, axis=0).toarray().reshape(-1)
else:
X_max = np.max(X, axis=0).reshape(-1)
X_max[X_max < 1] = 1
X_max[X_max > 50] = 50
self.constraints.append(self.cvx_x_pos <= X_max)
self.constraints.append(self.cvx_x_neg <= X_max)
kmax = int(np.ceil(np.max(X_max)))
self.cvx_env_pos = cvx.Variable(d)
self.cvx_env_neg = cvx.Variable(d)
for k in range(1, kmax + 1):
active = k <= (X_max)
self.constraints.append(
self.cvx_env_pos[active] >= self.cvx_x_pos[active] *
(2 * k - 1) - k * (k - 1))
self.constraints.append(
self.cvx_env_neg[active] >= self.cvx_x_neg[active] *
(2 * k - 1) - k * (k - 1))
if use_l2:
self.constraints.append(
(cvx.sum_entries(self.cvx_env_pos) -
2 * cvx_dot(self.cvx_centroid_pos, self.cvx_x_pos) +
cvx.sum_squares(self.cvx_centroid_pos)) < (
self.cvx_sphere_radius_pos**2))
self.constraints.append(
(cvx.sum_entries(self.cvx_env_neg) -
2 * cvx_dot(self.cvx_centroid_neg, self.cvx_x_neg) +
cvx.sum_squares(self.cvx_centroid_neg)) < (
self.cvx_sphere_radius_neg**2))
else:
if use_l2:
self.constraints.append(
cvx.pnorm(self.cvx_x_pos - self.cvx_centroid_pos, 2)**2 <
self.cvx_sphere_radius_pos**2)
self.constraints.append(
cvx.pnorm(self.cvx_x_neg - self.cvx_centroid_neg, 2)**2 <
self.cvx_sphere_radius_neg**2)
#!/usr/bin/python
import numpy as np
import cvxpy as cvx
from qcqp import *
n, m = 10, 15
np.random.seed(1)
A = np.random.randn(m, n)
b = np.random.randn(m, 1)
x = cvx.Variable(n)
obj = cvx.sum_squares(A * x - b)
cons = [cvx.square(x) == 1]
prob = cvx.Problem(cvx.Minimize(obj), cons)
qcqp = QCQP(prob)
# sample from the semidefinite relaxation
qcqp.suggest(SDR)
print("SDR lower bound: %.3f" % qcqp.sdr_bound)
f_cd, v_cd = qcqp.improve(COORD_DESCENT)
x_cd = x.value
print("Coordinate descent: objective %.3f, violation %.3f" % (f_cd, v_cd))
# SDR solution is cached and not solved again
qcqp.suggest(SDR)
f_dccp, v_dccp = qcqp.improve(DCCP)
print("Penalty CCP: objective %.3f, violation %.3f" % (f_dccp, v_dccp))
f_dccp, v_dccp = qcqp.improve(COORD_DESCENT, phase1=False)
x_dccp = x.value
(len(lines), 1))
t = np.linspace(0, 5, num=5001)
f = np.linspace(1, 100, num=100)
phi = np.array([[np.sin(2 * np.pi * fk * ti) for fk in f] for ti in t])
alphas = [0.00001, 0.0001, 0.001, 0.01, 0.1, 1, 10, 100, 1000, 10000]
residuals = []
xs = []
probvals = []
for alpha in alphas:
print(alpha)
x = cp.Variable((100, 1))
obj = cp.Minimize((alpha * cp.norm(x, 1)) +
cp.sum_squares(y_n - cp.matmul(phi, x)))
prob = cp.Problem(obj)
prob.solve()
residuals.append(cp.norm(y_n - (phi @ x)).value)
xs.append(x.value)
probvals.append(prob.value)
print(residuals)
print(probvals)
plt.plot(alphas, probvals)
plt.xscale('log')
plt.show()
for i in range(len(xs)):
plt.plot(range(1, 101), xs[i])
def test_intro(self) -> None:
"""Test examples from cvxpy.org introduction.
"""
import numpy
# cvx.Problem data.
m = 30
n = 20
numpy.random.seed(1)
A = numpy.random.randn(m, n)
b = numpy.random.randn(m)
# Construct the problem.
x = cvx.Variable(n)
objective = cvx.Minimize(cvx.sum_squares(A @ x - b))
constraints = [0 <= x, x <= 1]
prob = cvx.Problem(objective, constraints)
# The optimal objective is returned by p.solve().
prob.solve()
# The optimal value for x is stored in x.value.
print(x.value)
# The optimal Lagrange multiplier for a constraint
# is stored in constraint.dual_value.
print(constraints[0].dual_value)
########################################
# Create two scalar variables.
x = cvx.Variable()
y = cvx.Variable()
# Create two constraints.
constraints = [x + y == 1, x - y >= 1]
# Form objective.
obj = cvx.Minimize(cvx.square(x - y))
# Form and solve problem.
prob = cvx.Problem(obj, constraints)
prob.solve() # Returns the optimal value.
print("status:", prob.status)
print("optimal value", prob.value)
print("optimal var", x.value, y.value)
########################################
# Create two scalar variables.
x = cvx.Variable()
y = cvx.Variable()
# Create two constraints.
constraints = [x + y == 1, x - y >= 1]
# Form objective.
obj = cvx.Minimize(cvx.square(x - y))
# Form and solve problem.
prob = cvx.Problem(obj, constraints)
prob.solve() # Returns the optimal value.
print("status:", prob.status)
print("optimal value", prob.value)
print("optimal var", x.value, y.value)
self.assertEqual(prob.status, cvx.OPTIMAL)
self.assertAlmostEqual(prob.value, 1.0)
self.assertAlmostEqual(x.value, 1.0)
self.assertAlmostEqual(y.value, 0)
########################################
# Replace the objective.
prob = cvx.Problem(cvx.Maximize(x + y), prob.constraints)
print("optimal value", prob.solve())
self.assertAlmostEqual(prob.value, 1.0, places=3)
# Replace the constraint (x + y == 1).
constraints = prob.constraints
constraints[0] = (x + y <= 3)
prob = cvx.Problem(prob.objective, constraints)
print("optimal value", prob.solve())
self.assertAlmostEqual(prob.value, 3.0, places=2)
########################################
x = cvx.Variable()
# An infeasible problem.
prob = cvx.Problem(cvx.Minimize(x), [x >= 1, x <= 0])
prob.solve()
print("status:", prob.status)
print("optimal value", prob.value)
self.assertEqual(prob.status, cvx.INFEASIBLE)
self.assertAlmostEqual(prob.value, np.inf)
# An unbounded problem.
prob = cvx.Problem(cvx.Minimize(x))
prob.solve()
print("status:", prob.status)
print("optimal value", prob.value)
self.assertEqual(prob.status, cvx.UNBOUNDED)
self.assertAlmostEqual(prob.value, -np.inf)
########################################
# A scalar variable.
cvx.Variable()
# Column vector variable of length 5.
x = cvx.Variable(5)
# Matrix variable with 4 rows and 7 columns.
A = cvx.Variable((4, 7))
########################################
import numpy
# cvx.Problem data.
m = 10
n = 5
numpy.random.seed(1)
A = numpy.random.randn(m, n)
b = numpy.random.randn(m)
# Construct the problem.
x = cvx.Variable(n)
objective = cvx.Minimize(cvx.sum_squares(A @ x - b))
constraints = [0 <= x, x <= 1]
prob = cvx.Problem(objective, constraints)
print("Optimal value", prob.solve())
print("Optimal var")
print(x.value) # A numpy matrix.
self.assertAlmostEqual(prob.value, 4.14133859146)
########################################
# Positive scalar parameter.
m = cvx.Parameter(nonneg=True)
# Column vector parameter with unknown sign (by default).
cvx.Parameter(5)
# Matrix parameter with negative entries.
G = cvx.Parameter((4, 7), nonpos=True)
# Assigns a constant value to G.
G.value = -numpy.ones((4, 7))
########################################
# Create parameter, then assign value.
rho = cvx.Parameter(nonneg=True)
rho.value = 2
# Initialize parameter with a value.
rho = cvx.Parameter(nonneg=True, value=2)
########################################
import numpy
# cvx.Problem data.
n = 15
m = 10
numpy.random.seed(1)
A = numpy.random.randn(n, m)
b = numpy.random.randn(n)
# gamma must be positive due to DCP rules.
gamma = cvx.Parameter(nonneg=True)
# Construct the problem.
x = cvx.Variable(m)
error = cvx.sum_squares(A @ x - b)
obj = cvx.Minimize(error + gamma * cvx.norm(x, 1))
prob = cvx.Problem(obj)
# Construct a trade-off curve of ||Ax-b||^2 vs. ||x||_1
sq_penalty = []
l1_penalty = []
x_values = []
gamma_vals = numpy.logspace(-4, 6)
for val in gamma_vals:
gamma.value = val
prob.solve()
# Use expr.value to get the numerical value of
# an expression in the problem.
sq_penalty.append(error.value)
l1_penalty.append(cvx.norm(x, 1).value)
x_values.append(x.value)
########################################
import numpy
X = cvx.Variable((5, 4))
A = numpy.ones((3, 5))
# Use expr.size to get the dimensions.
print("dimensions of X:", X.size)
print("dimensions of sum(X):", cvx.sum(X).size)
print("dimensions of A @ X:", (A @ X).size)
# ValueError raised for invalid dimensions.
try:
A + X
except ValueError as e:
print(e)
def __init__(self,
d,
use_sphere=True,
use_slab=True,
non_negative=False,
less_than_one=False,
constrain_max_loss=False,
goal=None,
X=None):
assert goal in ['find_nearest_point', 'maximize_test_loss']
self.use_slab = use_slab
self.constrain_max_loss = constrain_max_loss
self.goal = goal
self.use_projection = not (non_negative or less_than_one or X)
if self.use_projection:
eff_d = 3 + (constrain_max_loss == True)
else:
eff_d = d
self.cvx_x = cvx.Variable(eff_d)
self.cvx_w = cvx.Parameter(eff_d)
self.cvx_centroid = cvx.Parameter(eff_d)
self.cvx_sphere_radius = cvx.Parameter(1)
self.cvx_x_c = self.cvx_x - self.cvx_centroid
if goal == 'find_nearest_point':
self.objective = cvx.Minimize(
cvx.pnorm(self.cvx_x - self.cvx_w, 2)**2)
elif goal == 'maximize_test_loss':
self.cvx_y = cvx.Parameter(1)
# No need for bias term
self.objective = cvx.Maximize(1 - self.cvx_y *
cvx_dot(self.cvx_w, self.cvx_x))
self.constraints = []
if use_sphere:
if X is not None:
if sparse.issparse(X):
X_max = X.max(axis=0).toarray().reshape(-1)
else:
X_max = np.max(X, axis=0).reshape(-1)
X_max[X_max < 1] = 1
X_max[X_max > 50] = 50
self.constraints.append(self.cvx_x <= X_max)
kmax = int(np.ceil(np.max(X_max)))
self.cvx_env = cvx.Variable(eff_d)
for k in range(1, kmax + 1):
active = k <= (X_max)
self.constraints.append(
self.cvx_env[active] >= self.cvx_x[active] *
(2 * k - 1) - k * (k - 1))
self.constraints.append(
(cvx.sum_entries(self.cvx_env) -
2 * cvx_dot(self.cvx_centroid, self.cvx_x) +
cvx.sum_squares(self.cvx_centroid)) < (
self.cvx_sphere_radius**2))
else:
self.constraints.append(
cvx.pnorm(self.cvx_x_c, 2)**2 < self.cvx_sphere_radius**2)
if use_slab:
self.cvx_centroid_vec = cvx.Parameter(eff_d)
self.cvx_slab_radius = cvx.Parameter(1)
self.constraints.append(
cvx_dot(self.cvx_centroid_vec, self.cvx_x_c) <
self.cvx_slab_radius)
self.constraints.append(
-cvx_dot(self.cvx_centroid_vec, self.cvx_x_c) <
self.cvx_slab_radius)
if non_negative:
self.constraints.append(self.cvx_x >= 0)
if less_than_one:
self.constraints.append(self.cvx_x <= 1)
if constrain_max_loss:
self.cvx_max_loss = cvx.Parameter(1)
self.cvx_constraint_w = cvx.Parameter(eff_d)
self.cvx_constraint_b = cvx.Parameter(1)
self.constraints.append(
1 - self.cvx_y * (cvx_dot(self.cvx_constraint_w, self.cvx_x) +
self.cvx_constraint_b) < self.cvx_max_loss)
self.prob = cvx.Problem(self.objective, self.constraints)
import cvxpy as cp
import numpy as np
m, n = 30, 20 # создаем матрицу и вектор (уравнений больше чем переменых)
A, b = np.random.randn(m, n), np.random.randn(m)
# Создаем вектор переменных
x = cp.Variable(n)
constraints = [0 <= x, x <= 1]
prob = cp.Problem(
objective=cp.Minimize(cp.sum_squares(A * x - b)),
constraints=constraints,
)
# The optimal objective value is returned by `prob.solve()`.
result = prob.solve_tsp()
# The optimal value for x is stored in `x.value`.
print(x.value)
# The optimal Lagrange multiplier for a constraint is stored in
# `constraint.dual_value`.
print(constraints[0].dual_value)
def test_absorb_lin_op(self):
"""Test absorb lin op operator.
"""
# norm1.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = norm1(mul_elemwise(-v, tmp), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0))
fn = norm1(mul_elemwise(-v, mul_elemwise(2 * v, tmp)), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(
x,
np.sign(v) * np.maximum(np.abs(v) - 5. * np.abs(v) / rho, 0))
new_prox = absorb_lin_op(new_prox)[0]
x = new_prox.prox(rho, v.copy())
new_v = 2 * v * v
self.assertItemsAlmostEqual(
x,
np.sign(new_v) *
np.maximum(np.abs(new_v) - 5. * np.abs(new_v) / rho, 0))
# nonneg.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = nonneg(mul_elemwise(-v, tmp), alpha=5.)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
self.assertItemsAlmostEqual(x, fn.prox(rho, -np.abs(v)))
# sum_squares.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
alpha = 5.
val = np.arange(10)
fn = sum_squares(mul_elemwise(-v, tmp), alpha=alpha, c=val)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(
cvx.Minimize(
cvx.sum_squares(cvx_x - v) * (rho / 2) +
5 * cvx.sum_squares(cvx.multiply(-v, cvx_x)) +
(val * -v).T @ cvx_x))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=3)
# Test scale.
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = norm1(10 * tmp)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(
cvx.Minimize(cvx.sum_squares(cvx_x - v) + cvx.norm(10 * cvx_x, 1)))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=3)
val = np.arange(10)
fn = norm1(10 * tmp, c=val, b=val, gamma=0.01)
rho = 2
new_prox = absorb_lin_op(fn)[0]
x = new_prox.prox(rho, v.copy())
cvx_x = cvx.Variable(10)
prob = cvx.Problem(cvx.Minimize(cvx.sum_squares(cvx_x - v) +
cvx.norm(10 * cvx_x - val, 1) + 10 * val.T * \
cvx_x + cvx.sum_squares(cvx_x)
))
prob.solve()
self.assertItemsAlmostEqual(x, cvx_x.value, places=2)
# sum_entries
tmp = Variable(10)
v = np.arange(10) * 1.0 - 5.0
fn = sum_entries(sum([10 * tmp, mul_elemwise(v, tmp)]))
funcs = absorb.absorb_all_lin_ops([fn])
c = __builtins__['sum']([func.c for func in funcs])
self.assertItemsAlmostEqual(c, v + 10, places=3)
constr += [
etahat[:,
t - 1] == tau[:, t] - M @ ntddot[:, t] - W @ ntdot[:, t]
]
# Trust region constraints.
constr += [cp.abs(nt[:] - ot[:]) <= rhos[i]]
# Torque limit.
constr += [cp.abs(tau[:]) <= taumax]
# Second arm can't fold back on first.
constr += [nt[1, :] <= math.pi, nt[1, :] >= -1 * math.pi]
# Establish objective function
objective = cp.Minimize(h * cp.sum_squares(tau[:]) +
lambdalambda * cp.sum(cp.abs(etahat[:])))
problem = cp.Problem(objective, constr)
optval = problem.solve(solver=cp.ECOS) # Solve...That...Problem!
# Calculate actual torque violations.
eta = np.zeros((2, N))
for t in range(1, N + 1):
# Dynamics equations. CONVERT TO PYTHON
t1 = nt.value[0, t]
t2 = nt.value[1, t]
t1dot = ntdot.value[0, t]
t2dot = ntdot.value[1, t]
thetalist = np.array([t1, t2])
def test_problem(self):
"""Test problem object.
"""
X = Variable((4, 2))
B = np.reshape(np.arange(8), (4, 2)) * 1.
prox_fns = [norm1(X), sum_squares(X, b=B)]
prob = Problem(prox_fns)
# prob.partition(quad_funcs = [prox_fns[0], prox_fns[1]])
prob.set_automatic_frequency_split(False)
prob.set_absorb(False)
prob.set_implementation(Impl['halide'])
prob.set_solver('admm')
prob.solve()
true_X = norm1(X).prox(2, B.copy())
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="pc")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs",
eps_rel=1e-6,
rho_0=1.0,
rho_scale=np.sqrt(2.0) * 2.0,
rho_max=2**16,
max_iters=20,
max_inner_iters=500,
verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# CG
prob = Problem(prox_fns)
prob.set_lin_solver("cg")
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
prob.solve(solver="hqs",
eps_rel=1e-6,
rho_0=1.0,
rho_scale=np.sqrt(2.0) * 2.0,
rho_max=2**16,
max_iters=20,
max_inner_iters=500,
verbose=False)
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Quad funcs.
prob = Problem(prox_fns)
prob.solve(solver="admm")
self.assertItemsAlmostEqual(X.value, true_X, places=2)
# Absorbing lin ops.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X, b=B)]
prob = Problem(prox_fns)
prob.set_absorb(True)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
cvx_X = cvx.Variable(4, 2)
cost = cvx.sum_squares(-2 * cvx_X - B) + cvx.norm(
5 * cvx.mul_elemwise(B, cvx_X), 1)
cvx_prob = cvx.Problem(cvx.Minimize(cost))
cvx_prob.solve(solver=cvx.SCS)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
prob.set_absorb(False)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
# Constant offsets.
prox_fns = [norm1(5 * mul_elemwise(B, X)), sum_squares(-2 * X - B)]
prob = Problem(prox_fns)
prob.solve(solver="admm", eps_rel=1e-6, eps_abs=1e-6)
self.assertItemsAlmostEqual(X.value, cvx_X.value, places=2)
elif sys.platform.startswith('darwin'):
FontPath = '/System/Library/Fonts/ヒラギノ角ゴシック W4.ttc'
elif sys.platform.startswith('linux'):
FontPath = '/usr/share/fonts/truetype/takao-gothic/TakaoPGothic.ttf'
jpfont = FontProperties(fname=FontPath)
#%% 収益率データの読み込み
R = pd.read_csv('asset_return_data.csv', index_col=0)
T = R.shape[0]
N = R.shape[1]
Mu = R.mean().values
Return_Dev = (R - Mu).values / np.sqrt(T)
#%% 下方半分散最小化問題の設定
Weight = cvx.Variable(N)
Deviation = cvx.Variable(T)
Target_Return = cvx.Parameter(nonneg=True)
Risk_Semivariance = cvx.sum_squares(Deviation)
Opt_Portfolio = cvx.Problem(cvx.Minimize(Risk_Semivariance),
[Weight.T*Mu == Target_Return,
cvx.sum(Weight) == 1.0,
Weight >= 0.0,
Deviation >= 0.0,
Return_Dev*Weight + Deviation >= 0.0])
#%% 最小下方半分散フロンティアの計算
V_Target = np.linspace(Mu.min(), Mu.max(), num=250)
V_Risk = np.zeros(V_Target.shape)
for idx, Target_Return.value in enumerate(V_Target):
Opt_Portfolio.solve(solver=cvx.ECOS)
V_Risk[idx] = np.sqrt(Risk_Semivariance.value)
#%% 最小下方半分散フロンティアのグラフの作成
fig1 = plt.figure(1, facecolor='w')
plt.plot(V_Risk, V_Target, 'k-')
def __update_ecc(self, nb_cost_mat, dis_k_vec, rw_constraints='inequality'):
# if self.__ds_name == 'Letter-high':
if self.__ged_options['edit_cost'] == 'LETTER':
raise Exception('Cannot compute for cost "LETTER".')
pass
# # method 1: set alpha automatically, just tune c_vir and c_eir by
# # LMS using cvxpy.
# alpha = 0.5
# coeff = 100 # np.max(alpha * nb_cost_mat[:,4] / dis_k_vec)
## if np.count_nonzero(nb_cost_mat[:,4]) == 0:
## alpha = 0.75
## else:
## alpha = np.min([dis_k_vec / c_vs for c_vs in nb_cost_mat[:,4] if c_vs != 0])
## alpha = alpha * 0.99
# param_vir = alpha * (nb_cost_mat[:,0] + nb_cost_mat[:,1])
# param_eir = (1 - alpha) * (nb_cost_mat[:,4] + nb_cost_mat[:,5])
# nb_cost_mat_new = np.column_stack((param_vir, param_eir))
# dis_new = coeff * dis_k_vec - alpha * nb_cost_mat[:,3]
#
# x = cp.Variable(nb_cost_mat_new.shape[1])
# cost = cp.sum_squares(nb_cost_mat_new * x - dis_new)
# constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])]]
# prob = cp.Problem(cp.Minimize(cost), constraints)
# prob.solve()
# edit_costs_new = x.value
# edit_costs_new = np.array([edit_costs_new[0], edit_costs_new[1], alpha])
# residual = np.sqrt(prob.value)
# # method 2: tune c_vir, c_eir and alpha by nonlinear programming by
# # scipy.optimize.minimize.
# w0 = nb_cost_mat[:,0] + nb_cost_mat[:,1]
# w1 = nb_cost_mat[:,4] + nb_cost_mat[:,5]
# w2 = nb_cost_mat[:,3]
# w3 = dis_k_vec
# func_min = lambda x: np.sum((w0 * x[0] * x[3] + w1 * x[1] * (1 - x[2]) \
# + w2 * x[2] - w3 * x[3]) ** 2)
# bounds = ((0, None), (0., None), (0.5, 0.5), (0, None))
# res = minimize(func_min, [0.9, 1.7, 0.75, 10], bounds=bounds)
# edit_costs_new = res.x[0:3]
# residual = res.fun
# method 3: tune c_vir, c_eir and alpha by nonlinear programming using cvxpy.
# # method 4: tune c_vir, c_eir and alpha by QP function
# # scipy.optimize.least_squares. An initial guess is required.
# w0 = nb_cost_mat[:,0] + nb_cost_mat[:,1]
# w1 = nb_cost_mat[:,4] + nb_cost_mat[:,5]
# w2 = nb_cost_mat[:,3]
# w3 = dis_k_vec
# func = lambda x: (w0 * x[0] * x[3] + w1 * x[1] * (1 - x[2]) \
# + w2 * x[2] - w3 * x[3]) ** 2
# res = optimize.root(func, [0.9, 1.7, 0.75, 100])
# edit_costs_new = res.x
# residual = None
elif self.__ged_options['edit_cost'] == 'LETTER2':
# # 1. if c_vi != c_vr, c_ei != c_er.
# nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
# x = cp.Variable(nb_cost_mat_new.shape[1])
# cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
## # 1.1 no constraints.
## constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])]]
# # 1.2 c_vs <= c_vi + c_vr.
# constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
# np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
## # 2. if c_vi == c_vr, c_ei == c_er.
## nb_cost_mat_new = nb_cost_mat[:,[0,3,4]]
## nb_cost_mat_new[:,0] += nb_cost_mat[:,1]
## nb_cost_mat_new[:,2] += nb_cost_mat[:,5]
## x = cp.Variable(nb_cost_mat_new.shape[1])
## cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
## # 2.1 no constraints.
## constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])]]
### # 2.2 c_vs <= c_vi + c_vr.
### constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
### np.array([2.0, -1.0, 0.0]).T@x >= 0.0]
#
# prob = cp.Problem(cp.Minimize(cost_fun), constraints)
# prob.solve()
# edit_costs_new = [x.value[0], x.value[0], x.value[1], x.value[2], x.value[2]]
# edit_costs_new = np.array(edit_costs_new)
# residual = np.sqrt(prob.value)
if not self.__triangle_rule and self.__allow_zeros:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif self.__triangle_rule and self.__allow_zeros:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01,
np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif not self.__triangle_rule and not self.__allow_zeros:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
prob.solve()
edit_costs_new = x.value
residual = np.sqrt(prob.value)
# elif method == 'inequality_modified':
# # c_vs <= c_vi + c_vr.
# nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
# x = cp.Variable(nb_cost_mat_new.shape[1])
# cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
# constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
# np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
# prob = cp.Problem(cp.Minimize(cost_fun), constraints)
# prob.solve()
# # use same costs for insertion and removal rather than the fitted costs.
# edit_costs_new = [x.value[0], x.value[0], x.value[1], x.value[2], x.value[2]]
# edit_costs_new = np.array(edit_costs_new)
# residual = np.sqrt(prob.value)
elif self.__triangle_rule and not self.__allow_zeros:
# c_vs <= c_vi + c_vr.
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif rw_constraints == '2constraints': # @todo: rearrange it later.
# c_vs <= c_vi + c_vr and c_vi == c_vr, c_ei == c_er.
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0,
np.array([1.0, -1.0, 0.0, 0.0, 0.0]).T@x == 0.0,
np.array([0.0, 0.0, 0.0, 1.0, -1.0]).T@x == 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
prob.solve()
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif self.__ged_options['edit_cost'] == 'NON_SYMBOLIC':
is_n_attr = np.count_nonzero(nb_cost_mat[:,2])
is_e_attr = np.count_nonzero(nb_cost_mat[:,5])
if self.__ds_name == 'SYNTHETICnew': # @todo: rearrenge this later.
# nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
nb_cost_mat_new = nb_cost_mat[:,[2,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
# constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
# np.array([0.0, 0.0, 0.0, 1.0, -1.0]).T@x == 0.0]
# constraints = [x >= [0.0001 for i in range(nb_cost_mat_new.shape[1])]]
constraints = [x >= [0.0001 for i in range(nb_cost_mat_new.shape[1])],
np.array([0.0, 1.0, -1.0]).T@x == 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
prob.solve()
# print(x.value)
edit_costs_new = np.concatenate((np.array([0.0, 0.0]), x.value,
np.array([0.0])))
residual = np.sqrt(prob.value)
elif not self.__triangle_rule and self.__allow_zeros:
if is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif is_n_attr and not is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value, np.array([0.0])))
residual = np.sqrt(prob.value)
elif not is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
residual = np.sqrt(prob.value)
else:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]),
x.value[2:], np.array([0.0])))
residual = np.sqrt(prob.value)
elif self.__triangle_rule and self.__allow_zeros:
if is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif is_n_attr and not is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0]).T@x >= 0.01,
np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value, np.array([0.0])))
residual = np.sqrt(prob.value)
elif not is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
residual = np.sqrt(prob.value)
else:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]),
x.value[2:], np.array([0.0])))
residual = np.sqrt(prob.value)
elif not self.__triangle_rule and not self.__allow_zeros:
if is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif is_n_attr and not is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value, np.array([0.0])))
residual = np.sqrt(prob.value)
elif not is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
residual = np.sqrt(prob.value)
else:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]),
x.value[2:], np.array([0.0])))
residual = np.sqrt(prob.value)
elif self.__triangle_rule and not self.__allow_zeros:
# c_vs <= c_vi + c_vr.
if is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif is_n_attr and not is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,2,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value, np.array([0.0])))
residual = np.sqrt(prob.value)
elif not is_n_attr and is_e_attr:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4,5]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])],
np.array([0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]), x.value[2:]))
residual = np.sqrt(prob.value)
else:
nb_cost_mat_new = nb_cost_mat[:,[0,1,3,4]]
x = cp.Variable(nb_cost_mat_new.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat_new @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat_new.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = np.concatenate((x.value[0:2], np.array([0.0]),
x.value[2:], np.array([0.0])))
residual = np.sqrt(prob.value)
elif self.__ged_options['edit_cost'] == 'CONSTANT': # @todo: node/edge may not labeled.
if not self.__triangle_rule and self.__allow_zeros:
x = cp.Variable(nb_cost_mat.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif self.__triangle_rule and self.__allow_zeros:
x = cp.Variable(nb_cost_mat.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat.shape[1])],
np.array([1.0, 0.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 1.0, 0.0, 0.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 1.0, 0.0, 0.0]).T@x >= 0.01,
np.array([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]).T@x >= 0.01,
np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif not self.__triangle_rule and not self.__allow_zeros:
x = cp.Variable(nb_cost_mat.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat.shape[1])]]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
elif self.__triangle_rule and not self.__allow_zeros:
x = cp.Variable(nb_cost_mat.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
constraints = [x >= [0.01 for i in range(nb_cost_mat.shape[1])],
np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
else:
raise Exception('The edit cost "', self.__ged_options['edit_cost'], '" is not supported for update progress.')
# # method 1: simple least square method.
# edit_costs_new, residual, _, _ = np.linalg.lstsq(nb_cost_mat, dis_k_vec,
# rcond=None)
# # method 2: least square method with x_i >= 0.
# edit_costs_new, residual = optimize.nnls(nb_cost_mat, dis_k_vec)
# method 3: solve as a quadratic program with constraints.
# P = np.dot(nb_cost_mat.T, nb_cost_mat)
# q_T = -2 * np.dot(dis_k_vec.T, nb_cost_mat)
# G = -1 * np.identity(nb_cost_mat.shape[1])
# h = np.array([0 for i in range(nb_cost_mat.shape[1])])
# A = np.array([1 for i in range(nb_cost_mat.shape[1])])
# b = 1
# x = cp.Variable(nb_cost_mat.shape[1])
# prob = cp.Problem(cp.Minimize(cp.quad_form(x, P) + q_T@x),
# [G@x <= h])
# prob.solve()
# edit_costs_new = x.value
# residual = prob.value - np.dot(dis_k_vec.T, dis_k_vec)
# G = -1 * np.identity(nb_cost_mat.shape[1])
# h = np.array([0 for i in range(nb_cost_mat.shape[1])])
x = cp.Variable(nb_cost_mat.shape[1])
cost_fun = cp.sum_squares(nb_cost_mat @ x - dis_k_vec)
constraints = [x >= [0.0 for i in range(nb_cost_mat.shape[1])],
# np.array([1.0, 1.0, -1.0, 0.0, 0.0]).T@x >= 0.0]
np.array([1.0, 1.0, -1.0, 0.0, 0.0, 0.0]).T@x >= 0.0,
np.array([0.0, 0.0, 0.0, 1.0, 1.0, -1.0]).T@x >= 0.0]
prob = cp.Problem(cp.Minimize(cost_fun), constraints)
self.__execute_cvx(prob)
edit_costs_new = x.value
residual = np.sqrt(prob.value)
# method 4:
return edit_costs_new, residual
def init_objective(self):
""" Initialize the objective function """
objective = [500*cvxpy.sum_squares(self.s0)]
return objective
def f_least_squares(m):
A = np.random.randn(m, n)
b = np.random.randn(m)
return cp.sum_squares(A*x - b)
def solve_opt_problem(A, b, t, n):
x = cp.Variable(n)
objective = cp.Minimize(cp.sum_squares(A @ x - b))
prob = cp.Problem(objective)
result = prob.solve(warm_start=True)
return x.value
def compute_compensation(self):
"""
Compute CoP and normalized leg stiffness compensation.
"""
# Force limits
lambda_max = max_force / (mass * height)
lambda_min = min_force / (mass * height)
omega_max = sqrt(lambda_max)
omega_min = sqrt(lambda_min)
# Measurements
Delta_com = self.pendulum.com.p - self.ref_com
Delta_comd = self.pendulum.com.pd - self.ref_comd
height = dot(self.contact.normal, self.pendulum.com.p - self.contact.p)
lambda_d = self.ref_lambda
measured_comd = self.pendulum.com.pd
nu_d = self.ref_vrp
omega_d = self.ref_omega
r_d_contact = self.ref_cop_contact
xi_d = self.ref_dcm
# Optimization variables
Delta_lambda = cvxpy.Variable(1)
Delta_nu = cvxpy.Variable(3)
Delta_omega = cvxpy.Variable(1)
Delta_r = cvxpy.Variable(2)
u = cvxpy.Variable(3)
# Linearized variation dynamics
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
# Pole placement
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
# Kinematic DCM height constraint
xi_z = self.ref_dcm[2] + Delta_xi[2] + 1.5 * sim.dt * Delta_xid[2]
# Cost function
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)
# Quadratic program
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()
# Read outputs from solution
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 minimize(self):
if self.verbose:
print('iter\t cost\t\t dnorm', end='')
if self.f.f_star() < np.inf:
print('\t\t gap', end='')
# compute first function and subgradient
self.f_x, self.g_x = self.f.function(self.x), self.f.jacobian(self.x)
ng = np.linalg.norm(self.g_x)
if self.eps < 0:
ng0 = -ng # norm of first subgradient
else:
ng0 = 1 # un-scaled stopping criterion
G = self.g_x # matrix of subgradients
F = self.f_x - self.g_x.dot(
self.x) # vector of translated function values
while True:
# construct the master problem
d = Variable(self.x.size)
v = Variable(1)
# each (fxi , gi , xi) gives the constraint:
#
# v >= fxi + gi^T * (x + d - xi) = gi^T * (x + d) + (fi - gi^T * xi)
#
# so we just keep the single constant fi - gi^T * xi instead of xi
M = [v >= F + G @ (self.x + d)]
if self.f.f_star() < np.inf:
# cheating: use information about f_star in the model
M += [v >= self.f.f_star()]
# objective function
c = v + self.mu * sum_squares(d) / 2
if self.is_verbose() and self.master_verbose:
print('\n')
# solve the master problem
Problem(Minimize(c), M).solve(solver=self.master_solver.upper(),
verbose=self.is_verbose()
and self.master_verbose)
try:
d = -d.value.ravel()
except AttributeError:
self.status = 'error'
break
v = v.value.item()
self.nd = np.linalg.norm(d)
# output statistics
if self.is_verbose():
print('\n{:4d}\t{: 1.4e}\t{: 1.4e}'.format(
self.iter, self.f_x, self.nd),
end='')
if self.f.f_star() < np.inf:
print('\t{: 1.4e}'.format((self.f_x - self.f.f_star()) /
max(abs(self.f.f_star()), 1)),
end='')
# stopping criteria
if self.mu * self.nd <= self.eps * ng0:
self.status = 'optimal'
break
if self.iter >= self.max_iter:
self.status = 'stopped'
break
last_x = self.x - d
# compute function and subgradient
fd, self.g_x = self.f.function(last_x), self.f.jacobian(last_x)
try:
self.callback()
except StopIteration:
break
if fd <= self.m_inf:
self.status = 'unbounded'
break
G = np.vstack((G, self.g_x))
F = np.hstack((F, fd - self.g_x.dot(last_x)))
if fd <= self.f_x + self.m1 * (v - self.f_x): # SS: serious step
self.x = last_x
self.f_x = fd
try:
self.check_lagrangian_dual_optimality()
except StopIteration:
break
else: # NS: null step
if self.f.ndim <= 3:
self.x0_history_ns.append(self.x[0])
self.x1_history_ns.append(self.x[1])
self.f_x_history_ns.append(self.f_x)
self.iter += 1
self.check_lagrangian_dual_conditions()
if self.verbose:
print('\n')
return self
epigraph("NORM_1", None, lambda: [cp.norm1(x) <= t]),
epigraph("NORM_NUCLEAR", None, lambda: [cp.norm(X, "nuc") <= t]),
epigraph("SUM_DEADZONE", None, lambda: [f_dead_zone() <= t]),
epigraph("SUM_EXP", None, lambda: [cp.sum_entries(cp.exp(x)) <= t]),
epigraph("SUM_HINGE", None, lambda: [f_hinge() <= t]),
epigraph("SUM_HINGE", None, lambda: [f_hinge_axis0() <= t_rvec]),
epigraph("SUM_HINGE", None, lambda: [f_hinge_axis1() <= t_vec]),
epigraph("SUM_INV_POS", None, lambda: [cp.sum_entries(cp.inv_pos(x)) <= t]),
epigraph("SUM_KL_DIV", None, lambda: [cp.sum_entries(cp.kl_div(p1,q1)) <= t]),
epigraph("SUM_LARGEST", None, lambda: [cp.sum_largest(x, 4) <= t]),
epigraph("SUM_LOGISTIC", None, lambda: [cp.sum_entries(cp.logistic(x)) <= t]),
epigraph("SUM_NEG_ENTR", None, lambda: [cp.sum_entries(-cp.entr(x)) <= t]),
epigraph("SUM_NEG_LOG", None, lambda: [cp.sum_entries(-cp.log(x)) <= t]),
epigraph("SUM_QUANTILE", None, lambda: [f_quantile() <= t]),
#epigraph("SUM_SQUARE", None, lambda: [f_quad_form() <= t]),
epigraph("SUM_SQUARE", None, lambda: [cp.sum_squares(x) <= t]),
]
def run_prox(prox_function_type, prob, v_map, lam=1, epigraph=False):
eval_prox_impl(prob, v_map, lam, prox_function_type, epigraph)
actual = {x: x.value for x in prob.variables()}
# Compare to solution with cvxpy
prob.objective.args[0] *= lam
prob.objective.args[0] += sum(
0.5*cp.sum_squares(x - v_map[x]) for x, v in v_map.items())
try:
prob.solve()
except cp.SolverError as e:
# If CVXPY fails with default, try again with SCS
prob.solve(solver=cp.SCS)
#B0_comb_m = np.matrix.transpose(np.matrix(B0_comb))
b_mul = np.matrix(A_comb) * np.matrix.transpose(np.matrix(x_comb))
b_mul = np.sum(b_mul, axis = 1)
b_dot = np.dot(A_comb, x_comb)
gamma = 0.0001
theta = 1
Ax = np.matrix(A_comb) * x
cost = cp.sum_squares(Ax - b_comb) + gamma*cp.norm(x, 1)
obj = cp.Minimize(cost)
constr = [x >= -0.7,x <= 0.01]
prob = cp.Problem(obj, constr)
opt_val = prob.solve()
solution = x.value
plt.figure()
def test_readme_examples(self) -> None:
import numpy
numpy.random.seed(1)
# cvx.Problem data.
m = 30
n = 20
A = numpy.random.randn(m, n)
b = numpy.random.randn(m)
# Construct the problem.
x = cvx.Variable(n)
objective = cvx.Minimize(cvx.sum_squares(A @ x - b))
constraints = [0 <= x, x <= 1]
p = cvx.Problem(objective, constraints)
# The optimal objective is returned by p.solve().
p.solve()
# The optimal value for x is stored in x.value.
print(x.value)
# The optimal Lagrange multiplier for a constraint
# is stored in constraint.dual_value.
print(constraints[0].dual_value)
####################################################
# Scalar variable.
a = cvx.Variable()
# Column vector variable of length 5.
x = cvx.Variable(5)
# Matrix variable with 4 rows and 7 columns.
A = cvx.Variable((4, 7))
####################################################
# Positive scalar parameter.
m = cvx.Parameter(nonneg=True)
# Column vector parameter with unknown sign (by default).
cvx.Parameter(5)
# Matrix parameter with negative entries.
G = cvx.Parameter((4, 7), nonpos=True)
# Assigns a constant value to G.
G.value = -numpy.ones((4, 7))
# Raises an error for assigning a value with invalid sign.
with self.assertRaises(Exception) as cm:
G.value = numpy.ones((4, 7))
self.assertEqual(str(cm.exception),
"Parameter value must be nonpositive.")
####################################################
a = cvx.Variable()
x = cvx.Variable(5)
# expr is an Expression object after each assignment.
expr = 2 * x
expr = expr - a
expr = cvx.sum(expr) + cvx.norm(x, 2)
####################################################
import numpy as np
# cvx.Problem data.
n = 10
m = 5
A = np.random.randn(n, m)
b = np.random.randn(n)
gamma = cvx.Parameter(nonneg=True)
# Construct the problem.
x = cvx.Variable(m)
objective = cvx.Minimize(
cvx.sum_squares(A @ x - b) + gamma * cvx.norm(x, 1))
p = cvx.Problem(objective)
# Assign a value to gamma and find the optimal x.
def get_x(gamma_value):
gamma.value = gamma_value
p.solve()
return x.value
gammas = np.logspace(-1, 2, num=2)
# Serial computation.
[get_x(value) for value in gammas]
####################################################
n = 10
mu = np.random.randn(1, n)
sigma = np.random.randn(n, n)
sigma = sigma.T.dot(sigma)
gamma = cvx.Parameter(nonneg=True)
gamma.value = 1
x = cvx.Variable(n)
# Constants:
# mu is the vector of expected returns.
# sigma is the covariance matrix.
# gamma is a cvx.Parameter that trades off risk and return.
# cvx.Variables:
# x is a vector of stock holdings as fractions of total assets.
expected_return = mu @ x
risk = cvx.quad_form(x, sigma)
objective = cvx.Maximize(expected_return - gamma * risk)
p = cvx.Problem(objective, [cvx.sum(x) == 1])
p.solve()
# The optimal expected return.
print(expected_return.value)
# The optimal risk.
print(risk.value)
###########################################
N = 50
M = 40
n = 10
data = []
for i in range(N):
data += [(1, np.random.normal(loc=1.0, scale=2.0, size=n))]
for i in range(M):
data += [(-1, np.random.normal(loc=-1.0, scale=2.0, size=n))]
# Construct problem.
gamma = cvx.Parameter(nonneg=True)
gamma.value = 0.1
# 'a' is a variable constrained to have at most 6 non-zero entries.
a = cvx.Variable(n) # mi.SparseVar(n, nonzeros=6)
b = cvx.Variable()
slack = [
cvx.pos(1 - label * (sample.T @ a - b)) for (label, sample) in data
]
objective = cvx.Minimize(cvx.norm(a, 2) + gamma * sum(slack))
p = cvx.Problem(objective)
# Extensions can attach new solve methods to the CVXPY cvx.Problem class.
# p.solve(method="admm")
p.solve()
# Count misclassifications.
errors = 0
for label, sample in data:
if label * (sample.T @ a - b).value < 0:
errors += 1
print("%s misclassifications" % errors)
print(a.value)
print(b.value)
noise = np.loadtxt("noise.csv", delimiter=",")
y = x @ c_true + 0.1 * (math.sqrt(n)) * noise
# # Reorder measurements, then censor
sort_ind = np.argsort(y)
y = y[sort_ind]
x = x[sort_ind]
D = (y[M] + y[M + 1]) / 2
y = y[:M]
print(y.shape)
print(x.shape)
c_hat = cp.Variable(n)
y_censored = cp.Variable(K - M)
Y = cp.hstack((y, y_censored))
objective = cp.Minimize(cp.sum_squares(x @ c_hat - Y))
constraints = [y_censored >= D]
prob = cp.Problem(objective, constraints)
prob.solve()
print(c_hat.value)
# print(y_censored.value)
residual = np.linalg.norm(c_true - c_hat.value) / np.linalg.norm(c_true)
print('residual for c_hat', residual)
print(
'#########################################################################'
)
c_hat = cp.Variable(n)
def tps_fit3_cvx(x_na, y_ng, bend_coef, rot_coef, wt_n):
"""
Use cvx instead of just matrix multiply.
Working with null space of matrices.
"""
if wt_n is None: wt_n = co.matrix(np.ones(len(x_na)))
n,d = x_na.shape
K_nn = tps_kernel_matrix(x_na)
_,_,VT = nlg.svd(np.c_[x_na,np.ones((x_na.shape[0],1))].T)
Nmat = VT.T[:,d+1:]
rot_coefs = np.diag(np.ones(d) * rot_coef if np.isscalar(rot_coef) else rot_coef)
A = cp.Variable(Nmat.shape[1],d)
B = cp.Variable(d,d)
c = cp.Variable(d,1)
Y = co.matrix(y_ng)
K = co.matrix(K_nn)
N = co.matrix(Nmat)
X = co.matrix(x_na)
W = co.matrix(np.diag(wt_n).copy())
R = co.matrix(rot_coefs)
ones = co.matrix(np.ones((n,1)))
constraints = []
# For correspondences
V1 = cp.Variable(n,d)
constraints.append(V1 == Y-K*N*A-X*B - ones*c.T)
V2 = cp.Variable(n,d)
constraints.append(V2 == cp.sqrt(W)*V1)
# For bending cost
Q = [] # for quadratic forms
for i in range(d):
Q.append(cp.quad_form(A[:,i], N.T*K*N))
# For rotation cost
# Element wise square root actually works here as R is diagonal and positive
V3 = cp.Variable(d,d)
constraints.append(V3 == cp.sqrt(R)*B)
# Orthogonality constraints for bending are taken care of already because working with the null space
#constraints.extend([X.T*A == 0, ones.T*A == 0])
# TPS objective
objective = cp.Minimize(cp.sum_squares(V2) + bend_coef*sum(Q) + cp.sum_squares(V3))
p = cp.Problem(objective, constraints)
p.solve(verbose=True)
return np.array(B.value), np.squeeze(np.array(c.value)) , Nmat.dot(np.array(A.value))