def sobbynorm(k1,k2, lnorm,theta,delta1,delta2,m): D1 = [] D2 = [] norm_list = [] for i in range(len(k1)): D1.append(utils.form_Dk(n=m,k=k1[i])*(delta1**(1/lnorm-k1[i]))) D2.append(utils.form_Dk(n=m,k=k2[i])*(delta2**(1/lnorm-k2[i]))) norm_list.append(cvx.norm(D1[i]*theta*D2[i].T,lnorm)) return np.sum(norm_list)
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 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 meshy_one(x,y,m,k=1,interp=1,mesh=None,lnorm=1,tune=50,eps=0.01,cvx_solver=0):
# interp = 0 for natural splines
# interp = 1 for banded piecewise polynomials
# 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
n = x.size
# Create D-matrix: specify n and k
if mesh==None:
mesh = np.linspace(min(x)-eps,max(x)+eps,m)
delta = np.diff(mesh)[0]
D = utils.form_Dk(n=m,k=k)*(delta**(1/lnorm-k))
# Create O-matrix: specify x and number of desired cuts
O = utils.interpO(data=x,mesh=mesh,k=k,key=interp)
# Solve convex problem.
theta = cvx.Variable(m)
obj = cvx.Minimize(0.5 * cvx.sum_squares(y - O*theta)
+ tune * cvx.norm(D*theta, lnorm) )
prob = cvx.Problem(obj)
prob.solve(solver=solvers[cvx_solver],verbose=False,max_iters = default_iter)
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,m,k) )
output = {'mesh': mesh, 'theta.hat': np.array(theta.value),'fitted':O.dot(np.array(theta.value)),'x':x,'y':y,'k':k,'interp':interp,'eps':eps,'m':m}
return output
def l1tf_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
n = x.size
# Create D-matrix: specify n and k
D = utils.form_Dk(n=n,k=k)
# Create falling factorial basis
H = fallfac(x=x, k=k)
print H.shape
# Solve convex problem.
theta = cvx.Variable(n)
obj = cvx.Minimize(0.5 * cvx.sum_squares(y - H*theta)
+ tune * cvx.norm(D*theta, 1) )
prob = cvx.Problem(obj)
prob.solve(solver=solvers[cvx_solver],verbose=False,max_iters = default_iter)
#print 'Solver status: ', prob.status
# Check for error.
#if prob.status != cvx.OPTIMAL:
# raise Exception("Solver did not converge!")
# 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': H.dot(np.array(theta.value)),'x':x,'y':y,'eps':eps}
return output
