def hanso(A, b, maxit, x0_init="random"):
"""
Runs a flovor HANSO (customizable via the x0_init parameter).
Parameters
----------
x0_init: string, optional (defautl "random")
initialization mode for HANSO: Possible values are:
"fista": run FISTA, and then switch to HANSO once energy starts
to increase
"random": initialize as usual (multivariate standard normal)
Raises
------
ValueError
"""
from hanso.hanso import hanso
from hanso.setx0 import setx0
nstart = 1
def fg_with_tv_plus_l1_penalty(x):
z = np.dot(A, x) - b
return (.5 * linalg.norm(z)**2 + lambd * l1(x),
np.dot(A.T, z) + lambd * grad_l1(x))
def fg_with_l1_penalty(x):
z = np.dot(A, x) - b
return (.5 * linalg.norm(z)**2 + lambd * l1(x),
np.dot(A.T, z) + lambd * grad_l1(x))
def fg_with_tv_penalty(x):
z = np.dot(A, x) - b
return (.5 * linalg.norm(z)**2 + lambd * tv(x),
np.dot(A.T, z) + lambd * grad_tv(x))
pobj = []
times = []
# penalty dependent gradient definition
if penalty_model == "l1":
fg = fg_with_l1_penalty
elif penalty_model == "tv":
fg = fg_with_tv_penalty
elif penalty_model == "tv+l1":
fg = fg_with_tv_plus_l1_penalty
else:
raise ValueError("Unknown penalty model: %s" % penalty_model)
if x0_init == "fista":
x0, pobj, times = fista(A, b, maxit=maxit, stop_if_energy_rises=True)
elif x0_init == "random":
x0 = setx0(A.shape[1], nstart)
else:
raise ValueError("Unknown value for x0_init parameter: %s" % x0_init)
maxit = maxit - len(pobj)
results = hanso(fg, x0=x0, sampgrad=True, maxit=maxit, nvec=0, verbose=2)
x = results[0]
_pobj = results[-1]
_times, _pobj = map(np.array, zip(*_pobj))
_times = concat_times(times, _times)
_pobj = list(pobj) + list(_pobj)
return x, _pobj, _times
def hanso(A, b, maxit, x0_init="random"):
"""
Runs a flovor HANSO (customizable via the x0_init parameter).
Parameters
----------
x0_init: string, optional (defautl "random")
initialization mode for HANSO: Possible values are:
"fista": run FISTA, and then switch to HANSO once energy starts
to increase
"random": initialize as usual (multivariate standard normal)
Raises
------
ValueError
"""
from hanso.hanso import hanso
from hanso.setx0 import setx0
nstart = 1
def fg_with_tv_plus_l1_penalty(x):
z = np.dot(A, x) - b
return (.5 * linalg.norm(z) ** 2 + lambd * l1(x),
np.dot(A.T, z) + lambd * grad_l1(x))
def fg_with_l1_penalty(x):
z = np.dot(A, x) - b
return (.5 * linalg.norm(z) ** 2 + lambd * l1(x),
np.dot(A.T, z) + lambd * grad_l1(x))
def fg_with_tv_penalty(x):
z = np.dot(A, x) - b
return (.5 * linalg.norm(z) ** 2 + lambd * tv(x),
np.dot(A.T, z) + lambd * grad_tv(x))
pobj = []
times = []
# penalty dependent gradient definition
if penalty_model == "l1":
fg = fg_with_l1_penalty
elif penalty_model == "tv":
fg = fg_with_tv_penalty
elif penalty_model == "tv+l1":
fg = fg_with_tv_plus_l1_penalty
else:
raise ValueError("Unknown penalty model: %s" % penalty_model)
if x0_init == "fista":
x0, pobj, times = fista(A, b, maxit=maxit,
stop_if_energy_rises=True)
elif x0_init == "random":
x0 = setx0(A.shape[1], nstart)
else:
raise ValueError("Unknown value for x0_init parameter: %s" % x0_init)
maxit = maxit - len(pobj)
results = hanso(fg,
x0=x0,
sampgrad=True,
maxit=maxit,
nvec=0,
verbose=2
)
x = results[0]
_pobj = results[-1]
_times, _pobj = map(np.array, zip(*_pobj))
_times = concat_times(times, _times)
_pobj = list(pobj) + list(_pobj)
return x, _pobj, _times
return x, _pobj, _times
maxit = 1000
# HANSO
hanso_x0_init_modes = [
"fista", # uncomment if penalty is l1 only
'random'
]
pobj_hanso = []
times_hanso = []
for x0_init in hanso_x0_init_modes:
optimizer = "HANSO (%s x0 init)" % x0_init
x_hanso, pobj, times = hanso(A, b, maxit, x0_init=x0_init)
pobj_hanso.append(pobj)
times_hanso.append(times)
fmin_hanso = loss_function(A, b, x_hanso)
print "fmin %s: %s" % (optimizer, fmin_hanso)
print
if penalty_model == "l1":
# ISTA
x_ista, pobj_ista, times_ista = ista(A, b, maxit)
fmin_ista = loss_function(A, b, x_ista)
print "xopt ISTA:", x_ista
print "fmin ISTA:", fmin_hanso
print
# FISTA
return x, _pobj, _times
maxit = 1000
# HANSO
hanso_x0_init_modes = [
"fista", # uncomment if penalty is l1 only
'random'
]
pobj_hanso = []
times_hanso = []
for x0_init in hanso_x0_init_modes:
optimizer = "HANSO (%s x0 init)" % x0_init
x_hanso, pobj, times = hanso(A, b, maxit, x0_init=x0_init)
pobj_hanso.append(pobj)
times_hanso.append(times)
fmin_hanso = loss_function(A, b, x_hanso)
print "fmin %s: %s" % (optimizer, fmin_hanso)
print
if penalty_model == "l1":
# ISTA
x_ista, pobj_ista, times_ista = ista(A, b, maxit)
fmin_ista = loss_function(A, b, x_ista)
print "xopt ISTA:", x_ista
print "fmin ISTA:", fmin_hanso
print
# FISTA