def solve_qp_constrained(P,q,nlabel,x0,**kwargs):
import solver_qp_constrained as solver
reload(solver)
## constrained solver
nvar = q.size
npixel = nvar/nlabel
F = sparse.bmat([
[sparse.bmat([[-sparse.eye(npixel,npixel) for i in range(nlabel-1)]])],
[sparse.eye(npixel*(nlabel-1),npixel*(nlabel-1))],
])
## quadratic objective
objective = solver.ObjectiveAPI(P, q, G=1, h=0, F=F,**kwargs)
## log barrier solver
t0 = kwargs.pop('logbarrier_initial_t',1.0)
mu = kwargs.pop('logbarrier_mu',20.0)
epsilon = kwargs.pop('logbarrier_epsilon',1e-3)
solver = solver.ConstrainedSolver(
objective,
t0=t0,
mu=mu,
epsilon=epsilon,
)
## remove zero entries in initial guess
xinit = x0.reshape((-1,nlabel),order='F')
xinit[xinit<1e-10] = 1e-3
xinit = (xinit/np.c_[np.sum(xinit, axis=1)]).reshape((-1,1),order='F')
x = solver.solve(xinit, **kwargs)
return x
def solve_qp_constrained(P,q,nlabel,x0,**kwargs):
import solver_qp_constrained as solver
reload(solver)
## constrained solver
nvar = q.size
npixel = nvar/nlabel
F = sparse.bmat([
[sparse.bmat([[-sparse.eye(npixel,npixel) for i in range(nlabel-1)]])],
[sparse.eye(npixel*(nlabel-1),npixel*(nlabel-1))],
])
## quadratic objective
objective = solver.ObjectiveAPI(P, q, G=1, h=0, F=F,**kwargs)
## log barrier solver
t0 = kwargs.pop('logbarrier_initial_t',1.0)
mu = kwargs.pop('logbarrier_mu',20.0)
epsilon = kwargs.pop('logbarrier_epsilon',1e-3)
solver = solver.ConstrainedSolver(
objective,
t0=t0,
mu=mu,
epsilon=epsilon,
)
## remove zero entries in initial guess
xinit = x0.reshape((-1,nlabel),order='F')
xinit[xinit<1e-10] = 1e-3
xinit = (xinit/np.c_[np.sum(xinit, axis=1)]).reshape((-1,1),order='F')
x = solver.solve(xinit, **kwargs)
return x
def solve_qp_ground_truth(P, q, list_GT, nlabel, **kwargs):
GT = np.asarray(list_GT).T
''' Ax >= b '''
N = P.shape[0] / nlabel
S = np.cumsum(GT, axis=1)
i_ = np.where(~GT)
rows = (i_[1] - S[i_]) * N + i_[0]
cols = i_[1] * N + i_[0]
G = sparse.coo_matrix(
(-np.ones(len(rows)), (rows, cols)),
shape=(N * (nlabel - 1), N * nlabel),
).tocsr()
G = G + sparse.bmat(
[[sparse.spdiags(list_GT[l],0,N,N) for l in range(nlabel)] \
for l2 in range(nlabel-1)]
)
h = kwargs.pop('ground_truth_margin', 0.0)
n = q.size
## positivity constraint
G = sparse.bmat([[G], [sparse.eye(n, n)]])
npixel = n / nlabel
F = sparse.bmat([
[
sparse.bmat(
[[-sparse.eye(npixel, npixel) for i in range(nlabel - 1)]])
],
[sparse.eye(npixel * (nlabel - 1), npixel * (nlabel - 1))],
])
## initial guess
list_GT_init = kwargs.pop('list_GT_init', None)
if list_GT_init is None:
xinit = np.asmatrix(np.asarray(list_GT).ravel()).T
else:
xinit = np.asmatrix(np.asarray(list_GT_init).ravel()).T
use_mosek = kwargs.pop('use_mosek', True)
if use_mosek:
import solver_mosek as solver
reload(solver)
logger.info('use mosek')
objective = solver.ObjectiveAPI(P, q, G=G, h=h, F=F, **kwargs)
constsolver = solver.ConstrainedSolver(objective, )
p = xinit.A.reshape((nlabel, -1)) + 1e-8
xinit = np.mat((p / np.sum(p, axis=0)).reshape(xinit.shape))
x = constsolver.solve(xinit)
minx = np.min(x)
maxx = np.max(x)
logger.info(
'Done solver ground truth constrained: x in [{:.3}, {:.3}]'.format(
minx, maxx))
logger.info('clipping x in [0,1]')
prob = np.clip(x.reshape((nlabel, -1)), 0, 1)
prob = prob / np.sum(prob, axis=0)
nx = prob.reshape(x.shape)
#check validity
ndiff = np.sum(np.argmax(prob, axis=0) != np.argmax(list_GT, axis=0))
logger.info('number incorrect pixels: {}'.format(ndiff))
return nx
## else: log barrier
import solver_qp_constrained as solver
reload(solver)
## quadratic objective
#objective = solver.ObjectiveAPI(P, q, G=G, h=h,**kwargs)
objective = solver.ObjectiveAPI(P, q, G=G, h=h, F=F, **kwargs)
## log barrier solver
t0 = kwargs.pop('logbarrier_initial_t', 1.0)
mu = kwargs.pop('logbarrier_mu', 20.0)
epsilon = kwargs.pop('logbarrier_epsilon', 1e-4)
modified = kwargs.pop('logbarrier_modified', False)
maxiter = kwargs.pop('logbarrier_maxiter', 10)
solver = solver.ConstrainedSolver(
objective,
t0=t0,
mu=mu,
epsilon=epsilon,
modified=modified,
)
## internal solver is newton's method
newton_a = kwargs.pop('newton_a', 0.4)
newton_b = kwargs.pop('newton_b', 0.8)
newton_epsilon = kwargs.pop('newton_epsilon', 1e-4)
newton_maxiter = kwargs.pop('newton_maxiter', 100)
p = xinit.A.reshape((nlabel, -1)) + 1e-8
xinit = np.mat((p / np.sum(p, axis=0)).reshape(xinit.shape))
x = solver.solve(
xinit,
a=newton_a,
b=newton_b,
epsilon=newton_epsilon,
maxiter=newton_maxiter,
)
minx = np.min(x)
maxx = np.max(x)
logger.info(
'Done solver ground truth constrained: x in [{:.3}, {:.3}]'.format(
minx, maxx))
logger.info('clipping x in [0,1]')
prob = np.clip(x.reshape((nlabel, -1)), 0, 1)
prob = prob / np.sum(prob, axis=0)
nx = prob.reshape(x.shape)
return nx
def solve_qp_ground_truth(P,q,list_GT,nlabel,**kwargs):
GT = np.asarray(list_GT).T
''' Ax >= b '''
N = P.shape[0]/nlabel
S = np.cumsum(GT,axis=1)
i_ = np.where(~GT)
rows = (i_[1]-S[i_])*N + i_[0]
cols = i_[1]*N + i_[0]
G = sparse.coo_matrix(
(-np.ones(len(rows)), (rows,cols)),
shape=(N*(nlabel-1),N*nlabel),
).tocsr()
G = G + sparse.bmat(
[[sparse.spdiags(list_GT[l],0,N,N) for l in range(nlabel)] \
for l2 in range(nlabel-1)]
)
h = kwargs.pop('ground_truth_margin',0.0)
n = q.size
## positivity constraint
G = sparse.bmat([[G], [sparse.eye(n,n)]])
npixel = n/nlabel
F = sparse.bmat([
[sparse.bmat([[-sparse.eye(npixel,npixel) for i in range(nlabel-1)]])],
[sparse.eye(npixel*(nlabel-1),npixel*(nlabel-1))],
])
## initial guess
list_GT_init = kwargs.pop('list_GT_init',None)
if list_GT_init is None:
xinit = np.asmatrix(np.asarray(list_GT).ravel()).T
else:
xinit = np.asmatrix(np.asarray(list_GT_init).ravel()).T
use_mosek = kwargs.pop('use_mosek', True)
if use_mosek:
import solver_mosek as solver
reload(solver)
logger.info('use mosek')
objective = solver.ObjectiveAPI(P, q, G=G, h=h,F=F,**kwargs)
constsolver = solver.ConstrainedSolver(
objective,
)
p = xinit.A.reshape((nlabel,-1)) + 1e-8
xinit = np.mat((p/np.sum(p,axis=0)).reshape(xinit.shape))
x = constsolver.solve(xinit)
minx = np.min(x)
maxx = np.max(x)
logger.info('Done solver ground truth constrained: x in [{:.3}, {:.3}]'.format(minx,maxx))
logger.info('clipping x in [0,1]')
prob = np.clip(x.reshape((nlabel,-1)), 0,1)
prob = prob / np.sum(prob,axis=0)
nx = prob.reshape(x.shape)
#check validity
ndiff = np.sum(np.argmax(prob, axis=0)!=np.argmax(list_GT,axis=0))
logger.info('number incorrect pixels: {}'.format(ndiff))
return nx
## else: log barrier
import solver_qp_constrained as solver
reload(solver)
## quadratic objective
#objective = solver.ObjectiveAPI(P, q, G=G, h=h,**kwargs)
objective = solver.ObjectiveAPI(P, q, G=G, h=h,F=F,**kwargs)
## log barrier solver
t0 = kwargs.pop('logbarrier_initial_t',1.0)
mu = kwargs.pop('logbarrier_mu',20.0)
epsilon = kwargs.pop('logbarrier_epsilon',1e-4)
modified = kwargs.pop('logbarrier_modified',False)
maxiter = kwargs.pop('logbarrier_maxiter', 10)
solver = solver.ConstrainedSolver(
objective,
t0=t0,
mu=mu,
epsilon=epsilon,
modified=modified,
)
## internal solver is newton's method
newton_a = kwargs.pop('newton_a', 0.4)
newton_b = kwargs.pop('newton_b', 0.8)
newton_epsilon = kwargs.pop('newton_epsilon', 1e-4)
newton_maxiter = kwargs.pop('newton_maxiter', 100)
p = xinit.A.reshape((nlabel,-1)) + 1e-8
xinit = np.mat((p/np.sum(p,axis=0)).reshape(xinit.shape))
x = solver.solve(
xinit,
a=newton_a,
b=newton_b,
epsilon=newton_epsilon,
maxiter=newton_maxiter,
)
minx = np.min(x)
maxx = np.max(x)
logger.info('Done solver ground truth constrained: x in [{:.3}, {:.3}]'.format(minx,maxx))
logger.info('clipping x in [0,1]')
prob = np.clip(x.reshape((nlabel,-1)), 0,1)
prob = prob / np.sum(prob,axis=0)
nx = prob.reshape(x.shape)
return nx