def test_1dmog(mus=[-2., 2.], sigs=[1., np.sqrt(3.)], pis=[0.5, 0.5], deg = 3, obsdeg = 6):
print 'testing 1d mixture of Gaussians'
# constraints on parameters here
K = len(mus)
mu,sig = sp.symbols('mu,sigma')
M = mm.MomentMatrix(deg, [mu, sig], morder='grevlex')
num_constrs = obsdeg + 1; # so observe num_constrs-1 moments
H = abs(hermite_coeffs(num_constrs))
constrs = [0]*num_constrs
for order in range(num_constrs):
for i in range(order+1):
constrs[order] = constrs[order] + H[order,i]* mu**(i) * sig**(order-i)
constrsval = 0
for k in range(K):
constrsval += pis[k]*constrs[order].evalf(subs={mu:mus[k], sig:sigs[k]})
constrs[order] -= constrsval
print constrs
cin = M.get_cvxopt_inputs(constrs[1:])
gs = [sig-0.2, 5-sig, sig+5, 10-mu, mu+10]
#gs = [sig-0.2]
locmatrices = [mm.LocalizingMatrix(M, g) for g in gs]
Ghs = [lm.get_cvxopt_Gh() for lm in locmatrices]
Gs=cin['G']# + [Gh['G'] for Gh in Ghs]
hs=cin['h']# + [Gh['h'] for Gh in Ghs]
sol = solvers.sdp(cin['c'],Gs=Gs, \
hs=hs, A=cin['A'], b=cin['b'])
## Q = cin['A'].T*cin['A']
## weight = 1;
## dims = {}
## dims['l'] = 0; dims['q'] = []; dims['s'] = [len(M.row_monos)]
## ipdb.set_trace()
## sol = solvers.coneqp(Q*weight, cin['A'].T*cin['b']*weight + cin['c'],G=Gs[0], \
## h=hs[0][:], dims = dims, A=cin['A'], b=cin['b'])
for i,mono in enumerate(M.matrix_monos):
trueval = 0;
if i>0:
for k in range(K):
trueval += pis[k]*mono.evalf(subs={mu:mus[k], sig:sigs[k]})
else:
trueval = 1
print '%s:\t%f\t%f' % (str(mono), sol['x'][i], trueval)
print M.extract_solutions_lasserre(sol['x'], Kmax=len(mus))
#import MomentMatrixSolver as mmsolver
#print mmsolver.alternating_solver(M, constrs, 2, maxiter=30000)
return M,sol
def polymom_univariate(xi, c, order):
constr = 0
H = abs(hermite_coeffs(order+1))
for i in range(order+1):
constr = constr + H[order,i]* xi**(i) * c**((order-i)/2)
return constr
def test_1dmog(mus=[-2., 2.],
sigs=[1., np.sqrt(3.)],
pis=[0.5, 0.5],
deg=3,
obsdeg=6):
print 'testing 1d mixture of Gaussians'
# constraints on parameters here
K = len(mus)
mu, sig = sp.symbols('mu,sigma')
M = mm.MomentMatrix(deg, [mu, sig], morder='grevlex')
num_constrs = obsdeg + 1
# so observe num_constrs-1 moments
H = abs(hermite_coeffs(num_constrs))
constrs = [0] * num_constrs
for order in range(num_constrs):
for i in range(order + 1):
constrs[order] = constrs[order] + H[order,
i] * mu**(i) * sig**(order - i)
constrsval = 0
for k in range(K):
constrsval += pis[k] * constrs[order].evalf(subs={
mu: mus[k],
sig: sigs[k]
})
constrs[order] -= constrsval
print constrs
cin = M.get_cvxopt_inputs(constrs[1:])
gs = [sig - 0.2, 5 - sig, sig + 5, 10 - mu, mu + 10]
#gs = [sig-0.2]
locmatrices = [mm.LocalizingMatrix(M, g) for g in gs]
Ghs = [lm.get_cvxopt_Gh() for lm in locmatrices]
Gs = cin['G'] # + [Gh['G'] for Gh in Ghs]
hs = cin['h'] # + [Gh['h'] for Gh in Ghs]
sol = solvers.sdp(cin['c'],Gs=Gs, \
hs=hs, A=cin['A'], b=cin['b'])
## Q = cin['A'].T*cin['A']
## weight = 1;
## dims = {}
## dims['l'] = 0; dims['q'] = []; dims['s'] = [len(M.row_monos)]
## ipdb.set_trace()
## sol = solvers.coneqp(Q*weight, cin['A'].T*cin['b']*weight + cin['c'],G=Gs[0], \
## h=hs[0][:], dims = dims, A=cin['A'], b=cin['b'])
for i, mono in enumerate(M.matrix_monos):
trueval = 0
if i > 0:
for k in range(K):
trueval += pis[k] * mono.evalf(subs={mu: mus[k], sig: sigs[k]})
else:
trueval = 1
print '%s:\t%f\t%f' % (str(mono), sol['x'][i], trueval)
print M.extract_solutions_lasserre(sol['x'], Kmax=len(mus))
#import MomentMatrixSolver as mmsolver
#print mmsolver.alternating_solver(M, constrs, 2, maxiter=30000)
return M, sol