def extract_solutions_lasserre(MM, ys, Kmax=10, tol=1e-6, maxdeg = None):
"""
extract solutions via (unstable) row reduction described by Lassarre and used in gloptipoly
MM is a moment matrix, and ys are its completed values
@params - Kmax: the maximum rank allowed to extract
@params - tol: singular values less than this is truncated.
@params - maxdeg: only extract from the top corner of the matrix up to maxdeg
"""
M = MM.numeric_instance(ys, maxdeg = maxdeg)
Us,Sigma,Vs=np.linalg.svd(M)
#
count = min(Kmax,sum(Sigma>tol))
# now using Lassarre's notation in the extraction section of
# "Moments, Positive Polynomials and their Applications"
T,Ut = util.srref(Vs[0:count,:])
if Sigma[count] <= tol:
print 'lost %.7f' % Sigma[count]
# inplace!
util.row_normalize_leadingone(Ut)
couldbes = np.where(Ut>0.9)
ind_leadones = np.zeros(Ut.shape[0], dtype=np.int)
for j in reversed(range(len(couldbes[0]))):
ind_leadones[couldbes[0][j]] = couldbes[1][j]
basis = [MM.row_monos[i] for i in ind_leadones]
dict_row_monos = dict_mono_to_ind(MM.row_monos)
Ns = {}
bl = len(basis)
# create multiplication matrix for each variable
for var in MM.vars:
Nvar = np.zeros((bl,bl))
for i,b in enumerate(basis):
Nvar[:,i] = Ut[ :,dict_row_monos[var*b] ]
Ns[var] = Nvar
N = np.zeros((bl,bl))
for var in Ns:
N+=Ns[var]*np.random.randn()
T,Q=scipy.linalg.schur(N)
sols = {}
quadf = lambda A, x : np.dot(x, np.dot(A,x))
for var in MM.vars:
sols[var] = np.array([quadf(Ns[var], Q[:,j]) for j in range(bl)])
#ipdb.set_trace()
return sols
def extract_solutions_lasserre(MM, ys, Kmax=10, tol=1e-6, maxdeg=None):
"""
extract solutions via (unstable) row reduction described by Lassarre and used in gloptipoly
MM is a moment matrix, and ys are its completed values
@params - Kmax: the maximum rank allowed to extract
@params - tol: singular values less than this is truncated.
@params - maxdeg: only extract from the top corner of the matrix up to maxdeg
"""
M = MM.numeric_instance(ys, maxdeg=maxdeg)
Us, Sigma, Vs = np.linalg.svd(M)
#
count = min(Kmax, sum(Sigma > tol))
# now using Lassarre's notation in the extraction section of
# "Moments, Positive Polynomials and their Applications"
T, Ut = util.srref(Vs[0:count, :])
if Sigma[count] <= tol:
print 'lost %.7f' % Sigma[count]
# inplace!
util.row_normalize_leadingone(Ut)
couldbes = np.where(Ut > 0.9)
ind_leadones = np.zeros(Ut.shape[0], dtype=np.int)
for j in reversed(range(len(couldbes[0]))):
ind_leadones[couldbes[0][j]] = couldbes[1][j]
basis = [MM.row_monos[i] for i in ind_leadones]
dict_row_monos = dict_mono_to_ind(MM.row_monos)
Ns = {}
bl = len(basis)
# create multiplication matrix for each variable
for var in MM.vars:
Nvar = np.zeros((bl, bl))
for i, b in enumerate(basis):
Nvar[:, i] = Ut[:, dict_row_monos[var * b]]
Ns[var] = Nvar
N = np.zeros((bl, bl))
for var in Ns:
N += Ns[var] * np.random.randn()
T, Q = scipy.linalg.schur(N)
sols = {}
quadf = lambda A, x: np.dot(x, np.dot(A, x))
for var in MM.vars:
sols[var] = np.array([quadf(Ns[var], Q[:, j]) for j in range(bl)])
#ipdb.set_trace()
return sols
def extract_solutions_lasserre_average(MM, ys, Kmax=10, tol=1e-6, numiter=10):
"""
extract solutions via (unstable) row reduction described by Lassarre and used in gloptipoly
MM is a moment matrix, and ys are its completed values
"""
M = MM.numeric_instance(ys)
Us,Sigma,Vs=np.linalg.svd(M)
#
count = min(Kmax,sum(Sigma>tol))
# now using Lassarre's notation in the extraction section of
# "Moments, Positive Polynomials and their Applications"
sols = {}
totalweight = 0;
for i in range(numiter):
T,Ut = util.srref(M[0:count,:])
if Sigma[count] <= tol:
print 'lost %.7f' % Sigma[count]
# inplace!
util.row_normalize_leadingone(Ut)
couldbes = np.where(Ut>0.9)
ind_leadones = np.zeros(Ut.shape[0], dtype=np.int)
for j in reversed(range(len(couldbes[0]))):
ind_leadones[couldbes[0][j]] = couldbes[1][j]
basis = [MM.row_monos[i] for i in ind_leadones]
dict_row_monos = dict_mono_to_ind(MM.row_monos)
Ns = {}
bl = len(basis)
# create multiplication matrix for each variable
for var in MM.vars:
Nvar = np.zeros((bl,bl))
for i,b in enumerate(basis):
Nvar[:,i] = Ut[ :,dict_row_monos[var*b] ]
Ns[var] = Nvar
N = np.zeros((bl,bl))
for var in Ns:
N+=Ns[var]*np.random.randn()
T,Q=scipy.linalg.schur(N)
quadf = lambda A, x : np.dot(x, np.dot(A,x))
for var in MM.vars:
sols[var] = np.array([quadf(Ns[var], Q[:,j]) for j in range(bl)])
return sols
def extract_solutions_lasserre_average(MM, ys, Kmax=10, tol=1e-6, numiter=10):
"""
extract solutions via (unstable) row reduction described by Lassarre and used in gloptipoly
MM is a moment matrix, and ys are its completed values
"""
M = MM.numeric_instance(ys)
Us, Sigma, Vs = np.linalg.svd(M)
#
count = min(Kmax, sum(Sigma > tol))
# now using Lassarre's notation in the extraction section of
# "Moments, Positive Polynomials and their Applications"
sols = {}
totalweight = 0
for i in range(numiter):
T, Ut = util.srref(M[0:count, :])
if Sigma[count] <= tol:
print 'lost %.7f' % Sigma[count]
# inplace!
util.row_normalize_leadingone(Ut)
couldbes = np.where(Ut > 0.9)
ind_leadones = np.zeros(Ut.shape[0], dtype=np.int)
for j in reversed(range(len(couldbes[0]))):
ind_leadones[couldbes[0][j]] = couldbes[1][j]
basis = [MM.row_monos[i] for i in ind_leadones]
dict_row_monos = dict_mono_to_ind(MM.row_monos)
Ns = {}
bl = len(basis)
# create multiplication matrix for each variable
for var in MM.vars:
Nvar = np.zeros((bl, bl))
for i, b in enumerate(basis):
Nvar[:, i] = Ut[:, dict_row_monos[var * b]]
Ns[var] = Nvar
N = np.zeros((bl, bl))
for var in Ns:
N += Ns[var] * np.random.randn()
T, Q = scipy.linalg.schur(N)
quadf = lambda A, x: np.dot(x, np.dot(A, x))
for var in MM.vars:
sols[var] = np.array([quadf(Ns[var], Q[:, j]) for j in range(bl)])
return sols
