def decompose(self):
"""
Gives an SOS decomposition of f if exists as a list of polynomials
of at most half degree of f.
This method also fills the 'Info' as 'minimize' does. In addition,
returns Info['is sos'] which is Boolean depending on the status of
sdp solver.
"""
n = self.NumVars
N0 = self.NumMonomials(n, self.MainPolyHlfDeg)
N1 = self.NumMonomials(n, self.MainPolyTotDeg)
self.MatSize = [N0, N1]
vec = self.MonomialsVec(self.MainPolyHlfDeg)
m = Matrix(1, N0, vec)
Mmnt = m.transpose() * m
Blck = [[] for i in range(N1)]
C = []
h = Matrix(self.Field, N0, N0, 0)
C.append(h)
decomp = []
for i in range(N1):
p = self.Monomials[i]
A = self.Calpha(p, Mmnt)
Blck[i].append(A)
from SDP import SDP
sos_sdp = SDP.sdp(solver=self.solver, Settings={'detail': self.detail})
sos_sdp.solve(C, self.PolyCoefFullVec(), Blck)
if sos_sdp.Info['Status'] == 'Optimal':
self.Info['status'] = 'Feasible'
GramMtx = Matrix(sos_sdp.Info['X'][0])
try:
self.Info[
'Message'] = "A SOS decomposition of the polynomial were found."
self.Info['is sos'] = True
H1 = GramMtx.cholesky()
tmpM = Matrix(1, N0, vec)
decomp = list(tmpM * H1)[0]
self.Info['Wall'] = sos_sdp.Info['Wall']
self.Info['CPU'] = sos_sdp.Info['CPU']
except:
self.Info[
'Message'] = "The given polynomial seems to be a sum of squares, but no SOS decomposition were extracted."
self.Info['is sos'] = False
self.Info['Wall'] = sos_sdp.Info['Wall']
self.Info['CPU'] = sos_sdp.Info['CPU']
else:
self.Info[
'Message'] = "The given polynomial is not a sum of squares."
self.Info['status'] = 'Infeasible'
self.Info['is sos'] = False
self.Info["Size"] = self.MatSize
return decomp
def decompose(self):
"""
Gives an SOS decomposition of f if exists as a list of polynomials
of at most half degree of f.
This method also fills the 'Info' as 'minimize' does. In addition,
returns Info['is sos'] which is Boolean depending on the status of
sdp solver.
"""
n = self.NumVars
N0 = self.NumMonomials(n, self.MainPolyHlfDeg)
N1 = self.NumMonomials(n, self.MainPolyTotDeg)
self.MatSize = [N0, N1]
vec = self.MonomialsVec(self.MainPolyHlfDeg)
m = Matrix(1, N0, vec)
Mmnt = m.transpose() * m
Blck = [[] for i in range(N1)]
C = []
h = Matrix(self.Field, N0, N0, 0)
C.append(h)
decomp = []
for i in range(N1):
p = self.Monomials[i]
A = self.Calpha(p, Mmnt)
Blck[i].append(A)
from SDP import SDP
sos_sdp = SDP.sdp(solver = self.solver, Settings = {'detail':self.detail})
sos_sdp.solve(C, self.PolyCoefFullVec(), Blck)
if sos_sdp.Info['Status'] == 'Optimal':
self.Info['status'] = 'Feasible'
GramMtx = Matrix(sos_sdp.Info['X'][0])
try:
self.Info['Message'] = "A SOS decomposition of the polynomial were found."
self.Info['is sos'] = True
H1 = GramMtx.cholesky();
tmpM = Matrix(1, N0, vec)
decomp = list(tmpM*H1)[0]
self.Info['Wall'] = sos_sdp.Info['Wall']
self.Info['CPU'] = sos_sdp.Info['CPU']
except:
self.Info['Message'] = "The given polynomial seems to be a sum of squares, but no SOS decomposition were extracted."
self.Info['is sos'] = False
self.Info['Wall'] = sos_sdp.Info['Wall']
self.Info['CPU'] = sos_sdp.Info['CPU']
else:
self.Info['Message'] = "The given polynomial is not a sum of squares."
self.Info['status'] = 'Infeasible'
self.Info['is sos']= False
self.Info["Size"] = self.MatSize
return decomp
def minimize(self):
"""
Solves the semidefinite program coming from the set of input
data and returns some information as outpu in 'Info'
'Info' carries the following information:
status':
either 'Optimal' or 'Infeasible' based on the status of
the solver.
'Message':
provides more detail on the final status of the solver
'min':
is the minimum computed for f over the set defined by
g1>=0,..., gm>=0. It is None, if the solver fails.
'Wall' & 'CPU':
wall time and CPU time spent by the solver.
'Size':
a list which gives the dimention of sdp matrices
"""
from SDP import SDP
sos_sdp = SDP.sdp(solver=self.solver, Settings={'detail': self.detail})
sos_sdp.solve(self.Matrice[0], self.Matrice[1], self.Matrice[2])
if sos_sdp.Info['Status'] == 'Optimal':
self.f_min = min(sos_sdp.Info['PObj'], sos_sdp.Info['DObj'])
self.Info = {
"min": self.f_min,
"Wall": sos_sdp.Info['Wall'],
"CPU": sos_sdp.Info['CPU']
}
self.Info['status'] = 'Optimal'
self.Info[
'Message'] = 'Feasible solution for moments of order ' + str(
self.Relaxation)
else:
self.f_min = None
self.Info['min'] = self.f_min
self.Info['status'] = 'Infeasible'
self.Info[
'Message'] = 'No feasible solution for moments of order ' + str(
self.Relaxation) + ' were found'
self.Info["Size"] = self.MatSize
return self.f_min
def fixSDP(self, msg, external, answer=False):
sdp = reduce2audio(SDP(msg.body))
if external:
url1 = self.zsession.locGetAddress()
url2 = self.zsession.locGetCtrlAddress()
else:
url1 = self.zsession.extGetAddress()
url2 = self.zsession.extGetCtrlAddress()
self.addrFromSDP[external] = fixConnection(sdp,
URL(url1[0], port=url1[1]),
URL(url2[0], port=url2[1]))
setBody(msg, sdp.toString())
if answer:
self.zsession.setAudioInfo(self.addrFromSDP[external][2])
if self.addrFromSDP[False] and self.addrFromSDP[True]:
url1, url2, _ = self.addrFromSDP[False]
self.zsession.locSetDstAddress((url1.host, url1.port))
self.zsession.locSetDstCtrlAddress((url2.host, url2.port))
url1, url2, _ = self.addrFromSDP[True]
self.zsession.extSetDstAddress((url1.host, url1.port))
self.zsession.extSetDstCtrlAddress((url2.host, url2.port))
self.zsession.addressesReady()
def minimize(self):
"""
Solves the semidefinite program coming from the set of input
data and returns some information as outpu in 'Info'
'Info' carries the following information:
status':
either 'Optimal' or 'Infeasible' based on the status of
the solver.
'Message':
provides more detail on the final status of the solver
'min':
is the minimum computed for f over the set defined by
g1>=0,..., gm>=0. It is None, if the solver fails.
'Wall' & 'CPU':
wall time and CPU time spent by the solver.
'Size':
a list which gives the dimention of sdp matrices
"""
from SDP import SDP
sos_sdp = SDP.sdp(solver = self.solver, Settings = {'detail':self.detail})
sos_sdp.solve(self.Matrice[0], self.Matrice[1], self.Matrice[2])
if sos_sdp.Info['Status'] == 'Optimal':
self.f_min = min(sos_sdp.Info['PObj'], sos_sdp.Info['DObj'])
self.Info = {"min":self.f_min, "Wall":sos_sdp.Info['Wall'], "CPU":sos_sdp.Info['CPU']}
self.Info['status'] = 'Optimal'
self.Info['Message'] = 'Feasible solution for moments of order ' + str(self.Relaxation)
else:
self.f_min = None
self.Info['min'] = self.f_min
self.Info['status'] = 'Infeasible'
self.Info['Message'] = 'No feasible solution for moments of order ' + str(self.Relaxation) + ' were found'
self.Info["Size"] = self.MatSize
return self.f_min
