def __init__(
self,
Prog,
Rng,
Settings={
'Order': 0,
'Solver': 'cvxopt',
'Iterations': 100,
'detail': True,
'tryKKT': 0
}):
"""
Initiates a SosTools object by input data, mainly polynomials
f and g1,..., gm
Arguments:
Prog:
is the list of polynomials f, g_1,..., gm, in the following
format:
[f, [g1,..., gm]]
Rng:
is the polynomial ring were f, g1,..., gm are coming from.
A typical format is:
PolynomialRing(base, 'x', n)
where
base is the base ring, such as
RR: Real numbers,
QQ: Rational numbers
ZZ: Integers
etc,
'x' is a generic name for indeterminate, and
n is the number of indeterminates.
Settings:
is a dictionary of options to configure the behavior of the
object as well as sdp solver.
The options are:
Order:
The order of sdp relaxation is (the ceiling of
half degree of f, g1,..., gm) + Order.
Solver:
'cvxopt',
'csdp',
'sdpa'.
by default is set to 'cvxopt', but based on available
sdp solvers can be chaned to 'csdp' and 'sdpa'.
Iterations:
The maximum number of iterations of the solver. The
default value is 100, and it currently just effects
'cvxopt' solver.
detail:
Boolean value, default is True. Set to False to hide
the sdp solver's progress output. Only works for 'cvxopt'.
tryKKT:
A positive integer number. If the solver encounters a
singular KKT matrix, it continues to iterate for this
given number of iterations. Only works for 'cvxopt'.
"""
self.MainPolynomial = Prog[0]
self.Field = self.MainPolynomial.base_ring()
self.Ring = Rng
self.vars = self.Ring.gens()
self.NumVars = len(self.vars)
###
f_tot_deg = self.MainPolynomial.total_degree()
if (f_tot_deg % 2) == 1:
f_half_deg = (f_tot_deg + 1) / 2
else:
f_half_deg = f_tot_deg / 2
self.MainPolyHlfDeg = f_half_deg
self.MainPolyTotDeg = f_tot_deg
###
self.Constraints = []
if len(Prog) > 1:
self.Constraints = Prog[1]
self.Constraints.append(self.vars[0]**0)
self.NumberOfConstraints = len(self.Constraints)
###
for g in self.Constraints:
tmp_deg = g.total_degree()
self.Degs.append(tmp_deg)
if (tmp_deg % 2) == 1:
self.HalfDegs.append((tmp_deg + 1) / 2)
else:
self.HalfDegs.append(tmp_deg / 2)
###
if 'Order' in Settings:
self.Ord = Settings['Order']
else:
self.Ord = 0
###
if 'Solver' in Settings:
self.solver = Settings['Solver']
else:
self.solver = 'cvxopt'
###
if 'detail' in Settings:
self.detail = Settings['detail']
else:
self.detail = True
###
if len(self.HalfDegs) > 0:
cns_half_deg_max = max(self.HalfDegs)
else:
cns_half_deg_max = 0
self.Relaxation = max(self.Relaxation, f_half_deg,
cns_half_deg_max) + self.Ord
###
self.Monomials = self.MonomialsVec(2 * self.Relaxation)
self.Info = {
'min': 0,
'CPU': 0,
'Wall': 0,
'status': 'Unknown',
'Message': '',
'is sos': False
}
from sage.interfaces.matlab import Matlab
try:
self.MATLAB = {
'available': True,
'gloptipoly': False,
'sedumi': False,
'sdpnal': False
}
a = Matlab()
path_str = a.get('path')
if path_str.find('gloptipoly') >= 0:
self.MATLAB['gloptipoly'] = True
if path_str.find('SeDuMi') >= 0:
self.MATLAB['sedumi'] = True
if path_str.find('SDPNAL') >= 0:
self.MATLAB['sdpnal'] = True
a.eval('quit;')
except:
self.MATLAB = {
'available': False,
'gloptipoly': False,
'sedumi': False,
'sdpnal': False
}
def __init__(self, Prog, Rng, Settings = {'Order':0, 'Solver':'cvxopt', 'Iterations':100, 'detail':True, 'tryKKT':0}):
"""
Initiates a SosTools object by input data, mainly polynomials
f and g1,..., gm
Arguments:
Prog:
is the list of polynomials f, g_1,..., gm, in the following
format:
[f, [g1,..., gm]]
Rng:
is the polynomial ring were f, g1,..., gm are coming from.
A typical format is:
PolynomialRing(base, 'x', n)
where
base is the base ring, such as
RR: Real numbers,
QQ: Rational numbers
ZZ: Integers
etc,
'x' is a generic name for indeterminate, and
n is the number of indeterminates.
Settings:
is a dictionary of options to configure the behavior of the
object as well as sdp solver.
The options are:
Order:
The order of sdp relaxation is (the ceiling of
half degree of f, g1,..., gm) + Order.
Solver:
'cvxopt',
'csdp',
'sdpa'.
by default is set to 'cvxopt', but based on available
sdp solvers can be chaned to 'csdp' and 'sdpa'.
Iterations:
The maximum number of iterations of the solver. The
default value is 100, and it currently just effects
'cvxopt' solver.
detail:
Boolean value, default is True. Set to False to hide
the sdp solver's progress output. Only works for 'cvxopt'.
tryKKT:
A positive integer number. If the solver encounters a
singular KKT matrix, it continues to iterate for this
given number of iterations. Only works for 'cvxopt'.
"""
self.MainPolynomial = Prog[0]
self.Field = self.MainPolynomial.base_ring()
self.Ring = Rng
self.vars = self.Ring.gens()
self.NumVars = len(self.vars)
###
f_tot_deg = self.MainPolynomial.total_degree()
if (f_tot_deg % 2) == 1:
f_half_deg = (f_tot_deg + 1)/2
else:
f_half_deg = f_tot_deg/2
self.MainPolyHlfDeg = f_half_deg
self.MainPolyTotDeg = f_tot_deg
###
self.Constraints = []
if len(Prog) > 1:
self.Constraints = Prog[1]
self.Constraints.append(self.vars[0]**0)
self.NumberOfConstraints = len(self.Constraints)
###
for g in self.Constraints:
tmp_deg = g.total_degree()
self.Degs.append(tmp_deg)
if (tmp_deg % 2) == 1:
self.HalfDegs.append((tmp_deg+1)/2)
else:
self.HalfDegs.append(tmp_deg/2)
###
if 'Order' in Settings:
self.Ord = Settings['Order']
else:
self.Ord = 0
###
if 'Solver' in Settings:
self.solver = Settings['Solver']
else:
self.solver = 'cvxopt'
###
if 'detail' in Settings:
self.detail = Settings['detail']
else:
self.detail = True
###
if len(self.HalfDegs) > 0 :
cns_half_deg_max = max(self.HalfDegs)
else:
cns_half_deg_max = 0
self.Relaxation = max(self.Relaxation,f_half_deg,cns_half_deg_max)+self.Ord
###
self.Monomials = self.MonomialsVec(2*self.Relaxation)
self.Info = {'min':0, 'CPU':0, 'Wall':0, 'status':'Unknown', 'Message':'', 'is sos':False}
from sage.interfaces.matlab import Matlab
try:
self.MATLAB = {'available':True, 'gloptipoly':False, 'sedumi':False, 'sdpnal':False}
a = Matlab()
path_str = a.get('path')
if path_str.find('gloptipoly') >= 0:
self.MATLAB['gloptipoly'] = True
if path_str.find('SeDuMi') >= 0:
self.MATLAB['sedumi'] = True
if path_str.find('SDPNAL') >= 0:
self.MATLAB['sdpnal'] = True
a.eval('quit;')
except:
self.MATLAB = {'available':False, 'gloptipoly':False, 'sedumi':False, 'sdpnal':False}
def CallMatlab(self, solver='sedumi'):
"""
"""
from sage.interfaces.matlab import Matlab
a = Matlab()
code_line = "mpol x " + str(self.NumVars)
a.eval(code_line)
code_line = "f = " + self.GloptiPolyStr(self.MainPolynomial) + ";"
a.eval(code_line)
code_line = "K = ["
for idx in range(self.NumberOfConstraints - 1):
if (idx < self.NumberOfConstraints - 1) and (self.Constraints[idx]
!= 1.0):
if code_line != "K = [":
code_line += ", "
code_line += self.GloptiPolyStr(self.Constraints[idx]) + ">= 0"
code_line += "];"
a.eval(code_line)
code_line = "P = msdp(min(f), K);"
a.eval(code_line)
if solver.lower() == 'sdpnal':
code_line = "[A,b,c,K] = msedumi(P);"
a.eval(code_line)
code_line = "opts = []; opts.tol = 1e-7;"
a.eval(code_line)
code_line = "[blk,At,C,B] = read_sedumi(A,b,c,K);"
a.eval(code_line)
code_line = "[obj,X,y,Z,info,runhist] = sdpnal(blk,At,C,B,opts);"
a.eval(code_line)
code_line = "res = -(obj(1)+obj(2))/2;"
a.eval(code_line)
RES = [eval(a.get("res"))]
code_line = "cputime = runhist.cputime(size(runhist.cputime,2));"
a.eval(code_line)
RES.append(eval(a.get('cputime')))
else:
code_line = "[status,obj] = msol(P)"
a.eval(code_line)
RES = [a.get("obj")]
a.eval("quit;")
return RES
def CallMatlab(self, solver = 'sedumi'):
"""
"""
from sage.interfaces.matlab import Matlab
a = Matlab()
code_line = "mpol x " + str(self.NumVars)
a.eval(code_line)
code_line = "f = " + self.GloptiPolyStr(self.MainPolynomial) + ";"
a.eval(code_line)
code_line = "K = ["
for idx in range(self.NumberOfConstraints - 1):
if (idx < self.NumberOfConstraints - 1) and (self.Constraints[idx] != 1.0):
if code_line != "K = [":
code_line += ", "
code_line += self.GloptiPolyStr(self.Constraints[idx]) + ">= 0"
code_line += "];"
a.eval(code_line)
code_line = "P = msdp(min(f), K);"
a.eval(code_line)
if solver.lower() == 'sdpnal':
code_line = "[A,b,c,K] = msedumi(P);"
a.eval(code_line)
code_line = "opts = []; opts.tol = 1e-7;"
a.eval(code_line)
code_line = "[blk,At,C,B] = read_sedumi(A,b,c,K);"
a.eval(code_line)
code_line = "[obj,X,y,Z,info,runhist] = sdpnal(blk,At,C,B,opts);"
a.eval(code_line)
code_line = "res = -(obj(1)+obj(2))/2;"
a.eval(code_line)
RES = [eval(a.get("res"))]
code_line = "cputime = runhist.cputime(size(runhist.cputime,2));"
a.eval(code_line)
RES.append(eval(a.get('cputime')))
else:
code_line = "[status,obj] = msol(P)"
a.eval(code_line)
RES = [a.get("obj")]
a.eval("quit;")
return RES