def ll_factorize(A):
"""
Solves LL of A using polymom
Assumes that diagonal elements of L are 1
M = L L^T; M_{ij} = \sum{k=1}^{min{i,j}} L_{ik} L_{jk}
"""
d, d_ = A.shape
assert d == d_ # Only triangular for now
l_vars = [(i,j) for i in xrange(d) for j in xrange(i+1)]
syms = ["l_%d%d"% (i+1,j+1) for i, j in l_vars]
R, syms = xring(",".join(syms), RR)
l_vars_ = dict(zip(l_vars, syms[:len(l_vars)]))
# Construct equations
def eqn(i,j):
return sum(l_vars_.get((i,k), 1 if i == k else 0) * l_vars_.get((j,k), 0) for k in xrange(min(i,j)+1))
I = [eqn(i,j) - A[i,j] for i in xrange(d) for j in xrange(i+1)]
I += [l_vars_.get((0,0)) - np.sqrt(A[0,0])]
return R, I
B = BB.BorderBasisFactory(1e-5).generate(R,I)
print B
V = B.zeros()
assert len(V) == 1
V = V[0]
L = zeros(d,d)
for idx, (i, j) in enumerate(l_vars):
L[i, j] = V[idx]
return L
def eigen_factorize(A):
"""
Solves LU of A using polymom
Assumes that diagonal elements of L are 1
"""
d, d_ = A.shape
assert d == d_ # Only triangular for now
syms = ["l"] + ["x_%d" % i for i in xrange(d)]
R, syms = xring(",".join(syms), RR)
l, xs = syms[0], syms[1:]
# Construct equations
def eqn(i):
return sum(A[i,j] * xs[j] for j in xrange(d))
I = [eqn(i) - l * xs[i] for i in xrange(d)]
I += [ xs[0] - 1.0 ]
#I += [ sum(xs[i]**2 for i in xrange(d)) - 1.0 ]
return R, I
B = BB.BorderBasisFactory(1e-5).generate(R,I)
V = B.zeros()
return R, I
def lu_factorize(A):
"""
Solves LU of A using polymom
Assumes that diagonal elements of L are 1
"""
d, d_ = A.shape
assert d == d_ # Only triangular for now
l_vars = [(i,j) for i in xrange(d) for j in xrange(i)]
u_vars = [(i,j) for i in xrange(d) for j in xrange(i, d)]
syms = ["l_%d%d"% (i+1,j+1) for i, j in l_vars] + ["u_%d%d"% (i+1,j+1) for i, j in u_vars]
R, syms = xring(",".join(syms), RR)
l_vars_ = dict(zip(l_vars, syms[:len(l_vars)]))
u_vars_ = dict(zip(u_vars, syms[len(l_vars):]))
# Construct equations
def eqn(i,j):
return sum(l_vars_.get((i,k), 1 if i == k else 0) * u_vars_.get((k,j), 0) for k in xrange(min(i,j)+1))
I = [eqn(i,j) - A[i,j] for i in xrange(d) for j in xrange(d)]
B = BB.BorderBasisFactory(1e-5).generate(R,I)
print B
V = B.zeros()
assert len(V) == 1
V = V[0]
L = np.eye(d)
U = np.zeros((d,d))
for idx, (i, j) in enumerate(l_vars):
L[i, j] = V[idx]
for idx, (i, j) in enumerate(u_vars):
U[i, j] = V[len(l_vars)+idx]
return L, U
def eigen_factorize(A):
"""
Solves LU of A using polymom
Assumes that diagonal elements of L are 1
"""
d, d_ = A.shape
assert d == d_ # Only triangular for now
syms = ["l"] + ["x_%d" % i for i in xrange(d)]
R, syms = xring(",".join(syms), RR)
l, xs = syms[0], syms[1:]
# Construct equations
def eqn(i):
return sum(A[i, j] * xs[j] for j in xrange(d))
I = [eqn(i) - l * xs[i] for i in xrange(d)]
I += [xs[0] - 1.0]
#I += [ sum(xs[i]**2 for i in xrange(d)) - 1.0 ]
return R, I
B = BB.BorderBasisFactory(1e-5).generate(R, I)
V = B.zeros()
return R, I
def cyclic(n, coefficient_ring=sp.FF(32003), order='grevlex'):
"""Return the cyclic-n ideal."""
R, gens = sp.xring('x:' + str(n), coefficient_ring, order)
F = [
sum(np.prod([gens[(i + k) % n] for k in range(d)]) for i in range(n))
for d in range(1, n)
]
return F + [np.product(gens) - 1]
def __init__(self, d, opt):
self.d = d
self.opt = opt
l_vars = [(i, j) for i in xrange(d) for j in xrange(i + 1)]
syms = ["l_%d%d" % (i + 1, j + 1) for i, j in l_vars]
self.R, self.syms = xring(",".join(syms), RR, order=grevlex)
self.l_vars = dict(zip(l_vars, self.syms))
def __init__(self, d, opt):
self.d = d
self.opt = opt
l_vars = [(i,j) for i in xrange(d) for j in xrange(i+1)]
syms = ["l_%d%d"% (i+1,j+1) for i, j in l_vars]
self.R, self.syms = xring(",".join(syms), RR, order=grevlex)
self.l_vars = dict(zip(l_vars, self.syms))
def generate_multivariate_problem(n_variables=10, n_equations=10):
syms = ['x%d' % i for i in xrange(1, n_variables + 1)]
R, syms = xring(','.join(syms), RR, order=grevlex)
I = [
sum(coeff * sym for coeff, sym in zip(coeffs, syms))
for coeffs in np.random.randn(n_variables, n_equations)
]
return R, I, [np.zeros(n_variables)]
def make_env(args):
"""Return the training environment for this run."""
if args.environment in ['CartPole-v0', 'CartPole-v1', 'LunarLander-v2']:
env = gym.make(args.environment)
elif args.binned:
dirname = "".join([
'data/bins/{0}-{1}-{2}'.format(args.variables, args.degree,
args.generators),
'-consts' if args.constants else "",
'-' + args.degree_distribution,
'-homog' if args.homogeneous else "",
'-pure' if args.pure else "",
])
ring = sp.xring('x:' + str(args.variables), sp.FF(32003), 'grevlex')[0]
ideal_gen = FromDirectoryIdealGenerator(dirname, ring)
env = BuchbergerEnv(ideal_gen,
elimination=args.elimination,
rewards=args.rewards)
env = LeadMonomialsWrapper(env, k=args.k)
elif args.environment == "MixedRandomBinomialIdeal":
ideal_gen = MixedRandomBinomialIdealGenerator(
args.variables,
list(range(5, args.degree + 1)),
list(range(4, args.generators + 1)),
constants=args.constants,
degrees=args.degree_distribution,
homogeneous=args.homogeneous,
pure=args.pure)
env = BuchbergerEnv(ideal_gen,
elimination=args.elimination,
rewards=args.rewards)
env = LeadMonomialsWrapper(env, k=args.k)
elif args.environment == "RandomPolynomialIdeal":
ideal_gen = RandomIdealGenerator(args.variables,
args.degree,
args.generators,
args.l,
constants=args.constants,
degrees=args.degree_distribution)
env = BuchbergerEnv(ideal_gen,
elimination=args.elimination,
rewards=args.rewards)
env = LeadMonomialsWrapper(env, k=args.k)
else:
ideal_gen = RandomBinomialIdealGenerator(
args.variables,
args.degree,
args.generators,
constants=args.constants,
degrees=args.degree_distribution,
homogeneous=args.homogeneous,
pure=args.pure)
env = BuchbergerEnv(ideal_gen,
elimination=args.elimination,
rewards=args.rewards)
env = LeadMonomialsWrapper(env, k=args.k)
return env
def __init__(self,
n,
d,
s,
lam,
coefficient_ring=sp.FF(32003),
order='grevlex',
constants=False,
degrees='uniform'):
self.ring = sp.xring('x:' + str(n), coefficient_ring, order)[0]
self.dist = self._make_dist(n, d, constants, degrees)
self.lam = lam
self.generators = s
self.bases = [basis(self.ring, i) for i in range(d + 1)]
def __init__(self,
n=3,
d=20,
s=10,
lam=0.5,
dist='uniform',
constants=False,
homogeneous=False,
coefficient_ring=sp.FF(32003),
order='grevlex'):
ring = sp.xring('x:' + str(n), coefficient_ring, order)[0]
self.s = s
self.lam = lam
self.homogeneous = homogeneous
self.bases = [basis(ring, i) for i in range(d + 1)]
self.rng = np.random.default_rng()
self.degree_dist = degree_distribution(ring,
d,
dist=dist,
constants=constants)
self.ring = ring
self.P = ring.domain.characteristic()
def generate_multivariate_problem(n_variables=10, n_equations=10):
syms = ["x%d" % i for i in xrange(1, n_variables + 1)]
R, syms = xring(",".join(syms), RR, order=grevlex)
I = [sum(coeff * sym for coeff, sym in zip(coeffs, syms)) for coeffs in np.random.randn(n_variables, n_equations)]
return R, I, [np.zeros(n_variables)]
def __init__(self, n_variables, n_equations):
self.n_variables, self.n_equations = n_variables, n_equations
syms = ['x%d' % i for i in xrange(1, n_variables + 1)]
self.R, self.syms = xring(','.join(syms), RR, order=grevlex)
def __init__(self, d, opt):
self.d = d
self.opt = opt
syms = ["l"] + ["x_%d" % (i + 1) for i in xrange(d)]
self.R, self.syms = xring(",".join(syms), RR, order=grevlex)
def __init__(self, n_variables, n_equations):
self.n_variables, self.n_equations = n_variables, n_equations
syms = ['x%d' % i for i in xrange(1, n_variables+1)]
self.R, self.syms = xring(','.join(syms), RR, order=grevlex)
def __init__(self, d, opt):
self.d = d
self.opt = opt
syms = ["l"] + ["x_%d" % (i+1) for i in xrange(d)]
self.R, self.syms = xring(",".join(syms), RR, order=grevlex)