def test_optimizePoly_unconstrained_poly(self):
n = 2
N = 20
X = np.random.uniform(-1.0, 1.0, (N, n))
# Function values for f and Poly object
f = self.ObjFun(X)
fparam = eq.Parameter(distribution='uniform',
lower=-1.,
upper=1.,
order=self.degf)
fParameters = [fparam for i in range(n)]
myBasis = eq.Basis('Total order')
fpoly = eq.Polyreg(fParameters,
myBasis,
training_inputs=X,
training_outputs=f)
for method in [
'BFGS', 'CG', 'Newton-CG', 'L-BFGS-B', 'Powell', 'Nelder-Mead',
'trust-ncg'
]:
Opt = eq.Optimization(method=method)
Opt.addObjective(Poly=fpoly)
x0 = np.random.uniform(-1.0, 1.0, n)
sol = Opt.optimizePoly(x0)
np.testing.assert_almost_equal(sol['x'].flatten(),
np.array([1.0, 1.0]),
decimal=3)
def test_optimizePoly_constrained_function(self):
n = 2
N = 20
X = np.random.uniform(-1.0, 1.0, (N, n))
# Function values for f and Poly object
f = self.ObjFun(X)
fparam = eq.Parameter(distribution='uniform',
lower=-1.,
upper=1.,
order=self.degf)
fParameters = [fparam for i in range(n)]
myBasis = eq.Basis('Total order')
fpoly = eq.Polyreg(fParameters,
myBasis,
training_inputs=X,
training_outputs=f)
g1Func = lambda x: self.ConFun1(x.reshape(1, -1))
g1Grad = lambda x: self.ConFun1_Deriv(x.flatten())
g1Hess = lambda x, v: self.ConFun1_Hess(x.flatten())
for method in ['trust-constr', 'SLSQP']:
Opt = eq.Optimization(method=method)
Opt.addObjective(Poly=fpoly)
Opt.addNonLinearIneqCon(self.boundsg1,
Function=g1Func,
jacFunction=g1Grad,
hessFunction=g1Hess)
Opt.addLinearEqCon(np.eye(n), np.ones(n))
x0 = np.zeros(n)
sol = Opt.optimizePoly(x0)
np.testing.assert_almost_equal(sol['x'].flatten(),
np.array([1.0, 1.0]),
decimal=2)
def test_optimizePoly_unconstrained_poly_subspace(self):
df = 2
n = 50
N = 5000
X = np.random.uniform(-1.0, 1.0, (N, n))
# Active subspace and values for f
U = sp.linalg.orth(np.random.rand(n, df))
u, f = self.ObjFun_Subspace(X, U)
fparam = eq.Parameter(distribution='uniform',
lower=-6.,
upper=6.,
order=self.degf)
fParameters = [fparam for i in range(df)]
myBasis = eq.Basis('Total order')
fpoly = eq.Polyreg(fParameters,
myBasis,
training_inputs=u,
training_outputs=f)
for method in [
'BFGS', 'CG', 'Newton-CG', 'L-BFGS-B', 'Powell', 'Nelder-Mead',
'trust-ncg'
]:
Opt = eq.Optimization(method=method)
Opt.addObjective(Poly=fpoly, subspace=U)
x0 = np.zeros(n)
sol = Opt.optimizePoly(x0)
np.testing.assert_almost_equal(np.dot(sol['x'], U).flatten(),
np.array([1.0, 1.0]),
decimal=3)
def test_optimizePoly_constrained_poly(self):
n = 2
N = 20
X = np.random.uniform(-1.0, 1.0, (N, n))
# Function values for f and Poly object
f = self.ObjFun(X)
fparam = eq.Parameter(distribution='uniform',
lower=-1.,
upper=1.,
order=self.degf)
fParameters = [fparam for i in range(n)]
myBasis = eq.Basis('Total order')
fpoly = eq.Polyreg(fParameters,
myBasis,
training_inputs=X,
training_outputs=f)
# Active subspace and values for g1
g1 = self.ConFun1(X)
g1param = eq.Parameter(distribution='uniform',
lower=-1.,
upper=1.,
order=self.degg1)
g1Parameters = [g1param for i in range(n)]
myBasis = eq.Basis('Total order')
g1poly = eq.Polyreg(g1Parameters,
myBasis,
training_inputs=X,
training_outputs=g1)
for method in ['trust-constr', 'SLSQP']:
Opt = eq.Optimization(method=method)
Opt.addObjective(Poly=fpoly)
Opt.addLinearIneqCon(np.eye(n), -np.ones(n), np.ones(n))
Opt.addNonLinearIneqCon(self.boundsg1, Poly=g1poly)
x0 = np.zeros(n)
sol = Opt.optimizePoly(x0)
np.testing.assert_almost_equal(sol['x'].flatten(),
np.array([1.0, 1.0]),
decimal=2)
def test_optimizePoly_constrained_poly_subspace(self):
df = 2
dg1 = 2
dg2 = 2
n = 50
N = 5000
X = np.random.uniform(-1.0, 1.0, (N, n))
# Active subspace and values for f
U = sp.linalg.orth(np.random.rand(n, df))
u, f = self.ObjFun_Subspace(X, U)
fparam = eq.Parameter(distribution='uniform',
lower=-6.,
upper=6.,
order=self.degf)
fParameters = [fparam for i in range(df)]
myBasis = eq.Basis('Total order')
fpoly = eq.Polyreg(fParameters,
myBasis,
training_inputs=u,
training_outputs=f)
# Active subspace and values for g1
W = sp.linalg.orth(np.random.rand(n, dg1))
w, g1 = self.ConFun1_Subspace(X, W)
g1param = eq.Parameter(distribution='uniform',
lower=-6.,
upper=6.,
order=self.degg1)
g1Parameters = [g1param for i in range(dg1)]
myBasis = eq.Basis('Total order')
g1poly = eq.Polyreg(g1Parameters,
myBasis,
training_inputs=w,
training_outputs=g1)
# Active subspace and values for g2
V = sp.linalg.orth(np.random.rand(n, dg2))
v, g2 = self.ConFun2_Subspace(X, V)
g2param = eq.Parameter(distribution='uniform',
lower=-6.,
upper=6.,
order=self.degg2)
g2Parameters = [g2param for i in range(dg2)]
myBasis = eq.Basis('Total order')
g2poly = eq.Polyreg(g2Parameters,
myBasis,
training_inputs=v,
training_outputs=g2)
for method in ['trust-constr', 'SLSQP']:
Opt = eq.Optimization(method=method)
Opt.addObjective(Poly=fpoly, subspace=U)
Opt.addBounds(-np.ones(n), np.ones(n))
Opt.addNonLinearIneqCon(self.boundsg1, Poly=g1poly, subspace=W)
Opt.addNonLinearEqCon(self.valg2, Poly=g2poly, subspace=V)
x0 = np.zeros(n)
sol = Opt.optimizePoly(x0)
np.testing.assert_almost_equal(np.dot(sol['x'], U).flatten(),
np.array([1.0, 1.0]),
decimal=3)