def test_exact():
np.random.seed(1)
M = 100
m = 10
n = 2
p = 5
# Samples
X = np.random.randn(M, m)
# Synthetic function
a = np.random.randn(m)
b = np.random.randn(m)
fX = np.dot(a, X.T)**2 + np.dot(b, X.T)**3
# Random point
U, _ = np.linalg.qr(np.random.randn(m, n))
# Actual ridge subspace
#U, _ = np.linalg.qr(np.vstack([a,b]).T)
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=True)
pra.fit(X, fX, U0=U, verbose=1)
# Because the data is an exact ridge function, we should (I think) converge to the global solution
for fX1, fX2 in zip(pra(X), fX):
print "%10.5e %10.5e" % (fX1, fX2)
assert np.all(np.isclose(pra(X), fX))
def test_same_solution(degree=5, dim=2):
np.random.seed(0)
X, fX, U = exact_data(M=1000, m=10, n=dim, p=degree)
bases = [
'arnoldi', 'legendre', 'monomial', 'chebyshev', 'laguerre', 'hermite'
]
#
#U0 = U + 0.01*np.random.randn(*U.shape)
U0 = None
for norm, bound in product([1, 2, np.inf],
[None]): # , 'lower', 'upper']):
print("=" * 50)
print("Norm", norm, "bound", bound)
Us = []
for basis in bases:
print('basis', basis)
pra = PolynomialRidgeApproximation(degree=5,
subspace_dimension=dim,
basis=basis,
bound=bound,
verbose=True)
pra.fit(X, fX, U0=U0)
Us.append(np.copy(pra.U))
angles = np.zeros((len(Us), len(Us)))
for (i, j) in zip(*np.triu_indices(len(Us))):
angles[i, j] = np.max(scipy.linalg.subspace_angles(Us[i], Us[j]))
print(angles)
assert np.max(
angles
) < 1e-10, "Did not find same solution using a different basis"
def test_fit_inf():
X, fX = exact_data()
pra = PolynomialRidgeApproximation(degree=3,
subspace_dimension=1,
norm=np.inf)
pra.fit(X, fX)
assert np.all(np.isclose(pra(X), fX))
def test_fit_two():
X, fX, Uopt = exact_data()
pra = PolynomialRidgeApproximation(degree=3,
subspace_dimension=1,
norm=2,
verbose=True)
pra.fit(X, fX)
assert np.all(np.isclose(pra(X), fX))
def test_profile(degree=3, subspace_dimension=1):
X, fX, Uopt = exact_data()
pra = PolynomialRidgeApproximation(degree=3,
subspace_dimension=1,
norm=2,
verbose=True)
pra.fit(X, fX)
Y = pra.U.T.dot(X.T).T
assert np.all(np.isclose(pra.profile(Y), pra(X)))
def test_affine():
X = np.random.randn(100, 5)
a = np.random.randn(5, )
y = X.dot(a)
pra = PolynomialRidgeApproximation(degree=1,
subspace_dimension=1,
bound='upper')
pra.fit(X, y)
assert np.all(np.isclose(y, pra(X)))
def test_affine():
X = np.random.randn(100, 5)
a = np.random.randn(5, )
y = X.dot(a)
pra = PolynomialRidgeApproximation(degree=1,
subspace_dimension=1,
bound='upper')
pra.fit(X, y)
assert np.all(np.isclose(y, pra(X)))
ang = scipy.linalg.subspace_angles(pra.U, a.reshape(-1, 1))
assert np.isclose(ang, 0)
pra = PolynomialRidgeApproximation(degree=1, subspace_dimension=1)
pra.fit(X, y)
assert np.all(np.isclose(y, pra(X)))
ang = scipy.linalg.subspace_angles(pra.U, a.reshape(-1, 1))
assert np.isclose(ang, 0)
def test_minimax_gradient():
np.random.seed(1)
M = 50
m = 5
n = 2
p = 5
# Samples
X = np.random.uniform(-1, 1, size=(M, m))
# Synthetic function
a = np.random.randn(m)
b = np.random.randn(m)
fX = np.dot(a, X.T)**2 + np.dot(b, X.T)**3
# Random point
U, _ = np.linalg.qr(np.random.randn(m, n))
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=False,
maxiter=0)
# Initialize subspace
pra.fit(X, fX)
#pra.set_scale(X, U)
#pra._fit_fixed_U_inf_norm(X, fX, U)
#c = pra.coef
c = np.random.randn(len(pra.Basis(p, dim=n)))
U_c = np.hstack([U.flatten(), c])
res = lambda U_c: pra._residual(X, fX, U_c)
jac = lambda U_c: pra._jacobian(X, fX, U_c)
print(res(U_c))
print(jac(U_c))
err = check_jacobian(U_c, res, jac)
assert err < 1e-6
def test_exact():
np.random.seed(1)
# M = 100
# m = 10
# n = 2
# p = 5
#
# # Samples
# X = np.random.randn(M,m)
#
# # Synthetic function
# a = np.random.randn(m)
# b = np.random.randn(m)
# fX = np.dot(a,X.T)**2 + np.dot(b, X.T)**3
M = 1000
m, n = 10, 2
p = 3
X, fX, Uopt = exact_data(M=M, m=m, n=n, p=p)
# Random point
U, _ = np.linalg.qr(np.random.randn(m, n))
# Actual ridge subspace
#U, _ = np.linalg.qr(np.vstack([a,b]).T)
#U += Uopt
for basis in ['legendre', 'arnoldi']:
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=True,
basis=basis,
verbose=True)
pra.fit(X, fX, U0=U)
# Because the data is an exact ridge function, we should (I think) converge to the global solution
for fX1, fX2 in zip(pra(X), fX):
print("%+10.5e %+10.5e | %10.5e" % (fX1, fX2, np.abs(fX1 - fX2)))
assert np.all(np.isclose(pra(X), fX))
try:
X = np.vstack([X0] + [job.args[0] for job in jobs])
except ValueError:
X = X0
# Normalize everything
Xdone_norm = total_domain.normalize(Xdone)
X_norm = total_domain.normalize(X)
# Now build ridge approximations
Us = []
for qoi in qois:
pra = PolynomialRidgeApproximation(subspace_dimension=1,
degree=3)
I = np.isfinite(Ydone[:, qoi])
pra.fit(Xdone_norm[I, :], Ydone[I, qoi])
Us.append(pra.U)
# Now do the sampling
Xnew_norm = stretch_sample(total_domain_norm,
Us,
X0=X_norm,
M=1,
verbose=True,
enrich=False)
print "Added %d new points" % Xnew_norm.shape[0]
Xnew = total_domain.unnormalize(Xnew_norm).reshape(1, -1)
for x in Xnew:
i += 1
ks = np.arange(150, 800, 2)
qois = [4, 21, 25]
#qois = [21,25]
for qoi in qois:
Iall = np.isfinite(Yall[:, qoi])
#norm = np.linalg.norm(Yall[Iall,qoi])
norm = (np.nanmax(Yall[Iall, qoi]) - np.nanmin(Yall[Iall, qoi])) * np.sqrt(
np.sum(Iall))
err_rand_vec = []
err_doe_vec = []
for k in ks:
I = np.isfinite(Yrand[:, qoi]) & (np.arange(Yrand.shape[0]) < k)
pra = PolynomialRidgeApproximation(degree=3,
subspace_dimension=1,
n_init=1)
pra.fit(Xrand_norm[I], Yrand[I, qoi])
#err_rand = np.mean(np.abs(pra.predict(Xall_norm[Iall]) - Yall[Iall,qoi]))/norm
err_rand = np.linalg.norm(
pra.predict(Xall_norm[Iall]) - Yall[Iall, qoi]) / norm
err_rand_vec.append(err_rand)
I = np.isfinite(Ydoe[:, qoi]) & (np.arange(Ydoe.shape[0]) < k)
pra.fit(Xdoe_norm[I], Ydoe[I, qoi])
err_doe = np.linalg.norm(
pra.predict(Xall_norm[Iall]) - Yall[Iall, qoi]) / norm
#err_doe = np.mean(np.abs(pra.predict(Xall_norm[Iall]) - Yall[Iall,qoi]))/norm
err_doe_vec.append(err_doe)
print "%4d: err rand %5.2e; doe %5.2e" % (k, err_rand, err_doe)
pgf = PGF()
pgf.add('k', ks)
pgf.add('doe', err_doe_vec)