def test_naca_grad():
nprocesses = max(1, multiprocessing.cpu_count() - 1)
try:
travis = os.environ['TRAVIS'] == 'true'
except KeyError:
travis = False
if travis:
# We limit number of dimensions and iteration count
# so entire test takes less than 10min on Travis-CI
naca = psdr.demos.NACA0012(n_upper=1,
n_lower=1,
verbose=True,
maxiter=200,
nprocesses=1)
x = 0.2 * np.ones(len(naca.domain))
err = check_jacobian(x, naca.eval, naca.grad, hvec=[1e-4])
print('maximum error', err)
assert err < 5e-2
else:
naca = psdr.demos.NACA0012(n_upper=1,
n_lower=1,
verbose=True,
maxiter=1000,
nprocesses=nprocesses)
x = 0.2 * np.ones(len(naca.domain))
err = check_jacobian(x, naca.eval, naca.grad, hvec=[1e-4])
print('maximum error', err)
assert err < 5e-4
def test_der(m=3, p=5, M=10):
X = np.random.randn(M, m)
bases = [
MonomialTensorBasis(m, p),
LegendreTensorBasis(m, p),
ChebyshevTensorBasis(m, p),
LaguerreTensorBasis(m, p),
HermiteTensorBasis(m, p),
]
for basis in bases:
obj = lambda x: basis.V(x.reshape(1, -1)).reshape(-1)
grad = lambda x: basis.DV(x.reshape(1, -1)).reshape(-1, m)
assert check_jacobian(X[0], obj, grad) < 1e-7
basis.set_scale(X)
obj = lambda x: basis.V(x.reshape(1, -1)).reshape(-1)
grad = lambda x: basis.DV(x.reshape(1, -1)).reshape(-1, m)
assert check_jacobian(X[0], obj, grad) < 1e-7
def test_jacobian(m, n, nout, Basis, degree):
np.random.seed(0)
M = 1000
U = np.random.randn(m, n)
X = np.random.uniform(-1, 1, size=(M, m))
fX = np.random.randn(M, nout)
r = _varpro_residual(U, X, fX, Basis, degree)
J = _varpro_jacobian(U, X, fX, Basis, degree)
res = lambda u: _varpro_residual(u.reshape(m, n), X, fX, Basis, degree)
jac = lambda u: _varpro_jacobian(u.reshape(m, n), X, fX, Basis, degree)
err = check_jacobian(U.flatten(), res, jac, hvec=[1e-6])
assert err < 1e-5
def test_jacobian_fixed(m, n, nf, nout, Basis, degree):
np.random.seed(0)
M = 1000
A = np.random.randn(m, m)
U, _ = np.linalg.qr(A, mode='complete')
Uf = np.copy(U[:, :nf])
Uc = np.copy(U[:, nf:])
mm = Uc.shape[1]
U, _ = np.linalg.qr(np.random.randn(mm, n))
X = np.random.uniform(-1, 1, size=(M, m))
fX = np.random.randn(M, nout)
res = lambda u: _varpro_residual_fixed(u.reshape(mm, n), X, fX, Basis,
degree, Uf, Uc)
jac = lambda u: _varpro_jacobian_fixed(u.reshape(mm, n), X, fX, Basis,
degree, Uf, Uc)
J = jac(U.flatten())
err = check_jacobian(U.flatten(), res, jac, hvec=[1e-6])
assert err < 1e-6