def test_varpro_jacobian():
np.random.seed(1)
M = 6
m = 2
n = 1
p = 2
# 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))
U_flat = U.flatten()
for basis in ['legendre', 'arnoldi']:
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=False,
basis=basis)
# This sets the basis
Y = (U.T @ X.T).T
# pra.basis = pra.Basis(pra.degree, Y)
#pra._varpro_jacobian(X, fX, U)
res = lambda U: pra._varpro_residual(X, fX, U)
jac = lambda U: pra._varpro_jacobian(X, fX, U)
err = check_jacobian(U_flat, res, jac, hvec=[1e-7])
assert err < 1e-6
# Check with scaling on
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=True)
#pra.set_scale(X, U)
res = lambda U: pra._varpro_residual(X, fX, U)
jac = lambda U: pra._varpro_jacobian(X, fX, U)
err = check_jacobian(U_flat, res, jac)
assert err < 1e-6
# Check with scaling on for Hermite basis
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=True,
basis='hermite')
# pra.set_scale(X, U)
res = lambda U: pra._varpro_residual(X, fX, U)
jac = lambda U: pra._varpro_jacobian(X, fX, U)
err = check_jacobian(U_flat, res, jac)
assert err < 1e-6
def test_varpro_jacobian():
np.random.seed(1)
M = 100
m = 10
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))
U_flat = U.flatten()
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=False)
res = lambda U: pra._varpro_residual(X, fX, U)
jac = lambda U: pra._varpro_jacobian(X, fX, U)
err = check_jacobian(U_flat, res, jac)
assert err < 1e-6
# Check with scaling on
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=True)
pra.set_scale(X, U)
res = lambda U: pra._varpro_residual(X, fX, U)
jac = lambda U: pra._varpro_jacobian(X, fX, U)
err = check_jacobian(U_flat, res, jac)
assert err < 1e-6
# Check with scaling on for Hermite basis
pra = PolynomialRidgeApproximation(degree=p,
subspace_dimension=n,
scale=True,
basis='hermite')
pra.set_scale(X, U)
res = lambda U: pra._varpro_residual(X, fX, U)
jac = lambda U: pra._varpro_jacobian(X, fX, U)
err = check_jacobian(U_flat, res, jac)
assert err < 1e-6