def test_lipschitz_approx_class():
r""" Integration testing
"""
fun = psdr.demos.OTLCircuit()
X = fun.domain.sample_grid(2)
lip = psdr.LipschitzMatrix()
lip.fit(grads=fun.grad(X))
lipapprox = LipschitzApproximation(lip.L, fun.domain)
X = fun.domain.sample(40)
fX = fun(X)
#fX += 0.1*np.random.randn(*fX.shape)
lipapprox.fit(X, fX[:, 0])
y = lipapprox(X)
print(fX[:, 0] - y)
err = np.max(np.abs(fX[:, 0] - y))
assert err < 1e-9
# Check identification of active subspace
for i in range(1, len(fun.domain)):
U = lip.U[:, :-i]
LUU = lip.L @ U @ U.T
lipapprox = LipschitzApproximation(LUU, fun.domain)
print(U.shape)
print(lipapprox.U.shape)
ang = subspace_angles(U, lipapprox.U)
print(ang)
assert np.max(ang) < 1e-7, "Did not correctly identify active subspace"
def test_lipschitz_fixed_U(N = 10, M = 20): np.random.seed(0) if True: fun = psdr.demos.HartmannMHD() X = fun.domain.sample(M) fX = fun(X)[:,0] Xg = fun.domain.sample(N) grads = fun.grad(Xg)[:,0,:] else: fun = psdr.demos.OTLCircuit() X = fun.domain.sample(M) fX = fun(X) Xg = fun.domain.sample(N) grads = fun.grad(Xg) m = len(fun.domain) #grads = np.zeros((0,m)) X = np.zeros((0,m)) fX = np.zeros((0,)) lipr = psdr.PartialLipschitzMatrix(m) U = np.eye(m) J, alpha = lipr._fixed_U(U, X, fX, grads, 0) lip = psdr.LipschitzMatrix(method = 'cvxpy') lip.fit(X = X, fX = fX, grads = grads) assert np.max(np.abs(lip.H - J)) < 1e-3
def test_shadow_lipschitz(): fun = psdr.demos.OTLCircuit() X = fun.domain.sample_grid(2) fX = fun(X) grads = fun.grad(X) lip = psdr.LipschitzMatrix() lip.fit(grads = grads) ax = lip.shadow_plot(X, fX) lip.shadow_uncertainty(fun.domain, X, fX, ax = ax, ngrid = 4, pgfname = 'test_shadow_uncertainty.dat') #assert filecmp.cmp(os.path.join(path, 'data/test_shadow_uncertainty.dat'), 'test_shadow_uncertainty.dat') # Test 2-d version ax = lip.shadow_plot(X, fX, dim = 2) # Test predefined axes fig, ax = plt.subplots() ax = lip.shadow_plot(X, fX, dim = 1, ax = ax) # Test specified U ax = lip.shadow_plot(X, fX, U = lip.U[:,0]) # Test specified U ax = lip.shadow_plot(X, fX, U = lip.U[:,0:2]) # Test specified U ax = lip.shadow_plot(X, fX, U = lip.U[:,0:2], dim = 2) # Test writing 2-D output lip.shadow_plot(X, fX, ax = None, pgfname = 'test_shadow_uncertainty_2d.dat')
def test_lipschitz_approx(norm, epsilon):
fun = psdr.demos.Borehole()
X = fun.domain.sample_grid(2)
lip = psdr.LipschitzMatrix()
lip.fit(grads=fun.grad(X))
# Now generate some random data
X = fun.domain.sample(50)
fX = fun(X)
# Implement for multiple ranks
for i in range(len(fun.domain)):
U = lip.U[:, :-i]
LUU = lip.L @ U @ U.T
np.random.seed(i)
fX += epsilon * np.random.randn(*fX.shape)
y = lipschitz_approximation_compatible_data(LUU,
X,
fX[:, 0],
norm=norm,
verbose=True)
err = check_lipschitz_eval(LUU, X, y)
print("error in data", err)
assert err < 1e-5
def lipschitz(X, fX, epsilon):
lip = psdr.LipschitzMatrix(epsilon=epsilon,
verbose=True,
abstol=1e-7,
reltol=1e-7,
feastol=1e-7)
lip.fit(X, fX)
return lip.L
def build_lipschitz(fun):
# Estimate the Lipschitz matrix
lip = psdr.LipschitzMatrix(verbose=True,
abstol=1e-7,
reltol=1e-7,
feastol=1e-7)
lip.fit(grads=fun.grad(fun.domain.sample_grid(4)))
L = lip.L
return L
def generate_X(fun, M):
np.random.seed(0)
X = fun.domain.sample(1000)
grads = fun.grad(X)
lip = psdr.LipschitzMatrix()
lip.fit(grads=grads)
L = lip.L
X = psdr.minimax_lloyd(fun.domain, M, L=L, verbose=True)
return X
def generate_X_maximin(fun, M):
np.random.seed(0)
X = fun.domain.sample(1000)
grads = fun.grad(X)
lip = psdr.LipschitzMatrix(verbose=True,
abstol=1e-7,
reltol=1e-7,
feastol=1e-7)
lip.fit(grads=grads)
L = lip.L
X0 = psdr.maximin_coffeehouse(fun.domain, M, L=L, verbose=True)
X = psdr.maximin_block(fun.domain, M, L=L, verbose=True, Xhat=X0)
return X
def test_lipschitz_partial(N = 30, M = 20):
np.random.seed(0)
if True:
fun = psdr.demos.HartmannMHD()
X = fun.domain.sample(M)
fX = fun(X)[:,0]
Xg = fun.domain.sample(N)
grads = fun.grad(Xg)[:,0,:]
else:
fun = psdr.demos.OTLCircuit()
X = fun.domain.sample(M)
fX = fun(X)
Xg = fun.domain.sample(N)
grads = fun.grad(Xg)
lip1 = psdr.PartialLipschitzMatrix(1, verbose = True, maxiter = 10)
lip2 = psdr.PartialLipschitzMatrix(2, verbose = True, maxiter = 10)
for lip in [lip1, lip2 ]:
for kwargs in [ {'X': X, 'fX': fX}, {'grads':grads}, {'X':X, 'fX': fX, 'grads': grads}]:
lip.fit(**kwargs)
err = check_lipschitz(lip.H, **kwargs)
print("error", err)
assert err > -1e-6, "constraints not satisfied"
# Check square-root L
err_L = np.max(np.abs(lip.H - lip.L.dot(lip.L)))
print("err L", err_L)
assert err_L < 1e-7
# If we fit an m-1 dimensional case we should get back the true Lipschitz matrix
# We avoid the low rank problem of points by considering gradients here
lip = psdr.LipschitzMatrix()
lip.fit(grads = grads)
H = lip.H
lip3 = psdr.PartialLipschitzMatrix(len(fun.domain)-1, verbose = True, U0 = lip.U[:,0:len(fun.domain)-1])
lip4 = psdr.PartialLipschitzMatrix(len(fun.domain), verbose = True)
for lip in [lip3, lip4]:
lip.fit(grads = grads)
err = np.max(np.abs(H - lip.H))
print('error', err)
assert err < 1e-4, "Did not identify true Lipschitz matrix"
names = []
# OTL circuit function
funs.append(psdr.demos.OTLCircuit())
names.append('otl')
# Borehole
funs.append(psdr.demos.Borehole())
names.append('borehole')
# Wing Weight
funs.append(psdr.demos.WingWeight())
names.append('wing')
act = psdr.ActiveSubspace()
lip = psdr.LipschitzMatrix()
m = max([len(fun.domain) for fun in funs])
pgf = PGF()
pgf.add('i', np.arange(1, m + 1))
for fun, name in zip(funs, names):
X = fun.domain.sample(1e3)
grads = fun.grad(X)
act.fit(grads)
lip.fit(grads=grads)
ew = np.nan * np.zeros(m)
ew[0:len(fun.domain)] = scipy.linalg.eigvalsh(act.C)[::-1]
pgf.add('%s_C' % name, ew)
ew[0:len(fun.domain)] = scipy.linalg.eigvalsh(lip.H)[::-1]
import numpy as np
import psdr, psdr.demos
np.random.seed(0)
#fun = psdr.demos.OTLCircuit()
fun = psdr.demos.Borehole()
X = fun.domain.sample(1e2)
grads = fun.grad(X)
lip = psdr.LipschitzMatrix(verbose=True)
lip.fit(grads=grads)
U = lip.U[:, 0:1]
print(U)
# setup an experimental design
X = psdr.minimax_design_1d(fun.domain, 20, L=U.T)
X2 = []
for x in X:
dom = fun.domain.add_constraints(A_eq=U.T, b_eq=U.T @ x)
X2.append(dom.sample_boundary(50))
X2 = np.vstack(X2)
fX2 = fun(X2)
pra = psdr.PolynomialRidgeApproximation(9, 1, norm=np.inf)
pra.fit_fixed_subspace(X2, fX2, U)
import psdr.demos from psdr.pgf import PGF np.random.seed(0) fun = psdr.demos.OTLCircuit() X = fun.domain.sample_grid(2) fX = fun(X) gradX = fun.grad(X) # Grid-based sampling Xg = fun.domain.sample_grid(8) fXg = fun(Xg) lip_mat = psdr.LipschitzMatrix() lip_con = psdr.LipschitzConstant() lip_mat.fit(grads=gradX) lip_con.fit(grads=gradX) # construct designs M = 100 ngrid = 100 X_iso = psdr.minimax_lloyd(fun.domain, M) X_lip = psdr.minimax_lloyd(fun.domain, M, L=lip_mat.L) # Fix ridge U = lip_mat.U[:, 0].copy() # Generate envelope of data
]
alg_names = ['random', 'LHS', 'minimax']
# Number of repetitions
Ms = [100, 100, 10]
Nsamp = 20
for fun, name in zip(funs, names):
# Estimate the Lipschitz matrix
np.random.seed(0)
X = np.vstack([fun.domain.sample(1000), fun.domain.sample_grid(2)])
grads = fun.grad(X)
lip = psdr.LipschitzMatrix(verbose=True,
reltol=1e-7,
abstol=1e-7,
feastol=1e-7)
lip.fit(grads=grads)
L = lip.L
plt.clf()
# Samples to use when estimating dispersion
#X0 = psdr.maximin_coffeehouse(fun.domain, 5000, L = L, N0 = 50)
X0 = np.vstack(
[psdr.random_sample(fun.domain, 5000),
fun.domain.sample_grid(2)])
plt.clf()
fun_true = psdr.Function(lambda x: partial_trace_fun(x, tol = 1e-4), domain)
X = fun.domain.sample_grid(10)
#np.random.seed(0)
#X = fun.domain.sample(200)
fX = fun(X)
fX_true = fun_true(X)
epsilon = float(max(np.abs(fX - fX_true)))
#epsilon = 0.2*np.max(np.abs(fX_true))
#print(np.max(fX_true))
#print(epsilon)
lip = psdr.LipschitzMatrix(verbose = True)
lip.fit(X, fX)
print("========noisy=========")
print("L", lip.L)
print(np.linalg.norm(lip.L, 'fro'))
ew, ev = np.linalg.eigh(lip.L)
print("ew", ew)
print("ev", ev)
lip.fit(X, fX_true)
print("========true=========")
print("L", lip.L)
print(np.linalg.norm(lip.L, 'fro'))
ew, ev = np.linalg.eigh(lip.L)
print("ew", ew)
print("ev", ev)