def downselect_morris_trajectories(samples, ntrajectories):
nvars = samples.shape[0]
assert samples.shape[1] % (nvars+1) == 0
ncandidate_trajectories = samples.shape[1]//(nvars+1)
# assert 10*ntrajectories<=ncandidate_trajectories
trajectories = np.reshape(
samples, (nvars, nvars+1, ncandidate_trajectories), order='F')
distances = np.zeros((ncandidate_trajectories, ncandidate_trajectories))
for ii in range(ncandidate_trajectories):
for jj in range(ii+1):
distances[ii, jj] = cdist(
trajectories[:, :, ii].T, trajectories[:, :, jj].T).sum()
distances[jj, ii] = distances[ii, jj]
get_combinations = combinations(
np.arange(ncandidate_trajectories), ntrajectories)
ncombinations = nchoosek(ncandidate_trajectories, ntrajectories)
print('ncombinations', ncombinations)
# values = np.empty(ncombinations)
best_index = None
best_value = -np.inf
for ii, index in enumerate(get_combinations):
value = np.sqrt(np.sum(
[distances[ix[0], ix[1]]**2 for ix in combinations(index, 2)]))
if value > best_value:
best_value = value
best_index = index
samples = trajectories[:, :, best_index].reshape(
nvars, ntrajectories*(nvars+1), order='F')
return samples
def test_barycentric_weights_1d(self):
eps = 1e-12
# test barycentric weights for uniform points using direct calculation
abscissa = np.linspace(-1, 1., 5)
weights = compute_barycentric_weights_1d(abscissa,
normalize_weights=False)
n = abscissa.shape[0] - 1
h = 2. / n
true_weights = np.empty((n + 1), np.double)
for j in range(n + 1):
true_weights[j] = (-1.)**(n - j) * nchoosek(
n, j) / (h**n * factorial(n))
assert np.allclose(true_weights, weights, eps)
# test barycentric weights for uniform points using analytical formula
# and with scaling on
weights = compute_barycentric_weights_1d(abscissa,
interval_length=1,
normalize_weights=False)
weights_analytical = equidistant_barycentric_weights(5)
ratio = weights / weights_analytical
# assert the two weights array differ by only a constant factor
assert np.allclose(np.min(ratio), np.max(ratio))
# test barycentric weights for clenshaw curtis points
level = 7
abscissa, tmp = clenshaw_curtis_pts_wts_1D(level)
n = abscissa.shape[0]
weights = compute_barycentric_weights_1d(abscissa,
normalize_weights=False,
interval_length=2)
true_weights = np.empty((n), np.double)
true_weights[0] = true_weights[n - 1] = 0.5
true_weights[1:n - 1] = [(-1)**ii for ii in range(1, n - 1)]
factor = true_weights[1] / weights[1]
assert np.allclose(true_weights / factor, weights, atol=eps)
# check barycentric weights are correctly computed regardless of
# order of points. Eventually ordering can effect numerical stability
# but not until very high level
abscissa, tmp = clenshaw_curtis_in_polynomial_order(level)
II = np.argsort(abscissa)
n = abscissa.shape[0]
weights = compute_barycentric_weights_1d(
abscissa,
normalize_weights=False,
interval_length=abscissa.max() - abscissa.min())
true_weights = np.empty((n), np.double)
true_weights[0] = true_weights[n - 1] = 0.5
true_weights[1:n - 1] = [(-1)**ii for ii in range(1, n - 1)]
factor = true_weights[1] / weights[II][1]
assert np.allclose(true_weights / factor, weights[II], eps)
num_samples = 65
abscissa, tmp = gauss_hermite_pts_wts_1D(num_samples)
weights = compute_barycentric_weights_1d(
abscissa,
normalize_weights=False,
interval_length=abscissa.max() - abscissa.min())
print(weights)
print(np.absolute(weights).max(), np.absolute(weights).min())
print(np.absolute(weights).max() / np.absolute(weights).min())