def wafp_sampling(self, indices, oversampling=10, weights=None,
sampler='idist', K=None, fast_sampler=True):
"""
Computes (indices.shape[0] + oversampling) points using the WAFP
strategy. This requires forming K random samples; the input sampler
determines which measure to take these random samples from.
"""
M = indices.shape[0] + oversampling
if K is None:
K = M + 40
else:
K = max(K, M)
if sampler == 'idist':
x = self.idist_mixture_sampling(K, indices, weights=weights,
fast_sampler=fast_sampler)
else:
raise ValueError('Unrecognized string "{0:s}" for input \
"sampler"'.format(sampler))
V = self.eval(x, indices)
# Precondition rows to have unit norm
V = np.multiply(V.T, 1/np.sqrt(np.sum(V**2, axis=1))).T
P = greedy_d_optimal(V, M)
return x[P, :]
def test_greedy_d_optimal_restart(self):
""" Greedy D-optimal designs with restart. """
N = int(200 * np.random.random_sample())
M = N + int(100 * np.random.random_sample())
c = np.random.random_sample()
p = int(c * M + (1 - c) * N)
A = np.random.randn(M, N) / np.sqrt(N)
P = greedy_d_optimal(A, p)
_, P2 = qr(A.T, pivoting=True, mode='r')
temp = A[P2[:N], :]
# G = np.dot(temp.T, temp)
# Ginvwm = np.dot(np.linalg.inv(G), A[P2[N:], :].T)
# Confirm greedy determinantal stuff
for q in range(p - N):
detvals = np.zeros(M - N - q)
for ind in range(M - N - q):
temp = A[np.append(P2[:(N + q)], P2[N + q + ind]), :]
detvals[ind] = np.linalg.det(np.dot(temp.T, temp))
maxind = np.argmax(detvals) + N + q
P2[[maxind, N + q]] = P2[[N + q, maxind]]
errstr = 'Failed for (N,M,p) = ({0:d}, {1:d}, {2:d})'.format(N, M, p)
self.assertEqual(np.linalg.norm(P - P2[:p], ord=np.inf), 0, msg=errstr)
def wafp_sampling_restart(self,
indices,
samples,
Nnewsamples,
weights=None,
sampler='idist',
fast_sampler=True):
"""
Computes Nnewsamples from a "restarted" WAFP procedure, from which the
input samples are already prescribed.
"""
if Nnewsamples == 0:
return samples
Mold = samples.shape[0]
V = self.eval(samples, indices)
# Precondition rows to have unit norm
V = np.multiply(V.T, 1 / np.sqrt(np.sum(V**2, axis=1))).T
# We'll do this slowly since adaptivity is hard.
# Generate Ncandidate new candidates, choose 1 new sample, repeat.
Ncandidates = 100
for q in range(Nnewsamples):
if sampler == 'idist':
x = self.idist_mixture_sampling(Ncandidates,
indices,
weights=weights,
fast_sampler=fast_sampler)
else:
raise ValueError('Unrecognized string "{0:s}" for input \
"sampler"'.format(sampler))
temp = self.eval(x, indices)
temp = np.multiply(temp.T, 1 / np.sqrt(np.sum(temp**2, axis=1))).T
A = np.vstack((V, temp))
P = greedy_d_optimal(A, Mold + q + 1, pstart=range(Mold + q))
# Append the new sample to both V and samples
V = np.vstack((V, A[P[-1], :]))
samples = np.vstack((samples, x[P[-1] - Mold - q, :]))
return samples
