def test_weights_ut_1d(self):
# UT weights in 1D
model = BayesSardModel(1,
self.ker_par_1d,
point_str='ut',
point_par=self.pt_par_ut)
alpha = np.array([[0, 1, 2]])
w, wc, wcc, emv, ivar = model.bq_weights(self.ker_par_1d, alpha)
# UT weights in 1D reproduced?
self.assertTrue(np.allclose(w, UnscentedTransform.weights(1)[0]))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))
# UT weights in 1D, different kappa and alpha
model = BayesSardModel(1,
self.ker_par_1d,
point_str='ut',
point_par={
'kappa': 2,
'alpha': 1
})
alpha = np.array([[0, 1, 2]])
w, wc, wcc, emv, ivar = model.bq_weights(self.ker_par_1d, alpha)
# UT weights in 1D reproduced?
self.assertTrue(
np.allclose(w,
UnscentedTransform.weights(1, kappa=2, alpha=1)[0]))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))
def test_weights_ut_5d(self):
model = BayesSardModel(5,
np.array([[1.0, 25, 25, 25, 25, 25]]),
point_str='ut')
alpha = np.hstack((np.zeros(
(5, 1)), np.eye(5), 2 * np.eye(5))).astype(np.int)
par = np.array([[1.0, 25, 25, 25, 25, 25]])
w, wc, wcc, emv, ivar = model.bq_weights(par, alpha)
# self.assertTrue(np.allclose(w, UnscentedTransform.weights(5, beta=0)[0]))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))
def test_weights_ut_2d(self):
# UT weights in 2D
par = np.array([[1.0, 1.0, 1]])
alpha = np.array([[0, 1, 0, 2, 0], [0, 0, 1, 0, 2]])
model = BayesSardModel(2,
par,
point_str='ut',
point_par=self.pt_par_ut)
w, wc, wcc, emv, ivar = model.bq_weights(par, alpha)
# UT weights reproduced in 2D?
self.assertTrue(np.allclose(w, UnscentedTransform.weights(2)[0]))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))
def test_weights_gh5_1d(self):
# GH-5 weights in 1D
model = BayesSardModel(1,
self.ker_par_1d,
point_str='gh',
point_par={'degree': 5})
alpha = np.array([[0, 1, 2, 3, 4]])
w, wc, wcc, emv, ivar = model.bq_weights(self.ker_par_1d, alpha)
# GH-5 weights in 1D reproduced?
self.assertTrue(
np.allclose(w, GaussHermiteTransform.weights(1, degree=5)))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))
def test_weights_gh3_2d(self):
# GH-3 weights in 2D
# there are 6 multivariate polynomials in 2D, UT has only 5 points in 2D
model = BayesSardModel(2,
self.ker_par_2d,
point_str='gh',
point_par={'degree': 3})
alpha = np.array([[0, 1, 0, 1, 2, 0, 1, 2, 2],
[0, 0, 1, 1, 0, 2, 2, 1, 2]])
par = np.array([[1.0, 1, 1]])
w, wc, wcc, emv, ivar = model.bq_weights(par, alpha)
self.assertTrue(np.allclose(w, GaussHermiteTransform.weights(2, 3)))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))
def test_weights_sr_1d(self):
# SR weights == UT weights for kappa=0 and alpha=1
model = BayesSardModel(1,
self.ker_par_1d,
point_str='ut',
point_par={
'kappa': 0,
'alpha': 1
})
alpha = np.array([[0, 1, 2]])
w, wc, wcc, emv, ivar = model.bq_weights(self.ker_par_1d, alpha)
# UT weights in 1D reproduced?
self.assertTrue(np.allclose(w[1:],
SphericalRadialTransform.weights(1)))
self.assertGreaterEqual(emv, 0)
self.assertGreaterEqual(ivar, 0)
# test positive definiteness
try:
la.cholesky(wc)
except la.LinAlgError:
self.fail("Weights not positive definite. Min eigval: {}".format(
la.eigvalsh(wc).min()))