def test_univariate_sim_only_x_only(self):
"""
Tests setup for univariate sim only where we only use an x input, not t.
"""
m = 700 # number of simulated observations
p = 3 # dimension of x (simulation inputs)
x = 0.5 * np.random.uniform(-1, 3, (m, p))
y = 5 * np.random.normal(0, 1, m) + 2
d = SepiaData(x_sim=x, y_sim=y, t_sim=None)
print('Testing univariate sim-only SepiaData...')
print(d)
self.assertTrue(d.obs_data is None)
self.assertTrue(d.sim_only)
self.assertTrue(d.scalar_out)
d.transform_xt()
self.assertTrue(np.all(np.min(d.sim_data.x_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.x_trans, 0) == 1))
d.standardize_y(center=False, scale=False)
self.assertEqual(d.sim_data.orig_y_sd, 1)
self.assertEqual(d.sim_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.sim_data.y, d.sim_data.y_std))
d.standardize_y(scale='columnwise')
self.assertTrue(np.allclose(d.sim_data.orig_y_sd, 5, rtol=0.1))
self.assertTrue(np.allclose(np.mean(d.sim_data.y_std, 0), 0, rtol=0.1))
self.assertTrue(np.allclose(np.std(d.sim_data.y_std, 0), 1, rtol=0.1))
self.assertTrue(d.sim_data.y.shape == d.sim_data.y_std.shape)
d.create_K_basis(10)
d.create_D_basis()
def setUp(self, m=100, n=1, nt_sim=50, nt_obs=20, n_theta=3, n_basis=5, sig_n=0.1, seed=42):
n_hier = 3
self.hier_idx = np.array([[0, 0, 0]])
#self.hier_idx = np.array([[1, 1, 1], [2, -1, 2]]) # TODO this fails for multivariate; cant use for univariate now
multi_data_list = []
univ_data_list = []
for si in range(n_hier):
multi_data_dict = generate_data.generate_multi_sim_and_obs(m=m, n=n, nt_sim=nt_sim, nt_obs=nt_obs,
n_theta=n_theta, n_basis=n_basis,
sig_n=sig_n, seed=seed)
univ_data_dict = generate_data.generate_univ_sim_and_obs(m=m, n=n, sig_n=sig_n, seed=seed)
d = SepiaData(t_sim=univ_data_dict['t_sim'], y_sim=univ_data_dict['y_sim'], y_obs=univ_data_dict['y_obs'])
d.transform_xt()
d.standardize_y()
univ_data_list.append(d)
d = SepiaData(t_sim=multi_data_dict['t_sim'], y_sim=multi_data_dict['y_sim'],
y_ind_sim=multi_data_dict['y_ind_sim'], y_obs=multi_data_dict['y_obs'],
y_ind_obs=multi_data_dict['y_ind_obs'])
d.transform_xt()
d.standardize_y()
d.create_K_basis(5)
d.create_D_basis('constant')
multi_data_list.append(d)
self.univ_model_list = [SepiaModel(d) for d in univ_data_list]
self.multi_model_list = [SepiaModel(d) for d in multi_data_list]
def test_univariate_sim_and_obs(self):
"""
Tests univiariate sim and obs where we pass in both x and t.
"""
m = 700 # number of simulated observations
p = 3 # dimension of x (sim/obs inputs)
q = 2 # dimension of t (extra sim inputs)
n = 5 # number of observed observations
x_sim = np.random.uniform(-1, 3, (m, p))
t = np.random.uniform(-10, 10, (m, q))
x_obs = np.random.uniform(-1.5, 3.5, (n, p))
y_sim = 5 * np.random.normal(0, 1, m) + 2
y_obs = 5 * np.random.normal(0, 1, n) + 1
d = SepiaData(x_sim=x_sim,
y_sim=y_sim,
t_sim=t,
x_obs=x_obs,
y_obs=y_obs)
print('Testing univariate sim and obs SepiaData...')
print(d)
self.assertTrue(d.obs_data is not None)
self.assertTrue(not d.sim_only)
self.assertTrue(d.scalar_out)
d.transform_xt()
self.assertTrue(np.all(np.min(d.sim_data.x_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.x_trans, 0) == 1))
self.assertTrue(np.all(np.min(d.sim_data.t_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.t_trans, 0) == 1))
d.transform_xt(-10, 10)
self.assertTrue(np.all(np.min(d.sim_data.x_trans, 0) == -10))
self.assertTrue(np.all(np.max(d.sim_data.x_trans, 0) == 10))
self.assertTrue(np.all(np.min(d.sim_data.t_trans, 0) == -10))
self.assertTrue(np.all(np.max(d.sim_data.t_trans, 0) == 10))
d.standardize_y(center=False, scale=False)
self.assertEqual(d.sim_data.orig_y_sd, 1)
self.assertEqual(d.sim_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.sim_data.y, d.sim_data.y_std))
self.assertEqual(d.obs_data.orig_y_sd, 1)
self.assertEqual(d.obs_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.obs_data.y, d.obs_data.y_std))
d.standardize_y(scale='columnwise')
self.assertTrue(np.allclose(d.sim_data.orig_y_sd, 5, rtol=0.1))
self.assertTrue(np.allclose(d.sim_data.orig_y_mean, 2, rtol=0.1))
self.assertTrue(np.allclose(np.mean(d.sim_data.y_std, 0), 0, rtol=0.1))
self.assertTrue(np.allclose(np.std(d.sim_data.y_std, 0), 1, rtol=0.1))
self.assertTrue(d.sim_data.y.shape == d.sim_data.y_std.shape)
self.assertTrue(np.allclose(d.obs_data.orig_y_sd, 5, rtol=0.1))
self.assertTrue(np.allclose(d.obs_data.orig_y_mean, 2, rtol=0.1))
self.assertTrue(d.obs_data.y.shape == d.obs_data.y_std.shape)
d.create_K_basis(10)
d.create_D_basis()
def setup_multi_sim_and_obs(m=100,
n=10,
nt_sim=20,
nt_obs=15,
noise_sd=0.1,
nx=5,
n_pc=10,
seed=42.,
n_lik=0,
n_mcmc=0,
n_pred=0,
fix_K=False):
try:
eng = matlab.engine.start_matlab()
eng.cd(root_path)
eng.addpath('matlab/', nargout=0)
res = eng.setup_multi_sim_and_obs(m,
n,
nt_sim,
nt_obs,
noise_sd,
nx,
n_pc,
seed,
n_lik,
n_mcmc,
n_pred,
nargout=1)
eng.quit()
except Exception as e:
print(e)
print(
'Matlab error; make sure matlab.engine installed, check Matlab code for errors.'
)
y = np.array(res['y'], dtype=float)
y_ind = np.array(res['y_ind'], dtype=float).squeeze()
xt = np.array(res['xt'], dtype=float)
y_obs = np.array(res['y_obs'], dtype=float)
y_ind_obs = np.array(res['y_ind_obs'], dtype=float).squeeze()
x_obs = np.array(res['x_obs'], dtype=float)
data = SepiaData(x_sim=xt[:, 0][:, None],
t_sim=xt[:, 1:],
y_sim=y,
y_ind_sim=y_ind,
x_obs=x_obs,
y_obs=y_obs,
y_ind_obs=y_ind_obs)
data.standardize_y()
data.transform_xt()
if fix_K: # means use the K from matlab - avoid issues with positive/negative component ambiguity
data.create_K_basis(n_pc, K=np.array(res['K']).T)
else:
data.create_K_basis(n_pc)
data.create_D_basis('constant')
print(data)
model = SepiaModel(data)
return model, res
def create_test_case():
n_obs = 2
n_sim = 5
p = 3
q = 4
ell_sim = 80
ell_obs = 20
t = np.random.uniform(0, 1, (n_sim, q))
x = 0.5 * np.ones((n_sim, p))
y_ind = np.linspace(0, 100, ell_sim)
y = 10 * np.random.normal(
0, 1,
(n_sim, 1)) * (y_ind[None, :] - 50)**2 / 75. + 20 * np.random.normal(
0, 1, (n_sim, 1)) * y_ind[None, :] + 20 * np.random.normal(
0, 1, (n_sim, 1))
x_obs = 0.5 * np.ones((n_obs, p))
y_obs_ind = np.linspace(10, 85, ell_obs)
y_obs = 10 * np.random.normal(0, 1, (n_obs, 1)) * (
y_obs_ind[None, :] - 50)**2 / 75. + 20 * np.random.normal(
0, 1, (n_obs, 1)) * y_obs_ind[None, :] + 20 * np.random.normal(
0, 1, (n_obs, 1))
data = SepiaData(x_sim=x,
t_sim=t,
y_sim=y,
y_ind_sim=y_ind,
x_obs=x_obs,
y_obs=y_obs,
y_ind_obs=y_obs_ind)
data.standardize_y()
data.transform_xt()
data.create_K_basis(n_pc=3)
data.create_D_basis('constant')
# Save as matfile for testing in matlab
savedict = {
't': t,
'y': y,
'y_obs': y_obs,
'D': data.obs_data.D,
'Kobs': data.obs_data.K,
'Ksim': data.sim_data.K,
'y_obs_std': data.obs_data.y_std,
'y_sim_std': data.sim_data.y_std,
'y_sd': data.sim_data.orig_y_sd
}
scipy.io.savemat('data/test_case_matlab.mat', savedict)
g = setup_model(data)
# Save pickle file of results
savedict = {'model': g, 'data': data}
with open('data/test_case_python_model.pkl', 'wb') as f:
pickle.dump(savedict, f)
def test_multivariate_sim_only_x_only(self):
"""
Tests setup for multivariate sim only where we only use an x input, not t.
"""
m = 700 # number of simulated observations
p = 3 # dimension of x (simulation inputs)
ell = 1000 # dimension of y output
pu = 3 # number of PCs
y_ind = np.linspace(0, 100, ell)
K_true = np.vstack([
0.5 * (np.sin(y_ind) + 1),
np.square(-y_ind + 50) / 2500, y_ind / 100
])
y = np.transpose(
np.log(1 + y_ind)[:, None] + np.dot(
K_true.T, 2 * np.array([1, 0.5, 0.2])[:, None] *
np.random.normal(0, 1, (pu, m))))
x = 0.5 * np.random.uniform(-1, 3, (m, p))
d = SepiaData(x_sim=x, y_sim=y, t_sim=None, y_ind_sim=y_ind)
print('Testing multivariate sim-only SepiaData...')
print(d)
self.assertTrue(d.obs_data is None)
self.assertTrue(d.sim_only)
self.assertTrue(not d.scalar_out)
d.transform_xt()
self.assertTrue(np.all(np.min(d.sim_data.x_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.x_trans, 0) == 1))
d.transform_xt(-10, 10)
self.assertTrue(np.all(np.min(d.sim_data.x_trans, 0) == -10))
self.assertTrue(np.all(np.max(d.sim_data.x_trans, 0) == 10))
d.standardize_y(center=False, scale=False)
self.assertEqual(d.sim_data.orig_y_sd, 1)
self.assertEqual(d.sim_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.sim_data.y, d.sim_data.y_std))
d.standardize_y(scale='columnwise')
self.assertTrue(
np.allclose(d.sim_data.orig_y_mean,
np.log(1 + y_ind),
rtol=0.1,
atol=0.5))
self.assertTrue(np.allclose(np.std(d.sim_data.y_std, 0), 1, rtol=0.1))
self.assertTrue(np.allclose(np.mean(d.sim_data.y_std, 0), 0, rtol=0.1))
self.assertTrue(d.sim_data.y.shape == d.sim_data.y_std.shape)
d.create_K_basis(3)
self.assertTrue(d.sim_data.K.shape == (pu, ell))
d.create_D_basis()
print(d)
def setUp(self, m=100, n=1, nt_sim=50, nt_obs=20, n_theta=3, n_basis=5, sig_n=0.1, seed=42):
multi_data_dict = generate_data.generate_multi_sim_and_obs(m=m, n=n, nt_sim=nt_sim, nt_obs=nt_obs,
n_theta=n_theta, n_basis=n_basis,
sig_n=sig_n, seed=seed)
univ_data_dict = generate_data.generate_univ_sim_and_obs(m=m, n=n, sig_n=sig_n, seed=seed)
d = SepiaData(t_sim=univ_data_dict['t_sim'], y_sim=univ_data_dict['y_sim'])
d.transform_xt()
d.standardize_y()
self.univ_sim_only_data = d
d = SepiaData(t_sim=univ_data_dict['t_sim'], y_sim=univ_data_dict['y_sim'], y_obs=univ_data_dict['y_obs'])
d.transform_xt()
d.standardize_y()
self.univ_sim_and_obs_data = d
d = SepiaData(t_sim=multi_data_dict['t_sim'], y_sim=multi_data_dict['y_sim'],
y_ind_sim=multi_data_dict['y_ind_sim'])
d.transform_xt()
d.standardize_y()
d.create_K_basis(5)
self.multi_sim_only_data = d
d = SepiaData(t_sim=multi_data_dict['t_sim'], y_sim=multi_data_dict['y_sim'],
y_ind_sim=multi_data_dict['y_ind_sim'], y_obs=multi_data_dict['y_obs'],
y_ind_obs=multi_data_dict['y_ind_obs'])
d.transform_xt()
d.standardize_y()
d.create_K_basis(5)
self.multi_sim_and_obs_noD_data = d
d = SepiaData(t_sim=multi_data_dict['t_sim'], y_sim=multi_data_dict['y_sim'],
y_ind_sim=multi_data_dict['y_ind_sim'], y_obs=multi_data_dict['y_obs'],
y_ind_obs=multi_data_dict['y_ind_obs'])
d.transform_xt()
d.standardize_y()
d.create_K_basis(5)
d.create_D_basis('linear')
self.multi_sim_and_obs_data = d
def setup_neddermeyer(seed=42., n_mcmc=100, sens=1, n_burn=0, n_lev=0):
try:
eng = matlab.engine.start_matlab()
eng.cd(root_path)
eng.addpath('matlab/', nargout=0)
#dataStruct = eng.neddeg(0, nargout=1)
res = eng.setup_neddermeyer(seed, n_mcmc, sens, n_burn, n_lev)
eng.quit()
except Exception as e:
print(e)
print(
'Matlab error; make sure matlab.engine installed, check Matlab code for errors.'
)
# get python model
import pickle
data_dict = pickle.load(
open('../../examples/Neddermeyer/pkls/nedderDataDict.pkl', 'rb'))
data = SepiaData(x_sim=data_dict['x_sim'],t_sim=data_dict['t_sim'],y_sim=data_dict['y_sim'],\
y_ind_sim=data_dict['y_ind_sim'],x_obs=data_dict['x_obs'],y_obs=data_dict['y_obs'],\
y_ind_obs=data_dict['y_ind_obs'])
data.transform_xt()
# set orig sim vals and Ksim
data.sim_data.orig_y_mean = data_dict['sim_orig_y_mean']
data.sim_data.orig_y_sd = data_dict['sim_orig_y_sd']
data.sim_data.y_std = data_dict['sim_y_std']
data.sim_data.K = data_dict['Ksim']
# set orig obs vals and Kobs
data.obs_data.orig_y_mean = data_dict['obs_orig_y_mean']
data.obs_data.orig_y_sd = data_dict['obs_orig_y_sd']
data.obs_data.y_std = data_dict['obs_orig_y_std']
data.obs_data.K = data_dict['Kobs']
# call create_D_basis
data.create_D_basis(D_obs=data_dict['Dobs'], D_sim=data_dict['Dsim'])
model = SepiaModel(data)
return model, res
def test_multivariate_sim_and_obs_lik(self):
"""
Tests log lik for multivariate sim and obs model
"""
d = SepiaData(t_sim=self.multi_data_dict['t_sim'],
y_sim=self.multi_data_dict['y_sim'],
y_ind_sim=self.multi_data_dict['y_ind_sim'],
y_obs=self.multi_data_dict['y_obs'],
y_ind_obs=self.multi_data_dict['y_ind_obs'])
print('Testing multivariate sim-only SepiaLogLik...', flush=True)
print(d, flush=True)
d.transform_xt()
d.standardize_y()
d.create_K_basis(5)
d.create_D_basis('linear')
model = setup_model(d)
model.logLik()
for param in model.params.mcmcList:
for cindex in range(int(np.prod(param.val_shape))):
model.logLik(cvar=param.name, cindex=cindex)
def test_multivariate_sim_and_obs_setup(self):
"""
Tests setup for multivariate sim and obs model with D
"""
d = SepiaData(t_sim=self.data_dict['t_sim'],
y_sim=self.data_dict['y_sim'],
y_ind_sim=self.data_dict['y_ind_sim'],
y_obs=self.data_dict['y_obs'],
y_ind_obs=self.data_dict['y_ind_obs'])
print(
'Testing multivariate sim and obs SepiaModelSetup with discrep...',
flush=True)
print(d, flush=True)
# Try it without doing standardization/transform/pc basis to be sure it doesn't break
model_notrans = setup_model(copy.deepcopy(d))
# Do explicit transformation
d.transform_xt()
d.standardize_y()
d.create_K_basis(n_pc=5)
d.create_D_basis(type='constant')
d.create_D_basis(type='linear')
custom_D = np.vstack(
[np.ones(d.obs_data.y.shape[1]), d.obs_data.y_ind])
d.create_D_basis(D_obs=custom_D)
model = setup_model(d)
# Check that either way gives same transformation
self.assertTrue(
np.allclose(model_notrans.data.sim_data.orig_y_mean,
model.data.sim_data.orig_y_mean))
self.assertTrue(
np.allclose(model_notrans.data.sim_data.orig_y_sd,
model.data.sim_data.orig_y_sd))
self.assertTrue(
np.allclose(model_notrans.data.sim_data.y_std,
model.data.sim_data.y_std))
self.assertTrue(
np.allclose(model_notrans.data.sim_data.t_trans,
model.data.sim_data.t_trans))
self.assertTrue(
np.allclose(model_notrans.data.obs_data.orig_y_mean,
model.data.obs_data.orig_y_mean))
self.assertTrue(
np.allclose(model_notrans.data.obs_data.orig_y_sd,
model.data.obs_data.orig_y_sd))
self.assertTrue(
np.allclose(model_notrans.data.obs_data.y_std,
model.data.obs_data.y_std))
# Check model components are set up as expected
self.assertTrue(not model.num.scalar_out)
self.assertTrue(not model.num.sim_only)
self.assertTrue(model.num.m == 100)
self.assertTrue(model.num.n == 1)
self.assertTrue(model.num.p == 1)
self.assertTrue(model.num.q == 3)
self.assertTrue(model.num.pu == 5)
self.assertTrue(model.num.pv == 2)
#self.assertTrue(np.allclose(model.num.w, model.data.sim_data.y_std)) # TODO compute projection
#self.assertTrue(np.allclose(model.num.u, model.data.obs_data.y_std)) # TODO compute projection
# self.assertTrue(np.allclose(model.num.v, model.data.obs_data.y_std)) # TODO compute projection
# Check parameter setup -- betaU
betaU = model.params.betaU
self.assertTrue(betaU.val_shape == (model.num.q + model.num.p,
model.num.pu))
self.assertTrue(betaU.prior.dist == 'Beta')
self.assertTrue(betaU.mcmc.stepType == 'BetaRho')
# Check parameter setup -- betaV
betaV = model.params.betaV
self.assertTrue(betaV.val_shape == (1, 1))
self.assertTrue(betaV.prior.dist == 'Beta')
self.assertTrue(betaV.mcmc.stepType == 'BetaRho')
# Check parameter setup -- lamUz
lamUz = model.params.lamUz
self.assertTrue(lamUz.val_shape == (1, model.num.pu))
self.assertTrue(lamUz.prior.dist == 'Gamma')
self.assertTrue(lamUz.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamUz
lamVz = model.params.lamVz
self.assertTrue(lamVz.val_shape == (1, 1))
self.assertTrue(lamVz.prior.dist == 'Gamma')
self.assertTrue(lamVz.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamWOs
lamWOs = model.params.lamWOs
self.assertTrue(lamWOs.val_shape == (1, 1))
self.assertTrue(lamWOs.prior.dist == 'Gamma')
self.assertTrue(lamWOs.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamWs
lamWs = model.params.lamWs
self.assertTrue(lamWs.val_shape == (1, model.num.pu))
self.assertTrue(lamWs.prior.dist == 'Gamma')
self.assertTrue(lamWs.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamOs
lamOs = model.params.lamOs
self.assertTrue(lamOs.val_shape == (1, 1))
self.assertTrue(lamOs.prior.dist == 'Gamma')
self.assertTrue(lamOs.mcmc.stepType == 'PropMH')
# Check parameter setup -- theta
theta = model.params.theta
self.assertTrue(theta.val_shape == (1, model.num.q))
self.assertTrue(theta.prior.dist == 'Normal')
self.assertTrue(theta.mcmc.stepType == 'Uniform')
self.assertTrue(np.allclose(theta.orig_range[0], 0))
self.assertTrue(np.allclose(theta.orig_range[1], 1))
mcmc_list_names = [p.name for p in model.params.mcmcList]
self.assertTrue(
set(mcmc_list_names) == set([
'betaU', 'betaV', 'lamUz', 'lamVz', 'lamWOs', 'lamWs', 'lamOs',
'theta'
]))
data.standardize_y()
data.create_K_basis(2)
# Generate D matrix with normal kernels
D_grid = h_sim # locations on which the kernels are centered
D_width = 1.5 # width of each kernel
pv = len(D_grid)
D_obs = np.zeros(shape=(data.obs_data.y_ind.shape[0], pv))
D_sim = np.zeros(shape=(data.sim_data.y_ind.shape[0], pv))
h_dense = data_dict['h_dense']
D_dense = np.zeros(shape=(h_dense.shape[0], pv))
for j in range(pv):
D_obs[:, j] = norm.pdf(h_field, D_grid[j], D_width)
D_sim[:, j] = norm.pdf(h_sim, D_grid[j], D_width)
D_dense[:, j] = norm.pdf(h_dense, D_grid[j], D_width)
data.create_D_basis(D_obs=D_obs.T, D_sim=D_sim)
#
# Data setup completed
#
nmcmc = 5000
#
# Standard mcmc reference model setup and sampling
#
model_ref = SepiaModel(data)
model_ref.tune_step_sizes(50, 20, verbose=False)
# burn in the model. This is qualitative, and needs to be assessed on trace plots
# This model is actually OK, but do 10 samples for 'burn-in'
model_ref.do_mcmc(10, prog=False)
# and discard those samples
model_ref.clear_samples()
D_obs = np.zeros(shape=(len(h_field), pv))
D_sim = np.zeros(shape=(len(h_sim), pv))
D_dense = np.zeros(shape=(len(h_dense), pv))
# create each kernel
for j in range(pv):
# create kernel j for each experiment
D_obs[:, j] = norm.pdf(h_field, D_grid[j], D_width)
D_sim[:, j] = norm.pdf(h_sim, D_grid[j], D_width)
D_dense[:, j] = norm.pdf(h_dense, D_grid[j], D_width)
# normalize D to match priors (not needed for D_obs, done in create_D_basis())
D_max = np.max(np.matmul(D_sim, D_sim.T))
D_sim = D_sim / np.sqrt(D_max)
D_dense = D_dense / np.sqrt(D_max)
data.create_D_basis(D_obs=D_obs.T)
plt.ylim(-.5, 1.5)
plt.xlim(0, 25)
plt.plot(h_dense, D_dense)
#plt.plot(h_field,D_obs)
plt.xlabel("Height (m)")
plt.ylabel("Basis elements d_i")
plt.title("D (dense grid)")
plt.show()
print(data)
#%% We can visually check that our principal component weights are reasonable.
# In an ideal setting, weights would follow a standard normal distribution.
data.plot_K_weights()
def test_predict_uv_from_multi_obs(self):
show_figs = True
exclude_burnin = True
n_pc = 2
seed = 42.
lamWOs_init = 50000. # use 0 to use default lamWOs initial value
nsamp = 100
nburn = 0
# Open data from matlab
script_path = os.path.dirname(os.path.realpath(__file__))
mat_fn = '%s/data/multi_sim_and_obs_mcmc_test.mat' % script_path
if os.path.isfile(mat_fn):
# if the matlab data is already in place, just load that
print(
'Found matfile, loading from multi_sim_and_obs_mcmc_test.mat \n'
)
matfile = scipy.io.loadmat(mat_fn)
else:
print('Generating matfile multi_sim_and_obs_mcmc_test.mat \n')
# Run matlab code, then open data from matlab
script_path = os.path.dirname(os.path.realpath(__file__))
# Run matlab code, then open data from matlab
try:
eng = matlab.engine.start_matlab()
eng.cd(script_path)
eng.addpath('matlab/', nargout=0)
eng.multi_sim_and_obs_mcmc_test(nsamp,
nburn,
seed,
lamWOs_init,
n_pc,
0,
nargout=0)
eng.quit()
matfile = scipy.io.loadmat(
'%s/data/multi_sim_and_obs_mcmc_test.mat' % script_path)
except Exception as e:
print(e)
print('make sure matlab.engine installed')
nburn = int(matfile['nburn'])
nsamp = int(matfile['nsamp'])
y_sim = matfile['y'].T
y_ind_sim = matfile['y_ind'].squeeze()
xt_sim = matfile['x']
y_obs = matfile['y_obs']
y_ind_obs = matfile['y_ind_obs'].squeeze()
x_obs = matfile['x_obs']
data = SepiaData(x_sim=xt_sim[:, 0][:, None],
t_sim=xt_sim[:, 1][:, None],
y_sim=y_sim,
y_ind_sim=y_ind_sim,
x_obs=x_obs,
y_obs=y_obs,
y_ind_obs=y_ind_obs)
data.standardize_y()
data.transform_xt()
data.create_K_basis(n_pc=n_pc)
data.create_D_basis(D=matfile['Dobs'].T)
print(data)
np.random.seed(int(seed))
model = setup_model(data)
if lamWOs_init > 0:
model.params.lamWOs.val = np.array([[lamWOs_init]])
t_start = time()
model.do_mcmc(nburn + nsamp)
t_end = time()
print('Python mcmc time %0.3g s' % (t_end - t_start))
print('Matlab mcmc time %0.3g s' % matfile['mcmc_time'])
np.random.seed(int(seed))
psamps = model.get_samples(0, sampleset=[0, 4], flat=True)
#pred = uvPred([0.5], psamps, model.num, model.data, returnMuSigma=True, useAltW=True)
pred = uvPred([0.5], psamps, model.num, model.data, returnMuSigma=True)
print('Samples of u are:')
print(pred.u.squeeze())
print('Matlab Samples of u are:')
print(matfile['pred2_u'].squeeze())
print('Samples of v are:')
print(pred.v.squeeze())
print('Matlab Samples of v are:')
print(matfile['pred2_v'].squeeze())
print('Mu are:')
print(pred.mu.squeeze())
print('Matlab Mu are:')
print(matfile['pred2_Myhat'])
print('Sigma are:')
print(pred.sigma.squeeze().reshape(14, 7).T)
print('Matlab Sigma are:')
print(matfile['pred2_Syhat'].squeeze())
print('Checking predicted realizations...')
self.assertTrue(
np.allclose(matfile['pred2_u'].squeeze(), pred.u.squeeze()))
self.assertTrue(
np.allclose(matfile['pred2_v'].squeeze(), pred.v.squeeze()))
print('Checking predicted means...')
self.assertTrue(
np.allclose(matfile['pred2_Myhat'].squeeze(), pred.mu.squeeze()))
print('Checking predicted sigmas...')
self.assertTrue(
np.allclose(matfile['pred2_Syhat'].squeeze(),
pred.sigma.squeeze().reshape(14, 7).T))
print('Done.')
print(data)
plt.plot(data.sim_data.y_ind, data.sim_data.y.T)
plt.plot(data.obs_data.y_ind, data.obs_data.y.T, 'k.', linewidth=3)
plt.title('Synthetic data (obs. in black)')
plt.xlabel('y index')
plt.ylabel('y')
plt.show()
#%%
data.transform_xt()
data.standardize_y('columnwise')
data.create_K_basis(5)
data.create_D_basis(type='linear')
print(data)
#%%
model = setup_model(data)
#%%
cachefile_name = 'multivariate_example_with_prediction.pkl'
import os.path
import pickle
use_save_file = False
y_ind_obs = matfile['y_ind_obs'].squeeze()
data = SepiaData(x_sim=x_sim[:, 0][:, None],
t_sim=x_sim[:, 1][:, None],
y_sim=y_sim,
y_ind_sim=y_ind_sim,
x_obs=x_obs,
y_obs=y_obs,
y_ind_obs=y_ind_obs)
print(data)
data.standardize_y()
assert np.allclose(data.sim_data.y_std, matfile['ystd'].T, rtol=0.01)
data.transform_xt()
data.create_K_basis(n_pc=2)
assert np.allclose(data.sim_data.K, matfile['Ksim'].T, rtol=0.01)
data.create_D_basis(D=matfile['Dsim'].T)
model = setup_model(data)
ll = model.logLik()
print('sepia log lik: %0.5g, gpmsa log lik: %0.5g' % (ll, matfile['ll']))
if (0):
nsamp = 100
model.do_mcmc(nsamp)
# Creates dict with each sampled variable name as key, array of samples (nsamp, ...) as value
samples_dict = {
p.name: np.array(p.mcmc.draws)
for p in model.params.mcmcList
}
with open(datadir+'desNative80x4Cg.txt','r') as f:
sim_data = np.loadtxt(f)
x_sim = sim_data[:,0:2] # x = {R, rho_ball}
t_sim = sim_data[:,2:4] # t = {C, g}
with open(datadir+'simHeights101x1','r') as f:
h_sim = np.loadtxt(f)
with open(datadir+'sims101x80Cg.txt','r') as f:
y_sim = np.loadtxt(f).T
# create sepia data object
data = SepiaData(x_sim = x_sim, t_sim = t_sim, y_ind_sim = h_sim, y_sim = y_sim,\
x_obs = x_obs, y_obs = y_obs, y_ind_obs = h_obs)
data.transform_xt()
data.standardize_y()
data.create_K_basis(3)
data.create_D_basis('linear')
print(data)
model = setup_model(data)
#%% Ragged data and model setup
y_obs_ragged = [np.array(field_data[0:3,4]),np.array(field_data[3:6,4]),\
np.array(field_data[6:9,4]),np.array(field_data[9:,4])]
h_obs_ragged = [np.array(field_data[0:3,3]),np.array(field_data[3:6,3]),\
np.array(field_data[6:9,3]),np.array(field_data[9:,3])]# observed heights
#y_obs = [np.array(field_data[0:3,4]),np.array(field_data[3:6,4]),\
# np.array(field_data[[7,9,11],4]),np.array(field_data[12:,4])]
#h_obs = [np.array(field_data[0:3,3]),np.array(field_data[3:6,3]),\
# np.array(field_data[[7,9,11],3]),np.array(field_data[12:,3])]# observed heights
print(y_obs)
def test_full_setup_LL_pred(self):
# Set up and check calibration model
x_obs = np.ones((3, 2)) * np.array([0.5, 0.75, 0.25]).reshape((-1, 1))
y_obs = np.block([[-0.1, 0.1], [-0.2, 0.3], [0.1, 0]])
# augment to also test more than scalar dimensions in x and t
x_sim_cal = np.hstack((0.5 * np.ones(
(self.x_sim.shape[0], 1)), self.x_sim[:, :1]))
t_sim_cal = self.x_sim[:, 1:]
xt_sim_sep = [np.array(0.5).reshape(1, 1)] + self.x_sim_kron
y_sim_std = (self.y_sim - np.mean(self.y_sim, axis=0).reshape(
1, -1)) / np.std(self.y_sim, axis=0, ddof=1).reshape(1, -1)
dc = SepiaData(x_sim=x_sim_cal,
t_sim=t_sim_cal,
y_sim=y_sim_std,
x_obs=x_obs,
y_obs=y_obs,
y_ind_sim=self.y_ind_sim,
y_ind_obs=self.y_ind_sim)
dc.create_K_basis(K=np.eye(2))
dc.create_D_basis(D_sim=np.eye(2), D_obs=np.eye(2))
dc.transform_xt(x_notrans=True, t_notrans=True)
dc.standardize_y(y_mean=0, y_sd=1)
print(dc)
cmod = SepiaModel(dc)
print('Calibration model LL=%f' % compute_log_lik(cmod))
kdc = SepiaData(xt_sim_sep=xt_sim_sep,
y_sim=y_sim_std,
x_obs=x_obs,
y_obs=y_obs,
y_ind_sim=self.y_ind_sim,
y_ind_obs=self.y_ind_sim)
kdc.create_K_basis(K=np.eye(2))
kdc.create_D_basis(D_sim=np.eye(2), D_obs=np.eye(2))
kdc.transform_xt(x_notrans=True, t_notrans=True)
kdc.standardize_y(y_mean=0, y_sd=1)
print(kdc)
kcmod = SepiaModel(kdc)
print('Calibration Sep model LL=%f' % compute_log_lik(kcmod))
self.assertAlmostEqual(compute_log_lik(cmod),
compute_log_lik(kcmod),
places=5)
print(
'Running MCMC on Calibration model in Sep pred mode, regular design'
)
np.random.seed(42)
t1 = time()
cmod.do_mcmc(10)
print('sampling time %f' % (time() - t1))
csamp = cmod.get_samples(sampleset=[cmod.get_last_sample_ind()])
cpred = SepiaFullPrediction(mode='Sep',
model=cmod,
samples=csamp,
storeMuSigma=True,
x_pred=np.array([0.5, 0.5]).reshape(
(1, -1)))
print(cpred.get_ysim())
csm, css = cpred.get_mu_sigma()
print(csm)
print(css)
print(
'Running MCMC on Calibration model in Sep pred mode, separable design'
)
np.random.seed(42)
t1 = time()
kcmod.do_mcmc(10)
print('sampling time %f' % (time() - t1))
kcsamp = kcmod.get_samples(sampleset=[kcmod.get_last_sample_ind()])
kcpred = SepiaFullPrediction(mode='Sep',
model=kcmod,
samples=kcsamp,
storeMuSigma=True,
x_pred=np.array([0.5, 0.5]).reshape(
(1, -1)))
print(kcpred.get_ysim())
kcsm, kcss = kcpred.get_mu_sigma()
print(kcsm)
print(kcss)
print('testing max difference which is %g' % np.max(abs(csm - kcsm)))
self.assertAlmostEqual(0, np.max(abs(csm - kcsm)))
print('testing max difference which is %g' % np.max(abs(css - kcss)))
self.assertAlmostEqual(0, np.max(abs(css - kcss)))
###### Timing for predictions
test_x_pred = np.random.rand(10, 2)
csamp = cmod.get_samples()
t1 = time()
cpred0 = SepiaFullPrediction(mode='notSep',
model=cmod,
samples=csamp,
storeMuSigma=True,
x_pred=test_x_pred)
print('predict time non-Sep in non-Sep mode %f' % (time() - t1))
t1 = time()
cpred = SepiaFullPrediction(mode='Sep',
model=cmod,
samples=csamp,
storeMuSigma=True,
x_pred=test_x_pred)
print('predict time non-sep in Sep mode %f' % (time() - t1))
kcsamp = kcmod.get_samples()
t1 = time()
kcpred = SepiaFullPrediction(mode='Sep',
model=kcmod,
samples=kcsamp,
storeMuSigma=True,
x_pred=test_x_pred)
print('predict time Sep %f' % (time() - t1))
pass
def test_multivariate_sim_and_obs_no_x(self):
"""
Tests multivariate sim and obs where we pass in t but not x (x is a dummy variable).
"""
m = 700 # number of simulated observations
ell_sim = 1000 # dimension of y output sim
ell_obs = 258 # dimension of y output obs
pu = 3 # number of PCs
q = 2 # dimension of t (extra sim inputs)
n = 5 # number of observed observations
y_ind_sim = np.linspace(0, 100, ell_sim)
K_true_sim = np.vstack([
0.5 * (np.sin(y_ind_sim) + 1),
np.square(-y_ind_sim + 50) / 2500, y_ind_sim / 100
])
y_sim = np.transpose(
np.log(1 + y_ind_sim)[:, None] + np.dot(
K_true_sim.T, 2 * np.array([1, 0.5, 0.2])[:, None] *
np.random.normal(0, 1, (pu, m))))
t = np.random.uniform(-10, 10, (m, q))
y_ind_obs = np.linspace(0, 100, ell_obs) + np.random.uniform(
-3, 3, ell_obs)
y_ind_obs[y_ind_obs < 0] = 0
K_true_obs = np.vstack([
0.5 * (np.sin(y_ind_obs) + 1),
np.square(-y_ind_obs + 50) / 2500, y_ind_obs / 100
])
y_obs = 10 + np.transpose(
np.log(1 + y_ind_obs)[:, None] + np.dot(
K_true_obs.T, 2 * np.array([1, 0.5, 0.2])[:, None] *
np.random.normal(0, 1, (pu, n))))
d = SepiaData(y_sim=y_sim,
t_sim=t,
y_ind_sim=y_ind_sim,
y_obs=y_obs,
y_ind_obs=y_ind_obs)
print('Testing multivariate sim and obs SepiaData...')
print(d)
self.assertTrue(d.obs_data is not None)
self.assertTrue(not d.sim_only)
self.assertTrue(not d.scalar_out)
d.transform_xt()
self.assertTrue(np.all(d.sim_data.x_trans == 0.5))
self.assertTrue(np.all(d.obs_data.x_trans == 0.5))
self.assertTrue(np.all(np.min(d.sim_data.t_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.t_trans, 0) == 1))
d.standardize_y(center=False, scale=False)
self.assertEqual(d.sim_data.orig_y_sd, 1)
self.assertEqual(d.sim_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.sim_data.y, d.sim_data.y_std))
self.assertEqual(d.obs_data.orig_y_sd, 1)
self.assertEqual(d.obs_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.obs_data.y, d.obs_data.y_std))
d.standardize_y(scale='columnwise')
self.assertTrue(
np.allclose(d.sim_data.orig_y_mean,
np.log(1 + y_ind_sim),
rtol=0.1,
atol=0.5))
self.assertTrue(np.allclose(np.mean(d.sim_data.y_std, 0), 0, rtol=0.1))
self.assertTrue(np.allclose(np.std(d.sim_data.y_std, 0), 1, rtol=0.1))
self.assertTrue(d.sim_data.y.shape == d.sim_data.y_std.shape)
self.assertTrue(
np.allclose(d.obs_data.orig_y_mean,
np.log(1 + y_ind_obs),
rtol=0.1,
atol=0.5))
self.assertTrue(d.obs_data.y.shape == d.obs_data.y_std.shape)
d.create_K_basis(3)
self.assertTrue(d.sim_data.K.shape == (pu, ell_sim))
self.assertTrue(d.obs_data.K.shape == (pu, ell_obs))
d.create_D_basis()
self.assertTrue(d.obs_data.D.shape == (1, ell_obs))
print(d)
def test_multivariate_sim_and_obs_ragged(self):
"""
Tests multivariate sim and obs where we pass in x and t but obs is ragged.
"""
m = 700 # number of simulated observations
p = 3 # dimension of x (simulation inputs)
ell_sim = 1000 # dimension of y output sim
pu = 3 # number of PCs
q = 2 # dimension of t (extra sim inputs)
n = 5 # number of observed observations
ell_obs = np.random.randint(100, 600, n)
y_ind_sim = np.linspace(0, 100, ell_sim)
K_true_sim = np.vstack([
0.5 * (np.sin(y_ind_sim) + 1),
np.square(-y_ind_sim + 50) / 2500, y_ind_sim / 100
])
y_sim = np.transpose(
np.log(1 + y_ind_sim)[:, None] + np.dot(
K_true_sim.T, 2 * np.array([1, 0.5, 0.2])[:, None] *
np.random.normal(0, 1, (pu, m))))
x_sim = 0.5 * np.random.uniform(-1, 3, (m, p))
t = np.random.uniform(-10, 10, (m, q))
y_ind_obs = [
np.linspace(0, 100, ell_obs[i]) +
np.random.uniform(-3, 3, ell_obs[i]) for i in range(len(ell_obs))
]
for yi in y_ind_obs:
yi[yi < 0] = 0
K_true_obs = [
np.vstack(
[0.5 * (np.sin(yi) + 1),
np.square(-yi + 50) / 2500, yi / 100]) for yi in y_ind_obs
]
y_obs = [
10 + np.squeeze(
np.log(1 + y_ind_obs[i])[:, None] + np.dot(
K_true_obs[i].T, 2 * np.array([1, 0.5, 0.2])[:, None] *
np.random.normal(0, 1, (pu, 1))))
for i in range(len(y_ind_obs))
]
x_obs = 0.5 * np.random.uniform(-1, 3, (n, p))
d = SepiaData(x_sim=x_sim,
y_sim=y_sim,
t_sim=t,
y_ind_sim=y_ind_sim,
x_obs=x_obs,
y_obs=y_obs,
y_ind_obs=y_ind_obs)
print('Testing multivariate sim and obs SepiaData...')
print(d)
self.assertTrue(d.obs_data is not None)
self.assertTrue(not d.sim_only)
self.assertTrue(not d.scalar_out)
d.transform_xt()
self.assertTrue(np.all(np.min(d.sim_data.x_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.x_trans, 0) == 1))
self.assertTrue(np.all(np.min(d.sim_data.t_trans, 0) == 0))
self.assertTrue(np.all(np.max(d.sim_data.t_trans, 0) == 1))
d.standardize_y(center=False, scale=False)
self.assertEqual(d.sim_data.orig_y_sd, 1)
self.assertEqual(d.sim_data.orig_y_mean, 0)
self.assertTrue(np.allclose(d.sim_data.y, d.sim_data.y_std))
#self.assertEqual(d.obs_data.orig_y_sd, 1)
#self.assertEqual(d.obs_data.orig_y_mean, 0)
#self.assertTrue(np.allclose(d.obs_data.y, d.obs_data.y_std))
d.standardize_y(scale='columnwise')
self.assertTrue(
np.allclose(d.sim_data.orig_y_mean,
np.log(1 + y_ind_sim),
rtol=0.1,
atol=0.5))
self.assertTrue(np.allclose(np.mean(d.sim_data.y_std, 0), 0, rtol=0.1))
self.assertTrue(np.allclose(np.std(d.sim_data.y_std, 0), 1, rtol=0.1))
self.assertTrue(d.sim_data.y.shape == d.sim_data.y_std.shape)
d.create_K_basis(3)
self.assertTrue(d.sim_data.K.shape == (pu, ell_sim))
d.create_D_basis()
print(d)
y_ind_sim = matfile['y_ind'].squeeze()
xt_sim = matfile['x']
y_obs = matfile['y_obs']
y_ind_obs = matfile['y_ind_obs'].squeeze()
x_obs = matfile['x_obs']
data = SepiaData(x_sim=xt_sim[:, 0][:, None],
t_sim=xt_sim[:, 1][:, None],
y_sim=y_sim,
y_ind_sim=y_ind_sim,
x_obs=x_obs,
y_obs=y_obs,
y_ind_obs=y_ind_obs)
data.standardize_y()
data.transform_xt()
data.create_K_basis(n_pc=2)
data.create_D_basis(D_obs=matfile['Dobs'].T)
print(data)
model = setup_model(data)
nsamp = int(matfile['nsamp'])
nburn = int(matfile['nburn'])
@timeit
def run_mcmc():
model.do_mcmc(nburn + nsamp)
print('Python mcmc time:')
run_mcmc()
def test_multivariate_sim_and_obs_lamVzGroups_setup(self):
"""
Tests setup for multivariate sim and obs model with D and lamVzGroups
"""
d = SepiaData(t_sim=self.data_dict['t_sim'],
y_sim=self.data_dict['y_sim'],
y_ind_sim=self.data_dict['y_ind_sim'],
y_obs=self.data_dict['y_obs'],
y_ind_obs=self.data_dict['y_ind_obs'])
print(
'Testing multivariate sim and obs SepiaModelSetup with discrep...',
flush=True)
print(d, flush=True)
# Do explicit transformation
d.transform_xt()
d.standardize_y()
d.create_K_basis(n_pc=5)
custom_D = np.vstack([
np.ones(d.obs_data.y.shape[1]), d.obs_data.y_ind,
d.obs_data.y_ind**2
])
d.create_D_basis(D_obs=custom_D)
lamVzGroup = [0, 1, 1]
model = setup_model(d, lamVzGroup=lamVzGroup)
# Check model components are set up as expected
self.assertTrue(not model.num.scalar_out)
self.assertTrue(not model.num.sim_only)
self.assertTrue(model.num.m == 100)
self.assertTrue(model.num.n == 1)
self.assertTrue(model.num.p == 1)
self.assertTrue(model.num.q == 3)
self.assertTrue(model.num.pu == 5)
self.assertTrue(model.num.pv == 3)
# Check parameter setup -- betaU
betaU = model.params.betaU
self.assertTrue(betaU.val_shape == (model.num.q + model.num.p,
model.num.pu))
self.assertTrue(betaU.prior.dist == 'Beta')
self.assertTrue(betaU.mcmc.stepType == 'BetaRho')
# Check parameter setup -- betaV
betaV = model.params.betaV
self.assertTrue(betaV.val_shape == (1, 2))
self.assertTrue(betaV.prior.dist == 'Beta')
self.assertTrue(betaV.mcmc.stepType == 'BetaRho')
# Check parameter setup -- lamUz
lamUz = model.params.lamUz
self.assertTrue(lamUz.val_shape == (1, model.num.pu))
self.assertTrue(lamUz.prior.dist == 'Gamma')
self.assertTrue(lamUz.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamUz
lamVz = model.params.lamVz
self.assertTrue(lamVz.val_shape == (1, 2))
self.assertTrue(lamVz.prior.dist == 'Gamma')
self.assertTrue(lamVz.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamWOs
lamWOs = model.params.lamWOs
self.assertTrue(lamWOs.val_shape == (1, 1))
self.assertTrue(lamWOs.prior.dist == 'Gamma')
self.assertTrue(lamWOs.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamWs
lamWs = model.params.lamWs
self.assertTrue(lamWs.val_shape == (1, model.num.pu))
self.assertTrue(lamWs.prior.dist == 'Gamma')
self.assertTrue(lamWs.mcmc.stepType == 'PropMH')
# Check parameter setup -- lamOs
lamOs = model.params.lamOs
self.assertTrue(lamOs.val_shape == (1, 1))
self.assertTrue(lamOs.prior.dist == 'Gamma')
self.assertTrue(lamOs.mcmc.stepType == 'PropMH')
# Check parameter setup -- theta
theta = model.params.theta
self.assertTrue(theta.val_shape == (1, model.num.q))
self.assertTrue(theta.prior.dist == 'Normal')
self.assertTrue(theta.mcmc.stepType == 'Uniform')
self.assertTrue(np.allclose(theta.orig_range[0], 0))
self.assertTrue(np.allclose(theta.orig_range[1], 1))
mcmc_list_names = [p.name for p in model.params.mcmcList]
self.assertTrue(
set(mcmc_list_names) == set([
'betaU', 'betaV', 'lamUz', 'lamVz', 'lamWOs', 'lamWs', 'lamOs',
'theta'
]))
