print(f"Model took {tock - tick:.1f} seconds")
A_true = truth["A"]
A_est = model.theta_[model.parameter_names.index("A")]
# Get exact transformation.
R = utils.exact_rotation_matrix(A_true, A_est)
# Now make it a valid rotation matrix.
try:
L = linalg.cholesky(R.T @ R)
R = R @ linalg.solve(L, np.eye(data_kwds["n_latent_factors"]))
except:
R = utils.find_rotation_matrix(A_true, A_est, full_output=False)
model.rotate(R)
scatter_kwds = dict(s=1, rasterized=True, c="#000000")
fig = plt.figure(figsize=(7.5, 3.09))
gs = gridspec.GridSpec(2, 3, height_ratios=[1, 4], width_ratios=[1, 1, 1])
A_est = model.theta_[model.parameter_names.index("A")]
xs = [A_true.flatten(), truth["scores"].flatten(), truth["psi"].flatten()]
ys = [
A_est.flatten(),
Js, Ks, gJs, gKs, converged, meta, X_H, label_names = contents
# Get best model.
J_best_mml, K_best_mml = grid_search.best(Js, Ks, meta["message_length"])
comparison_model = meta["best_models"]["mml"]
# Perform rotation.
A_est = comparison_model.theta_[comparison_model.parameter_names.index("A")]
if A_est.shape == A_target.shape:
for rotation in range(max_rotations):
A_est = comparison_model.theta_[comparison_model.parameter_names.index("A")]
R, p_opt, cov, *_ = utils.find_rotation_matrix(A_target, A_est,
full_output=True)
R_opt = utils.exact_rotation_matrix(A_target, A_est,
p0=np.random.uniform(-np.pi, np.pi, comparison_model.n_latent_factors**2))
AL = linalg.cholesky(R_opt.T @ R_opt)
R_opt2 = R_opt @ linalg.solve(AL, np.eye(comparison_model.n_latent_factors))
chi1 = np.sum(np.abs(A_est @ R - A_target))
chi2 = np.sum(np.abs(A_est @ R_opt2 - A_target))
R = R_opt2 if chi2 < chi1 else R
# Now make it a valid rotation matrix.
comparison_model.rotate(R)
A_astrophysical[idx, i] = 1.0 / count
A_astrophysical /= np.clip(np.sqrt(np.sum(A_astrophysical, axis=0)), 1, np.inf)
# Un-assigned columns
for column_index in np.where(np.all(A_astrophysical == 0, axis=0))[0]:
print(f"Warning: unassigned column index: {column_index}")
A_astrophysical[:, column_index] = np.random.normal(0, 1e-2, size=D)
if config["correct_A_astrophysical"]:
AL = linalg.cholesky(A_astrophysical.T @ A_astrophysical)
A_astrophysical = A_astrophysical @ linalg.solve(
AL, np.eye(model.n_latent_factors))
R, p_opt, cov, *_ = utils.find_rotation_matrix(A_astrophysical,
A_est,
full_output=True)
R_opt = utils.exact_rotation_matrix(A_astrophysical,
A_est,
p0=np.random.uniform(
-np.pi, np.pi,
model.n_latent_factors**2))
# WTF check R_opt.
AL = linalg.cholesky(R_opt.T @ R_opt)
R_opt2 = R_opt @ linalg.solve(AL, np.eye(model.n_latent_factors))
chi1 = np.sum(np.abs(A_est @ R - A_astrophysical))
chi2 = np.sum(np.abs(A_est @ R_opt2 - A_astrophysical))