in_labels = ['mu', 'rho', 'dpdx', 'eta', 'B0'] # Set the number of parameter (m) and active subspace dimension (n) m, n = 5, 4 # Obtain M input samples drawn uniformly from the input space M = 100 X_norm = 2*np.random.rand(M, m) - 1 X_phys = utils_analytic.normalized_to_physical(X=X_norm) # Run simulation on sample inputs f = utils_analytic.func(X_phys, QofI=QofI) df_phys = utils_analytic.grad(X_phys, QofI=QofI) # Scale data so parameters are in [-1,1] df_norm = utils_analytic.physical_to_normalized(df=df_phys) ############################################################################### ##### Local Linear Approximation Gradients ############################################################################### # Estimate gradients using local linear approximation df_local_linear = active_subspaces.gradients.local_linear_gradients(X_phys, f) # Scale data so parameters are in [-1,1] df_local_linear = utils_analytic.physical_to_normalized(df=df_local_linear) # Compute the active/inactive subspaces # NOTE: The gradient is normalized for this computation sub = active_subspaces.subspaces.Subspaces() sub.compute(df_local_linear/np.linalg.norm(df_local_linear, axis=1).reshape((df_local_linear.shape[0], 1)))
in_labels = ['mu', 'rho', 'dpdx', 'eta', 'B0'] # Set the number of parameter (m) and active subspace dimension (n) m, n = 5, 4 # Obtain M input samples drawn uniformly from the input space M = 100 X_norm = 2*np.random.rand(M, m) - 1 X_phys = utils_analytic.normalized_to_physical(X=X_norm) # Run simulation on sample inputs f = utils_analytic.func(X_phys, QofI=QofI) df_phys = utils_analytic.grad(X_phys, QofI=QofI) # Scale data so parameters are in [-1,1] df_norm = utils_analytic.physical_to_normalized(df=df_phys) # Compute the active/inactive subspaces # NOTE: The gradient is normalized for this computation sub = active_subspaces.subspaces.Subspaces() sub.compute(df_norm/np.linalg.norm(df_norm, axis=1).reshape((df_norm.shape[0], 1))) # Rewrite the active/inactive subspace variables to be n-dimensional sub.W1, sub.W2 = sub.eigenvectors[:,:n], sub.eigenvectors[:,n:] sub.W1 = sub.W1.reshape(m, n) sub.W2 = sub.W2.reshape(m, m-n) # Define the active/inactive variables Y, Z = np.dot(X_norm, sub.W1), np.dot(X_norm, sub.W2) # Plot the active subspace info
