udns = dns[:,2]*utau f = interp1d(ydns, udns) utarget = f(eqn.y) beta_prior = eqn.beta.copy() sigma_obs = 1e-10 sigma_prior = 1.0 eqn.objective = BayesianObjectiveU(utarget, beta_prior, sigma_obs, sigma_prior) inverse_solver = InverseSolver(eqn) inverse_solver.maxiter = 10 inverse_solver.stepsize = 0.1 inverse_solver.algo = "gn" eqn = inverse_solver.solve() plt.figure(11) plt.semilogx(eqn.yp, up_prior, 'g-', label=r'Prior') plt.semilogx(eqn.yp, eqn.up, 'r-', label=r'Posterior') plt.semilogx(eqn.yp[::5], utarget[::5]/utau, 'b.', label=r'DNS') plt.xlabel(r"$y^+$") plt.ylabel(r"$u^+$") plt.legend(loc=2) plt.tight_layout() plt.savefig("figs/inverse_matchu_u.pdf") plt.figure(4) beta11, beta12, beta22, beta33 = get_beta(eqn.beta) plt.semilogx(eqn.yp, beta11, 'r-', label=r'R11') plt.semilogx(eqn.yp, beta12, 'g-', label=r'R12')
if obs_cov_type == "scalar": objective.cov_obs_inv = np.linalg.inv(np.eye(ngrid-2)*sigma_obs**2) elif obs_cov_type == "vector": Cov_ = np.eye(ngrid-2) for i in range(ngrid-2): Cov_[i,i] = sigma_vector[i]**2 objective.cov_obs_inv = np.linalg.inv(Cov_) elif obs_cov_type == "matrix": objective.cov_obs_inv = np.linalg.inv(Cov[1:-1,1:-1]) else: raise ValueError("Wrong argument for covariance matrix type.") heat = HeatModel(T_inf, ngrid=ngrid) heat.solve() xi, Ti = heat.x, heat.T.copy() heat.objective = objective inverse = InverseSolver(heat) inverse.maxiter = 30 inverse.nsamples = 2 heat = inverse.solve() xf, Tf = heat.x, heat.T beta_map = heat.beta.astype(np.float64) beta_prior = beta_prior.astype(np.float64) data = data.astype(np.float64) sigma_obsv = np.ones_like(beta_map)*sigma_obs sigma_priorv = np.ones_like(beta_map)*sigma_prior np.savetxt("mcmc_input_cov.dat", Cov) np.savetxt('mcmc_input.dat', np.c_[data, np.sqrt(np.diag(Cov)), beta_prior, sigma_priorv, beta_map])