import numpy as np import scipy.optimize as so def phid(Wd, K, m, d_obs): """ Wd = data weighting matrix K = complex valued forward model kernel m = model d_obs = observed data """ #print("phid=", np.linalg.norm(np.dot(Wd, np.abs(np.dot(K,m)) - d_obs))**2 / len(d_obs) ) return np.linalg.norm(np.dot(Wd, np.abs(np.dot(K,m)) - d_obs))**2 def phim(Wm, m): """ Wm = model weighting matrix x = model """ return np.linalg.norm(np.dot(Wm, m))**2 def PHI(m, Wd, K, d_obs, Wm, alphastar): """ Global objective function x = model to be fit Wd = data weighting matrix K = complex forward modelling kernel d_obs = observed data (modulus) Wm = model weighting matrix alphastar = regularisation to use """ return phid(Wd, K, m, d_obs) + alphastar*phim(Wm, m) # main def nonlinearinversion( x0, Wd, K, d_obs, Wm, alphastar): print("Performing non-linear inversion") args = (Wd, K, d_obs, Wm, alphastar) #return so.minimize(PHI, np.zeros(len(x0)), args, 'Nelder-Mead') bounds = np.zeros((len(x0),2)) bounds[:,0] = x0*0.75 bounds[:,1] = x0*1.25 #bounds[:,0] = 0 #bounds[:,1] = np.max(x0)*1.25 return so.minimize(PHI, x0, args, 'L-BFGS-B', bounds=bounds) # Works well #return so.minimize(PHI, x0, args, 'Powell', bounds=bounds) # Slow but works #return so.minimize(PHI, x0, args, 'trust-constr', bounds=bounds) # very Slow #return so.minimize(PHI, x0, args, 'TNC', bounds=bounds) # slow #return so.minimize(PHI, x0, args, 'SLSQP', bounds=bounds) # slow