def genStateData(fstate, sim): logging.info("generating state data for optimization result") tj.DIM = DIM = sim['DIM'] tj.N = N = sim['N'] tj.SIGMA = SIGMA = sim['SIGMA'] order = sim['order'] if order < 1: fstate = np.append(fstate, np.zeros(N*DIM**2)) # append mu_1 if order < 2: fstate = np.append(fstate, np.zeros(N*DIM*tj.triuDim())) # append mu_2 fstate = tj.triangular_to_state(fstate) (t_span, y_span) = tj.integrate( fstate ) # save result np.save('output/state_data',y_span) np.save('output/time_data',t_span) np.save('output/setup',[N,DIM,SIGMA])
def match(sim,SIGMA,weights,initial=None,initialMomentum=None,gradTol=None,order=2,scalegrad=True, maxIter=150, visualize=False, visualizeIterations=False): """ Perform matching using the supplied similarity measure, the two_jet flow and scipy's optimizer. A gradient check can be performed for the initial value. The initial value is either zero of supplied as a parameter. Order specifies the order of the particle jets Weights determines the split between energy (weights[0]) and match term (weights[1]) """ # set flow parameters DIM = tj.DIM = sim['DIM'] N = tj.N = sim['N'] tj.SIGMA = SIGMA logging.info("Flow parameters: weights %s, order %d, SIGMA %g, scalegrad %s, gradTol %s, maxIter %d, visualize %s, visualizeIterations %s",weights,order,SIGMA,scalegrad,gradTol,maxIter,visualize,visualizeIterations) # initial guess (x0moving) if not initialMomentum: p = np.zeros([N,DIM]) mu_1 = np.zeros([N,DIM,DIM]) mu_2 = np.zeros([N,DIM,DIM,DIM]) else: p = initialMomentum[0] mu_1 = initialMomentum[1] mu_2 = initialMomentum[2] if not initial: (q,q_1,q_2) = (np.zeros([N,DIM]), np.outer(np.ones(N),np.eye(DIM)).reshape([N,DIM,DIM]), np.zeros([N,DIM,DIM,DIM])) elif len(initial) == 1: (q,q_1,q_2) = (initial[0], np.outer(np.ones(N),np.eye(DIM)).reshape([N,DIM,DIM]), np.zeros([N,DIM,DIM,DIM])) elif len(initial) == 2: (q,q_1,q_2) = (initial[0], initial[1], np.zeros([N,DIM,DIM,DIM])) elif len(initial) == 3: (q,q_1,q_2) = initial x0 = tj.weinstein_darboux_to_state(q, q_1, q_2, p, mu_1, mu_2)# initial guess + zeros assert(np.allclose(x0,tj.triangular_to_state(tj.state_to_triangular(x0)))) x0 = tj.state_to_triangular(x0) # we do not need to optimize over symmetric indices sizeqs = x0.size/2 x0nonmoving = x0[0:sizeqs] # for now, the point positions are fixed if order == 0: x0moving = x0[sizeqs:sizeqs+p.size] # only p is optimized for elif order == 1: x0moving = x0[sizeqs:sizeqs+p.size+mu_1.size] # only p,mu_1 is optimized for else: x0moving = x0[sizeqs:x0.size] # p,mu_1,mu_2 is optimized for # optimization functions fsim = lambda x: F(sim, x0nonmoving, x, weights=weights, order=order, scalegrad=scalegrad, visualize=visualizeIterations) f = lambda x: F(sim, x0nonmoving, x, weights=weights, adjint=False, order=order, scalegrad=scalegrad, visualize=visualizeIterations) fgrad = lambda x: F(sim, x0nonmoving, x, weights=weights, order=order, scalegrad=scalegrad, visualize=visualizeIterations)[1] ## debug #fsim = lambda x: Fdisp(sim, x0nonmoving, x, weights=weights, order=order, scalegrad=scalegrad) #f = lambda x: Fdisp(sim, x0nonmoving, x, weights=weights, adjint=False, order=order, scalegrad=scalegrad) #fgrad = lambda x: Fdisp(sim, x0nonmoving, x, weights=weights, order=order, scalegrad=scalegrad)[1] if gradTol != None: # non-zero starting point res = minimize(fsim, x0moving, method='BFGS', jac=True, options={'disp': True, 'maxiter': 50}) x0moving = res.x # grad check for similarity F(sim, x0nonmoving, x0moving, weights=weights, adjint=True, order=order, scalegrad=scalegrad,simGradCheck=True,energyGradCheck=True) # grad check full system #f = lambda x: F(sim, x0nonmoving, x, weights=[0,1], adjint=False, order=order, scalegrad=False, visualize=visualizeIterations) #fgrad = lambda x: F(sim, x0nonmoving, x, weights=[0,1], order=order, scalegrad=False, visualize=visualizeIterations)[1] logging.info("computing finite difference approximation of gradient") findiffgrad = approx_fprime(x0moving,f,1e-7) compgrad = fgrad(x0moving) graderr = np.max(abs(findiffgrad-compgrad)) logging.info("gradient numerical check error: %e",graderr) if abs(graderr) > gradTol: logging.warning("finite diff gradient: " + str(findiffgrad)) logging.warning("computed gradient: " + str(compgrad)) logging.warning("difference: " + str(findiffgrad-compgrad)) #return None # gradient check not passed # change optimization method to e.g. BFGS after debugging res = minimize(fsim, x0moving, method='BFGS', jac=True, options={'disp': True, 'maxiter': maxIter}) #res = fmin_bfgs(f, x0moving, fprime=fgrad, disp=True, full_output=True) #res = fmin_cg(f, x0moving, fprime=fgrad, disp=True, full_output=True) #res = fmin_l_bfgs_b(f, x0moving, fprime=fgrad, disp=0) # visualize result if visualize: F(sim, x0nonmoving, res.x, weights=weights, adjint=False, order=order, scalegrad=scalegrad, visualize=True) return (np.append(x0nonmoving,res.x),res)
def F(sim, nonmoving, x, weights=None, adjint=True, order=2, scalegrad=None, simGradCheck=False, energyGradCheck=False, visualize=False): """ Function that scipy's optimize function will call for returning the value and gradient for a given x. The forward and adjoint integration is called from this function using the values supplied by the similarity measure. """ N = sim['N'] DIM = sim['DIM'] i = 0 q = np.reshape( nonmoving[i:(i+N*DIM)] , [N,DIM] ) tj.gaussian.N = N tj.gaussian.DIM = DIM tj.gaussian.SIGMA = tj.SIGMA K,DK,D2K,D3K,D4K,D5K,D6K = tj.derivatives_of_kernel(q,q) # input state0 = np.append(nonmoving, x) if order < 1: state0 = np.append(state0, np.zeros(N*DIM**2)) # append mu_1 if order < 2: state0 = np.append(state0, np.zeros(N*DIM*tj.triuDim())) # append mu_2 # shift from triangular to symmetric state0 = tj.triangular_to_state(state0) triunonmoving = nonmoving triux = x nonmoving = state0[0:state0.size/2] x = state0[state0.size/2:] # rescale if scalegrad: #logging.debug("rescaling, SIGMA " + str(tj.SIGMA)) q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 ) if order >= 1: mu0_1 = tj.SIGMA*mu0_1 if order == 2: mu0_2 = tj.SIGMA*mu0_2 state0 = tj.weinstein_darboux_to_state(q0,q0_1,q0_2,p0,mu0_1,mu0_2) q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 ) # flow (t_span, y_span) = tj.integrate(state0) stateT = y_span[-1] # debug qT,qT_1,qT_2,pT,muT_1,muT_2 = tj.state_to_weinstein_darboux( stateT ) #logging.info("q0: " + str(q0)) #logging.info("p0_2: " + str(p0)) #logging.info("qT: " + str(qT)) logging.info("||p0||: " + str(np.linalg.norm(p0))) logging.info("||mu0_1||: " + str(np.linalg.norm(mu0_1))) logging.info("||mu0_2||: " + str(np.linalg.norm(mu0_2))) #if order >= 1: #logging.info("q0_1: " + str(q0_1)) #logging.info("qT_1: " + str(qT_1)) #logging.info("mu0_1: " + str(mu0_1)) #if order >= 2: #logging.info("q0_2: " + str(q0_2)) #logging.info("qT_2: " + str(qT_2)) #logging.info("mu0_2: " + str(mu0_2)) #logging.info("qT-q0: " + str(qT-q0)) #logging.info("qT_1-q0_1: " + str(qT_1-q0_1)) #logging.info("qT_2-q0_2: " + str(qT_2-q0_2)) simT = sim['f'](stateT, state0=state0, visualize=visualize) # debug #logging.info('match term (before flow/after flow/diff): ' + str(sim['f'](state0)[0]) + '/' + str(simT[0]) + '/' + str(sim['f'](state0)[0]-simT[0])) logging.info('match term after flow: ' + str(simT[0])) Ediff = tj.Hamiltonian(q0,p0,mu0_1,mu0_2) # path energy from Hamiltonian logging.info('Hamiltonian: ' + str(Ediff)) if not adjint: return weights[1]*simT[0]+weights[0]*Ediff dq = simT[1][0] if order >= 1: dq_1 = simT[1][1] else: dq_1 = np.zeros(q0_1.shape) if order >= 2: dq_2 = simT[1][2] else: dq_2 = np.zeros(q0_2.shape) logging.info("||dq||: " + str(np.linalg.norm(dq))) logging.info("||dq_1||: " + str(np.linalg.norm(dq_1))) logging.info("||dq_2||: " + str(np.linalg.norm(dq_2))) ds1 = tj.weinstein_darboux_to_state(dq,dq_1,dq_2,np.zeros(dq.shape),np.zeros(dq_1.shape),np.zeros(dq_2.shape),N,DIM) if simGradCheck: logging.info("computing finite difference approximation of sim gradient") fsim = lambda x: sim['f'](np.hstack( (x,stateT[x.size:],) ), state0=state0)[0] findiffgrad = approx_fprime(stateT[0:N*DIM+N*DIM**2+N*DIM**3],fsim,1e-5) compgrad = ds1[0:N*DIM+N*DIM**2+N*DIM**3] graderr = np.max(abs(findiffgrad-compgrad)) logging.debug("sim gradient numerical check error: %e",graderr) logging.debug("finite diff gradient: " + str(findiffgrad)) logging.debug("computed gradient: " + str(compgrad)) logging.debug("difference: " + str(findiffgrad-compgrad)) if energyGradCheck: logging.info("computing finite difference approximation of energy gradient") fsim = lambda x: tj.Hamiltonian(q0,np.reshape(x[0:N*DIM],[N,DIM]),np.reshape(x[N*DIM:N*DIM+N*DIM**2],[N,DIM,DIM]),np.reshape(x[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3],[N,DIM,DIM,DIM])) findiffgrad = approx_fprime(np.hstack((p0.flatten(),mu0_1.flatten(),mu0_2.flatten(),)),fsim,1e-7) compgrad = tj.grad_Hamiltonian(q0,p0,mu0_1,mu0_2) graderr = np.max(abs(findiffgrad-compgrad)) logging.debug("energy gradient numerical check error: %e",graderr) logging.debug("finite diff gradient: " + str(findiffgrad)) logging.debug("computed gradient: " + str(compgrad)) logging.debug("difference: " + str(findiffgrad-compgrad)) (t_span, y_span) = tj.adj_integrate(stateT,ds1) adjstate0 = y_span[-1] assert(nonmoving.size+x.size<=adjstate0.size/2) gradE = tj.grad_Hamiltonian(q0,p0,mu0_1,mu0_2) assert(adjstate0.size/2-nonmoving.size == gradE.size) # gradE doesn't include point variations currently gradE = gradE[0:x.size] grad0 = weights[1]*adjstate0[adjstate0.size/2+nonmoving.size:adjstate0.size/2+nonmoving.size+x.size] + weights[0]*gradE # transported gradient + grad of energy adjstate0[adjstate0.size/2+nonmoving.size:adjstate0.size/2+nonmoving.size+grad0.size] = grad0 grad0 = tj.state_to_triangular(adjstate0[adjstate0.size/2:adjstate0.size])[triunonmoving.size:triunonmoving.size+triux.size] grad0 = np.ndarray.flatten(grad0) # rescale if scalegrad: if order >= 1: grad0[N*DIM:N*DIM+N*DIM**2] = tj.SIGMA*grad0[N*DIM:N*DIM+N*DIM**2] if order == 2: grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3] = tj.SIGMA*grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3] # visualization dq0,dq0_1,dq0_2,dp0,dmu0_1,dmu0_2 = tj.state_to_weinstein_darboux( adjstate0[adjstate0.size/2:adjstate0.size],N,DIM ) #logging.info("dp0: " + str(dp0)) logging.info("||dp0|| final: " + str(np.linalg.norm(dp0))) #logging.info("dmu0_1: " + str(dmu0_1)) logging.info("||dmu0_1|| final: " + str(np.linalg.norm(dmu0_1))) #logging.info("dmu0_2: " + str(dmu0_2)) logging.info("||dmu0_2|| final: " + str(np.linalg.norm(dmu0_2))) #logging.info("adjstate0: " + str(adjstate0)) #logging.info("grad0: " + str(grad0)) #plt.figure(0) #plt.quiver(q0[:,0],q0[:,1],dp0[:,0],dp0[:,1]) ## pause #raw_input("F: Press ENTER to continue") return (weights[1]*simT[0]+weights[0]*Ediff, grad0)
def Fdisp(sim, nonmoving, x, adjint=True, weights=None, order=2, scalegrad=None): """ As F above but using linear displacement instead of integrating the flows. For testing. """ # input N = sim['N'] # debug DIM = sim['DIM'] # debug tj.gaussian.N = N tj.gaussian.DIM = DIM tj.gaussian.SIGMA = tj.SIGMA #x = np.append(x, np.zeros(N*DIM**3)) # debug state0 = np.append(nonmoving, x) if order < 1: state0 = np.append(state0, np.zeros(N*DIM**2)) # append mu_1 if order < 2: state0 = np.append(state0, np.zeros(N*DIM**3)) # append mu_2 # shift from triangular to symmetric #assert(np.allclose(state0,tj.state_to_triangular(tj.triangular_to_state(state0)))) state0 = tj.triangular_to_state(state0) triunonmoving = nonmoving triux = x nonmoving = state0[0:state0.size/2] x = state0[state0.size/2:] # rescale if scalegrad: #logging.debug("rescaling, SIGMA " + str(tj.SIGMA)) q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 ) if order >= 1: mu0_1 = tj.SIGMA*mu0_1 if order == 2: mu0_2 = tj.SIGMA*mu0_2 state0 = tj.weinstein_darboux_to_state(q0,q0_1,q0_2,p0,mu0_1,mu0_2) q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 ) # displacement qT = q0+p0 qT_1 = q0_1+mu0_1 qT_2 = q0_2+mu0_2 stateT = tj.weinstein_darboux_to_state(qT,qT_1,qT_2,p0,mu0_1,mu0_2) # debug #qT,qT_1,qT_2,pT,muT_1,muT_2 = tj.state_to_weinstein_darboux( stateT ) #logging.info("q0_1: " + str(q0_1)) #logging.info("q0_2: " + str(q0_2)) #logging.info("p0: " + str(p0)) #logging.info("mu0_1: " + str(mu0_1)) #logging.info("mu0_2: " + str(mu0_2)) #logging.info("qT: " + str(qT)) #logging.info("qT_1: " + str(qT_1)) #logging.info("qT_2: " + str(qT_2)) #logging.info("qT-q0: " + str(qT-q0)) #logging.info("qT_1-q0_1: " + str(qT_1-q0_1)) #logging.info("qT_2-q0_2: " + str(qT_2-q0_2)) logging.info("||p0||: " + str(np.linalg.norm(p0))) logging.info("||mu0_1||: " + str(np.linalg.norm(mu0_1))) logging.info("||mu0_2||: " + str(np.linalg.norm(mu0_2))) simT = sim['f'](stateT) # debug logging.info('match term (after flow): ' + str(simT[0])) Ediff = tj.Hamiltonian(q0,p0,mu0_1,mu0_2) # path energy from Hamiltonian logging.info('Hamiltonian: ' + str(Ediff)) if not adjint: return weights[1]*simT[0]+weights[0]*Ediff dq = simT[1][0] if order >= 1: dq_1 = simT[1][1] else: dq_1 = np.zeros([N,DIM,DIM]) if order >= 2: dq_2 = simT[1][2] else: dq_2 = np.zeros([N,DIM,DIM,DIM]) ds1 = tj.weinstein_darboux_to_state(np.zeros(dq.shape),np.zeros(dq_1.shape),np.zeros(dq_2.shape),dq,dq_1,dq_2,sim['N'],sim['DIM']) adjstate0 = np.append(np.zeros(ds1.size), ds1) assert(nonmoving.size+x.size==adjstate0.size/2) gradE = tj.grad_Hamiltonian(q0,p0,mu0_1,mu0_2) assert(adjstate0.size/2-nonmoving.size == gradE.size) # gradE doesn't include point variations currently grad0 = np.array(weights[1]*adjstate0[adjstate0.size/2+nonmoving.size:] + weights[0]*gradE) # transported gradient + grad of energy # get from symmetric to triangular form #assert(np.allclose(adjstate0[adjstate0.size/2:adjstate0.size],tj.triangular_to_state(tj.state_to_triangular(adjstate0[adjstate0.size/2:adjstate0.size])))) grad0 = tj.state_to_triangular(adjstate0[adjstate0.size/2:adjstate0.size])[triunonmoving.size:triunonmoving.size+triux.size] grad0 = np.ndarray.flatten(grad0) # rescale if scalegrad: if order >= 1: grad0[N*DIM:N*DIM+N*DIM**2] = tj.SIGMA*grad0[N*DIM:N*DIM+N*DIM**2] if order == 2: grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3] = tj.SIGMA*grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3] # debug #grad0 = grad0[0:N*DIM+N*DIM**2] logging.info("||dq||: " + str(np.linalg.norm(dq))) logging.info("||dq_1||: " + str(np.linalg.norm(dq_1))) logging.info("||dq_2||: " + str(np.linalg.norm(dq_2))) #logging.info("grad0: " + str(grad0)) ## pause #raw_input("Fdisp: Press ENTER to continue") return (weights[1]*simT[0]+weights[0]*Ediff, grad0)