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 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)