def func(abg):
'rediscretize:'
xmin = FPMultiPhiSolver.calculate_xmin(S.getTf(), abg, S._theta)
dt = FPMultiPhiSolver.calculate_dt(S._dx, abg, xmin, factor = 2.)
# print abg, dt, S._dx, xmin
S.rediscretize(S._dx, dt, S.getTf(), xmin)
'Solve it:'
# print abg
# start = time.clock()
Fs = S.c_solve(abg)
# solve_end = time.clock()
spike_t_indexes = mleBinnedTrain.getTindxs(S._ts)
# t_indxs_end = time.clock();
# print abg, ' : solvetime = %f; indx_time = %f'%(solve_end - start, t_indxs_end - solve_end)
'form (approximate) likelihood:'
pdf = -diff(Fs[:,:,-1], axis = 1) / S._dt;
likelihoods = pdf[minus_idxs, spike_t_indexes]*minus_weights + \
pdf[plus_idxs, spike_t_indexes]*plus_weights
if amin(likelihoods) <= .0:
likelihoods[likelihoods<=.0] = 1e-8
'Return '
return -sum(log(likelihoods))
def func(abg):
xmin = FPMultiPhiSolver.calculate_xmin(S.getTf(), abg)
dt = FPMultiPhiSolver.calculate_dt(S._dx, abg, xmin)
S.rediscretize(S._dx, dt, S.getTf(), xmin)
'Solve it:'
Fss = S.c_solve(abg);
Fs = Fss[:,:,-1];
Ss = S.transformSurvivorData(binnedTrain)
Ls = Fs - Ss
'Return '
G = .5*sum(Ls*Ls)*S._dt
print 'abg = ', abg, '; G=', G
# G = .0;
# for phi, phi_idx in zip(S._phis, xrange(S._num_phis() )):
# unique_Is = bins[phi]['unique_Is']
# SDF = bins[phi]['SDF']
# Ls = SDF - interp(unique_Is, ts, Fs[phi_idx,:])
# G += sum(Ls*Ls)
del Fss, Fs, Ss, Ls;
return G
def func(abgt):
'Solve it:'
abg = abgt[:3]
xmin = FPMultiPhiSolver.calculate_xmin(S.getTf(), abg)
dt = FPMultiPhiSolver.calculate_dt(S._dx, abg, xmin)
S.rediscretize(S._dx, dt, S.getTf(), xmin)
Fs = S.solve_tau(abgt, visualize=False)[:,:,-1]
Ss = S.transformSurvivorData(binnedTrain)
Ls = Fs - Ss
'Return '
G = .5*sum(Ls*Ls)*S._dt
return G
def obtainRenewalDensities(phis, abg, theta, Tf):
xmin = FPMultiPhiSolver.calculate_xmin(Tf, abg)
dx = .025; dt = FPMultiPhiSolver.calculate_dt(dx, abg, xmin, factor = 5.)
S = FPMultiPhiSolver(theta, phis,
dx, dt, Tf, xmin);
Fs = S.solve(abg)
ts = S._ts;
iG = squeeze(Fs[:, :,-1])
g = -diff(iG)/ S._dt;
t_mids = (S._ts[1:]+S._ts[:-1])/2.0
return g, S._ts ,t_mids
def loglikelihood(abg):
'rediscretize:'
xmin = FPMultiPhiSolver.calculate_xmin(S.getTf(), abg, S._theta)
dt = FPMultiPhiSolver.calculate_dt(S._dx, abg, xmin)
S.rediscretize(S._dx, dt, S.getTf(), xmin)
'Solve it:'
Fs = S.c_solve(abg)
spike_t_indexes = mleBinnedTrain.getTindxs(S._ts)
'form (approximate) likelihood:'
pdf = -diff(Fs[:,:,-1], axis = 1) / S._dt;
likelihoods = pdf[minus_idxs, spike_t_indexes]*minus_weights +\
pdf[plus_idxs, spike_t_indexes]*plus_weights
# if amin(likelihoods) <= .0:
# likelihoods[likelihoods<=.0] = 1e-8
normalized_log_likelihood = sum(log(likelihoods))
'Return '
return -normalized_log_likelihood
def func(abg):
xmin = FPMultiPhiSolver.calculate_xmin(S.getTf(), abg, S._theta)
dt = FPMultiPhiSolver.calculate_dt(S._dx, abg, xmin)
S.rediscretize(S._dx, dt, S.getTf(), xmin)
'Solve it:'
Fss = S.c_solve(abg)
Fs = Fss[:,:,-1]
Ss = S.transformSurvivorData(binnedTrain)
lSups = amax(abs(Fs - Ss) , axis = 1)
'Return '
G = dot(weight_vector, lSups)
if verbose:
print 'abg = ', abg, '; G=', G
return G
def func(abg):
xmin = FPMultiPhiSolver.calculate_xmin(S.getTf(), abg)
dt = FPMultiPhiSolver.calculate_dt(S._dx, abg, xmin)
S.rediscretize(S._dx, dt, S.getTf(), xmin)
'Solve it:'
Fss = S.c_solve(abg)
Fs = Fss[:,:,-1]
Ss = S.transformSurvivorData(binnedTrain)
Ls = Fs - Ss
'Return '
G = .5*sum( dot(weight_vector, Ls*Ls) )*S._dt / sum(weight_vector)
# 'clean up'
# del Fss, Fs, Ss, Ls;
print 'abg = ', abg, '; G=', G
return G
def calculateExactSDFs():
N_phi = 4;
print 'N_phi = ', N_phi
phis = 2*pi*array([0,.25, .5, .75])
for regime_idx, regime_name in enumerate(['superT', 'superSin', 'crit','subT']):
# for regime_name in ['superT']:
regime_label = 'sinusoidal_spike_train_N=1000_' + regime_name + '_12'
binnedTrain = BinnedSpikeTrain.initFromFile(regime_label, phis)
Tf = binnedTrain.getTf()
print 'Tf = ', Tf
theta = binnedTrain.theta;
print 'theta = ', theta
ps = binnedTrain._Train._params
abg_true = array((ps._alpha, ps._beta, ps._gamma))
abg = abg_true
xmin = FPMultiPhiSolver.calculate_xmin(Tf, abg, theta)
# dx = .0125# dx = .0125; ;
dx = .0125;
dt = FPMultiPhiSolver.calculate_dt(dx, abg, xmin, factor = 5.)
print 'xmin = ', xmin, ', dx, dt = ', dx, dt
S = FPMultiPhiSolver(theta, phis,
dx, dt, Tf, xmin)
S.setTf(Tf)
Fs = S.c_solve(abg)
ts = S._ts;
filename= RESULTS_DIR + '/Fs_%s'%regime_name
print 'saving Fs to ', filename
savez(filename, ts=ts,
Gs=squeeze(Fs[:,:,-1]),
phis=phis,
Tf = Tf);
def MixedEstimator(abg_init, binnedTrain, dp_tol = 1e-2):
phis = binnedTrain.bins.keys();
theta = binnedTrain.theta
dp = dp_tol*2.0;
abg = abg_init
while dp > dp_tol:
Tf = binnedTrain.getTf()
xmin = FPMultiPhiSolver.calculate_xmin(Tf, abg)
dx = FPMultiPhiSolver.calculate_dx(abg, xmin)
dt = FPMultiPhiSolver.calculate_dt(dx, abg, xmin, factor = 8.)
S = FPMultiPhiSolver(theta, phis,
dx, dt, Tf, xmin)
Fs = S.solve(abg, visualize=False)
Ss = S.transformSurvivorData(binnedTrain)
Ls = Fs[:,:,-1] - Ss
Nus = S.solveAdjoint(abg, Ls)
dGdp = S.estimateParameterGradient(abg, Fs, Nus)
from numpy.linalg.linalg import norm
dG_normalized = dGdp/ norm(dGdp)
dp = FortetLineEstimator(binnedTrain, abg, dG_normalized, dp_tol)
abg = abg - dp*dG_normalized
print 'dG = ', dG_normalized
print 'dp = ', dp
print 'abg = (%.3g, %.3g, %.3g)'%(abg[0],abg[1],abg[2])
print '-'
return abg
def adapted_sandbox(save_figs=False):
# file_name = 'sinusoidal_spike_train_N=1000_subT_11'
# file_name = 'sinusoidal_spike_train_N=1000_superSin_13'
N_samples = 16;
N_phi_per_quarter = 4;
N_phi = 4*N_phi_per_quarter;
normalized_phis = getAdaptedPhis(N_phi_per_quarter)
diFs = empty((4, 3, N_samples))
errors = empty((4, 2, N_samples))
seed(2013)
for regime_idx, tag in enumerate(['superSin', 'crit', 'superT', 'subT']):
file_name = 'sinusoidal_spike_train_N=1000_%s_13'%tag
binnedTrain = BinnedSpikeTrain.initFromFile(file_name, normalized_phis)
theta = binnedTrain.theta;
real_phis = normalized_phis * 2.0 * pi / theta;
for sample_idx in xrange(N_samples):
phi_star,I_star = binnedTrain.getRandomPhiInterval()
print 'phi_star, I_star: ', phi_star, I_star
phi_m, phi_minus, phi_plus = getApproximatePhis(phi_star, real_phis,theta)
delta_phi_minus_weight, delta_phi_plus_weight = getDeltaPhiWeights(phi_star, phi_minus, phi_plus)
solver_phis = [phi_star, phi_m, phi_minus, phi_plus]
ps = binnedTrain._Train._params
abg = array((ps._alpha, ps._beta, ps._gamma))
Tf = I_star + .2;
dx = .025;
x_min = FPMultiPhiSolver.calculate_xmin(Tf, abg, theta)
dt = FPMultiPhiSolver.calculate_dt(dx,abg, x_min, factor = 1.0)
S = FPMultiPhiSolver(theta, solver_phis,
dx, dt, Tf, x_min)
S.setTf(Tf)
Fth = S.c_solve(abg)[:,:,-1]
ts = S._ts;
tm_idx, tp_idx = gettsIndex(ts, I_star)
diF_star = -diff(Fth[0, [tm_idx, tp_idx]]) / (S._dt)
diF_m = -diff(Fth[1, [tm_idx, tp_idx]]) / (S._dt)
diF_plus_minus = -(diff(Fth[2, [tm_idx, tp_idx]])*delta_phi_minus_weight + \
diff(Fth[3, [tm_idx, tp_idx]])*delta_phi_plus_weight)/ (S._dt)
# print 'di_F: %.4f,%.4f,%.4f' %(diF_star, diF_m, diF_plus_minus)
# print 'error: %.4f,%.4f' %(abs(diF_star - diF_m), abs(diF_star-diF_plus_minus) )
diFs[regime_idx, :, sample_idx] = r_[diF_star, diF_m, diF_plus_minus]
errors[regime_idx, :, sample_idx] = r_[abs(diF_star - diF_m), abs(diF_star-diF_plus_minus)]
figure()
plot(errors[regime_idx, 0,:], 'b', label='F_m')
plot(errors[regime_idx, 1,:], 'r', label='F_min + F_plus')
legend(); title(tag, fontsize = 32)
from numpy import save
save('Ls_adapted',diFs)
save('errors_adapted', errors)
def thetas_sandbox(save_figs=False):
N_samples = 100;
N_phi = 64;
normalized_phis = linspace(1/(2.*N_phi), 1. - 1/ (2.*N_phi), N_phi)
#results banks:
# seed(2013)
thetas = [10, 20]
likelihoods = empty((len(thetas), 4, N_samples))
errors = empty((len(thetas), 3, N_samples))
base_name = 'sinusoidal_spike_train_N=1000_critical_theta='
for regime_idx, theta in enumerate(thetas):
sample_id = 17
regime_name = 'theta%d'%theta
regime_label = base_name + '%d'%theta
file_name = regime_label + '_%d'%sample_id
print file_name
binnedTrain = BinnedSpikeTrain.initFromFile(file_name, normalized_phis)
theta = binnedTrain.theta;
real_phis = normalized_phis * 2.0 * pi / theta;
for sample_idx in xrange(N_samples):
phi_star,I_star = binnedTrain.getRandomPhiInterval()
print 'phi_star_normalized, I_star: %.3f, %.3f' %(phi_star/ (2*pi/theta), I_star)
phi_m, phi_minus, phi_plus = getApproximatePhis(phi_star, real_phis,theta)
delta_phi_minus_weight, delta_phi_plus_weight = getDeltaPhiWeights(phi_star, phi_minus, phi_plus)
#phi_star_idx = 0; phi_m_idx = 1; etc...
solver_phis = [phi_star, phi_m, phi_minus, phi_plus]
# print 'solver_phis = ', solver_phis
# print 'weights = %.3f, %.3f'%(delta_phi_minus_weight, delta_phi_plus_weight)
ps = binnedTrain._Train._params
abg_true = array((ps._alpha, ps._beta, ps._gamma))
abg = abg_true
Tf = I_star + .2;
dx = .025;
x_min = FPMultiPhiSolver.calculate_xmin(Tf, abg, theta)
dt = FPMultiPhiSolver.calculate_dt(dx,abg, x_min, factor = 1.0)
S = FPMultiPhiSolver(theta, solver_phis,
dx, dt, Tf, x_min)
S.setTf(Tf)
Fs = S.c_solve(abg)
Fth = Fs[:,:,-1]
# Fth_phis = S.solveFphi(abg, Fs)[:,:,-1]
ts = S._ts;
tm_idx, tp_idx = gettsIndex(ts, I_star)
delta_t = S._dt
delta_phi = phi_star - phi_m
#various approximations to the likelihood, L
L_star = -diff(Fth[0, [tm_idx, tp_idx]]) / (delta_t)
L_m = -diff(Fth[1, [tm_idx, tp_idx]]) / (delta_t)
L_plus_minus = -(diff(Fth[2, [tm_idx, tp_idx]])*delta_phi_minus_weight + \
diff(Fth[3, [tm_idx, tp_idx]])*delta_phi_plus_weight)/ (delta_t)
# gradphi_g = -diff(Fth_phis[1, [tm_idx, tp_idx]]) / (delta_t);
# logL_gradphi = log(L_m) + delta_phi * gradphi_g / L_m
# L_gradphi = exp(logL_gradphi)
L_gradphi = L_plus_minus
# print 'di_F: %.4f,%.4f,%.4f' %(diF_star, diF_m, diF_plus_minus)
# print 'error: %.4f,%.4f' %(abs(diF_star - diF_m), abs(diF_star-diF_plus_minus) )
likelihoods[regime_idx, :, sample_idx] = r_[L_star,
L_m,
L_plus_minus,
L_gradphi]
errors[regime_idx, :, sample_idx] = r_[abs(L_star - L_m),
abs(L_star-L_plus_minus),
abs(L_star - L_gradphi)]
figure()
plot(errors[regime_idx, 0,:], 'b', label='F_m')
plot(errors[regime_idx, 1,:], 'r', label='F_min + F_plus')
legend(); title('theta= %.2f'%theta, fontsize = 32)
from numpy import save
save('likelihoods_thetas',likelihoods)
save('errors_thetas', errors)
def supersin_sandbox(N_phi = 32):
N_sub_samples = 10
N_samples = N_sub_samples*5;
normalized_phis = linspace(1/(2.*N_phi), 1. - 1/ (2.*N_phi), N_phi)
#results banks:
likelihoods = empty((4, 4, N_samples))
errors = empty((4, 3, N_samples))
seed(2013)
for regime_idx, tag in enumerate(['superSin']):
file_name = 'sinusoidal_spike_train_N=1000_%s_22'%(tag)
print file_name
binnedTrain = BinnedSpikeTrain.initFromFile(file_name, normalized_phis)
theta = binnedTrain.theta;
real_phis = normalized_phis * 2.0 * pi / theta;
for sample_idx in xrange(N_samples):
if 0 == mod(sample_idx, N_sub_samples):
train_id = randint(1,101)
file_name = 'sinusoidal_spike_train_N=1000_%s_%d'%(tag, train_id)
print file_name
binnedTrain = BinnedSpikeTrain.initFromFile(file_name, normalized_phis)
phi_star,I_star = binnedTrain.getRandomPhiInterval()
print 'phi_star_normalized, I_star: %.3f, %.3f' %(phi_star/ (2*pi/theta), I_star)
phi_m, phi_minus, phi_plus = getApproximatePhis(phi_star, real_phis,theta)
delta_phi_minus_weight, delta_phi_plus_weight = getDeltaPhiWeights(phi_star, phi_minus, phi_plus)
#phi_star_idx = 0; phi_m_idx = 1; etc...
solver_phis = [phi_star, phi_m, phi_minus, phi_plus]
# print 'solver_phis = ', solver_phis
# print 'weights = %.3f, %.3f'%(delta_phi_minus_weight, delta_phi_plus_weight)
ps = binnedTrain._Train._params
abg_true = array((ps._alpha, ps._beta, ps._gamma))
abg = abg_true
Tf = I_star + .2;
dx = .025;
x_min = FPMultiPhiSolver.calculate_xmin(Tf, abg, theta)
dt = FPMultiPhiSolver.calculate_dt(dx,abg, x_min, factor = 1.0)
S = FPMultiPhiSolver(theta, solver_phis,
dx, dt, Tf, x_min)
S.setTf(Tf)
Fs = S.c_solve(abg)
Fth = Fs[:,:,-1]
Fth_phis = S.solveFphi(abg, Fs)[:,:,-1]
ts = S._ts;
tm_idx, tp_idx = gettsIndex(ts, I_star)
delta_t = S._dt
delta_phi = phi_star - phi_m
#various approximations to the likelihood, L
L_star = -diff(Fth[0, [tm_idx, tp_idx]]) / (delta_t)
L_m = -diff(Fth[1, [tm_idx, tp_idx]]) / (delta_t)
L_plus_minus = -(diff(Fth[2, [tm_idx, tp_idx]])*delta_phi_minus_weight + \
diff(Fth[3, [tm_idx, tp_idx]])*delta_phi_plus_weight)/ (delta_t)
gradphi_g = -diff(Fth_phis[1, [tm_idx, tp_idx]]) / (delta_t);
logL_gradphi = log(L_m) + delta_phi * gradphi_g / L_m
L_gradphi = exp(logL_gradphi)
'sanity check'
approx_Fth_phi = .5 * sum(Fth[0, [tm_idx, tp_idx]] - Fth[1, [tm_idx, tp_idx]]) / (phi_star - phi_m)
lFth_phi = .5* (sum(Fth_phis[1, [tm_idx, tp_idx]]))
if (approx_Fth_phi * lFth_phi < .0):
print 'sanity inverse: approx:%.3f , adjoint_calc: %.3f'%(approx_Fth_phi,lFth_phi)
if (.0 >= L_star*L_m*L_plus_minus*L_gradphi):
print 'negative likelihood encountered'
# print 'di_F: %.4f,%.4f,%.4f' %(diF_star, diF_m, diF_plus_minus)
# print 'error: %.4f,%.4f' %(abs(diF_star - diF_m), abs(diF_star-diF_plus_minus) )
likelihoods[regime_idx, :, sample_idx] = r_[L_star,
L_m,
L_plus_minus,
L_gradphi]
errors[regime_idx, :, sample_idx] = r_[abs(L_star - L_m),
abs(L_star-L_plus_minus),
abs(L_star - L_gradphi)]
figure()
plot(errors[regime_idx, 0,:], 'b', label='F_m')
plot(errors[regime_idx, 1,:], 'r', label='F_min + F_plus')
legend(); title(tag, fontsize = 32)
from numpy import save
save('likelihoods_supersin',likelihoods)
save('errors_supersin', errors)
def AdjointEstimator():
N_phi = 20;
print 'N_phi = ', N_phi
phis = linspace(1/(2.*N_phi), 1. - 1/ (2.*N_phi), N_phi)
file_name = 'sinusoidal_spike_train_N=1000_crit_1'
print file_name
binnedTrain = BinnedSpikeTrain.initFromFile(file_name, phis)
phi_omit = None
binnedTrain.pruneBins(phi_omit, N_thresh = 100, T_thresh = 10.0)
print 'N_bins = ', len(binnedTrain.bins.keys())
Tf = binnedTrain.getTf()
print 'Tf = ', Tf
phis = binnedTrain.bins.keys();
theta = binnedTrain.theta
ps = binnedTrain._Train._params
abg_true = array((ps._alpha, ps._beta, ps._gamma))
print 'abg_true = ', abg_true
abg = abg_true
xmin = FPMultiPhiSolver.calculate_xmin(Tf, abg)
dx = FPMultiPhiSolver.calculate_dx(abg, xmin)
dt = FPMultiPhiSolver.calculate_dt(dx, abg, xmin, factor = 8.)
print 'xmin, dx, dt = ', xmin, dx, dt
S = FPMultiPhiSolver(theta, phis,
dx, dt, Tf, xmin)
abg_init = initialize5(binnedTrain)
print 'abg_init = ', abg_init
# start = time.clock()
# abg_est = TNCEstimator(S, binnedTrain, abg_init)
# print 'Est. time = ', time.clock() - start
# print 'abg_est = ', abg_est
# start = time.clock()
# abg_est = NMEstimator(S, binnedTrain, abg_init)
# print 'Est. time = ', time.clock() - start
# print 'abg_est = ', abg_est
#
# start = time.clock()
# abg_est = COBYLAEstimator(S, binnedTrain, abg_init)
# print 'Est. time = ', time.clock() - start
# print 'abg_est = ', abg_est
# start = time.clock()
# abg_est = CGEstimator(S, binnedTrain, abg_init)
# print 'Est. time = ', time.clock() - start
# print 'abg_est = ', abg_est
start = time.clock()
abg_est = BFGSEstimator(S, binnedTrain, abg_init)
print 'Est. time = ', time.clock() - start
print 'abg_est = ', abg_est
