def main(data,gf,param,outfile):
'''
Nt: number of time steps
Nx: number of positions
Dx: spatial dimensions of coordinates and displacements
Ns: number of slip basis functions per slip direction
Ds: number of slip directions
Nv: number of fluidity basis functions
total: number of state parameters (Ns*Ds + Nv + 2*Nx*Dx)
Parameters
----------
data: \ mask : (Nt,Nx) boolean array
\ mean : (Nt,Nx,Dx) array
\ covariance : (Nt,Nx,Dx,Dx) array
\ metadata \ position : (Nx,Dx) array
time : (Nt,) array
prior: \ mean : (total,) array
\ covariance : (total,total) array
gf: \ elastic : (Ns,Ds,Nx,Dx) array
\ viscoelastic : (Ns,Ds,Dv,Nx,Dx) array
\ metadata \ position : (Nx,Dx) array
reg: \ regularization : (*,total) array
params: user parameter dictionary
Returns
-------
out: \ slip_integral \ mean : (Nt,Ns,Ds) array
\ uncertainty :(Nt,Ns,Ds) array
\ slip \ mean : (Nt,Ns,Ds) array
\ uncertainty : (Nt,Ns,Ds) array
\ slip_derivative \ mean : (Nt,Ns,Ds) array
\ uncertainty : (Nt,Ns,Ds) array
\ fluidity \ mean : (Nv,) array
\ uncertainty : (Nv,) array
\ secular_velocity \ mean : (Nx,Dx) array
\ uncertainty : (Nx,Dx) array
\ baseline_displacement \ mean : (Nx,Dx) array
\ uncertainty : (Nx,Dx) array
'''
F = gf['slip'][...]
G = gf['fluidity'][...]
coseismic_times = np.array(param['coseismic_times'])
afterslip_start_times = param['afterslip_start_times']
afterslip_end_times = param['afterslip_end_times']
afterslip_times = zip(afterslip_start_times,afterslip_end_times)
afterslip_times = np.array(afterslip_times)
time = data['time'][:]
slip_scale = 1.0 # meter
relax_scale = 1.0 # year
time_scale = np.std(time)
time_shift = np.mean(time) # years
disp_scale = 1.0 # meter
# shift is different for each time series
disp_shift = np.mean(data['mean'],0)
# scale greens functions
# F is originally in meters disp per meter slip
F /= disp_scale/slip_scale
# G is originally in meters/year disp per meter slip*fluidity
G /= (disp_scale/time_scale)/(slip_scale/relax_scale)
time -= time_shift
time /= time_scale
coseismic_times -= time_shift
coseismic_times /= time_scale
afterslip_times -= time_shift
afterslip_times /= time_scale
param['initial_slip_variance'] /= slip_scale**2
param['fluidity_variance'] *= relax_scale**2
param['secular_velocity_variance'] /= (disp_scale/time_scale)**2
param['baseline_displacement_variance'] /= disp_scale**2
# define slip functions and slip jacobian here
slip_func,slip_jac = steps_and_ramps(coseismic_times,
afterslip_times)
Nst = len(coseismic_times) + len(afterslip_start_times)
Ns,Ds,Nv,Nx,Dx = np.shape(G)
Nt = len(time)
# check for consistency between input
assert data['mean'].shape == (Nt,Nx,Dx)
assert data['variance'].shape == (Nt,Nx,Dx)
assert F.shape == (Ns,Ds,Nx,Dx)
assert G.shape == (Ns,Ds,Nv,Nx,Dx)
p = state_parser(Nst,Ns,Ds,Nv,Nx,Dx)
if param['solver'] == 'bvls':
solver = modest.bvls
upper_bound = 1e6*np.ones(p['total'])
lower_bound = -1e6*np.ones(p['total'])
# all inferred fluidities will be positive
lower_bound[p['fluidity']] = 0
# all inferred left lateral slip will be positive
left_lateral_indices = np.array(p['slip'][:,:,0],copy=True)
thrust_indices = np.array(p['slip'][:,:,1],copy=True)
upper_bound[left_lateral_indices] = 0.0
solver_args = (lower_bound,upper_bound)
solver_kwargs = {}
if param['solver'] == 'lstsq':
solver = modest.lstsq
solver_args = ()
solver_kwargs = {}
elif param['solver'] == 'lsmr':
solver = modest.lsmr
solver_args = ()
solver_kwargs = {}
elif param['solver'] == 'lgmres':
solver = modest.lgmres
solver_args = ()
solver_kwargs = {'tol':1e-8,'maxiter':1000}
elif param['solver'] == 'dgs':
solver = modest.dgs
solver_args = ()
solver_kwargs = {}
#fprior = prior.create_formatted_prior(param,p,slip_model='parameterized')
Xprior,Cprior = prior.create_prior(param,p,slip_model='parameterized')
reg_matrix = reg.create_regularization(param,p,slip_model='parameterized')
reg_rows = len(reg_matrix)
setup_output_file(outfile,p,
data['name'][...],
data['position'][...],
data['time'][...])
Xprior,Cprior = modest.nonlin_lstsq(
regularization,
np.zeros(reg_rows),
Xprior,
data_covariance=np.eye(reg_rows),
prior_covariance=Cprior,
system_args=(reg_matrix,),
jacobian=regularization_jacobian,
jacobian_args=(reg_matrix,),
maxitr=param['maxitr'],
solver=solver,
solver_args=solver_args,
solver_kwargs=solver_kwargs,
LM_damping=True,
output=['solution','solution_covariance'])
time_indices = range(Nt)
block_time_indices = modest.misc.divide_list(time_indices,param['time_blocks'])
for i in block_time_indices:
outfile['data/mean'][i,...] = data['mean'][i,...]
outfile['data/mask'][i,...] = data['mask'][i,...]
outfile['data/covariance'][i,...] = data['variance'][i,...]
di = data['mean'][i,...]
di -= disp_shift
di /= disp_scale
di_mask = np.array(data['mask'][i,:],dtype=bool)
# expand to three dimensions
di_mask = np.repeat(di_mask[...,None],3,-1)
di = di[~di_mask]
Cdi = data['variance'][i,...]
Cdi /= disp_scale**2
Cdi = Cdi[~di_mask]
Xprior,Cprior = modest.nonlin_lstsq(
observation,
di,
Xprior,
data_covariance=Cdi,
prior_covariance=Cprior,
system_args=(time[i],F,G,p,slip_func,di_mask),
jacobian=observation_jacobian,
jacobian_args=(time[i],F,G,p,slip_func,slip_jac,di_mask),
solver=solver,
solver_args=solver_args,
solver_kwargs=solver_kwargs,
maxitr=param['maxitr'],
LM_damping=True,
LM_param=1.0,
rtol=1e-2,
atol=1e-2,
output=['solution','solution_covariance'])
post_mean_scaled,post_cov_scaled = Xprior,Cprior
post_mean = np.copy(post_mean_scaled)
post_mean[p['baseline_displacement']] *= disp_scale
post_mean[p['baseline_displacement']] += disp_shift
post_mean[p['secular_velocity']] *= (disp_scale/time_scale)
post_mean[p['slip']] *= slip_scale
post_mean[p['fluidity']] /= relax_scale
for i in range(Nt):
outfile['state/all'][i,:] = post_mean
outfile['state/baseline_displacement'][i,...] = post_mean[p['baseline_displacement']]
outfile['state/secular_velocity'][i,...] = post_mean[p['secular_velocity']]
outfile['state/slip'][i,...] = slip_func(post_mean[p['slip']],time[i])
outfile['state/slip_derivative'][i,...] = slip_func(post_mean[p['slip']],time[i],diff=1)
outfile['state/fluidity'][i,...] = post_mean[p['fluidity']]
# compute predicted data
logger.info('computing predicted data')
error = 0.0
count = 0
for i in range(Nt):
predicted = observation_t(post_mean_scaled,
time[i],
F,G,p,slip_func)
# change back to meters
predicted *= disp_scale
predicted += disp_shift
residual = outfile['data/mean'][i,...] - predicted
covariance = outfile['data/covariance'][i,...]
data_mask = np.array(outfile['data/mask'][i,...],dtype=bool)
error += L2(residual,covariance,data_mask)
count += np.sum(~data_mask)
outfile['predicted/mean'][i,...] = predicted
mask = np.zeros(p['total'])
mask[p['secular_velocity']] = 1.0
mask[p['baseline_displacement']] = 1.0
mask_post_mean = post_mean_scaled*mask
tectonic = observation_t(mask_post_mean,
time[i],
F,G,p,
slip_func)
tectonic *= disp_scale
tectonic += disp_shift
outfile['tectonic/mean'][i,...] = tectonic
mask = np.zeros(p['total'])
mask[p['slip']] = 1.0
mask_post_mean = post_mean_scaled*mask
elastic = observation_t(mask_post_mean,
time[i],
F,G,p,
slip_func)
elastic *= disp_scale
outfile['elastic/mean'][i,...] = elastic
visc = (outfile['predicted/mean'][i,...] -
outfile['tectonic/mean'][i,...] -
outfile['elastic/mean'][i,...])
outfile['viscous/mean'][i,...] = visc
logger.info('total RMSE: %s' % np.sqrt(error/count))
return
def main(data,gf,param,outfile):
'''
Nt: number of time steps
Nx: number of positions
Dx: spatial dimensions of coordinates and displacements
Ns: number of slip basis functions per slip direction
Ds: number of slip directions
Nv: number of fluidity basis functions
total: number of state parameters (Ns*Ds + Nv + 2*Nx*Dx)
Parameters
----------
data: \ mask : (Nt,Nx) boolean array
\ mean : (Nt,Nx,Dx) array
\ covariance : (Nt,Nx,Dx,Dx) array
\ metadata \ position : (Nx,Dx) array
time : (Nt,) array
prior: \ mean : (total,) array
\ covariance : (total,total) array
gf: \ elastic : (Ns,Ds,Nx,Dx) array
\ viscoelastic : (Ns,Ds,Dv,Nx,Dx) array
\ metadata \ position : (Nx,Dx) array
reg: \ regularization : (*,total) array
params: user parameter dictionary
Returns
-------
out: \ slip_integral \ mean : (Nt,Ns,Ds) array
\ uncertainty :(Nt,Ns,Ds) array
\ slip \ mean : (Nt,Ns,Ds) array
\ uncertainty : (Nt,Ns,Ds) array
\ slip_derivative \ mean : (Nt,Ns,Ds) array
\ uncertainty : (Nt,Ns,Ds) array
\ fluidity \ mean : (Nv,) array
\ uncertainty : (Nv,) array
\ secular_velocity \ mean : (Nx,Dx) array
\ uncertainty : (Nx,Dx) array
\ baseline_displacement \ mean : (Nx,Dx) array
\ uncertainty : (Nx,Dx) array
'''
# set attributes of outfile
outfile.attrs.update(param)
outfile.attrs.update(gf.attrs)
outfile.attrs.update(data.attrs)
F = gf['slip'][...]
G = gf['fluidity'][...]
alpha = param['slip_acceleration_variance']
jump_factor = param['jump_variance_factor']
jump_times = param['jump_times']
time = data['time'][:]
Ns,Ds,Nv,Nx,Dx = np.shape(G)
Nt = len(time)
# check for consistency between input
assert np.shape(data['mean']) == (Nt,Nx,Dx)
assert np.shape(data['covariance']) == (Nt,Nx,Dx,Dx)
assert np.shape(F) == (Ns,Ds,Nx,Dx)
assert np.shape(G) == (Ns,Ds,Nv,Nx,Dx)
p = state_parser(Ns,Ds,Nv,Nx,Dx)
fprior = prior.create_formatted_prior(param,p)
Xprior,Cprior = prior.create_prior(fprior,p)
freg = reg.create_formatted_regularization(param,p)
reg_matrix = reg.create_regularization(freg,p)
reg_rows = len(reg_matrix)
kalman = modest.KalmanFilter(
Xprior,Cprior,
observation_augmented,
obs_args=(F,G,p,reg_matrix),
ojac=observation_jacobian_augmented,
ojac_args=(F,G,p,reg_matrix),
trans=transition,
trans_args=(p,),
tjac=transition_jacobian,
tjac_args=(p,),
pcov=process_covariance,
pcov_args=(alpha,p),
core=False,
solver_kwargs={'maxitr':param['maxitr']},
temp_file=param['history_file'])
# prepare outfile file
# copy over data file
outfile.create_dataset('data/mean',shape=np.shape(data['mean']))
outfile.create_dataset('data/mask',shape=np.shape(data['mask']),dtype=bool)
outfile.create_dataset('data/covariance',shape=np.shape(data['covariance']))
outfile['data/name'] = data['name'][...]
outfile['data/position'] = data['position'][...]
outfile['data/time'] = data['time'][...]
outfile.create_dataset('predicted/mean',shape=np.shape(data['mean']))
outfile.create_dataset('predicted/covariance',shape=np.shape(data['covariance']))
outfile['predicted/name'] = data['name'][...]
outfile['predicted/mask'] = np.array(0.0*data['mask'][...],dtype=bool)
outfile['predicted/position'] = data['position'][...]
outfile['predicted/time'] = data['time'][...]
outfile.create_dataset('tectonic/mean',shape=np.shape(data['mean']))
outfile.create_dataset('tectonic/covariance',shape=np.shape(data['covariance']))
outfile['tectonic/name'] = data['name'][...]
outfile['tectonic/mask'] = np.array(0.0*data['mask'][...],dtype=bool)
outfile['tectonic/position'] = data['position'][...]
outfile['tectonic/time'] = data['time'][...]
outfile.create_dataset('elastic/mean',shape=np.shape(data['mean']))
outfile.create_dataset('elastic/covariance',shape=np.shape(data['covariance']))
outfile['elastic/name'] = data['name'][...]
outfile['elastic/mask'] = np.array(0.0*data['mask'][...],dtype=bool)
outfile['elastic/position'] = data['position'][...]
outfile['elastic/time'] = data['time'][...]
outfile.create_dataset('viscous/mean',shape=np.shape(data['mean']))
outfile.create_dataset('viscous/covariance',shape=np.shape(data['covariance']))
outfile['viscous/name'] = data['name'][...]
outfile['viscous/mask'] = np.array(0.0*data['mask'][...],dtype=bool)
outfile['viscous/position'] = data['position'][...]
outfile['viscous/time'] = data['time'][...]
a = np.ones((Nt,Nx))
b = np.eye(3)
c = 1e-10*np.einsum('ij,kl',a,b)
outfile['predicted/covariance'][...] = c
outfile['tectonic/covariance'][...] = c
outfile['elastic/covariance'][...] = c
outfile['viscous/covariance'][...] = c
outfile.create_dataset('state/all',shape=(Nt,p['total']))
for k in ['baseline_displacement',
'secular_velocity',
'slip_integral',
'slip',
'slip_derivative',
'fluidity']:
outfile.create_dataset('state/' + k,shape=(Nt,)+np.shape(p[k]))
outfile['state/time'] = data['time'][...]
logger.info('starting Kalman filter iterations')
for i in range(Nt):
outfile['data/mean'][i,...] = data['mean'][i,...]
outfile['data/mask'][i,...] = data['mask'][i,...]
outfile['data/covariance'][i,...] = data['covariance'][i,...]
di = flat_data(data['mean'][i,...])
di = np.hstack((di,np.zeros(reg_rows)))
di_mask = np.array(data['mask'][i,:],dtype=bool)
# expand to three dimensions
di_mask = np.repeat(di_mask[:,None],3,1)
di_mask = flat_data(di_mask)
di_mask = np.hstack((di_mask,np.zeros(reg_rows,dtype=bool)))
Cdi = flat_cov(data['covariance'][i,...])
Cdi = scipy.linalg.block_diag(Cdi,np.eye(reg_rows))
if np.all(time[i] < jump_times):
kalman.pcov_args = (0.0*alpha,p)
kalman.next(di,Cdi,time[i],mask=di_mask)
kalman.pcov_args = (alpha,p)
elif (i != 0) & np.any((time[i] > jump_times) & (time[i-1] <= jump_times)):
logger.info('increasing slip variance by %sx when updating '
'from t=%s to t=%s' % (jump_factor,time[i-1],time[i]))
kalman.pcov_args = (jump_factor*alpha,p)
kalman.next(di,Cdi,time[i],mask=di_mask)
kalman.pcov_args = (alpha,p)
else:
kalman.next(di,Cdi,time[i],mask=di_mask)
print(kalman.get_posterior()[0][p['fluidity']])
logger.info('starting Rauch-Tung-Striebel smoothing')
kalman.smooth()
for i in range(Nt):
outfile['state/all'][i,:] = kalman.history['smooth'][i,:]
for k in ['baseline_displacement',
'secular_velocity',
'slip_integral',
'slip',
'slip_derivative',
'fluidity']:
outfile['state/' + k][i,...] = np.array(kalman.history['smooth'])[i,p[k]]
# compute predicted data
logger.info('computing predicted data')
error = 0.0
for i in range(Nt):
predicted = observation(outfile['state/all'][i],
time[i],
F,G,p,flatten=False)
residual = outfile['data/mean'][i,...] - predicted
covariance = outfile['data/covariance'][i,...]
data_mask = np.array(outfile['data/mask'][i,...],dtype=bool)
error += RMSE(residual,covariance,data_mask)
outfile['predicted/mean'][i,...] = predicted
mask = np.zeros(p['total'])
mask[p['secular_velocity']] = 1.0
mask[p['baseline_displacement']] = 1.0
state = outfile['state/all'][i]*mask
outfile['tectonic/mean'][i,...] = observation(
state,
time[i],
F,G,p,
flatten=False)
mask = np.zeros(p['total'])
mask[p['slip']] = 1.0
state = outfile['state/all'][i]*mask
outfile['elastic/mean'][i,...] = observation(
state,
time[i],
F,G,p,
flatten=False)
visc = (outfile['predicted/mean'][i,...] -
outfile['tectonic/mean'][i,...] -
outfile['elastic/mean'][i,...])
outfile['viscous/mean'][i,...] = visc
logger.info('total RMSE: %s' % error)
return
