def ffcn_bar(self, t, x, x_bar, f, f_bar, p, p_bar, u, u_bar):
if self.traced == False:
dims = {'x': x.size, 'p': p.size, 'u': u.size}
self.trace(dims)
v = self.txpu_to_v(t,x,p,u)
adolc.zos_forward(123, v, 1)
v_bar = adolc.fos_reverse(123, f_bar)
self.bar_v_to_txpu(v, v_bar, x, x_bar, p, p_bar, u, u_bar)
def reduced_functional(m):
"""
Apply the Okada model by unrolling the tape and compute the QoI.
"""
J = sum(adolc.zos_forward(tape_tag, m, keep=1))
op.J_progress.append(J)
return J
def fov_reverse(self,arg):
(m,q,u,n,z,x,y) = arg
adolc.set_nested_ctx(self.tag_ext_fct,1)
ny = adolc.zos_forward(self.tag_ext_fct,2,2,1,x)
nz = adolc.fov_reverse(self.tag_ext_fct,2,2,q,u)
np.copyto(z,nz)
return 1
def zos_forward(self,arg):
(n,yin,m,yout) = arg
adolc.set_nested_ctx(self.tag_ext_fct,1)
ny = adolc.zos_forward(self.tag_ext_fct,2,2,0,yin)
adolc.set_nested_ctx(self.tag_ext_fct,0)
np.copyto(yout,ny)
return 1
def okada_source(m, keep=1):
"""
Compute the dislocation field due to a (flattened) array of
active control parameters by replaying pyadolc's tape.
:kwarg keep: toggle whether to flag for a reverse propagation.
"""
return adolc.zos_forward(tape_tag, m, keep=1)
def set_initial_condition(self,
prob,
annotate_source=False,
unroll_tape=False,
**kwargs):
"""
Set initial condition using the Okada parametrisation [Okada 85].
Uses code from GeoCLAW found in `geoclaw/src/python/geoclaw/dtopotools.py`.
[Okada 85] Yoshimitsu Okada, "Surface deformation due to shear and tensile faults in a
half-space", Bulletin of the Seismological Society of America, Vol. 75, No. 4,
pp.1135--1154, (1985).
:arg prob: :class:`AdaptiveTsunamiProblem` solver object.
:kwarg annotate_source: toggle annotation of the rupture process using pyadolc.
:kwarg tag: non-negative integer label for tape.
"""
# separate_faults = kwargs.get('separate_faults', True)
separate_faults = kwargs.get('separate_faults', False)
subtract_from_bathymetry = kwargs.pop('subtract_from_bathymetry', True)
tag = kwargs.get('tag', 0)
# Create fault topography...
if unroll_tape:
# ... by unrolling ADOL-C's tape
import adolc
F = adolc.zos_forward(tag, self.input_vector, keep=1)
if separate_faults:
F = np.sum(F.reshape(self.num_subfaults, len(self.indices)),
axis=0)
surf = self.interpolate_dislocation_field(prob, data=F)
else:
# ... by running the Okada model
self.create_topography(annotate=annotate_source, **kwargs)
surf = self.interpolate_dislocation_field(prob)
# Assume zero initial velocity and interpolate into the elevation space
u, eta = prob.fwd_solutions[0].split()
u.assign(0.0)
eta.interpolate(surf)
# Subtract initial surface from the bathymetry field
if subtract_from_bathymetry:
self.subtract_surface_from_bathymetry(prob, surf=surf)
return surf
Np = size(p) Nq = size(q) Nv = size(v) Nm = 100 ts = linspace(0,10,Nm) # TAPING THE INTEGRATOR adolc.trace_on(1) av = adolc.adouble(v) adolc.independent(av) ax = explicit_euler(av[0],f,ts,av[:Np],av[Np:]) adolc.dependent(ax) adolc.trace_off() # COMPUTING FUNCTION AND JACOBIAN FROM THE TAPE y = adolc.zos_forward(1,v,0) J = adolc.jacobian(1,v) x_plot = plot(ts, y,'b') x_analytical_plot = plot(ts,phi(ts,p,q),'b.') xp0_plot = plot(ts, J[:,0], 'g') xp0_analytical_plot = plot(ts, phip0(ts,p,q), 'g.') xp1_plot = plot(ts, J[:,1], 'r') xp1_analytical_plot = plot(ts, phip1(ts,p,q), 'r.') show() print J
# PERFORM PARAMETER ESTIMATION
def dFdp(p, q, ts, Sigma, etas):
v[:Np] = p[:]
return adolc.jacobian(1, v)[:, :Np]
res = scipy.optimize.leastsq(F,
p,
args=(q, ts, Sigma, etas),
Dfun=dFdp,
full_output=True)
# plotting solution of parameter estimation and starting point
p[0] += 3
p[1] += 2.
x = explicit_euler(p[0], f, ts, p, q)
y = adolc.zos_forward(2, v, 0)
p[0] -= 3
p[1] -= 2.
starting_plot = plot(ts, x)
x = explicit_euler(p[0], f, ts, p, q)
correct_plot = plot(ts, x, 'b.')
meas_plot = plot(ts, etas, 'r.')
x = explicit_euler(res[0][0], f, ts, res[0], q)
est_plot = plot(ts, x)
plot(ts, etas, 'r.')
hplot = plot(ts, y, 'g.')
xlabel(r'time $t$ []')
ylabel(r'measurement function $h(t,x,p,q)$')
legend((meas_plot, starting_plot, correct_plot, est_plot, hplot),
Np = size(p) Nq = size(q) Nv = size(v) Nm = 100 ts = linspace(0, 10, Nm) # TAPING THE INTEGRATOR adolc.trace_on(1) av = adolc.adouble(v) adolc.independent(av) ax = explicit_euler(av[0], f, ts, av[:Np], av[Np:]) adolc.dependent(ax) adolc.trace_off() # COMPUTING FUNCTION AND JACOBIAN FROM THE TAPE y = adolc.zos_forward(1, v, 0) J = adolc.jacobian(1, v) x_plot = plot(ts, y, 'b') x_analytical_plot = plot(ts, phi(ts, p, q), 'b.') xp0_plot = plot(ts, J[:, 0], 'g') xp0_analytical_plot = plot(ts, phip0(ts, p, q), 'g.') xp1_plot = plot(ts, J[:, 1], 'r') xp1_analytical_plot = plot(ts, phip1(ts, p, q), 'r.') show() print J
ax = explicit_euler(av[0],f,ts,av[:Np],av[Np:])
ay = measurement_model(ax, av[:Np],av[Np:])
for m in range(Nm):
y[m] = adolc.depends_on(ay[m])
adolc.trace_off()
# PERFORM PARAMETER ESTIMATION
def dFdp(p,q,ts,Sigma, etas):
v[:Np] = p[:]
return adolc.jacobian(1,v)[:,:Np]
res = scipy.optimize.leastsq(F,p,args=(q,ts,Sigma,etas), Dfun = dFdp, full_output = True)
# plotting solution of parameter estimation and starting point
p[0]+=3; p[1] += 2.
x = explicit_euler(p[0],f,ts,p,q)
y = adolc.zos_forward(2,v,0)
p[0]-= 3; p[1] -= 2.
starting_plot = plot(ts,x)
x = explicit_euler(p[0],f,ts,p,q)
correct_plot = plot(ts,x,'b.')
meas_plot = plot(ts,etas,'r.')
x = explicit_euler(res[0][0],f,ts,res[0],q)
est_plot = plot(ts,x)
plot(ts,etas,'r.')
hplot = plot(ts,y,'g.')
xlabel(r'time $t$ []')
ylabel(r'measurement function $h(t,x,p,q)$')
legend((meas_plot,starting_plot,correct_plot,est_plot,hplot),('measurements','initial guess','true','estimated','measurement model'))
title('Parameter Estimation')
