def test_adjoint_F(self, shape, kernel, space_order, nbpml, save,
Eu, Erec, Ev, Esrca):
"""
Unlike `test_adjoint_F` in test_adjoint.py, here we explicitly check the norms
of all Operator-evaluated Functions. The numbers we check against are derived
"manually" from sequential runs of test_adjoint::test_adjoint_F
"""
tn = 500. # Final time
nrec = 130 # Number of receivers
# Create solver from preset
solver = acoustic_setup(shape=shape, spacing=[15. for _ in shape], kernel=kernel,
nbpml=nbpml, tn=tn, space_order=space_order, nrec=nrec,
preset='layers-isotropic', dtype=np.float64)
# Run forward operator
rec, u, _ = solver.forward(save=save)
assert np.isclose(norm(u), Eu, rtol=Eu*1.e-8)
assert np.isclose(norm(rec), Erec, rtol=Erec*1.e-8)
# Run adjoint operator
srca, v, _ = solver.adjoint(rec=rec)
assert np.isclose(norm(v), Ev, rtol=Ev*1.e-8)
assert np.isclose(norm(srca), Esrca, rtol=Esrca*1.e-8)
# Adjoint test: Verify <Ax,y> matches <x, A^Ty> closely
term1 = inner(srca, solver.geometry.src)
term2 = norm(rec)**2
assert np.isclose((term1 - term2)/term1, 0., rtol=1.e-10)
t0 = 0.
tn = 1300.
dt = model.critical_dt
nt = int(1 + (tn - t0) / dt)
time_axis = np.linspace(t0, tn, nt)
# Source
f1 = 0.008
src1 = RickerSource(name='src', grid=model.grid, f0=f1, time=time_axis)
src1.coordinates.data[0, :] = np.array(model.domain_size) * 0.5
src1.coordinates.data[0, -1] = 20.
# Receiver for observed data
rec_t = Receiver(name='rec_t', grid=model.grid, npoint=301, ntime=nt)
rec_t.coordinates.data[:, 0] = np.linspace(0., 3000., num=301)
rec_t.coordinates.data[:, 1] = 20.
# Test data and source
d_hat, u1, _ = forward(model, src1.coordinates.data, rec_t.coordinates.data,
src1.data)
# Adjoint
q0, _, _ = adjoint(model, d_hat, src1.coordinates.data, rec_t.coordinates.data)
# Adjoint test
a = inner(d_hat, d_hat)
b = inner(q0, src1)
print("Adjoint test F")
print("a = %2.2e, b = %2.2e, diff = %2.2e: " % (a, b, a - b))
print("Relative error: ", a / b - 1)
rec_t.coordinates.data,
src.data,
save=True)
# Forward
print("Forward")
_, u0, _ = forward(model,
src.coordinates.data,
rec_t.coordinates.data,
src.data,
save=True)
# gradient
print("Adjoint J")
dm_hat, _ = gradient(model, dD_hat, rec_t.coordinates.data, u0)
# Adjoint test
a = model.critical_dt * inner(dD_hat, dD_hat)
b = inner(dm_hat, model.dm)
if is_tti:
c = np.linalg.norm(u0[0].data.flatten() - u0l[0].data.flatten(), np.inf)
else:
c = np.linalg.norm(u0.data.flatten() - u0l.data.flatten(), np.inf)
print("Difference between saving with forward and born", c)
print("Adjoint test J")
print("a = %2.2e, b = %2.2e, diff = %2.2e: " % (a, b, a - b))
print("Relative error: ", a / b - 1)