def test_precomputed_interpolation_time():
""" Test interpolation with PrecomputedSparseFunction which accepts
precomputed values for interpolation coefficients, but this time
with a TimeFunction
"""
shape = (101, 101)
points = [(.05, .9), (.01, .8), (0.07, 0.84)]
origin = (0, 0)
grid = Grid(shape=shape, origin=origin)
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
u = TimeFunction(name='u', grid=grid, space_order=0, save=5)
for it in range(5):
u.data[it, :] = it
gridpoints, interpolation_coeffs = precompute_linear_interpolation(points,
grid, origin)
sf = PrecomputedSparseTimeFunction(name='s', grid=grid, r=r, npoint=len(points),
nt=5, gridpoints=gridpoints,
interpolation_coeffs=interpolation_coeffs)
assert sf.data.shape == (5, 3)
eqn = sf.interpolate(u)
op = Operator(eqn)
op(time_m=0, time_M=4)
for it in range(5):
assert np.allclose(sf.data[it, :], it)
def test_precomputed_interpolation_time():
""" Test interpolation with PrecomputedSparseFunction which accepts
precomputed values for interpolation coefficients, but this time
with a TimeFunction
"""
shape = (101, 101)
points = [(.05, .9), (.01, .8), (0.07, 0.84)]
origin = (0, 0)
grid = Grid(shape=shape, origin=origin)
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
u = TimeFunction(name='u', grid=grid, space_order=0, save=5)
for it in range(5):
u.data[it, :] = it
gridpoints, interpolation_coeffs = precompute_linear_interpolation(points,
grid, origin)
sf = PrecomputedSparseTimeFunction(name='s', grid=grid, r=r, npoint=len(points),
nt=5, gridpoints=gridpoints,
interpolation_coeffs=interpolation_coeffs)
assert sf.data.shape == (5, 3)
eqn = sf.interpolate(u)
op = Operator(eqn)
op(time_m=0, time_M=4)
for it in range(5):
assert all(np.isclose(sf.data[it, :], it))
def run(r, srcpd, layout):
initial_model_filename = "overthrust_3D_initial_model.h5"
tn = 5
so = 6
dtype = np.float32
datakey = "m0"
nbl = 40
dt = 1.75
time_axis = TimeAxis(start=0, stop=tn, step=dt)
nt = time_axis.num
model = overthrust_model_iso(initial_model_filename, datakey, so, nbl,
dtype)
shape = model.shape
grid = model.grid
origin = (0, 0, 0)
spacing = model.spacing
coeffs = kaiser(M=r, beta=6.31)
# What we accepted as a parameter was sources per dimension. We are going to lay them out on a grid so square the number
nsrc = srcpd * srcpd
if layout == 'grid':
src_coordinates = define_sources_grid(srcpd, model, r)
elif layout == 'hemisphere':
src_coordinates = define_sources_hemisphere(srcpd, model)
else:
print("Invalid layout: %s" % layout)
return
gridpoints = [
tuple((int(floor((point[i] - origin[i]) / grid.spacing[i])) - r / 2)
for i in range(len(point))) for point in src_coordinates
]
src = PrecomputedSparseTimeFunction(name="src",
grid=grid,
npoint=nsrc,
r=r,
gridpoints=gridpoints,
interpolation_coeffs=coeffs,
nt=nt)
ricker = RickerSource(time_range=time_axis,
grid=grid,
name="ricker",
f0=0.008)
for p in range(nsrc):
src.data[:, p] = ricker.wavelet
m = model.m
# Create symbols for forward wavefield, source and receivers
u = TimeFunction(name='u',
grid=grid,
save=None,
time_order=2,
space_order=so)
rec = Receiver(name='rec', grid=grid, time_range=time_axis, npoint=nsrc)
s = model.grid.stepping_dim.spacing
# Define PDE and update rule
eq_time = solve(model.m * u.dt2 - u.laplace + model.damp * u.dt, u.forward)
# Time-stepping stencil.
eqns = [
Eq(u.forward, eq_time, subdomain=model.grid.subdomains['physdomain'])
]
# Construct expression to inject source values
src_term = src.inject(field=u.forward, expr=src * s**2 / m)
# Create interpolation expression for receivers
rec_term = rec.interpolate(expr=u)
# Substitute spacing terms to reduce flops
op = Operator(eqns + src_term + rec_term,
subs=model.spacing_map,
name='Forward')
op.apply(dt=dt)
print("u_norm", np.linalg.norm(u.data))
