def test_interpolation_msf():
grid = Grid(shape=(4, 4))
r = 2 # Because we interpolate across 2 neighbouring points in each dimension
nt = 10
m0 = TimeFunction(name="m0",
grid=grid,
space_order=0,
save=nt,
time_order=0)
m1 = TimeFunction(name="m1",
grid=grid,
space_order=0,
save=nt,
time_order=0)
mat = scipy.sparse.coo_matrix((0, 0), dtype=np.float32)
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=mat, nt=nt)
eqns = sf.inject(field=m0.forward, expr=sf.dt2)
eqns += sf.inject(field=m1.forward, expr=sf.dt2)
op0 = Operator(eqns)
op1 = Operator(eqns, opt=('advanced', {'linearize': True}))
assert 'm0L0' in str(op1)
# There used to be a bug causing the jit compilation to fail because of
# the writing to `const int` variables
assert op0.cfunction
assert op1.cfunction
def test_precomputed_subpoints_inject_dt2(self):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
nt = 10
m = TimeFunction(name="m",
grid=grid,
space_order=0,
save=None,
time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
matrix = scipy.sparse.coo_matrix(np.array([[1], [1]],
dtype=np.float32))
sf = MatrixSparseTimeFunction(name="s",
grid=grid,
r=r,
matrix=matrix,
nt=nt,
time_order=2)
# Lookup the exact point
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.gridpoints.data[1, 0] = 39
sf.gridpoints.data[1, 1] = 39
sf.interpolation_coefficients[x].data[1, 0] = 1.0
sf.interpolation_coefficients[x].data[1, 1] = 2.0
sf.interpolation_coefficients[y].data[1, 0] = 1.0
sf.interpolation_coefficients[y].data[1, 1] = 2.0
# Single timestep, -0.5*1e-6, so that with dt=0.001, the .dt2 == 1 at t=1
sf.data[1, 0] = -5e-7
step = [Eq(m.forward, m)]
inject = sf.inject(field=m.forward, expr=sf.dt2)
op = Operator(step + inject)
sf.manual_scatter()
op(time_m=1, time_M=1, dt=0.001)
sf.manual_gather()
assert m.data[0, 40, 40] == pytest.approx(6.0) # 1 + 1 + 4
assert m.data[0, 40, 41] == pytest.approx(2.0)
assert m.data[0, 41, 40] == pytest.approx(2.0)
assert m.data[0, 41, 41] == pytest.approx(4.0)
assert m.data[0, 39, 39] == pytest.approx(1.0)
assert m.data[0, 39, 40] == pytest.approx(2.0)
assert m.data[0, 40, 39] == pytest.approx(2.0)
def test_msf_interpolate():
""" Test interpolation with MatrixSparseTimeFunction 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)
matrix = scipy.sparse.eye(len(points))
sf = MatrixSparseTimeFunction(
name='s', grid=grid, r=r, matrix=matrix, nt=5
)
sf.gridpoints.data[:] = gridpoints
sf.coefficients_x.data[:] = interpolation_coeffs[:, 0, :]
sf.coefficients_y.data[:] = interpolation_coeffs[:, 0, :]
assert sf.data.shape == (5, 3)
eqn = sf.interpolate(u)
op = Operator(eqn)
print(op)
sf.manual_scatter()
op(time_m=0, time_M=4)
sf.manual_gather()
for it in range(5):
assert np.allclose(sf.data[it, :], it)
# Now test injection
u.data[:] = 0
eqn_inject = sf.inject(field=u, expr=sf)
op2 = Operator(eqn_inject)
print(op2)
op2(time_m=0, time_M=4)
# There should be 4 points touched for each source point
# (5, 90), (1, 80), (7, 84) and x+1, y+1 for each
nzt, nzx, nzy = np.nonzero(u.data)
assert np.all(np.unique(nzx) == np.array([1, 2, 5, 6, 7, 8]))
assert np.all(np.unique(nzy) == np.array([80, 81, 84, 85, 90, 91]))
assert np.all(np.unique(nzt) == np.array([1, 2, 3, 4]))
# 12 points x 4 timesteps
assert nzt.size == 48
def test_precomputed_subpoints_inject(self):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
nt = 10
m = TimeFunction(name="m",
grid=grid,
space_order=0,
save=None,
time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
# Single two-component source with coefficients both +1
matrix = scipy.sparse.coo_matrix(np.array([[1], [1]],
dtype=np.float32))
sf = MatrixSparseTimeFunction(name="s",
grid=grid,
r=r,
matrix=matrix,
nt=nt)
# Lookup the exact point
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.gridpoints.data[1, 0] = 39
sf.gridpoints.data[1, 1] = 39
sf.interpolation_coefficients[x].data[1, 0] = 1.0
sf.interpolation_coefficients[x].data[1, 1] = 2.0
sf.interpolation_coefficients[y].data[1, 0] = 1.0
sf.interpolation_coefficients[y].data[1, 1] = 2.0
sf.data[0, 0] = 1.0
step = [Eq(m.forward, m)]
inject = sf.inject(field=m.forward, expr=sf)
op = Operator(step + inject)
sf.manual_scatter()
op(time_m=0, time_M=0)
sf.manual_gather()
assert m.data[1, 40, 40] == 6.0 # 1 + 1 + 4
assert m.data[1, 40, 41] == 2.0
assert m.data[1, 41, 40] == 2.0
assert m.data[1, 41, 41] == 4.0
assert m.data[1, 39, 39] == 1.0
assert m.data[1, 39, 40] == 2.0
assert m.data[1, 40, 39] == 2.0
def test_precomputed_subpoints_inject(self, rxy, par_dim_index):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
if isinstance(rxy, tuple):
r = {grid.dimensions[0]: rxy[0], grid.dimensions[1]: rxy[1]}
else:
r = rxy
par_dim = grid.dimensions[par_dim_index]
nt = 10
m = TimeFunction(name="m",
grid=grid,
space_order=0,
save=None,
time_order=1)
# Put some data in there to ensure it acts additively
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
# Single two-component source with coefficients both +1
matrix = scipy.sparse.coo_matrix(np.array([[1], [1]],
dtype=np.float32))
sf = MatrixSparseTimeFunction(name="s",
grid=grid,
r=r,
par_dim=par_dim,
matrix=matrix,
nt=nt)
coeff_size_x = sf.interpolation_coefficients[x].data.shape[1]
coeff_size_y = sf.interpolation_coefficients[y].data.shape[1]
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.gridpoints.data[1, 0] = 39
sf.gridpoints.data[1, 1] = 39
sf.interpolation_coefficients[x].data[
0, :] = 1.0 + np.arange(coeff_size_x)
sf.interpolation_coefficients[y].data[
0, :] = 1.0 + np.arange(coeff_size_y)
sf.interpolation_coefficients[x].data[
1, :] = 1.0 + np.arange(coeff_size_x)
sf.interpolation_coefficients[y].data[
1, :] = 1.0 + np.arange(coeff_size_y)
sf.data[0, 0] = 1.0
step = [Eq(m.forward, m)]
inject = sf.inject(field=m.forward, expr=sf)
op = Operator(step + inject)
sf.manual_scatter()
op(time_m=0, time_M=0)
sf.manual_gather()
check_coeffs = self._pure_python_coeffs(sf)
expected_data1 = (
m.data[0] +
np.tensordot(np.array(sf.data[0, :]), check_coeffs, axes=1))
assert np.all(m.data[1] == expected_data1)