def test_adjoint_inject_interpolate(self, shape, coords, npoints=19):
"""
Verify that p.inject is the adjoint of p.interpolate for a
devito SparseFunction p
"""
grid = Grid(shape)
a = Function(name="a", grid=grid)
a.data[:] = 0.
c = Function(name='c', grid=grid)
c.data[:] = 27.
assert a.grid == c.grid
# Inject receiver
p = SparseFunction(name="p", grid=grid, npoint=npoints)
for i, r in enumerate(coords):
p.coordinates.data[:, i] = np.linspace(r[0], r[1], npoints)
p.data[:] = 1.2
expr = p.inject(field=a, expr=p)
# Read receiver
p2 = SparseFunction(name="p2", grid=grid, npoint=npoints)
for i, r in enumerate(coords):
p2.coordinates.data[:, i] = np.linspace(r[0], r[1], npoints)
expr2 = p2.interpolate(expr=c)
Operator(expr + expr2)(a=a, c=c)
# < P x, y > - < x, P^T y>
# Px => p2
# y => p
# x => c
# P^T y => a
term1 = np.dot(p2.data.reshape(-1), p.data.reshape(-1))
term2 = np.dot(c.data.reshape(-1), a.data.reshape(-1))
assert np.isclose((term1-term2) / term1, 0., atol=1.e-6)
def test_scheduling_sparse_functions(self):
"""Tests loop scheduling in presence of sparse functions."""
grid = Grid((10, 10))
time = grid.time_dim
u1 = TimeFunction(name="u1", grid=grid, save=10, time_order=2)
u2 = TimeFunction(name="u2", grid=grid, time_order=2)
sf1 = SparseFunction(name='sf1', grid=grid, npoint=1, ntime=10)
sf2 = SparseFunction(name='sf2', grid=grid, npoint=1, ntime=10)
# Deliberately inject into u1, rather than u1.forward, to create a WAR w/ eqn3
eqn1 = Eq(u1.forward, u1 + 2.0 - u1.backward)
eqn2 = sf1.inject(u1, expr=sf1)
eqn3 = Eq(u2.forward, u2 + 2*u2.backward - u1.dt2)
eqn4 = sf2.interpolate(u2)
op = Operator([eqn1] + eqn2 + [eqn3] + eqn4)
trees = retrieve_iteration_tree(op)
assert len(trees) == 4
# Time loop not shared due to the WAR
assert trees[0][0].dim is time and trees[0][0] is trees[1][0] # this IS shared
assert trees[1][0] is not trees[2][0]
assert trees[2][0].dim is time and trees[2][0] is trees[3][0] # this IS shared
# Now single, shared time loop expected
eqn2 = sf1.inject(u1.forward, expr=sf1)
op = Operator([eqn1] + eqn2 + [eqn3] + eqn4)
trees = retrieve_iteration_tree(op)
assert len(trees) == 4
assert all(trees[0][0] is i[0] for i in trees)
def test_default_composite_functions(self):
"""
Test the default argument derivation for composite functions.
"""
grid = Grid(shape=(5, 6, 7))
f = TimeFunction(name='f', grid=grid)
s = SparseFunction(name='s', grid=grid, npoint=3, nt=4)
s.coordinates.data[:, 0] = np.arange(0., 3.)
s.coordinates.data[:, 1] = np.arange(1., 4.)
s.coordinates.data[:, 2] = np.arange(2., 5.)
op = Operator(s.interpolate(f))
expected = {
's': s.data,
's_coords': s.coordinates.data,
# Default dimensions of the sparse data
'p_size': 3,
'p_s': 0,
'p_e': 3,
'd_size': 3,
'p_s': 0,
'p_e': 3,
'time_size': 4,
'time_s': 0,
'time_e': 4,
}
self.verify_arguments(op.arguments(), expected)
def test_interpolation_wodup(self):
grid = Grid(shape=(4, 4), extent=(3.0, 3.0))
f = Function(name='f', grid=grid, space_order=0)
f.data[:] = 4.
if grid.distributor.myrank == 0:
coords = [(0.5, 0.5), (0.5, 2.5), (2.5, 0.5), (2.5, 2.5)]
else:
coords = []
sf = SparseFunction(name='sf',
grid=grid,
npoint=len(coords),
coordinates=coords)
sf.data[:] = 0.
# This is the situation at this point
# O is a grid point
# * is a sparse point
#
# O --- O --- O --- O
# | * | | * |
# O --- O --- O --- O
# | | | |
# O --- O --- O --- O
# | * | | * |
# O --- O --- O --- O
op = Operator(sf.interpolate(expr=f))
op.apply()
assert np.all(sf.data == 4.)
def test_interpolation_dup(self):
"""
Test interpolation operator when the sparse points are replicated over
multiple MPI ranks.
"""
grid = Grid(shape=(4, 4), extent=(3.0, 3.0))
x, y = grid.dimensions
# Init Function+data
f = Function(name='f', grid=grid)
f.data[:] = np.array([[1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3],
[4, 4, 4, 4]])
coords = np.array([(0.5, 0.5), (1.5, 2.5), (1.5, 1.5), (2.5, 1.5)])
sf = SparseFunction(name='sf',
grid=grid,
npoint=len(coords),
coordinates=coords)
sf.data[:] = 0.
# Global view (left) and local view (right, after domain decomposition)
# O is a grid point
# x is a halo point
# A, B, C, D are sparse points
# Rank0 Rank1
# O --- O --- O --- O O --- O --- x x --- O --- O
# | A | | | | A | | | | |
# O --- O --- O --- O O --- O --- x x --- O --- O
# | | C | B | --> | | C | | C | B |
# O --- O --- O --- O x --- x --- x x --- x --- x
# | | D | | Rank2 Rank3
# O --- O --- O --- O x --- x --- x x --- x --- x
# | | C | | C | B |
# O --- O --- x x --- O --- O
# | | D | | D | |
# O --- O --- x x --- O --- O
#
# The initial `f.data` is (global view)
#
# 1. --- 1. --- 1. --- 1.
# | | | |
# 2. --- 2. --- 2. --- 2.
# | | | |
# 3. --- 3. --- 3. --- 3.
# | | | |
# 4. --- 4. --- 4. --- 4.
#
# Expected `sf.data` (global view)
#
# 1.5 --- 2.5 --- 2.5 --- 3.5
op = Operator(sf.interpolate(expr=f))
op.apply()
assert np.all(sf.data == [1.5, 2.5, 2.5, 3.5][grid.distributor.myrank])
def test_edge_sparse():
"""
Test that interpolation uses the correct point for the edge case
where the sparse point is at the origin with non rational grid spacing.
Due to round up error the interpolation would use the halo point instead of
the point (0, 0) without the factorizaion of the expressions.
"""
grid = Grid(shape=(16, 16), extent=(225., 225.), origin=(25., 35.))
u = unit_box(shape=(16, 16), grid=grid)
u._data_with_outhalo[:u.space_order, :] = -1
u._data_with_outhalo[:, :u.space_order] = -1
sf1 = SparseFunction(name='s', grid=u.grid, npoint=1)
sf1.coordinates.data[0, :] = (25.0, 35.0)
expr = sf1.interpolate(u)
subs = {d.spacing: v for d, v in zip(u.grid.dimensions, u.grid.spacing)}
op = Operator(expr, subs=subs)
op()
assert sf1.data[0] == 0
def test_interpolation_dx():
"""
Test interpolation of a SparseFunction from a Derivative of
a Function.
"""
u = unit_box(shape=(11, 11))
sf1 = SparseFunction(name='s', grid=u.grid, npoint=1)
sf1.coordinates.data[0, :] = (0.5, 0.5)
op = Operator(sf1.interpolate(u.dx))
assert sf1.data.shape == (1, )
u.data[:] = 0.0
u.data[5, 5] = 4.0
u.data[4, 5] = 2.0
u.data[6, 5] = 2.0
op.apply()
# Exactly in the middle of 4 points, only 1 nonzero is 4
assert sf1.data[0] == pytest.approx(-20.0)
def test_operator_leakage_sparse():
"""
Test to ensure that :class:`Operator` creation does not cause
memory leaks for :class:`SparseFunction` symbols.
"""
grid = Grid(shape=(5, 6))
a = Function(name='a', grid=grid)
s = SparseFunction(name='s', grid=grid, npoint=1, nt=1)
w_a = weakref.ref(a)
w_s = weakref.ref(s)
# Create operator and delete everything again
op = Operator(s.interpolate(a))
w_op = weakref.ref(op)
del op
del s
del a
clear_cache()
# Test whether things are still hanging around
assert w_a() is None
assert w_s() is None
assert w_op() is None
def test_interpolation_dup(self):
"""
Test interpolation operator when the sparse points are replicated over
multiple MPI ranks.
"""
grid = Grid(shape=(4, 4), extent=(3.0, 3.0))
x, y = grid.dimensions
# Init Function+data
f = Function(name='f', grid=grid)
glb_pos_map = grid.distributor.glb_pos_map
if LEFT in glb_pos_map[x]:
f.data[:] = [[1., 1.], [2., 2.]]
else:
f.data[:] = [[3., 3.], [4., 4.]]
if grid.distributor.myrank == 0:
coords = [(0.5, 0.5), (1.5, 2.5), (1.5, 1.5), (2.5, 1.5)]
else:
coords = []
sf = SparseFunction(name='sf',
grid=grid,
npoint=len(coords),
coordinates=coords)
sf.data[:] = 0.
# Global view (left) and local view (right, after domain decomposition)
# O is a grid point
# x is a halo point
# A, B, C, D are sparse points
# Rank0 Rank1
# O --- O --- O --- O O --- O --- x x --- O --- O
# | A | | | | A | | | | |
# O --- O --- O --- O O --- O --- x x --- O --- O
# | | C | B | --> | | C | | C | B |
# O --- O --- O --- O x --- x --- x x --- x --- x
# | | D | | Rank2 Rank3
# O --- O --- O --- O x --- x --- x x --- x --- x
# | | C | | C | B |
# O --- O --- x x --- O --- O
# | | D | | D | |
# O --- O --- x x --- O --- O
#
# The initial `f.data` is (global view)
#
# 1. --- 1. --- 1. --- 1.
# | | | |
# 2. --- 2. --- 2. --- 2.
# | | | |
# 3. --- 3. --- 3. --- 3.
# | | | |
# 4. --- 4. --- 4. --- 4.
#
# Expected `sf.data` (global view)
#
# 1.5 --- 2.5 --- 2.5 --- 3.5
op = Operator(sf.interpolate(expr=f))
op.apply()
if grid.distributor.myrank == 0:
assert np.all(sf.data == [1.5, 2.5, 2.5, 3.5])
else:
assert sf.data.size == 0