def test_no_index(self):
"""Test behaviour when the ConditionalDimension is used as a symbol in
an expression."""
nt = 19
grid = Grid(shape=(11, 11))
time = grid.time_dim
u = TimeFunction(name='u', grid=grid)
assert(grid.stepping_dim in u.indices)
v = Function(name='v', grid=grid)
factor = 4
time_subsampled = ConditionalDimension('t_sub', parent=time, factor=factor)
eqns = [Eq(u.forward, u + 1), Eq(v, v + u*u*time_subsampled)]
op = Operator(eqns)
op.apply(t_M=nt-2)
assert np.all(np.allclose(u.data[(nt-1) % 3], nt-1))
# expected result is 1024
# v = u[0]**2 * 0 + u[4]**2 * 1 + u[8]**2 * 2 + u[12]**2 * 3 + u[16]**2 * 4
# with u[t] = t
# v = 16 * 1 + 64 * 2 + 144 * 3 + 256 * 4 = 1600
assert np.all(np.allclose(v.data, 1600))
def test_halo_indexing(self):
"""
Tests packing/unpacking data in :class:`Function` objects when some halo
region is present.
"""
domain_shape = (16, 16, 16)
grid = Grid(shape=domain_shape)
u = Function(name='yu3D', grid=grid, space_order=2)
assert u.shape == u.data.shape == domain_shape
assert u._shape_with_inhalo == u.data_with_halo.shape == (20, 20, 20)
assert u.shape_with_halo == u._shape_with_inhalo # W/o MPI, these two coincide
# Test simple insertion and extraction
u.data_with_halo[0, 0, 0] = 1.
u.data[0, 0, 0] = 2.
assert u.data_with_halo[0, 0, 0] == 1.
assert u.data[0, 0, 0] == 2.
assert u.data_with_halo[2, 2, 2] == 2.
# Test negative indices
u.data_with_halo[-1, -1, -1] = 3.
assert u.data[-1, -1, -1] == 0.
assert u.data_with_halo[-1, -1, -1] == 3.
def test_function_wo(self):
grid = Grid(shape=(3, 3, 3))
i = Dimension(name='i')
f = Function(name='f', shape=(1, ), dimensions=(i, ), grid=grid)
u = TimeFunction(name='u', grid=grid)
eqns = [Eq(u.forward, u + 1), Eq(f[0], u[0, 0, 0, 0])]
op = Operator(eqns, opt='noop')
assert len(op.body[1].header) == 2
assert len(op.body[1].footer) == 2
assert op.body[1].header[0].value ==\
('omp target enter data map(to: u[0:u_vec->size[0]]'
'[0:u_vec->size[1]][0:u_vec->size[2]][0:u_vec->size[3]])')
assert str(op.body[1].header[1]) == ''
assert str(op.body[1].footer[0]) == ''
assert op.body[1].footer[1].contents[0].value ==\
('omp target update from(u[0:u_vec->size[0]]'
'[0:u_vec->size[1]][0:u_vec->size[2]][0:u_vec->size[3]])')
assert op.body[1].footer[1].contents[1].value ==\
('omp target exit data map(release: u[0:u_vec->size[0]]'
'[0:u_vec->size[1]][0:u_vec->size[2]][0:u_vec->size[3]])')
def test_subdimleft_notparallel(self):
"""
Tests application of an Operator consisting of a subdimension
defined over different sub-regions, explicitly created through the
use of SubDimensions.
This tests that flow direction is not being automatically inferred
from whether the subdimension is on the left or right boundary.
"""
grid = Grid(shape=(20, 20))
x, y = grid.dimensions
t = grid.stepping_dim
thickness = 4
u = TimeFunction(name='u', save=None, grid=grid, space_order=1, time_order=0)
xl = SubDimension.left(name='xl', parent=x, thickness=thickness)
yi = SubDimension.middle(name='yi', parent=y,
thickness_left=thickness, thickness_right=thickness)
# Flows inward (i.e. forward) rather than outward
eq = Eq(u[t+1, xl, yi], u[t+1, xl-1, yi] + 1)
op = Operator([eq])
iterations = FindNodes(Iteration).visit(op)
assert all(i.is_Affine and i.is_Sequential for i in iterations if i.dim == xl)
assert all(i.is_Affine and i.is_Parallel for i in iterations if i.dim == yi)
op.apply(time_m=1, time_M=1)
assert all(np.all(u.data[0, :thickness, thickness+i] == [1, 2, 3, 4])
for i in range(12))
assert np.all(u.data[0, thickness:] == 0)
assert np.all(u.data[0, :, thickness+12:] == 0)
def test_empty_arrays(self):
"""
MFE for issue #1641.
"""
grid = Grid(shape=(4, 4), extent=(3.0, 3.0))
f = TimeFunction(name='f', grid=grid, space_order=0)
f.data[:] = 1.
sf1 = SparseTimeFunction(name='sf1', grid=grid, npoint=0, nt=10)
sf2 = SparseTimeFunction(name='sf2', grid=grid, npoint=0, nt=10)
assert sf1.size == 0
assert sf2.size == 0
eqns = sf1.inject(field=f, expr=sf1 + sf2 + 1.)
op = Operator(eqns)
op.apply()
assert np.all(f.data == 1.)
# Again, but with a MatrixSparseTimeFunction
mat = scipy.sparse.coo_matrix((0, 0), dtype=np.float32)
sf = MatrixSparseTimeFunction(name="s",
grid=grid,
r=2,
matrix=mat,
nt=10)
assert sf.size == 0
eqns = sf.interpolate(f)
op = Operator(eqns)
sf.manual_scatter()
op(time_m=0, time_M=9)
sf.manual_gather()
assert np.all(f.data == 1.)
def test_precomputed_interpolation():
""" Test interpolation with PrecomputedSparseFunction which accepts
precomputed values for coefficients
"""
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
def init(data):
for i in range(data.shape[0]):
for j in range(data.shape[1]):
data[i,
j] = sin(grid.spacing[0] * i) + sin(grid.spacing[1] * j)
return data
m = Function(name='m', grid=grid, initializer=init, space_order=0)
gridpoints, coefficients = precompute_linear_interpolation(
points, grid, origin)
sf = PrecomputedSparseFunction(name='s',
grid=grid,
r=r,
npoint=len(points),
gridpoints=gridpoints,
coefficients=coefficients)
eqn = sf.interpolate(m)
op = Operator(eqn)
op()
expected_values = [sin(point[0]) + sin(point[1]) for point in points]
assert (all(np.isclose(sf.data, expected_values, rtol=1e-6)))
def test_simple_indexing(self):
"""Test data packing/unpacking via basic indexing."""
grid = Grid(shape=(16, 16, 16))
u = Function(name='yu3D', grid=grid, space_order=0)
# Test simple insertion and extraction
u.data[0, 1, 1] = 1.
assert u.data[0, 0, 0] == 0.
assert u.data[0, 1, 1] == 1.
assert np.all(u.data == u.data[:, :, :])
assert 1. in u.data[0]
assert 1. in u.data[0, 1]
# Test negative indices
assert u.data[0, -15, -15] == 1.
u.data[6, 0, 0] = 1.
assert u.data[-10, :, :].sum() == 1.
# Test setting whole array to given value
u.data[:] = 3.
assert np.all(u.data == 3.)
# Test insertion of single value into block
u.data[5, :, 5] = 5.
assert np.all(u.data[5, :, 5] == 5.)
# Test extraction of block with negative indices
sliced = u.data[-11, :, -11]
assert sliced.shape == (16, )
assert np.all(sliced == 5.)
# Test insertion of block into block
block = np.ndarray(shape=(1, 16, 1), dtype=np.float32)
block.fill(4.)
u.data[4:5, :, 4:5] = block
assert np.all(u.data[4, :, 4] == block)
def __init__(self,
origin,
spacing,
shape,
space_order,
nbpml=20,
dtype=np.float32):
self.shape = shape
self.nbpml = int(nbpml)
self.origin = tuple([dtype(o) for o in origin])
# Origin of the computational domain with PML to inject/interpolate
# at the correct index
origin_pml = tuple(
[dtype(o - s * nbpml) for o, s in zip(origin, spacing)])
phydomain = PhysicalDomain(self.nbpml)
shape_pml = np.array(shape) + 2 * self.nbpml
# Physical extent is calculated per cell, so shape - 1
extent = tuple(np.array(spacing) * (shape_pml - 1))
self.grid = Grid(extent=extent,
shape=shape_pml,
origin=origin_pml,
dtype=dtype,
subdomains=phydomain)
def test_tasking_fused(self):
nt = 10
bundle0 = Bundle()
grid = Grid(shape=(10, 10, 10), subdomains=bundle0)
tmp = Function(name='tmp', grid=grid)
u = TimeFunction(name='u', grid=grid, save=nt)
v = TimeFunction(name='v', grid=grid, save=nt)
w = TimeFunction(name='w', grid=grid)
eqns = [Eq(w.forward, w + 1),
Eq(tmp, w.forward),
Eq(u.forward, tmp, subdomain=bundle0),
Eq(v.forward, tmp, subdomain=bundle0)]
op = Operator(eqns, opt=('tasking', 'fuse', 'orchestrate'))
# Check generated code
assert len(retrieve_iteration_tree(op)) == 5
locks = [i for i in FindSymbols().visit(op) if isinstance(i, Lock)]
assert len(locks) == 1 # Only 1 because it's only `tmp` that needs protection
assert len(op._func_table) == 2
exprs = FindNodes(Expression).visit(op._func_table['copy_device_to_host0'].root)
assert len(exprs) == 19
assert str(exprs[12]) == 'int id = sdata0->id;'
assert str(exprs[13]) == 'const int time = sdata0->time;'
assert str(exprs[14]) == 'lock0[0] = 1;'
assert exprs[15].write is u
assert exprs[16].write is v
assert str(exprs[17]) == 'lock0[0] = 2;'
assert str(exprs[18]) == 'sdata0->flag = 1;'
op.apply(time_M=nt-2)
assert np.all(u.data[nt-1] == 9)
assert np.all(v.data[nt-1] == 9)
def test_subdimensions(self):
nt = 10
grid = Grid(shape=(10, 10, 10))
x, y, z = grid.dimensions
xi = SubDimension.middle(name='xi', parent=x, thickness_left=2, thickness_right=2)
yi = SubDimension.middle(name='yi', parent=y, thickness_left=2, thickness_right=2)
zi = SubDimension.middle(name='zi', parent=z, thickness_left=2, thickness_right=2)
u = TimeFunction(name='u', grid=grid, save=nt)
u1 = TimeFunction(name='u', grid=grid, save=nt)
eqn = Eq(u.forward, u + 1).xreplace({x: xi, y: yi, z: zi})
op0 = Operator(eqn, opt='noop')
op1 = Operator(eqn, opt='buffering')
# Check generated code
assert len(retrieve_iteration_tree(op1)) == 2
assert len([i for i in FindSymbols().visit(op1) if i.is_Array]) == 1
op0.apply(time_M=nt-2)
op1.apply(time_M=nt-2, u=u1)
assert np.all(u.data == u1.data)
def test_composite_full(self):
nt = 10
grid = Grid(shape=(4, 4))
u = TimeFunction(name='u', grid=grid, save=nt)
v = TimeFunction(name='v', grid=grid, save=nt)
u1 = TimeFunction(name='u', grid=grid, save=nt)
v1 = TimeFunction(name='v', grid=grid, save=nt)
eqns = [Eq(u.forward, u + v + 1),
Eq(v.forward, u + v + v.backward)]
op0 = Operator(eqns, opt=('noop', {'gpu-fit': (u, v)}))
op1 = Operator(eqns, opt=('buffering', 'tasking', 'streaming', 'orchestrate'))
# Check generated code
assert len(retrieve_iteration_tree(op1)) == 9
assert len([i for i in FindSymbols().visit(op1) if isinstance(i, Lock)]) == 2
op0.apply(time_M=nt-2)
op1.apply(time_M=nt-2, u=u1, v=v1)
assert np.all(u.data == u1.data)
assert np.all(v.data == v1.data)
def test_streaming_postponed_deletion(self):
nt = 10
grid = Grid(shape=(10, 10, 10))
u = TimeFunction(name='u', grid=grid)
v = TimeFunction(name='v', grid=grid)
usave = TimeFunction(name='usave', grid=grid, save=nt)
u1 = TimeFunction(name='u', grid=grid)
v1 = TimeFunction(name='v', grid=grid)
for i in range(nt):
usave.data[i, :] = i
eqns = [Eq(u.forward, u + usave),
Eq(v.forward, v + u.forward.dx + usave)]
op0 = Operator(eqns, opt=('noop', {'gpu-fit': usave}))
op1 = Operator(eqns, opt=('streaming', 'orchestrate'))
op0.apply(time_M=nt-1)
op1.apply(time_M=nt-1, u=u1, v=v1)
assert np.all(u.data == u1.data)
assert np.all(v.data == v1.data)
def test_shape(self):
class sd0(SubDomain):
name = 'd0'
def define(self, dimensions):
x, y = dimensions
return {x: ('middle', 1, 6), y: ('middle', 1, 1)}
s_d0 = sd0()
class sd1(SubDomain):
name = 'd1'
def define(self, dimensions):
x, y = dimensions
return {x: ('right', 4), y: ('left', 2)}
s_d1 = sd1()
class sd2(SubDomain):
name = 'd2'
def define(self, dimensions):
x, y = dimensions
return {x: ('left', 3), y: ('middle', 1, 2)}
s_d2 = sd2()
grid = Grid(shape=(10, 10), subdomains=(s_d0, s_d1, s_d2))
assert grid.subdomains['domain'].shape == (10, 10)
assert grid.subdomains['interior'].shape == (8, 8)
assert grid.subdomains['d0'].shape == (3, 8)
assert grid.subdomains['d1'].shape == (4, 2)
assert grid.subdomains['d2'].shape == (3, 7)
def test_basic(self):
grid = Grid(shape=(3, 3, 3))
u = TimeFunction(name='u', grid=grid)
op = Operator(Eq(u.forward, u + 1),
platform='nvidiaX',
language='openacc')
trees = retrieve_iteration_tree(op)
assert len(trees) == 1
assert trees[0][1].pragmas[0].value ==\
'acc parallel loop collapse(3)'
assert op.body[1].header[0].value ==\
('acc enter data copyin(u[0:u_vec->size[0]]'
'[0:u_vec->size[1]][0:u_vec->size[2]][0:u_vec->size[3]])')
assert str(op.body[1].footer[0]) == ''
assert op.body[1].footer[1].contents[0].value ==\
('acc exit data copyout(u[0:u_vec->size[0]]'
'[0:u_vec->size[1]][0:u_vec->size[2]][0:u_vec->size[3]])')
assert op.body[1].footer[1].contents[1].value ==\
('acc exit data delete(u[0:u_vec->size[0]]'
'[0:u_vec->size[1]][0:u_vec->size[2]][0:u_vec->size[3]])')
def __init__(self,
origin,
spacing,
shape,
space_order,
nbl=20,
dtype=np.float32,
subdomains=(),
damp_mask=False):
self.shape = shape
self.nbl = int(nbl)
self.origin = tuple([dtype(o) for o in origin])
# Origin of the computational domain with boundary to inject/interpolate
# at the correct index
origin_pml = tuple(
[dtype(o - s * nbl) for o, s in zip(origin, spacing)])
phydomain = PhysicalDomain(self.nbl)
subdomains = subdomains + (phydomain, )
shape_pml = np.array(shape) + 2 * self.nbl
# Physical extent is calculated per cell, so shape - 1
extent = tuple(np.array(spacing) * (shape_pml - 1))
self.grid = Grid(extent=extent,
shape=shape_pml,
origin=origin_pml,
dtype=dtype,
subdomains=subdomains)
if self.nbl != 0:
# Create dampening field as symbol `damp`
self.damp = Function(name="damp", grid=self.grid)
initialize_damp(self.damp, self.nbl, self.spacing, mask=damp_mask)
self._physical_parameters = ['damp']
else:
self.damp = 1 if damp_mask else 0
self._physical_parameters = []
def test_dimension_sort(self, expr, expected):
"""
Tests that ``dimension_sort()`` provides meaningful Dimension orderings.
"""
grid = Grid(shape=(10, 10))
p = Dimension('p')
r = Dimension('r')
d = Dimension('d')
time = grid.time_dim # noqa
x, y = grid.dimensions
a = Function(name='a', dimensions=(time, p), shape=(10, 1)) # noqa
b = Function(name='b', dimensions=(time, x, y),
shape=(10, 10, 10)) # noqa
c = Function(
name='c',
shape=(1, 2), # noqa
dimensions=(p, d),
dtype=np.int32)
f = Function(name='f', dimensions=(p, r), shape=(1, 1)) # noqa
expr = eval(expr)
assert list(dimension_sort(expr)) == eval(expected)
def test_iteration_parallelism_3d(self, exprs, atomic, parallel):
"""Tests detection of PARALLEL_* properties."""
grid = Grid(shape=(10, 10, 10))
time = grid.time_dim # noqa
t = grid.stepping_dim # noqa
x, y, z = grid.dimensions # noqa
p = Dimension(name='p')
d = Dimension(name='d')
rx = Dimension(name='rx')
ry = Dimension(name='ry')
rz = Dimension(name='rz')
u = Function(name='u', grid=grid) # noqa
v = TimeFunction(name='v', grid=grid, save=None) # noqa
cx = Function(name='coeff_x', dimensions=(p, rx), shape=(1, 2)) # noqa
cy = Function(name='coeff_y', dimensions=(p, ry), shape=(1, 2)) # noqa
cz = Function(name='coeff_z', dimensions=(p, rz), shape=(1, 2)) # noqa
gp = Function(name='gridpoints', dimensions=(p, d), shape=(1, 3)) # noqa
src = Function(name='src', dimensions=(p,), shape=(1,)) # noqa
rcv = Function(name='rcv', dimensions=(time, p), shape=(100, 1), space_order=0) # noqa
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = eval(e)
# Use 'openmp' here instead of 'advanced' to disable loop blocking
op = Operator(exprs, dle='openmp')
iters = FindNodes(Iteration).visit(op)
assert all([i.is_ParallelAtomic for i in iters if i.dim.name in atomic])
assert all([not i.is_ParallelAtomic for i in iters if i.dim.name not in atomic])
assert all([i.is_Parallel for i in iters if i.dim.name in parallel])
assert all([not i.is_Parallel for i in iters if i.dim.name not in parallel])
def test_shifted(self):
nt = 19
grid = Grid(shape=(11, 11))
time = grid.time_dim
u = TimeFunction(name='u', grid=grid)
assert (grid.stepping_dim in u.indices)
u2 = TimeFunction(name='u2', grid=grid, save=nt)
assert (time in u2.indices)
factor = 4
time_subsampled = ConditionalDimension('t_sub',
parent=time,
factor=factor)
usave = TimeFunction(name='usave',
grid=grid,
save=2,
time_dim=time_subsampled)
assert (time_subsampled in usave.indices)
t_sub_shift = Constant(name='t_sub_shift', dtype=np.int32)
eqns = [
Eq(u.forward, u + 1.),
Eq(u2.forward, u2 + 1.),
Eq(usave.subs(time_subsampled, time_subsampled - t_sub_shift), u)
]
op = Operator(eqns)
# Starting at time_m=10, so time_subsampled - t_sub_shift is in range
op.apply(time_m=10, time_M=nt - 2, t_sub_shift=3)
assert np.all(np.allclose(u.data[0], 8))
assert np.all([np.allclose(u2.data[i], i - 10) for i in range(10, nt)])
assert np.all(
[np.allclose(usave.data[i], 2 + i * factor) for i in range(2)])
def test_array_reduction(self, so, dim):
"""
Test generation of OpenMP reduction clauses involving Function's.
"""
grid = Grid(shape=(3, 3, 3))
d = grid.dimensions[dim]
f = Function(name='f', shape=(3,), dimensions=(d,), grid=grid, space_order=so)
u = TimeFunction(name='u', grid=grid)
op = Operator(Inc(f, u + 1), opt=('openmp', {'par-collapse-ncores': 1}))
iterations = FindNodes(Iteration).visit(op)
assert "reduction(+:f[0:f_vec->size[0]])" in iterations[1].pragmas[0].value
try:
op(time_M=1)
except:
# Older gcc <6.1 don't support reductions on array
info("Un-supported older gcc version for array reduction")
assert True
return
assert np.allclose(f.data, 18)
def test_streaming_two_buffers(self, opt, ntmps, nfuncs):
nt = 10
grid = Grid(shape=(4, 4))
u = TimeFunction(name='u', grid=grid)
usave = TimeFunction(name='usave', grid=grid, save=nt)
vsave = TimeFunction(name='vsave', grid=grid, save=nt)
for i in range(nt):
usave.data[i, :] = i
vsave.data[i, :] = i
eqn = Eq(u.forward, u + usave + vsave)
op = Operator(eqn, opt=opt)
# Check generated code
assert len(op._func_table) == nfuncs
assert len([i for i in FindSymbols().visit(op) if i.is_Array]) == ntmps
op.apply(time_M=nt - 2)
assert np.all(u.data[0] == 56)
assert np.all(u.data[1] == 72)
def test_multiple_subnests_v1(self):
"""
Unlike ``test_multiple_subnestes_v0``, now we use the ``cire-rotate=True``
option, which trades some of the inner parallelism for a smaller working set.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions
t = grid.stepping_dim
f = Function(name='f', grid=grid)
u = TimeFunction(name='u', grid=grid, space_order=3)
eqn = Eq(u.forward, ((u[t, x, y, z] + u[t, x+1, y+1, z+1])*3*f +
(u[t, x+2, y+2, z+2] + u[t, x+3, y+3, z+3])*3*f + 1))
op = Operator(eqn, opt=('advanced', {'openmp': True,
'cire-mincost-sops': 1,
'cire-rotate': True,
'par-nested': 0,
'par-collapse-ncores': 1,
'par-dynamic-work': 0}))
trees = retrieve_iteration_tree(op._func_table['bf0'].root)
assert len(trees) == 2
assert trees[0][0] is trees[1][0]
assert trees[0][0].pragmas[0].value ==\
'omp for collapse(2) schedule(dynamic,1)'
assert not trees[0][2].pragmas
assert not trees[0][3].pragmas
assert trees[0][4].pragmas[0].value == ('omp parallel for collapse(1) '
'schedule(dynamic,1) '
'num_threads(nthreads_nested)')
assert not trees[1][2].pragmas
assert trees[1][3].pragmas[0].value == ('omp parallel for collapse(1) '
'schedule(dynamic,1) '
'num_threads(nthreads_nested)')
def test_injection_wodup_wtime(self):
"""
Just like ``test_injection_wodup``, but using a SparseTimeFunction
instead of a SparseFunction. Hence, the data scattering/gathering now
has to correctly pack/unpack multidimensional arrays.
"""
grid = Grid(shape=(4, 4), extent=(3.0, 3.0))
save = 3
f = TimeFunction(name='f', grid=grid, save=save, space_order=0)
f.data[:] = 0.
coords = np.array([(0.5, 0.5), (0.5, 2.5), (2.5, 0.5), (2.5, 2.5)])
sf = SparseTimeFunction(name='sf', grid=grid, nt=save,
npoint=len(coords), coordinates=coords)
sf.data[0, :] = 4.
sf.data[1, :] = 8.
sf.data[2, :] = 12.
op = Operator(sf.inject(field=f, expr=sf + 1))
op.apply()
assert np.all(f.data[0] == 1.25)
assert np.all(f.data[1] == 2.25)
assert np.all(f.data[2] == 3.25)
def test_operator_leakage_function():
"""
Test to ensure that Operator creation does not cause memory leaks for (Time)Functions.
"""
grid = Grid(shape=(5, 6))
f = Function(name='f', grid=grid)
g = TimeFunction(name='g', grid=grid)
# Take weakrefs to test whether symbols are dead or alive
w_f = weakref.ref(f)
w_g = weakref.ref(g)
# Create operator and delete everything again
op = Operator(Eq(f, 2 * g))
w_op = weakref.ref(op)
del op
del f
del g
clear_cache()
# Test whether things are still hanging around
assert w_f() is None
assert w_g() is None
assert w_op() is None
def test_bcs(self):
"""
Tests application of an Operator consisting of multiple equations
defined over different sub-regions, explicitly created through the
use of SubDimensions.
"""
grid = Grid(shape=(20, 20))
x, y = grid.dimensions
t = grid.stepping_dim
thickness = 4
u = TimeFunction(name='u', save=None, grid=grid, space_order=0, time_order=1)
xleft = SubDimension.left(name='xleft', parent=x, thickness=thickness)
xi = SubDimension.middle(name='xi', parent=x,
thickness_left=thickness, thickness_right=thickness)
xright = SubDimension.right(name='xright', parent=x, thickness=thickness)
yi = SubDimension.middle(name='yi', parent=y,
thickness_left=thickness, thickness_right=thickness)
t_in_centre = Eq(u[t+1, xi, yi], 1)
leftbc = Eq(u[t+1, xleft, yi], u[t+1, xleft+1, yi] + 1)
rightbc = Eq(u[t+1, xright, yi], u[t+1, xright-1, yi] + 1)
op = Operator([t_in_centre, leftbc, rightbc])
op.apply(time_m=1, time_M=1)
assert np.all(u.data[0, :, 0:thickness] == 0.)
assert np.all(u.data[0, :, -thickness:] == 0.)
assert all(np.all(u.data[0, i, thickness:-thickness] == (thickness+1-i))
for i in range(thickness))
assert all(np.all(u.data[0, -i, thickness:-thickness] == (thickness+2-i))
for i in range(1, thickness + 1))
assert np.all(u.data[0, thickness:-thickness, thickness:-thickness] == 1.)
def test_symbolic_factor(self):
"""
Test ConditionalDimension with symbolic factor (provided as a Constant).
"""
g = Grid(shape=(4, 4, 4))
u = TimeFunction(name='u', grid=g, time_order=0)
fact = Constant(name='fact', dtype=np.int32, value=4)
tsub = ConditionalDimension(name='tsub', parent=g.time_dim, factor=fact)
usave = TimeFunction(name='usave', grid=g, time_dim=tsub, save=4)
op = Operator([Eq(u, u + 1), Eq(usave, u)])
op.apply(time=7) # Use `fact`'s default value, 4
assert np.all(usave.data[0] == 1)
assert np.all(usave.data[1] == 5)
u.data[:] = 0.
op.apply(time=7, fact=2)
assert np.all(usave.data[0] == 1)
assert np.all(usave.data[1] == 3)
assert np.all(usave.data[2] == 5)
assert np.all(usave.data[3] == 7)
def test_basic(self):
nt = 19
grid = Grid(shape=(11, 11))
time = grid.time_dim
u = TimeFunction(name='u', grid=grid)
assert(grid.stepping_dim in u.indices)
u2 = TimeFunction(name='u2', grid=grid, save=nt)
assert(time in u2.indices)
factor = 4
time_subsampled = ConditionalDimension('t_sub', parent=time, factor=factor)
usave = TimeFunction(name='usave', grid=grid, save=(nt+factor-1)//factor,
time_dim=time_subsampled)
assert(time_subsampled in usave.indices)
eqns = [Eq(u.forward, u + 1.), Eq(u2.forward, u2 + 1.), Eq(usave, u)]
op = Operator(eqns)
op.apply(t_M=nt-2)
assert np.all(np.allclose(u.data[(nt-1) % 3], nt-1))
assert np.all([np.allclose(u2.data[i], i) for i in range(nt)])
assert np.all([np.allclose(usave.data[i], i*factor)
for i in range((nt+factor-1)//factor)])
def test_subdim_middle(self):
"""
Tests that instantiating SubDimensions using the classmethod
constructors works correctly.
"""
grid = Grid(shape=(4, 4, 4))
x, y, z = grid.dimensions
t = grid.stepping_dim # noqa
u = TimeFunction(name='u', grid=grid) # noqa
xi = SubDimension.middle(name='xi',
parent=x,
thickness_left=1,
thickness_right=1)
eqs = [Eq(u.forward, u + 1)]
eqs = [e.subs(x, xi) for e in eqs]
op = Operator(eqs)
u.data[:] = 1.0
op.apply(time_M=1)
assert np.all(u.data[1, 0, :, :] == 1)
assert np.all(u.data[1, -1, :, :] == 1)
assert np.all(u.data[1, 1:3, :, :] == 2)
def test_at_is_actually_working(shape, expected):
"""
Check that autotuning is actually running when switched on,
in both 2D and 3D operators.
"""
grid = Grid(shape=shape)
infield = Function(name='infield', grid=grid)
infield.data[:] = np.arange(reduce(mul, shape), dtype=np.int32).reshape(shape)
outfield = Function(name='outfield', grid=grid)
stencil = Eq(outfield.indexify(), outfield.indexify() + infield.indexify()*3.0)
op = Operator(stencil, dle=('blocking', {'openmp': False,
'blockinner': True,
'blockalways': True}))
# Run with whatever `configuration` says (by default, basic+preemptive)
op(infield=infield, outfield=outfield, autotune=True)
assert op._state['autotuning'][-1]['runs'] == 4
assert op._state['autotuning'][-1]['tpr'] == 1
# Now try `aggressive` autotuning
configuration['autotuning'] = 'aggressive'
op(infield=infield, outfield=outfield, autotune=True)
assert op._state['autotuning'][-1]['runs'] == expected
assert op._state['autotuning'][-1]['tpr'] == 1
configuration['autotuning'] = configuration._defaults['autotuning']
# Try again, but using the Operator API directly
op(infield=infield, outfield=outfield, autotune='aggressive')
assert op._state['autotuning'][-1]['runs'] == expected
assert op._state['autotuning'][-1]['tpr'] == 1
# Similar to above
op(infield=infield, outfield=outfield, autotune=('aggressive', 'preemptive'))
assert op._state['autotuning'][-1]['runs'] == expected
assert op._state['autotuning'][-1]['tpr'] == 1
return skipper(True, "mpi4py/MPI not installed")
continue
# Skip if an unsupported backend
if i == configuration['backend']:
return skipper(True, "`%s` backend unsupported" % i)
try:
_, noi = i.split('no')
if noi != configuration['backend']:
return skipper(True, "`%s` backend unsupported" % i)
except ValueError:
pass
return skipper(False, "")
# Testing dimensions for space and time
grid = Grid(shape=(3, 3, 3))
time = grid.time_dim
t = grid.stepping_dim
x, y, z = grid.dimensions
def scalar(name):
return Scalar(name=name)
def array(name, shape, dimensions, scope='heap'):
return Array(name=name, shape=shape, dimensions=dimensions, scope=scope)
def constant(name):
return Constant(name=name)
p[0, :] = 0
p[nx-1, :] = 0
p[:, 0] = 0
p[:, ny-1] = 0
plot_field(p, xmax=xmax, ymax=ymax, view=(30, 225))
from devito import Grid, Function, TimeFunction, Operator, configuration, Eq, solve
# Silence the runtime performance logging
configuration['log_level'] = 'ERROR'
# Now with Devito we will turn `p` into `TimeFunction` object
# to make all the buffer switching implicit
grid = Grid(shape=(nx, ny), extent=(1., 2.))
p = Function(name='p', grid=grid, space_order=2)
pd = Function(name='pd', grid=grid, space_order=2)
p.data[:] = 0.
pd.data[:] = 0.
# Initialise the source term `b`
b = Function(name='b', grid=grid)
b.data[:] = 0.
b.data[int(nx / 4), int(ny / 4)] = 100
b.data[int(3 * nx / 4), int(3 * ny / 4)] = -100
# Create Laplace equation base on `pd`
eq = Eq(pd.laplace, b, subdomain=grid.interior)
# Let SymPy solve for the central stencil point
stencil = solve(eq, pd)
