def test_capture_vector_temporaries(self):
"""
Check that all vector temporaries appearing in a offloaded stencil
equation are: ::
* mapped to a YASK grid, directly in Python-land,
* so no memory needs to be allocated in C-land, and
* passed down to the generated code, and
* re-initializaed to 0. at each operator application
"""
grid = Grid(shape=(4, 4, 4))
u = TimeFunction(name='yu4D', grid=grid, space_order=0)
v = Function(name='yv3D', grid=grid, space_order=0)
eqs = [Eq(u.forward, u + cos(v)*2. + cos(v)*cos(v)*3.)]
op = Operator(eqs)
# Sanity check of the generated code
assert 'posix_memalign' not in str(op)
assert 'run_solution' in str(op)
# No data has been allocated for the temporaries yet
assert list(op.yk_solns.values())[0].grids['r1'].is_storage_allocated() is False
op.apply(yu4D=u, yv3D=v, time=0)
# Temporary data has already been released after execution
assert list(op.yk_solns.values())[0].grids['r1'].is_storage_allocated() is False
assert np.all(v.data == 0.)
assert np.all(u.data[1] == 5.)
def test_subsampling(self):
"""
Tests (time) subsampling support. This stresses the compiler as two
different YASK kernels need to be generated.
"""
grid = Grid(shape=(8, 8))
time = grid.time_dim
nt = 9
u = TimeFunction(name='u', grid=grid)
u.data_with_halo[:] = 0.
# Setup subsampled function
factor = 4
nsamples = (nt+factor-1)//factor
times = ConditionalDimension('t_sub', parent=time, factor=factor)
usave = TimeFunction(name='usave', grid=grid, save=nsamples, time_dim=times)
eqns = [Eq(u.forward, u + 1.), Eq(usave, u)]
op = Operator(eqns)
op.apply(time=nt-1)
# Check numerical correctness
assert np.all(usave.data[0] == 0.)
assert np.all(usave.data[1] == 4.)
assert np.all(usave.data[2] == 8.)
# Check code generation
solns = FindNodes(ForeignExpression).visit(op)
assert len(solns) == 2
assert all('run_solution' in str(i) for i in solns)
def test_subsampled_fd(self):
"""
Test that the symbolic interface is working for space subsampled
functions.
"""
nt = 19
grid = Grid(shape=(12, 12), extent=(11, 11))
u = TimeFunction(name='u', grid=grid, save=nt, space_order=2)
assert(grid.time_dim in u.indices)
# Creates subsampled spatial dimensions and according grid
dims = tuple([ConditionalDimension(d.name+'sub', parent=d, factor=2)
for d in u.grid.dimensions])
grid2 = Grid((6, 6), dimensions=dims)
u2 = TimeFunction(name='u2', grid=grid2, save=nt, space_order=1)
for i in range(nt):
for j in range(u2.data_with_halo.shape[2]):
u2.data_with_halo[i, :, j] = np.arange(u2.data_with_halo.shape[2])
eqns = [Eq(u.forward, u + 1.), Eq(u2.forward, u2.dx)]
op = Operator(eqns, dse="advanced")
op.apply(time_M=nt-2)
# Verify that u2[1, x,y]= du2/dx[0, x, y]
assert np.allclose(u.data[-1], nt-1)
assert np.allclose(u2.data[1], 0.5)
def test_fd_space_staggered(self, space_order, stagger):
"""
This test compares the discrete finite-difference scheme against polynomials
For a given order p, the finite difference scheme should
be exact for polynomials of order p
:param derivative: name of the derivative to be tested
:param space_order: space order of the finite difference stencil
"""
clear_cache()
# dummy axis dimension
nx = 100
xx = np.linspace(-1, 1, nx)
dx = xx[1] - xx[0]
# Symbolic data
grid = Grid(shape=(nx,), dtype=np.float32)
x = grid.dimensions[0]
# Location of the staggered function
if stagger == left:
off = -.5
side = -x
xx2 = xx - off * dx
elif stagger == right:
off = .5
side = x
xx2 = xx[:-1] - off * dx
else:
off = 0
side = NODE
xx2 = xx
u = Function(name="u", grid=grid, space_order=space_order, staggered=(side,))
du = Function(name="du", grid=grid, space_order=space_order)
# Define polynomial with exact fd
coeffs = np.ones((space_order-1,), dtype=np.float32)
polynome = sum([coeffs[i]*x**i for i in range(0, space_order-1)])
polyvalues = np.array([polynome.subs(x, xi) for xi in xx2], np.float32)
# Fill original data with the polynomial values
u.data[:] = polyvalues
# True derivative of the polynome
Dpolynome = diff(polynome)
Dpolyvalues = np.array([Dpolynome.subs(x, xi) for xi in xx], np.float32)
# FD derivative, symbolic
u_deriv = generic_derivative(u, deriv_order=1, fd_order=space_order,
dim=x, stagger=stagger)
# Compute numerical FD
stencil = Eq(du, u_deriv)
op = Operator(stencil, subs={x.spacing: dx})
op.apply()
# Check exactness of the numerical derivative except inside space_brd
space_border = space_order
error = abs(du.data[space_border:-space_border] -
Dpolyvalues[space_border:-space_border])
assert np.isclose(np.mean(error), 0., atol=1e-3)
def test_mixed_blocking_nthreads():
grid = Grid(shape=(64, 64, 64))
f = TimeFunction(name='f', grid=grid)
op = Operator(Eq(f.forward, f + 1.), dle=('advanced', {'openmp': True}))
op.apply(time=100, autotune=True)
assert op._state['autotuning'][0]['runs'] == 6
assert op._state['autotuning'][0]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][0]['tuned']) == 3
assert 'nthreads' in op._state['autotuning'][0]['tuned']
def test_mode_destructive():
"""Test autotuning in destructive mode."""
grid = Grid(shape=(64, 64, 64))
f = TimeFunction(name='f', grid=grid, time_order=0)
op = Operator(Eq(f, f + 1.), dle=('advanced', {'openmp': False}))
op.apply(time=100, autotune=('basic', 'destructive'))
# AT is expected to have executed 30 timesteps (6 block shapes, 5 timesteps each)
# The operator runs for 101 timesteps
# So, overall, f.data[0] is incremented 131 times
assert np.all(f.data == 131)
def test_acoustic_wo_src_wo_rec(self):
"""
Test that the acoustic wave equation runs without crashing in absence
of sources and receivers.
"""
dt = self.model.critical_dt
self.u.data[:] = 0.0
op = Operator(self.eqn, subs=self.model.spacing_map)
assert 'run_solution' in str(op)
op.apply(u=self.u, m=self.m, damp=self.damp, time=10, dt=dt)
assert np.linalg.norm(self.u.data[:]) == 0.0
def test_operator_timefunction():
grid = Grid(shape=(3, 3, 3))
f = TimeFunction(name='f', grid=grid, save=3)
op = Operator(Eq(f.forward, f + 1))
op.apply(time=0)
pkl_op = pickle.dumps(op)
new_op = pickle.loads(pkl_op)
assert str(op) == str(new_op)
new_op.apply(time_m=1, time_M=1, f=f)
assert np.all(f.data[2] == 2)
def test_operator_function():
grid = Grid(shape=(3, 3, 3))
f = Function(name='f', grid=grid)
op = Operator(Eq(f, f + 1))
op.apply()
pkl_op = pickle.dumps(op)
new_op = pickle.loads(pkl_op)
assert str(op) == str(new_op)
new_op.apply(f=f)
assert np.all(f.data == 2)
def test_multiple_threads():
"""
Test autotuning when different ``num_threads`` for a given OpenMP parallel
region are attempted.
"""
grid = Grid(shape=(64, 64, 64))
v = TimeFunction(name='v', grid=grid)
op = Operator(Eq(v.forward, v + 1), dle=('blocking', {'openmp': True}))
op.apply(time_M=0, autotune='max')
assert op._state['autotuning'][0]['runs'] == 60 # Would be 30 with `aggressive`
assert op._state['autotuning'][0]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][0]['tuned']) == 3
def run_simulation(save=False, dx=0.01, dy=0.01, a=0.5, timesteps=100):
nx, ny = int(1 / dx), int(1 / dy)
dx2, dy2 = dx**2, dy**2
dt = dx2 * dy2 / (2 * a * (dx2 + dy2))
grid = Grid(shape=(nx, ny))
u = TimeFunction(name='u', grid=grid, save=timesteps if save else None,
initializer=initializer, time_order=1, space_order=2)
eqn = Eq(u.dt, a * (u.dx2 + u.dy2))
stencil = solve(eqn, u.forward)
op = Operator(Eq(u.forward, stencil))
op.apply(time=timesteps-2, dt=dt)
return u.data[timesteps - 1]
def test_mode_runtime_backward():
"""Test autotuning in runtime mode."""
grid = Grid(shape=(64, 64, 64))
f = TimeFunction(name='f', grid=grid)
op = Operator(Eq(f.backward, f + 1.), dle=('advanced', {'openmp': False}))
summary = op.apply(time=101, autotune=('basic', 'runtime'))
# AT is expected to have attempted 6 block shapes
assert op._state['autotuning'][0]['runs'] == 6
# AT is expected to have executed 30 timesteps
assert summary['section0'].itershapes[0][0] == 101-30
assert np.all(f.data[0] == 101)
assert np.all(f.data[1] == 100)
def test_acoustic_w_src_wo_rec(self):
"""
Test that the acoustic wave equation runs without crashing in absence
of receivers.
"""
dt = self.model.critical_dt
self.u.data[:] = 0.0
eqns = self.eqn
eqns += self.src.inject(field=self.u.forward, expr=self.src * dt**2 / self.m)
op = Operator(eqns, subs=self.model.spacing_map)
assert 'run_solution' in str(op)
op.apply(u=self.u, m=self.m, damp=self.damp, src=self.src, dt=dt)
exp_u = 154.05
assert np.isclose(np.linalg.norm(self.u.data[:]), exp_u, atol=exp_u*1.e-2)
def test_discarding_runs():
grid = Grid(shape=(64, 64, 64))
f = TimeFunction(name='f', grid=grid)
op = Operator(Eq(f.forward, f + 1.), dle=('advanced', {'openmp': True}))
op.apply(time=100, nthreads=4, autotune='aggressive')
assert op._state['autotuning'][0]['runs'] == 20
assert op._state['autotuning'][0]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][0]['tuned']) == 3
assert op._state['autotuning'][0]['tuned']['nthreads'] == 4
# With 1 < 4 threads, the AT eventually tries many more combinations
op.apply(time=100, nthreads=1, autotune='aggressive')
assert op._state['autotuning'][1]['runs'] == 30
assert op._state['autotuning'][1]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][1]['tuned']) == 3
assert op._state['autotuning'][1]['tuned']['nthreads'] == 1
def test_collapsing(self):
grid = Grid(shape=(3, 3, 3))
u = TimeFunction(name='u', grid=grid)
op = Operator(Eq(u.forward, u + 1), dle=('blocking', 'openmp'))
# Does it compile? Honoring the OpenMP specification isn't trivial
assert op.cfunction
# Does it produce the right result
op.apply(t_M=9)
assert np.all(u.data[0] == 10)
iterations = FindNodes(Iteration).visit(op._func_table['bf0'])
assert iterations[0].pragmas[0].value == 'omp for collapse(2) schedule(static,1)'
assert iterations[2].pragmas[0].value ==\
('omp parallel for collapse(2) schedule(static,1) num_threads(%d)'
% nhyperthreads())
def test_makeit_ssa(exprs, exp_u, exp_v):
"""
A test building Operators with non-trivial sequences of input expressions
that push hard on the `makeit_ssa` utility function.
"""
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
u = Function(name='u', grid=grid) # noqa
v = Function(name='v', grid=grid) # noqa
s = Scalar(name='s') # noqa
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = eval(e)
op = Operator(exprs)
op.apply()
assert np.all(u.data == exp_u)
assert np.all(v.data == exp_v)
def test_mpi_operator():
grid = Grid(shape=(4,))
f = TimeFunction(name='f', grid=grid)
g = TimeFunction(name='g', grid=grid)
# Using `sum` creates a stencil in `x`, which in turn will
# trigger the generation of code for MPI halo exchange
op = Operator(Eq(f.forward, f.sum() + 1))
op.apply(time=2)
pkl_op = pickle.dumps(op)
new_op = pickle.loads(pkl_op)
assert str(op) == str(new_op)
new_op.apply(time=2, f=g)
assert np.all(f.data[0] == [2., 3., 3., 3.])
assert np.all(f.data[1] == [3., 6., 7., 7.])
assert np.all(g.data[0] == f.data[0])
assert np.all(g.data[1] == f.data[1])
def test_const_change(self):
"""
Test that Constand.data can be set as required.
"""
n = 5
t = Constant(name='t', dtype=np.int32)
grid = Grid(shape=(2, 2))
x, y = grid.dimensions
f = TimeFunction(name='f', grid=grid, save=n+1)
f.data[:] = 0
eq = Eq(f.dt-1)
stencil = Eq(f.forward, solve(eq, f.forward))
op = Operator([stencil])
op.apply(time_m=0, time_M=n-1, dt=1)
check = Function(name='check', grid=grid)
eq_test = Eq(check, f[t, x, y])
op_test = Operator([eq_test])
for j in range(0, n+1):
t.data = j # Ensure constant is being updated correctly
op_test.apply(t=t)
assert(np.amax(check.data[:], axis=None) == j)
assert(np.amin(check.data[:], axis=None) == j)
def test_constants(self):
"""
Check that :class:`Constant` objects are treated correctly.
"""
grid = Grid(shape=(4, 4, 4))
c = Constant(name='c', value=2., dtype=grid.dtype)
p = SparseTimeFunction(name='points', grid=grid, nt=1, npoint=1)
u = TimeFunction(name='yu4D', grid=grid, space_order=0)
u.data[:] = 0.
op = Operator([Eq(u.forward, u + c), Eq(p[0, 0], 1. + c)])
assert 'run_solution' in str(op)
op.apply(yu4D=u, c=c, time=9)
# Check YASK did its job and could read constant grids w/o problems
assert np.all(u.data[0] == 20.)
# Check the Constant could be read correctly even in Devito-land, i.e.,
# outside of run_solution
assert p.data[0][0] == 3.
# Check re-executing with another constant gives the correct result
c2 = Constant(name='c', value=5.)
op.apply(yu4D=u, c=c2, time=2)
assert np.all(u.data[0] == 30.)
assert np.all(u.data[1] == 35.)
assert p.data[0][0] == 6.
def _new_operator3(shape, blockshape=None, dle=None):
blockshape = as_tuple(blockshape)
grid = Grid(shape=shape)
spacing = 0.1
a = 0.5
c = 0.5
dx2, dy2 = spacing**2, spacing**2
dt = dx2 * dy2 / (2 * a * (dx2 + dy2))
# Allocate the grid and set initial condition
# Note: This should be made simpler through the use of defaults
u = TimeFunction(name='u', grid=grid, time_order=1, space_order=(2, 2, 2))
u.data[0, :] = np.arange(reduce(mul, shape), dtype=np.int32).reshape(shape)
# Derive the stencil according to devito conventions
eqn = Eq(u.dt, a * (u.dx2 + u.dy2) - c * (u.dxl + u.dyl))
stencil = solve(eqn, u.forward)
op = Operator(Eq(u.forward, stencil), dle=dle)
blocksizes = get_blocksizes(op, dle, grid, blockshape)
op.apply(u=u, t=10, dt=dt, **blocksizes)
return u.data[1, :], op
def execute_devito(ui, spacing=0.01, a=0.5, timesteps=500):
"""Execute diffusion stencil using the devito Operator API."""
nx, ny = ui.shape
dx2, dy2 = spacing**2, spacing**2
dt = dx2 * dy2 / (2 * a * (dx2 + dy2))
# Allocate the grid and set initial condition
# Note: This should be made simpler through the use of defaults
grid = Grid(shape=(nx, ny))
u = TimeFunction(name='u', grid=grid, time_order=1, space_order=2)
u.data[0, :] = ui[:]
# Derive the stencil according to devito conventions
eqn = Eq(u.dt, a * (u.dx2 + u.dy2))
stencil = solve(eqn, u.forward)
op = Operator(Eq(u.forward, stencil))
# Execute the generated Devito stencil operator
tstart = time.time()
op.apply(u=u, t=timesteps, dt=dt)
runtime = time.time() - tstart
log("Devito: Diffusion with dx=%0.4f, dy=%0.4f, executed %d timesteps in %f seconds"
% (spacing, spacing, timesteps, runtime))
return u.data[1, :], runtime
def test_acoustic_w_src_w_rec(self):
"""
Test that the acoustic wave equation forward operator produces the correct
results when running a 3D model also used in ``test_adjointA.py``.
"""
dt = self.model.critical_dt
self.u.data[:] = 0.0
eqns = self.eqn
eqns += self.src.inject(field=self.u.forward, expr=self.src * dt**2 / self.m)
eqns += self.rec.interpolate(expr=self.u)
op = Operator(eqns, subs=self.model.spacing_map)
assert 'run_solution' in str(op)
op.apply(u=self.u, m=self.m, damp=self.damp, src=self.src, rec=self.rec, dt=dt)
# The expected norms have been computed "by hand" looking at the output
# of test_adjointA's forward operator w/o using the YASK backend.
exp_u = 154.05
exp_rec = 212.15
assert np.isclose(np.linalg.norm(self.u.data[:]), exp_u, atol=exp_u*1.e-2)
assert np.isclose(np.linalg.norm(self.rec.data.reshape(-1)), exp_rec,
atol=exp_rec*1.e-2)
def test_multiple_blocking():
"""
Test that if there are more than one blocked Iteration nests, then
the autotuner works "incrementally" -- it starts determining the best block
shape for the first Iteration nest, then it moves on to the second one,
then the third, etc. IOW, the autotuner must not be attempting the
cartesian product of all possible block shapes across the various
blocked nests.
"""
grid = Grid(shape=(64, 64, 64))
u = TimeFunction(name='u', grid=grid, space_order=2)
v = TimeFunction(name='v', grid=grid)
op = Operator([Eq(u.forward, u + 1), Eq(v.forward, u.forward.dx2 + v + 1)],
dle=('blocking', {'openmp': False}))
# First of all, make sure there are indeed two different loop nests
assert 'bf0' in op._func_table
assert 'bf1' in op._func_table
# 'basic' mode
op.apply(time_M=0, autotune='basic')
assert op._state['autotuning'][0]['runs'] == 12 # 6 for each Iteration nest
assert op._state['autotuning'][0]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][0]['tuned']) == 4
# 'aggressive' mode
op.apply(time_M=0, autotune='aggressive')
assert op._state['autotuning'][1]['runs'] == 60
assert op._state['autotuning'][1]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][1]['tuned']) == 4
# With OpenMP, we tune over one more argument (`nthreads`), though the AT
# will only attempt one value
op = Operator([Eq(u.forward, u + 1), Eq(v.forward, u.forward.dx2 + v + 1)],
dle=('blocking', {'openmp': True}))
op.apply(time_M=0, autotune='basic')
assert op._state['autotuning'][0]['runs'] == 12
assert op._state['autotuning'][0]['tpr'] == options['squeezer'] + 1
assert len(op._state['autotuning'][0]['tuned']) == 5
def test_dynamic_nthreads(self):
grid = Grid(shape=(16, 16, 16))
f = TimeFunction(name='f', grid=grid)
op = Operator(Eq(f.forward, f + 1.), dle='openmp')
# Check num_threads appears in the generated code
# Not very elegant, but it does the trick
assert 'num_threads(nthreads)' in str(op)
# Check `op` accepts the `nthreads` kwarg
op.apply(time=0)
op.apply(time_m=1, time_M=1, nthreads=4)
assert np.all(f.data[0] == 2.)
# Check the actual value assumed by `nthreads`
assert op.arguments(time=0)['nthreads'] == NThreads.default_value()
assert op.arguments(time=0, nthreads=123)['nthreads'] == 123 # user supplied
def test_multiple_middle(self):
"""
Test Operator with two basic 'middle' subdomains defined.
"""
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: ('middle', 6, 1), y: ('middle', 1, 1)}
s_d1 = sd1()
grid = Grid(shape=(10, 10), subdomains=(s_d0, s_d1))
f = Function(name='f', grid=grid, dtype=np.int32)
eq0 = Eq(f, f+1, subdomain=grid.subdomains['d0'])
eq1 = Eq(f, f+2, subdomain=grid.subdomains['d1'])
Operator([eq0, eq1])()
expected = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 2, 2, 2, 2, 2, 2, 2, 2, 0],
[0, 2, 2, 2, 2, 2, 2, 2, 2, 0],
[0, 2, 2, 2, 2, 2, 2, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=np.int32)
assert((np.array(f.data) == expected).all())
def initialize_damp(damp, nbl, spacing, mask=False):
"""
Initialise damping field with an absorbing boundary layer.
Parameters
----------
damp : Function
The damping field for absorbing boundary condition.
nbl : int
Number of points in the damping layer.
spacing :
Grid spacing coefficient.
mask : bool, optional
whether the dampening is a mask or layer.
mask => 1 inside the domain and decreases in the layer
not mask => 0 inside the domain and increase in the layer
"""
dampcoeff = 1.5 * np.log(1.0 / 0.001) / (nbl)
eqs = [Eq(damp, 1.0)] if mask else []
for d in damp.dimensions:
# left
dim_l = SubDimension.left(name='abc_%s_l' % d.name,
parent=d,
thickness=nbl)
pos = Abs((nbl - (dim_l - d.symbolic_min) + 1) / float(nbl))
val = dampcoeff * (pos - sin(2 * np.pi * pos) / (2 * np.pi))
val = -val if mask else val
eqs += [Inc(damp.subs({d: dim_l}), val / d.spacing)]
# right
dim_r = SubDimension.right(name='abc_%s_r' % d.name,
parent=d,
thickness=nbl)
pos = Abs((nbl - (d.symbolic_max - dim_r) + 1) / float(nbl))
val = dampcoeff * (pos - sin(2 * np.pi * pos) / (2 * np.pi))
val = -val if mask else val
eqs += [Inc(damp.subs({d: dim_r}), val / d.spacing)]
# TODO: Figure out why yask doesn't like it with dse/dle
Operator(eqs, name='initdamp', dse='noop', dle='noop')()
def test_multiple_loop_nests(self):
"""
Compute a simple stencil S, preceded by an "initialization loop" I and
followed by a "random loop" R.
* S is the trivial equation ``u[t+1,x,y,z] = u[t,x,y,z] + 1``;
* I initializes ``u`` to 0;
* R adds 2 to another field ``v`` along the ``z`` dimension but only
over the planes ``[x=0, y=2]`` and ``[x=0, y=5]``.
Out of these three loop nests, only S should be "offloaded" to YASK; indeed,
I is outside the time loop, while R does not loop over space dimensions.
This test checks that S is the only loop nest "offloaded" to YASK, and
that the numerical output is correct.
"""
u = TimeData(name='yu4D',
shape=(12, 12, 12),
dimensions=(x, y, z),
space_order=0)
v = TimeData(name='yv4D',
shape=(12, 12, 12),
dimensions=(x, y, z),
space_order=0)
v.data[:] = 0.
eqs = [
Eq(u.indexed[0, x, y, z], 0),
Eq(u.indexed[1, x, y, z], 0),
Eq(u.forward, u + 1.),
Eq(v.indexed[t + 1, 0, 2, z], v.indexed[t + 1, 0, 2, z] + 2.),
Eq(v.indexed[t + 1, 0, 5, z], v.indexed[t + 1, 0, 5, z] + 2.)
]
op = Operator(eqs, subs={t.spacing: 1})
op(yu4D=u, yv4D=v, t=1)
assert 'run_solution' in str(op)
assert len(retrieve_iteration_tree(op)) == 3
assert np.all(u.data[0] == 0.)
assert np.all(u.data[1] == 1.)
assert np.all(v.data[0] == 0.)
assert np.all(v.data[1, 0, 2] == 2.)
assert np.all(v.data[1, 0, 5] == 2.)
def BornOperator(model, source, receiver, space_order=4,
kernel='OT2', **kwargs):
"""
Constructor method for the Linearized Born operator in an acoustic media
:param model: :class:`Model` object containing the physical parameters
:param source: :class:`PointData` object containing the source geometry
:param receiver: :class:`PointData` object containing the acquisition geometry
:param time_order: Time discretization order
:param space_order: Space discretization order
"""
m, damp = model.m, model.damp
# Create source and receiver symbols
src = PointSource(name='src', grid=model.grid, time_range=source.time_range,
npoint=source.npoint)
rec = Receiver(name='rec', grid=model.grid, time_range=receiver.time_range,
npoint=receiver.npoint)
# Create wavefields and a dm field
u = TimeFunction(name="u", grid=model.grid, save=None,
time_order=2, space_order=space_order)
U = TimeFunction(name="U", grid=model.grid, save=None,
time_order=2, space_order=space_order)
dm = Function(name="dm", grid=model.grid, space_order=0)
s = model.grid.stepping_dim.spacing
eqn1 = iso_stencil(u, m, s, damp, kernel)
eqn2 = iso_stencil(U, m, s, damp, kernel, q=-dm*u.dt2)
# Add source term expression for u
source = src.inject(field=u.forward, expr=src * s**2 / m,
offset=model.nbpml)
# Create receiver interpolation expression from U
receivers = rec.interpolate(expr=U, offset=model.nbpml)
# Substitute spacing terms to reduce flops
return Operator(eqn1 + source + eqn2 + receivers, subs=model.spacing_map,
name='Born', **kwargs)
def test_cire():
grid = Grid(shape=(4, 4, 4))
u = TimeFunction(name='u', grid=grid, space_order=2)
u1 = TimeFunction(name='u', grid=grid, space_order=2)
eqn = Eq(u.forward, u.dy.dy + 1.)
op0 = Operator(eqn, opt=('advanced', {'cire-mingain': 0}))
op1 = Operator(eqn,
opt=('advanced', {
'linearize': True,
'cire-mingain': 0
}))
# Check generated code
assert 'uL0' not in str(op0)
assert 'uL0' in str(op1)
op0.apply(time_M=10)
op1.apply(time_M=10, u=u1)
assert np.all(u.data == u1.data)
def test_drop_redundants_after_fusion(self):
"""
Test for detection of redundant aliases that get exposed after
Cluster fusion.
"""
grid = Grid(shape=(10, 10))
t = cos(Function(name="t", grid=grid))
p = sin(Function(name="p", grid=grid))
a = TimeFunction(name="a", grid=grid)
b = TimeFunction(name="b", grid=grid)
c = TimeFunction(name="c", grid=grid)
d = TimeFunction(name="d", grid=grid)
e = TimeFunction(name="e", grid=grid)
f = TimeFunction(name="f", grid=grid)
s1 = SparseTimeFunction(name="s1", grid=grid, npoint=1, nt=2)
eqns = [
Eq(a.forward, t * a.dx + p * b.dy),
Eq(b.forward, p * b.dx + p * t * a.dy)
]
eqns += s1.inject(field=a.forward, expr=s1)
eqns += s1.inject(field=b.forward, expr=s1)
eqns += [
Eq(c.forward, t * p * a.forward.dx + b.forward.dy),
Eq(d.forward, t * d.dx + e.dy + p * a.dt),
Eq(e.forward, p * d.dx + e.dy + t * b.dt)
]
eqns += [Eq(f.forward, t * p * e.forward.dx + p * d.forward.dy)]
op = Operator(eqns)
arrays = [i for i in FindSymbols().visit(op) if i.is_Array]
assert len(arrays) == 2
assert all(i._mem_heap and not i._mem_external for i in arrays)
def test_iteration_parallelism_2d(self, exprs, atomic, parallel):
"""Tests detection of PARALLEL_* properties."""
grid = Grid(shape=(10, 10))
time = grid.time_dim # noqa
t = grid.stepping_dim # noqa
x, y = grid.dimensions # noqa
p = Dimension(name='p')
d = Dimension(name='d')
rx = Dimension(name='rx')
ry = Dimension(name='ry')
u = Function(name='u', grid=grid) # noqa
v = TimeFunction(name='v', grid=grid, save=None) # noqa
w = TimeFunction(name='w', 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
gp = Function(name='gridpoints', dimensions=(p, d),
shape=(1, 2)) # 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)
op = Operator(exprs, opt='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 ForwardOperator(model, geometry, space_order=4, save=False, kernel='OT2', **kwargs):
"""
Construct a forward modelling operator in an acoustic medium with density.
Parameters
----------
model : Model
Object containing the physical parameters.
geometry : AcquisitionGeometry
Geometry object that contains the source (SparseTimeFunction) and
receivers (SparseTimeFunction) and their position.
space_order : int, optional
Space discretization order.
save : int or Buffer, optional
Saving flag, True saves all time steps. False saves three timesteps.
Defaults to False.
"""
m, damp, irho = model.m, model.damp, model.irho
# Create symbols for forward wavefield, source and receivers
u = TimeFunction(name='u', grid=model.grid,
save=geometry.nt if save else None,
time_order=2, space_order=space_order)
src = PointSource(name='src', grid=geometry.grid, time_range=geometry.time_axis,
npoint=geometry.nsrc)
rec = Receiver(name='rec', grid=geometry.grid, time_range=geometry.time_axis,
npoint=geometry.nrec)
s = model.grid.stepping_dim.spacing
eqn = density_stencil(u, m, s, damp, irho)
# Construct expression to inject source values
src_term = src.inject(field=u.forward, expr=src*s**2/(irho*m))
# Create interpolation expression for receivers
rec_term = rec.interpolate(expr=u)
# Substitute spacing terms to reduce flops
return Operator(eqn + src_term + rec_term, subs=model.spacing_map,
name='Forward', **kwargs)
def test_misc_dims(self):
"""
Tests grid-independent :class:`Function`s, which require YASK's "misc"
dimensions.
"""
dx = Dimension(name='dx')
grid = Grid(shape=(10, 10))
x, y = grid.dimensions
time = grid.time_dim
u = TimeFunction(name='u', grid=grid, time_order=1, space_order=4, save=4)
c = Function(name='c', dimensions=(x, dx), shape=(10, 5))
step = Eq(u.forward, (
u[time, x-2, y] * c[x, 0]
+ u[time, x-1, y] * c[x, 1]
+ u[time, x, y] * c[x, 2]
+ u[time, x+1, y] * c[x, 3]
+ u[time, x+2, y] * c[x, 4]))
for i in range(10):
c.data[i, 0] = 1.0+i
c.data[i, 1] = 1.0+i
c.data[i, 2] = 3.0+i
c.data[i, 3] = 6.0+i
c.data[i, 4] = 5.0+i
u.data[:] = 0.0
u.data[0, 2, :] = 2.0
op = Operator(step)
assert 'run_solution' in str(op)
op(time_m=0, time_M=0)
assert(np.all(u.data[1, 0, :] == 10.0))
assert(np.all(u.data[1, 1, :] == 14.0))
assert(np.all(u.data[1, 2, :] == 10.0))
assert(np.all(u.data[1, 3, :] == 8.0))
assert(np.all(u.data[1, 4, :] == 10.0))
assert(np.all(u.data[1, 5:10, :] == 0.0))
def test_at_w_mpi():
"""Make sure autotuning works in presence of MPI. MPI ranks work
in isolation to determine the best block size, locally."""
grid = Grid(shape=(8, 8))
t = grid.stepping_dim
x, y = grid.dimensions
f = TimeFunction(name='f', grid=grid, time_order=1)
f.data_with_halo[:] = 1.
eq = Eq(f.forward, f[t, x, y-1] + f[t, x, y+1])
op = Operator(eq, dle=('advanced', {'openmp': False, 'blockinner': True}))
op.apply(time=-1, autotune=('basic', 'runtime'))
# Nothing really happened, as not enough timesteps
assert np.all(f.data_ro_domain[0] == 1.)
assert np.all(f.data_ro_domain[1] == 1.)
# The 'destructive' mode writes directly to `f` for whatever timesteps required
# to perform the autotuning. Eventually, the result is complete garbage; note
# also that this autotuning mode disables the halo exchanges
op.apply(time=-1, autotune=('basic', 'destructive'))
assert np.all(f._data_ro_with_inhalo.sum() == 904)
# Check the halo hasn't been touched during AT
glb_pos_map = grid.distributor.glb_pos_map
if LEFT in glb_pos_map[y]:
assert np.all(f._data_ro_with_inhalo[:, :, -1] == 1)
else:
assert np.all(f._data_ro_with_inhalo[:, :, 0] == 1)
# Finally, try running w/o AT, just to be sure nothing was broken
f.data_with_halo[:] = 1.
op.apply(time=2)
if LEFT in glb_pos_map[y]:
assert np.all(f.data_ro_domain[1, :, 0] == 5.)
assert np.all(f.data_ro_domain[1, :, 1] == 7.)
assert np.all(f.data_ro_domain[1, :, 2:4] == 8.)
else:
assert np.all(f.data_ro_domain[1, :, 4:6] == 8)
assert np.all(f.data_ro_domain[1, :, 6] == 7)
assert np.all(f.data_ro_domain[1, :, 7] == 5)
def test_tti_v2_rewrite_aggressive_opcounts(space_order, expected):
grid = Grid(shape=(3, 3, 3))
s = 0.00067
u = TimeFunction(name='u', grid=grid, space_order=space_order)
v = TimeFunction(name='v', grid=grid, space_order=space_order)
f = Function(name='f', grid=grid)
g = Function(name='g', grid=grid)
m = Function(name='m', grid=grid)
e = Function(name='e', grid=grid)
d = Function(name='d', grid=grid)
ang0 = cos(f)
ang1 = sin(f)
ang2 = cos(g)
ang3 = sin(g)
H1u = (ang1 * ang1 * ang2 * ang2 * u.dx2 +
ang1 * ang1 * ang3 * ang3 * u.dy2 + ang0 * ang0 * u.dz2 +
2 * ang1 * ang1 * ang3 * ang2 * u.dxdy +
2 * ang0 * ang1 * ang3 * u.dydz + 2 * ang0 * ang1 * ang2 * u.dxdz)
H2u = -H1u + u.laplace
H1v = (ang1 * ang1 * ang2 * ang2 * v.dx2 +
ang1 * ang1 * ang3 * ang3 * v.dy2 + ang0 * ang0 * v.dz2 +
2 * ang1 * ang1 * ang3 * ang2 * v.dxdy +
2 * ang0 * ang1 * ang3 * v.dydz + 2 * ang0 * ang1 * ang2 * v.dxdz)
H2v = -H1v + v.laplace
eqns = [
Eq(u.forward, (2 * u - u.backward) + s**2 / m * (e * H2u + H1v)),
Eq(v.forward, (2 * v - v.backward) + s**2 / m * (d * H2v + H1v))
]
op = Operator(eqns, dse='aggressive')
sections = list(op._profiler._sections.values())
assert len(sections) == 2
assert sections[0].sops == 4
assert sections[1].sops == expected
def test_adjoint_inject_interpolate(shape, coords, npoints=19):
a = unit_box(shape=shape)
a.data[:] = 0.
c = unit_box(shape=shape, name='c')
c.data[:] = 27.
# Inject receiver
p = points(a.grid, ranges=coords, npoints=npoints)
p.data[:] = 1.2
expr = p.inject(field=a, expr=p)
# Read receiver
p2 = points(a.grid, name='points2', ranges=coords, npoints=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_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, dle=('noop', {'openmp': True}))
assert len(op.body[2].header) == 1
assert len(op.body[2].footer) == 1
assert op.body[2].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 op.body[2].footer[0].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[2].footer[0].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 AdjointOperator(model, geometry, space_order=4, kernel='sls', time_order=2, **kwargs):
"""
Construct an adjoint modelling operator in a viscoacoustic medium.
Parameters
----------
model : Model
Object containing the physical parameters.
geometry : AcquisitionGeometry
Geometry object that contains the source (SparseTimeFunction) and
receivers (SparseTimeFunction) and their position.
space_order : int, optional
Space discretization order.
kernel : selects a visco-acoustic equation from the options below:
sls (Standard Linear Solid) :
1st order - Blanch and Symes (1995) / Dutta and Schuster (2014)
viscoacoustic equation
2nd order - Bai et al. (2014) viscoacoustic equation
ren - Ren et al. (2014) viscoacoustic equation
deng_mcmechan - Deng and McMechan (2007) viscoacoustic equation
Defaults to sls 2nd order.
"""
if time_order == 1:
va = VectorTimeFunction(name="va", grid=model.grid, time_order=time_order,
space_order=space_order)
kwargs.update({'v': va})
pa = TimeFunction(name="pa", grid=model.grid, time_order=time_order,
space_order=space_order, staggered=NODE)
# Equations kernels
eq_kernel = kernels[kernel]
eqn = eq_kernel(model, geometry, pa, forward=False, **kwargs)
src_term, rec_term = src_rec(pa, model, geometry, forward=False)
# Substitute spacing terms to reduce flops
return Operator(eqn + src_term + rec_term, subs=model.spacing_map,
name='Adjoint', **kwargs)
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) present(u)'
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 GradientOperator(model, source, receiver, space_order=4, save=True,
kernel='OT2', **kwargs):
"""
Constructor method for the gradient operator in an acoustic media
:param model: :class:`Model` object containing the physical parameters
:param source: :class:`PointData` object containing the source geometry
:param receiver: :class:`PointData` object containing the acquisition geometry
:param time_order: Time discretization order
:param space_order: Space discretization order
"""
m, damp = model.m, model.damp
# Gradient symbol and wavefield symbols
grad = Function(name='grad', grid=model.grid)
u = TimeFunction(name='u', grid=model.grid, save=source.nt if save
else None, time_order=2, space_order=space_order)
v = TimeFunction(name='v', grid=model.grid, save=None,
time_order=2, space_order=space_order)
rec = Receiver(name='rec', grid=model.grid, ntime=receiver.nt,
npoint=receiver.npoint)
s = model.grid.stepping_dim.spacing
eqn = iso_stencil(v, m, s, damp, kernel, forward=False)
if kernel == 'OT2':
gradient_update = Eq(grad, grad - u.dt2 * v)
elif kernel == 'OT4':
gradient_update = Eq(grad, grad - (u.dt2 +
s**2 / 12.0 * u.laplace2(m**(-2))) * v)
else:
error("Unrecognized kernel, has to be OT2 or OT4")
# Add expression for receiver injection
receivers = rec.inject(field=v.backward, expr=rec * s**2 / m,
offset=model.nbpml)
# Substitute spacing terms to reduce flops
return Operator(eqn + receivers + [gradient_update], subs=model.spacing_map,
name='Gradient', **kwargs)
def test_subdomain_dim(self):
"""
Test that all dimensions including ones used as an expression
are replaced by the subdimension dimensions.
"""
class sd0(SubDomain):
name = 'd0'
def define(self, dimensions):
x, y = dimensions
return {x: ('middle', 1, 6), y: ('middle', 1, 1)}
s_d0 = sd0()
grid = Grid(shape=(10, 10), subdomains=(s_d0, ))
x, y = grid.dimensions
x1, y1 = s_d0.dimensions
f = Function(name='f', grid=grid, dtype=np.int32)
eq0 = Eq(f, x * f + y, subdomain=grid.subdomains['d0'])
with timed_region('x'):
expr = Operator._lower_exprs([eq0])[0]
assert expr.rhs == x1 * f[x1 + 1, y1 + 1] + y1
def initialize_damp(damp, padsizes, spacing, abc_type="damp", fs=False):
"""
Initialize damping field with an absorbing boundary layer.
Parameters
----------
damp : Function
The damping field for absorbing boundary condition.
nbl : int
Number of points in the damping layer.
spacing :
Grid spacing coefficient.
mask : bool, optional
whether the dampening is a mask or layer.
mask => 1 inside the domain and decreases in the layer
not mask => 0 inside the domain and increase in the layer
"""
eqs = [Eq(damp, 1.0 if abc_type == "mask" else 0.0)]
for (nbl, nbr), d in zip(padsizes, damp.dimensions):
if not fs or d is not damp.dimensions[-1]:
dampcoeff = 1.5 * np.log(1.0 / 0.001) / (nbl)
# left
dim_l = SubDimension.left(name='abc_%s_l' % d.name, parent=d,
thickness=nbl)
pos = Abs((nbl - (dim_l - d.symbolic_min) + 1) / float(nbl))
val = dampcoeff * (pos - sin(2*np.pi*pos)/(2*np.pi))
val = -val if abc_type == "mask" else val
eqs += [Inc(damp.subs({d: dim_l}), val/d.spacing)]
# right
dampcoeff = 1.5 * np.log(1.0 / 0.001) / (nbr)
dim_r = SubDimension.right(name='abc_%s_r' % d.name, parent=d,
thickness=nbr)
pos = Abs((nbr - (d.symbolic_max - dim_r) + 1) / float(nbr))
val = dampcoeff * (pos - sin(2*np.pi*pos)/(2*np.pi))
val = -val if abc_type == "mask" else val
eqs += [Inc(damp.subs({d: dim_r}), val/d.spacing)]
Operator(eqs, name='initdamp')()
def ForwardOperator(model, geometry, space_order=4, save=False, **kwargs):
"""
Construct method for the forward modelling operator in an elastic media.
Parameters
----------
model : Model
Object containing the physical parameters.
geometry : AcquisitionGeometry
Geometry object that contains the source (SparseTimeFunction) and
receivers (SparseTimeFunction) and their position.
space_order : int, optional
Space discretization order.
save : int or Buffer
Saving flag, True saves all time steps, False saves three buffered
indices (last three time steps). Defaults to False.
"""
wave = kernels[model.grid.dim]
pde = wave(model, space_order, geometry.nt if save else None, geometry)
# Substitute spacing terms to reduce flops
return Operator(pde, subs=model.spacing_map, name='Forward', **kwargs)
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', language='openmp')
assert len(op.body.maps) == 1
assert op.body.maps[0].pragmas[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 len(op.body.unmaps) == 2
assert op.body.unmaps[0].pragmas[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.unmaps[1].pragmas[0].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]]) if(devicerm)')
def test_catch_largest_time_invariant(self):
"""
Make sure the DSE extracts the largest time-invariant sub-expressions
such that its operation count exceeds a certain threshold.
"""
grid = Grid((10, 10))
a = Function(name="a", grid=grid, space_order=4)
b = Function(name="b", grid=grid, space_order=4)
c = Function(name="c", grid=grid, space_order=4)
d = Function(name="d", grid=grid, space_order=4)
e = TimeFunction(name="e", grid=grid, space_order=4)
deriv = (sqrt((a - 2*b)/c) * e.dx).dy + (sqrt((d - 2*c)/a) * e.dy).dx
op = Operator(Eq(e.forward, deriv + e))
# We expect two temporary Arrays, one for each `sqrt` subexpr
arrays = [i for i in FindSymbols().visit(op) if i.is_Array]
assert len(arrays) == 2
assert all(i._mem_heap and not i._mem_external for i in arrays)
def test_blocking(self, opt):
grid = Grid(shape=(3, 3, 3))
u = TimeFunction(name='u', grid=grid)
op = Operator(Eq(u.forward, u + 1),
platform='nvidiaX',
language='openmp',
opt=opt)
trees = retrieve_iteration_tree(op)
assert len(trees) == 1
tree = trees[0]
assert len(tree) == 7
assert all(i.dim.is_Block for i in tree[1:7])
assert op.parameters[3] is tree[1].step
assert op.parameters[6] is tree[2].step
assert op.parameters[9] is tree[3].step
assert tree[1].pragmas[0].value ==\
'omp target teams distribute parallel for collapse(3)'
def test_streaming_postponed_deletion(self):
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=10)
eqns = [
Eq(u.forward, u + usave),
Eq(v.forward, v + u.forward.dx + usave)
]
op = Operator(eqns,
platform='nvidiaX',
language='openacc',
opt=('streaming', 'orchestrate'))
sections = FindNodes(Section).visit(op)
assert len(sections) == 2
assert str(sections[1].body[0].body[0].footer[1]) ==\
('#pragma acc exit data delete(usave[time:1][0:usave_vec->size[1]]'
'[0:usave_vec->size[2]][0:usave_vec->size[3]])')
def test_scheduling_after_rewrite():
"""Tests loop scheduling after DSE-induced expression hoisting."""
grid = Grid((10, 10))
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)
const = Function(name="const", grid=grid, space_order=2)
# Deliberately inject into u1, rather than u1.forward, to create a WAR
eqn1 = Eq(u1.forward, u1 + sin(const))
eqn2 = sf1.inject(u1.forward, expr=sf1)
eqn3 = Eq(u2.forward, u2 - u1.dt2 + sin(const))
op = Operator([eqn1] + eqn2 + [eqn3])
trees = retrieve_iteration_tree(op)
# Check loop nest structure
assert len(trees) == 4
assert all(i.dim == j
for i, j in zip(trees[0], grid.dimensions)) # time invariant
assert trees[1][0].dim == trees[2][0].dim == trees[3][
0].dim == grid.time_dim
def test_inject_from_field(shape, coords, result, npoints=19):
"""Test point injection from a second field along a line
through the middle of the grid.
"""
a = unit_box(shape=shape)
spacing = a.data[tuple([1 for _ in shape])]
a.data[:] = 0.
b = DenseData(name='b', shape=a.data.shape)
b.data[:] = 1.
p = points(ranges=coords, npoints=npoints)
expr = p.inject(field=a, expr=b)
Operator(expr,
subs={
x.spacing: spacing,
y.spacing: spacing,
z.spacing: spacing
})(a=a, b=b)
indices = [slice(4, 6, 1) for _ in coords]
indices[0] = slice(1, -1, 1)
assert np.allclose(a.data[indices], result, rtol=1.e-5)
def test_basic(self):
grid = Grid(shape=(3, 3, 3))
u = TimeFunction(name='u', grid=grid)
op = Operator(Eq(u.forward, u + 1))
trees = retrieve_iteration_tree(op)
assert len(trees) == 1
assert trees[0][1].pragmas[0].value ==\
'omp target teams distribute parallel for collapse(3)'
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].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_parameters(self):
"""
Tests that we can actually generate code for a trivial operator
using constant and array data objects.
"""
grid = Grid(shape=(3,))
a_dense = Function(name='a_dense', grid=grid)
const = Constant(name='constant')
eqn = Eq(a_dense, a_dense + 2.*const)
op = Operator(eqn)
assert len(op.parameters) == 5
assert op.parameters[0].name == 'a_dense'
assert op.parameters[0].is_Tensor
assert op.parameters[1].name == 'constant'
assert op.parameters[1].is_Scalar
assert op.parameters[2].name == 'timers'
assert op.parameters[2].is_Object
assert op.parameters[3].name == 'x_M'
assert op.parameters[3].is_Scalar
assert op.parameters[4].name == 'x_m'
assert op.parameters[4].is_Scalar
assert 'a_dense[x + 1] = 2.0F*constant + a_dense[x + 1]' in str(op)
def test_array_rw(self):
grid = Grid(shape=(3, 3, 3))
f = Function(name='f', grid=grid)
u = TimeFunction(name='u', grid=grid, space_order=2)
eqn = Eq(u.forward, u*cos(f*2))
op = Operator(eqn)
assert len(op.body[1].header) == 7
assert str(op.body[1].header[0]) == 'float (*r1)[y_size][z_size];'
assert op.body[1].header[1].text ==\
'posix_memalign((void**)&r1, 64, sizeof(float[x_size][y_size][z_size]))'
assert op.body[1].header[2].value ==\
'omp target enter data map(alloc: r1[0:x_size][0:y_size][0:z_size])'
assert len(op.body[1].footer) == 6
assert str(op.body[1].footer[0]) == ''
assert op.body[1].footer[1].value ==\
'omp target exit data map(delete: r1[0:x_size][0:y_size][0:z_size])'
assert op.body[1].footer[2].text == 'free(r1)'
def test_timeparallel_reduction(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)
op = Operator(Inc(f[0], u + 1), opt='noop')
trees = retrieve_iteration_tree(op)
assert len(trees) == 1
tree = trees[0]
assert tree.root.is_Sequential
assert all(i.is_ParallelRelaxed and not i.is_Parallel
for i in tree[1:])
# The time loop is not in OpenMP canonical form, so it won't be parallelized
assert not tree.root.pragmas
assert len(tree[1].pragmas) == 1
assert tree[1].pragmas[0].value ==\
('omp target teams distribute parallel for collapse(3)'
' reduction(+:f[0])')
def test_expr_like_lowering(self):
"""
Test the lowering of an expr-like ConditionalDimension's condition.
This test makes an Operator that should indexify and lower the condition
passed in the Conditional Dimension
"""
grid = Grid(shape=(3, 3))
g1 = Function(name='g1', grid=grid)
g2 = Function(name='g2', grid=grid)
g1.data[:] = 0.49
g2.data[:] = 0.49
x, y = grid.dimensions
ci = ConditionalDimension(name='ci',
parent=y,
condition=Le((g1 + g2), 1.01 * (g1 + g2)))
f = Function(name='f', shape=grid.shape, dimensions=(x, ci))
Operator(Eq(f, g1 + g2)).apply()
assert np.all(f.data[:] == g1.data[:] + g2.data[:])
def test_no_fusion_convoluted(self):
"""
Conceptually like `test_no_fusion_simple`, but with more expressions
and non-trivial data flow.
"""
grid = Grid(shape=(4, 4, 4))
time = grid.time_dim
f = TimeFunction(name='f', grid=grid)
g = Function(name='g', grid=grid)
h = Function(name='h', grid=grid)
ctime = ConditionalDimension(name='ctime',
parent=time,
condition=time > 4)
eqns = [
Eq(f.forward, f + 1),
Eq(h, f + 1),
Eq(g, f + 1, implicit_dims=[ctime]),
Eq(f.forward, f + 1, implicit_dims=[ctime]),
Eq(f.forward, f + 1),
Eq(g, f + 1)
]
op = Operator(eqns)
exprs = FindNodes(Expression).visit(op._func_table['bf0'].root)
assert len(exprs) == 3
assert exprs[1].expr.rhs is exprs[0].output
assert exprs[2].expr.rhs is exprs[0].output
exprs = FindNodes(Expression).visit(op._func_table['bf1'].root)
assert len(exprs) == 3
exprs = FindNodes(Expression).visit(op._func_table['bf2'].root)
assert len(exprs) == 3
assert exprs[1].expr.rhs is exprs[0].output
assert exprs[2].expr.rhs is exprs[0].output
def mat_vec(A, x, b, optimize):
"""``Ax = b``."""
op = Operator(Inc(b, A*x), dle=optimize)
op.apply()
info('Executed `Ax = b`')
def transpose_mat_vec(A, x, b, optimize):
"""``A -> A^T, A^Tx = b``."""
i, j = A.indices
op = Operator([Inc(b, A[j, i]*x)], dle=optimize)
op.apply()
info('Executed `A^Tx = b`')
def mat_mat(A, B, C, optimize):
"""``AB = C``."""
op = Operator(Inc(C, A*B), dle=optimize)
op.apply()
info('Executed `AB = C`')
def mat_mat_sum(A, B, C, D, optimize):
"""``AB + AC = D``."""
op = Operator(Inc(D, A*B + A*C), dle=optimize)
op.apply()
info('Executed `AB + AC = D`')
def chain_contractions(A, B, C, D, E, F, optimize):
"""``AB + AC = D, DE = F``."""
op = Operator([Inc(D, A*B + A*C), Inc(F, D*E)], dle=optimize)
op.apply()
info('Executed `AB + AC = D, DE = F`')
