def test_fd_adjoint(self, so, ndim, derivative, adjoint_name):
grid = Grid(shape=tuple([51] * ndim), extent=tuple([25] * ndim))
x = grid.dimensions[0]
f = Function(name='f', grid=grid, space_order=so)
f_deriv = Function(name='f_deriv', grid=grid, space_order=so)
g = Function(name='g', grid=grid, space_order=so)
g_deriv = Function(name='g_deriv', grid=grid, space_order=so)
# Fill f and g with smooth cos/sin
Operator(
[Eq(g, x * cos(2 * np.pi * x / 5)),
Eq(f, sin(2 * np.pi * x / 8))]).apply()
# Check symbolic expression are expected ones for the adjoint .T
deriv = getattr(f, derivative)
coeff = 1 if derivative == 'dx2' else -1
expected = coeff * getattr(f, derivative).evaluate.subs(
{x.spacing: -x.spacing})
assert simplify(deriv.T.evaluate) == simplify(bypass_uneval(expected))
# Compute numerical derivatives and verify dot test
# i.e <f.dx, g> = <f, g.dx.T>
eq_f = Eq(f_deriv, deriv)
eq_g = Eq(g_deriv, getattr(g, derivative).T)
op = Operator([eq_f, eq_g])
op()
a = np.dot(f_deriv.data.reshape(-1), g.data.reshape(-1))
b = np.dot(g_deriv.data.reshape(-1), f.data.reshape(-1))
assert np.isclose(1 - a / b, 0, atol=1e-5)
def trig_func(model):
"""
Trigonometric function of the tilt and azymuth angles.
"""
try:
theta = model.theta
except AttributeError:
theta = 0
costheta = cos(theta)
sintheta = sin(theta)
if model.dim == 3:
try:
phi = model.phi
except AttributeError:
phi = 0
cosphi = cos(phi)
sinphi = sin(phi)
return costheta, sintheta, cosphi, sinphi
return costheta, sintheta
def test_simd_space_invariant(self):
"""
Similar to test_space_invariant_v3, testing simd vectorization happens
in the correct place.
"""
grid = Grid(shape=(10, 10, 10))
x, y, z = grid.dimensions
f = Function(name='f', grid=grid)
eq = Inc(f, cos(x * y) + cos(x * z))
op = Operator(eq, opt=('advanced', {'openmp': True}))
iterations = FindNodes(Iteration).visit(op)
assert 'omp for collapse(1) schedule(static,1)' in iterations[
0].pragmas[0].value
assert 'omp simd' in iterations[1].pragmas[0].value
assert 'omp simd' in iterations[3].pragmas[0].value
op.apply()
assert np.isclose(np.linalg.norm(f.data), 37.1458, rtol=1e-5)
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, language='openmp')
assert len(op.body.allocs) == 1
assert str(op.body.allocs[0]) ==\
('float * r0_vec = (float *)'
'omp_target_alloc(x_size*y_size*z_size*sizeof(float),'
'omp_get_default_device());')
assert len(op.body.maps) == 2
assert all('r0' not in str(i) for i in op.body.maps)
assert len(op.body.frees) == 1
assert str(op.body.frees[0]) ==\
'omp_target_free(r0_vec,omp_get_default_device());'
assert len(op.body.unmaps) == 3
assert all('r0' not in str(i) for i in op.body.unmaps)
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, language='openmp')
assert len(op.body[2].header) == 7
assert str(op.body[2].header[0]) == 'float (*r0)[y_size][z_size];'
assert op.body[2].header[1].text ==\
'posix_memalign((void**)&r0, 64, sizeof(float[x_size][y_size][z_size]))'
assert op.body[2].header[2].value ==\
('omp target enter data map(alloc: r0[0:x_size][0:y_size][0:z_size])'
'')
assert len(op.body[2].footer) == 6
assert str(op.body[2].footer[0]) == ''
assert op.body[2].footer[1].value ==\
('omp target exit data map(delete: r0[0:x_size][0:y_size][0:z_size])'
' if((x_size != 0) && (y_size != 0) && (z_size != 0))')
assert op.body[2].footer[2].text == 'free(r0)'