def test_sub_dimension_cache():
"""
Test that SubDimensions with same name but different attributes do not
alias to the same SubDimension. Conversely, if the name and the attributes
are the same, they must alias to the same SubDimension.
"""
x = Dimension('x')
xi0 = SubDimension.middle('xi', x, 1, 1)
xi1 = SubDimension.middle('xi', x, 1, 1)
assert xi0 is xi1
xl0 = SubDimension.left('xl', x, 2)
xl1 = SubDimension.left('xl', x, 2)
assert xl0 is xl1
xl2asxi = SubDimension.left('xi', x, 2)
assert xl2asxi is not xl1
assert xl2asxi is not xi1
xr0 = SubDimension.right('xr', x, 1)
xr1 = SubDimension.right('xr', x, 1)
assert xr0 is xr1
def test_sub_dimension(self):
"""Test that different SubDimensions have different hash value."""
d0 = Dimension(name='d')
d1 = Dimension(name='d', spacing=Scalar(name='s'))
di0 = SubDimension.middle('di', d0, 1, 1)
di1 = SubDimension.middle('di', d1, 1, 1)
assert hash(di0) != hash(d0)
assert hash(di0) != hash(di1)
dl0 = SubDimension.left('dl', d0, 2)
assert hash(dl0) != hash(di0)
def test_sub_dimension(self):
"""
Test that SubDimensions with same name but different attributes do not
alias to the same SubDimension. Conversely, if the name and the attributes
are the same, they must alias to the same SubDimension.
"""
x = Dimension('x')
xi0 = SubDimension.middle('xi', x, 1, 1)
xi1 = SubDimension.middle('xi', x, 1, 1)
assert xi0 is xi1
xl0 = SubDimension.left('xl', x, 2)
xl1 = SubDimension.left('xl', x, 2)
assert xl0 is xl1
xl2asxi = SubDimension.left('xi', x, 2)
assert xl2asxi is not xl1
assert xl2asxi is not xi1
xr0 = SubDimension.right('xr', x, 1)
xr1 = SubDimension.right('xr', x, 1)
assert xr0 is xr1
def test_bcs(self):
"""
Tests application of an Operator consisting of multiple equations
defined over different sub-regions, explicitly created through the
use of :class:`SubDimension`s.
"""
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_size(self):
"""Check the symbolic size of all possible SubDimensions is as expected."""
grid = Grid(shape=(4,))
x, = grid.dimensions
thickness = 4
xleft = SubDimension.left(name='xleft', parent=x, thickness=thickness)
assert xleft.symbolic_size == xleft.thickness.left[0]
xi = SubDimension.middle(name='xi', parent=x,
thickness_left=thickness, thickness_right=thickness)
assert xi.symbolic_size == (x.symbolic_max - x.symbolic_min -
xi.thickness.left[0] - xi.thickness.right[0] + 1)
xright = SubDimension.right(name='xright', parent=x, thickness=thickness)
assert xright.symbolic_size == xright.thickness.right[0]
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 :class:`SubDimension`s.
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 initialize_damp(damp, padsizes, spacing, fs=False):
"""
Initialise damping field with an absorbing boundary layer.
Includes basic constant Q setup (not interfaced yet) and assumes that
the peak frequency is 1/(10 * spacing).
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
"""
lqmin = np.log(.1)
lqmax = np.log(100)
w0 = 1 / (10 * np.max(spacing))
z = damp.dimensions[-1]
eqs = [Eq(damp, 1)]
for (nbl, nbr), d in zip(padsizes, damp.dimensions):
if not fs or d is not z:
nbl = max(5, nbl - 10) if d is z else nbl
# left
dim_l = SubDimension.left(name='abc_%s_l' % d.name,
parent=d,
thickness=nbl)
pos = Abs(dim_l - d.symbolic_min) / float(nbl)
eqs.append(
Eq(damp.subs({d: dim_l}), Min(damp.subs({d: dim_l}), pos)))
# right
dim_r = SubDimension.right(name='abc_%s_r' % d.name,
parent=d,
thickness=nbr)
pos = Abs(d.symbolic_max - dim_r) / float(nbr)
eqs.append(Eq(damp.subs({d: dim_r}), Min(damp.subs({d: dim_r}), pos)))
eqs.append(Eq(damp, w0 / exp(lqmin + damp * (lqmax - lqmin))))
Operator(eqs, name='initdamp')()
def test_iteration_property_vector(self, exprs, expected):
"""Tests detection of vector Iterations when using subdimensions."""
grid = Grid(shape=(20, 20))
x, y = grid.dimensions # noqa
t = grid.time_dim # noqa
# The leftmost 10 elements
yleft = SubDimension.left(name='yleft', parent=y, thickness=10) # noqa
u = TimeFunction(name='u', grid=grid, save=10, time_order=0, space_order=1) # 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)
iterations = FindNodes(Iteration).visit(op)
vectorizable = [i.dim.name for i in iterations if i.is_Vectorizable]
assert set(vectorizable) == set(expected)
def test_bcs_basic(self):
"""
Test MPI in presence of boundary condition loops. Here, no halo exchange
is expected (as there is no stencil in the computed expression) but we
check that:
* the left BC loop is computed by the leftmost rank only
* the right BC loop is computed by the rightmost rank only
"""
grid = Grid(shape=(20, ))
x = grid.dimensions[0]
t = grid.stepping_dim
thickness = 4
u = TimeFunction(name='u', grid=grid, 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)
t_in_centre = Eq(u[t + 1, xi], 1)
leftbc = Eq(u[t + 1, xleft], u[t + 1, xleft + 1] + 1)
rightbc = Eq(u[t + 1, xright], u[t + 1, xright - 1] + 1)
op = Operator([t_in_centre, leftbc, rightbc])
op.apply(time_m=1, time_M=1)
glb_pos_map = u.grid.distributor.glb_pos_map
if LEFT in glb_pos_map[x]:
assert np.all(u.data_ro_domain[0, thickness:] == 1.)
assert np.all(
u.data_ro_domain[0, :thickness] == range(thickness + 1, 1, -1))
else:
assert np.all(u.data_ro_domain[0, :-thickness] == 1.)
assert np.all(
u.data_ro_domain[0, -thickness:] == range(2, thickness + 2))
def test_subdimleft_parallel(self):
"""
Tests application of an Operator consisting of a subdimension
defined over different sub-regions, explicitly created through the
use of :class:`SubDimension`s.
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=0,
time_order=1)
xl = SubDimension.left(name='xl', parent=x, thickness=thickness)
yi = SubDimension.middle(name='yi',
parent=y,
thickness_left=thickness,
thickness_right=thickness)
# Can be done in parallel
eq = Eq(u[t + 1, xl, yi], u[t, xl, yi] + 1)
op = Operator([eq])
iterations = FindNodes(Iteration).visit(op)
assert all(i.is_Affine and i.is_Parallel for i in iterations
if i.dim in [xl, yi])
op.apply(time_m=0, time_M=0)
assert np.all(u.data[1, 0:thickness, 0:thickness] == 0)
assert np.all(u.data[1, 0:thickness, -thickness:] == 0)
assert np.all(u.data[1, 0:thickness, thickness:-thickness] == 1)
assert np.all(u.data[1, thickness + 1:, :] == 0)
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 test_nofission_as_unprofitable():
"""
Test there's no fission if not gonna increase number of collapsable loops.
"""
grid = Grid(shape=(20, 20))
x, y = grid.dimensions
t = grid.stepping_dim
yl = SubDimension.left(name='yl', parent=y, thickness=4)
yr = SubDimension.right(name='yr', parent=y, thickness=4)
u = TimeFunction(name='u', grid=grid)
eqns = [
Eq(u.forward, u[t + 1, x, y + 1] + 1.).subs(y, yl),
Eq(u.forward, u[t + 1, x, y - 1] + 1.).subs(y, yr)
]
op = Operator(eqns, opt='fission')
assert_structure(op, ['t,x,yl', 't,x,yr'], 't,x,yl,yr')
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) / (40)
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_cache_blocking_structure_subdims():
"""
Test that:
* With local SubDimensions no-blocking is expected.
* With non-local SubDimensions, blocking is expected.
"""
grid = Grid(shape=(4, 4, 4))
x, y, z = grid.dimensions
xi, yi, zi = grid.interior.dimensions
t = grid.stepping_dim
xl = SubDimension.left(name='xl', parent=x, thickness=4)
f = TimeFunction(name='f', grid=grid)
assert xl.local
# Local SubDimension -> no blocking expected
op = Operator(Eq(f[t + 1, xl, y, z], f[t, xl, y, z] + 1))
assert_blocking(op, {})
# Non-local SubDimension -> blocking expected
op = Operator(Eq(f.forward, f + 1, subdomain=grid.interior))
bns, _ = assert_blocking(op, {'i0x0_blk0'})
trees = retrieve_iteration_tree(bns['i0x0_blk0'])
tree = trees[0]
assert len(tree) == 5
assert tree[
0].dim.is_Incr and tree[0].dim.parent is xi and tree[0].dim.root is x
assert tree[
1].dim.is_Incr and tree[1].dim.parent is yi and tree[1].dim.root is y
assert tree[2].dim.is_Incr and tree[2].dim.parent is tree[0].dim and\
tree[2].dim.root is x
assert tree[3].dim.is_Incr and tree[3].dim.parent is tree[1].dim and\
tree[3].dim.root is y
assert not tree[
4].dim.is_Incr and tree[4].dim is zi and tree[4].dim.parent is z
def test_nontrivial_operator(self):
"""
Test MPI in a non-trivial scenario: ::
* 9 processes logically organised in a 3x3 cartesian grid (as opposed to
most tests in this module, which only use 2 or 4 processed);
* star-like stencil expression;
* non-trivial Higdon-like BCs;
* simultaneous presence of TimeFunction(grid), Function(grid), and
Function(dimensions)
"""
size_x, size_y = 9, 9
tkn = 2
# Grid and Dimensions
grid = Grid(shape=(
size_x,
size_y,
))
x, y = grid.dimensions
t = grid.stepping_dim
# SubDimensions to implement BCs
xl, yl = [SubDimension.left('%sl' % d.name, d, tkn) for d in [x, y]]
xi, yi = [
SubDimension.middle('%si' % d.name, d, tkn, tkn) for d in [x, y]
]
xr, yr = [SubDimension.right('%sr' % d.name, d, tkn) for d in [x, y]]
# Functions
u = TimeFunction(name='f', grid=grid)
m = Function(name='m', grid=grid)
c = Function(name='c', grid=grid, dimensions=(x, ), shape=(size_x, ))
# Data initialization
u.data_with_halo[:] = 0.
m.data_with_halo[:] = 1.
c.data_with_halo[:] = 0.
# Equations
c_init = Eq(c, 1.)
eqn = Eq(u[t + 1, xi, yi], u[t, xi, yi] + m[xi, yi] + c[xi] + 1.)
bc_left = Eq(u[t + 1, xl, yi], u[t + 1, xl + 1, yi] + 1.)
bc_right = Eq(u[t + 1, xr, yi], u[t + 1, xr - 1, yi] + 1.)
bc_top = Eq(u[t + 1, xi, yl], u[t + 1, xi, yl + 1] + 1.)
bc_bottom = Eq(u[t + 1, xi, yr], u[t + 1, xi, yr - 1] + 1.)
op = Operator([c_init, eqn, bc_left, bc_right, bc_top, bc_bottom])
op.apply(time=0)
# Expected (global view):
# 0 0 5 5 5 5 5 0 0
# 0 0 4 4 4 4 4 0 0
# 5 4 3 3 3 3 3 4 5
# 5 4 3 3 3 3 3 4 5
# 5 4 3 3 3 3 3 4 5
# 5 4 3 3 3 3 3 4 5
# 0 0 4 4 4 4 4 0 0
# 0 0 5 5 5 5 5 0 0
assert np.all(u.data_ro_domain[0] == 0) # The write occures at t=1
glb_pos_map = u.grid.distributor.glb_pos_map
# Check cornes
if LEFT in glb_pos_map[x] and LEFT in glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[0, 0, 5], [0, 0, 4], [5, 4, 3]])
elif LEFT in glb_pos_map[x] and RIGHT in glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[5, 0, 0], [4, 0, 0], [3, 4, 5]])
elif RIGHT in glb_pos_map[x] and LEFT in glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[5, 4, 3], [0, 0, 4], [0, 0, 5]])
elif RIGHT in glb_pos_map[x] and RIGHT in glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[3, 4, 5], [4, 0, 0], [5, 0, 0]])
# Check sides
if not glb_pos_map[x] and LEFT in glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[5, 4, 3], [5, 4, 3], [5, 4, 3]])
elif not glb_pos_map[x] and RIGHT in glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[3, 4, 5], [3, 4, 5], [3, 4, 5]])
elif LEFT in glb_pos_map[x] and not glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[5, 5, 5], [4, 4, 4], [3, 3, 3]])
elif RIGHT in glb_pos_map[x] and not glb_pos_map[y]:
assert np.all(
u.data_ro_domain[1] == [[3, 3, 3], [4, 4, 4], [5, 5, 5]])
# Check center
if not glb_pos_map[x] and not glb_pos_map[y]:
assert np.all(u.data_ro_domain[1] == 3)
