def test_adjoint_inject_interpolate(self, shape, coords, npoints=19):
"""
Verify that p.inject is the adjoint of p.interpolate for a
devito SparseFunction p
"""
a = unit_box(shape=shape)
a.data[:] = 0.
c = unit_box(shape=shape, name='c', grid=a.grid)
c.data[:] = 27.
assert a.grid == c.grid
# 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_adjoint_inject_interpolate(self, shape, coords, npoints=19):
"""
Verify that p.inject is the adjoint of p.interpolate for a
devito SparseFunction p
"""
a = unit_box(shape=shape)
a.data[:] = 0.
c = unit_box(shape=shape, name='c', grid=a.grid)
c.data[:] = 27.
assert a.grid == c.grid
# 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_interpolate_array(shape, coords, npoints=20):
"""Test generic point interpolation testing the x-coordinate of an
abitrary set of points going across the grid.
"""
a = unit_box(shape=shape)
p = points(a.grid, coords, npoints=npoints)
xcoords = p.coordinates.data[:, 0]
expr = p.interpolate(a)
Operator(expr)(a=a, points=p.data[:])
assert np.allclose(p.data[:], xcoords, rtol=1e-6)
def test_interpolate_array(shape, coords, npoints=20):
"""Test generic point interpolation testing the x-coordinate of an
abitrary set of points going across the grid.
"""
a = unit_box(shape=shape)
p = points(a.grid, coords, npoints=npoints)
xcoords = p.coordinates.data[:, 0]
expr = p.interpolate(a)
Operator(expr)(a=a, points=p.data[:])
assert np.allclose(p.data[:], xcoords, rtol=1e-6)
def test_inject(shape, coords, result, npoints=19):
"""Test point injection with a set of points forming a line
through the middle of the grid.
"""
a = unit_box(shape=shape)
a.data[:] = 0.
p = points(a.grid, ranges=coords, npoints=npoints)
expr = p.inject(a, FLOAT(1.))
Operator(expr)(a=a)
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_interpolate_custom(shape, coords, npoints=20):
"""Test generic point interpolation testing the x-coordinate of an
abitrary set of points going across the grid.
"""
a = unit_box(shape=shape)
p = custom_points(a.grid, coords, npoints=npoints)
xcoords = p.coordinates.data[:, 0]
p.data[:] = 1.
expr = p.interpolate(a * p.indices[0])
Operator(expr)(a=a)
assert np.allclose(p.data[0, :], 0.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[1, :], 1.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[2, :], 2.0 * xcoords, rtol=1e-6)
def test_inject(shape, coords, result, npoints=19):
"""Test point injection with a set of points forming a line
through the middle of the grid.
"""
a = unit_box(shape=shape)
a.data[:] = 0.
p = points(a.grid, ranges=coords, npoints=npoints)
expr = p.inject(a, FLOAT(1.))
Operator(expr)(a=a)
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_interpolate_custom(shape, coords, npoints=20):
"""Test generic point interpolation testing the x-coordinate of an
abitrary set of points going across the grid.
"""
a = unit_box(shape=shape)
p = custom_points(a.grid, coords, npoints=npoints)
xcoords = p.coordinates.data[:, 0]
p.data[:] = 1.
expr = p.interpolate(a * p.indices[0])
Operator(expr)(a=a)
assert np.allclose(p.data[0, :], 0.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[1, :], 1.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[2, :], 2.0 * xcoords, rtol=1e-6)
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)
a.data[:] = 0.
b = Function(name='b', grid=a.grid)
b.data[:] = 1.
p = points(a.grid, ranges=coords, npoints=npoints)
expr = p.inject(field=a, expr=b)
Operator(expr)(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_interpolate_indexed(shape, coords, npoints=20):
"""Test generic point interpolation testing the x-coordinate of an
abitrary set of points going across the grid. Unlike other tests,
here we interpolate an expression built using the indexed notation.
"""
a = unit_box(shape=shape)
p = custom_points(a.grid, coords, npoints=npoints)
xcoords = p.coordinates.data[:, 0]
p.data[:] = 1.
expr = p.interpolate(a[a.grid.dimensions] * p.indices[0])
Operator(expr)(a=a)
assert np.allclose(p.data[0, :], 0.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[1, :], 1.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[2, :], 2.0 * xcoords, rtol=1e-6)
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)
a.data[:] = 0.
b = Function(name='b', grid=a.grid)
b.data[:] = 1.
p = points(a.grid, ranges=coords, npoints=npoints)
expr = p.inject(field=a, expr=b)
Operator(expr)(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_interpolate_indexed(shape, coords, npoints=20):
"""Test generic point interpolation testing the x-coordinate of an
abitrary set of points going across the grid. Unlike other tests,
here we interpolate an expression built using the indexed notation.
"""
a = unit_box(shape=shape)
p = custom_points(a.grid, coords, npoints=npoints)
xcoords = p.coordinates.data[:, 0]
p.data[:] = 1.
expr = p.interpolate(a[a.grid.dimensions] * p.indices[0])
Operator(expr)(a=a)
assert np.allclose(p.data[0, :], 0.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[1, :], 1.0 * xcoords, rtol=1e-6)
assert np.allclose(p.data[2, :], 2.0 * xcoords, rtol=1e-6)
def test_interpolation_dx():
"""
Test interpolation of a SparseFunction from a Derivative of
a Function.
"""
u = unit_box(shape=(11, 11))
sf1 = SparseFunction(name='s', grid=u.grid, npoint=1)
sf1.coordinates.data[0, :] = (0.5, 0.5)
op = Operator(sf1.interpolate(u.dx))
assert sf1.data.shape == (1, )
u.data[:] = 0.0
u.data[5, 5] = 4.0
u.data[4, 5] = 2.0
u.data[6, 5] = 2.0
op.apply()
# Exactly in the middle of 4 points, only 1 nonzero is 4
assert sf1.data[0] == pytest.approx(-20.0)