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test_msparse.py
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/
test_msparse.py
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from math import floor
import pytest
import numpy as np
import scipy.sparse
from devito import Grid, TimeFunction, Eq, Operator, MatrixSparseTimeFunction
class TestMatrixSparseTimeFunction(object):
def _precompute_linear_interpolation(self, points, grid, origin):
""" Sample precompute function that, given point and grid information
precomputes gridpoints and coefficients according to a linear
scheme to be used in PrecomputedSparseFunction.
"""
gridpoints = [
tuple(
floor((point[i] - origin[i]) / grid.spacing[i]) for i in range(len(point))
)
for point in points
]
coefficients = np.zeros((len(points), 2, 2))
for i, point in enumerate(points):
for d in range(grid.dim):
coefficients[i, d, 0] = (
(gridpoints[i][d] + 1) * grid.spacing[d] - point[d]
) / grid.spacing[d]
coefficients[i, d, 1] = (
point[d] - gridpoints[i][d] * grid.spacing[d]
) / grid.spacing[d]
return gridpoints, coefficients
def test_precomputed_interpolation(self):
shape = (101, 101)
points = [(0.05, 0.9), (0.01, 0.8), (0.07, 0.84)]
origin = (0, 0)
grid = Grid(shape=shape, origin=origin)
x, y = grid.dimensions
r = 2
nt = 10
m = TimeFunction(name="m", grid=grid, space_order=0, save=nt, time_order=0)
for it in range(nt):
m.data[it, :] = it
gridpoints, coefficients = self._precompute_linear_interpolation(
points, grid, origin
)
mat = scipy.sparse.eye(len(points), dtype=np.float32)
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=mat, nt=nt)
sf.gridpoints.data[:] = gridpoints
sf.interpolation_coefficients[x].data[:] = coefficients[:, 0, :]
sf.interpolation_coefficients[y].data[:] = coefficients[:, 1, :]
eqn = sf.interpolate(m)
op = Operator(eqn)
sf.manual_scatter()
# args = op.arguments(time_m=0, time_M=9)
op(time_m=0, time_M=9)
sf.manual_gather()
for it in range(nt):
assert np.all(sf.data[it, :] == pytest.approx(it))
def test_precomputed_interpolation_empty(self):
shape = (101, 101)
origin = (0, 0)
grid = Grid(shape=shape, origin=origin)
x, y = grid.dimensions
# because we interpolate across 2 neighbouring points in each dimension
r = 2
nt = 10
m = TimeFunction(name="m", grid=grid, space_order=0, save=nt, time_order=0)
for it in range(nt):
m.data[it, :] = it
mat = scipy.sparse.coo_matrix((0, 0), dtype=np.float32)
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=mat, nt=nt)
eqn = sf.interpolate(m)
op = Operator(eqn)
sf.manual_scatter()
op(time_m=0, time_M=9)
sf.manual_gather()
# There are no receivers, so nothing to assert here
def test_precomputed2(self):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
nt = 10
m = TimeFunction(name="m", grid=grid, space_order=0, save=None, time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
matrix = scipy.sparse.eye(1, dtype=np.float32)
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=matrix, nt=nt)
# Lookup the exact point
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.data[:] = 0.0
step = [Eq(m.forward, m)]
interp = sf.interpolate(m)
op = Operator(step + interp)
sf.manual_scatter()
op(time_m=0, time_M=0)
sf.manual_gather()
assert sf.data[0, 0] == 1.0
def test_precomputed_subpoints(self):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
nt = 10
m = TimeFunction(name="m", grid=grid, space_order=0, save=None, time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
# Two-location source with 2 coefficients the same
matrix = scipy.sparse.coo_matrix(np.array([[1], [1]], dtype=np.float32))
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=matrix, nt=nt)
# Lookup the exact point
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.gridpoints.data[1, 0] = 39
sf.gridpoints.data[1, 1] = 39
sf.interpolation_coefficients[x].data[1, 0] = 1.0
sf.interpolation_coefficients[x].data[1, 1] = 2.0
sf.interpolation_coefficients[y].data[1, 0] = 1.0
sf.interpolation_coefficients[y].data[1, 1] = 2.0
sf.data[:] = 0.0
step = [Eq(m.forward, m)]
interp = sf.interpolate(m)
op = Operator(step + interp)
sf.manual_scatter()
op(time_m=0, time_M=0)
sf.manual_gather()
assert sf.data[0, 0] == 5.0
def test_precomputed_subpoints_inject(self):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
nt = 10
m = TimeFunction(name="m", grid=grid, space_order=0, save=None, time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
# Single two-component source with coefficients both +1
matrix = scipy.sparse.coo_matrix(np.array([[1], [1]], dtype=np.float32))
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=matrix, nt=nt)
# Lookup the exact point
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.gridpoints.data[1, 0] = 39
sf.gridpoints.data[1, 1] = 39
sf.interpolation_coefficients[x].data[1, 0] = 1.0
sf.interpolation_coefficients[x].data[1, 1] = 2.0
sf.interpolation_coefficients[y].data[1, 0] = 1.0
sf.interpolation_coefficients[y].data[1, 1] = 2.0
sf.data[0, 0] = 1.0
step = [Eq(m.forward, m)]
inject = sf.inject(field=m.forward, expr=sf)
op = Operator(step + inject)
sf.manual_scatter()
op(time_m=0, time_M=0)
sf.manual_gather()
assert m.data[1, 40, 40] == 6.0 # 1 + 1 + 4
assert m.data[1, 40, 41] == 2.0
assert m.data[1, 41, 40] == 2.0
assert m.data[1, 41, 41] == 4.0
assert m.data[1, 39, 39] == 1.0
assert m.data[1, 39, 40] == 2.0
assert m.data[1, 40, 39] == 2.0
def test_precomputed_subpoints_inject_dt2(self):
shape = (101, 101)
grid = Grid(shape=shape)
x, y = grid.dimensions
r = 2 # Constant for linear interpolation
# because we interpolate across 2 neighbouring points in each dimension
nt = 10
m = TimeFunction(name="m", grid=grid, space_order=0, save=None, time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
matrix = scipy.sparse.coo_matrix(np.array([[1], [1]], dtype=np.float32))
sf = MatrixSparseTimeFunction(
name="s", grid=grid, r=r, matrix=matrix, nt=nt, time_order=2
)
# Lookup the exact point
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.gridpoints.data[1, 0] = 39
sf.gridpoints.data[1, 1] = 39
sf.interpolation_coefficients[x].data[1, 0] = 1.0
sf.interpolation_coefficients[x].data[1, 1] = 2.0
sf.interpolation_coefficients[y].data[1, 0] = 1.0
sf.interpolation_coefficients[y].data[1, 1] = 2.0
# Single timestep, -0.5*1e-6, so that with dt=0.001, the .dt2 == 1 at t=1
sf.data[1, 0] = -5e-7
step = [Eq(m.forward, m)]
inject = sf.inject(field=m.forward, expr=sf.dt2)
op = Operator(step + inject)
sf.manual_scatter()
op(time_m=1, time_M=1, dt=0.001)
sf.manual_gather()
assert m.data[0, 40, 40] == pytest.approx(6.0) # 1 + 1 + 4
assert m.data[0, 40, 41] == pytest.approx(2.0)
assert m.data[0, 41, 40] == pytest.approx(2.0)
assert m.data[0, 41, 41] == pytest.approx(4.0)
assert m.data[0, 39, 39] == pytest.approx(1.0)
assert m.data[0, 39, 40] == pytest.approx(2.0)
assert m.data[0, 40, 39] == pytest.approx(2.0)
@pytest.mark.parallel(mode=4)
def test_mpi(self):
# Shape chosen to get a source in multiple ranks
shape = (91, 91)
grid = Grid(shape=shape)
x, y = grid.dimensions
# because we interpolate across 2 neighbouring points in each dimension
r = 2
nt = 10
# NOTE: halo on function (space_order//2?) must be at least >= r
m = TimeFunction(name="m", grid=grid, space_order=4, save=None, time_order=1)
m.data[:] = 0.0
m.data[:, 40, 40] = 1.0
m.data[:, 50, 50] = 1.0
# only rank 0 is allowed to have points
if grid.distributor.myrank == 0:
# A single dipole source - so two rows, one column
matrix = scipy.sparse.coo_matrix(np.array([[1], [-1]], dtype=np.float32))
else:
matrix = scipy.sparse.coo_matrix((0, 0), dtype=np.float32)
sf = MatrixSparseTimeFunction(name="s", grid=grid, r=r, matrix=matrix, nt=nt)
if grid.distributor.myrank == 0:
# First component of the dipole at 40, 40
sf.gridpoints.data[0, 0] = 40
sf.gridpoints.data[0, 1] = 40
sf.interpolation_coefficients[x].data[0, 0] = 1.0
sf.interpolation_coefficients[x].data[0, 1] = 2.0
sf.interpolation_coefficients[y].data[0, 0] = 1.0
sf.interpolation_coefficients[y].data[0, 1] = 2.0
sf.gridpoints.data[1, 0] = 50
sf.gridpoints.data[1, 1] = 50
sf.interpolation_coefficients[x].data[1, 0] = 2.0
sf.interpolation_coefficients[x].data[1, 1] = 2.0
sf.interpolation_coefficients[y].data[1, 0] = 2.0
sf.interpolation_coefficients[y].data[1, 1] = 2.0
op = Operator(sf.interpolate(m))
sf.manual_scatter()
args = op.arguments(time_m=0, time_M=9)
print("rank %d: %s" % (grid.distributor.myrank, str(args)))
op.apply(time_m=0, time_M=0)
sf.manual_gather()
for i in range(grid.distributor.nprocs):
print("==== from rank %d" % i)
if i == grid.distributor.myrank:
print(repr(sf.data))
grid.distributor.comm.Barrier()
if grid.distributor.myrank == 0:
assert sf.data[0, 0] == -3.0 # 1 * (1 * 1) * 1 + (-1) * (2 * 2) * 1