def test_collocation_interpolation_identity():
# Check if interpolation followed by collocation on the same grid
# is the identity
rect = odl.IntervalProd([0, 0], [1, 1])
part = odl.uniform_partition_fromintv(rect, [4, 2])
space = odl.FunctionSpace(rect)
dspace = odl.rn(part.size)
coll_op_c = PointCollocation(space, part, dspace, order='C')
coll_op_f = PointCollocation(space, part, dspace, order='F')
interp_ops_c = [
NearestInterpolation(space, part, dspace, variant='left', order='C'),
NearestInterpolation(space, part, dspace, variant='right', order='C'),
LinearInterpolation(space, part, dspace, order='C'),
PerAxisInterpolation(space, part, dspace, order='C',
schemes=['linear', 'nearest'])]
interp_ops_f = [
NearestInterpolation(space, part, dspace, variant='left', order='F'),
NearestInterpolation(space, part, dspace, variant='right', order='F'),
LinearInterpolation(space, part, dspace, order='F'),
PerAxisInterpolation(space, part, dspace, order='F',
schemes=['linear', 'nearest'])]
values = np.arange(1, 9, dtype='float64')
for interp_op_c in interp_ops_c:
ident_values = coll_op_c(interp_op_c(values))
assert all_almost_equal(ident_values, values)
for interp_op_f in interp_ops_f:
ident_values = coll_op_f(interp_op_f(values))
assert all_almost_equal(ident_values, values)
def test_collocation_interpolation_identity():
"""Check if collocation is left-inverse to interpolation."""
# Interpolation followed by collocation on the same grid should be
# the identity
rect = odl.IntervalProd([0, 0], [1, 1])
part = odl.uniform_partition_fromintv(rect, [4, 2])
space = odl.FunctionSpace(rect)
tspace = odl.rn(part.shape)
coll_op = PointCollocation(space, part, tspace)
interp_ops = [
NearestInterpolation(space, part, tspace, variant='left'),
NearestInterpolation(space, part, tspace, variant='right'),
LinearInterpolation(space, part, tspace),
PerAxisInterpolation(space,
part,
tspace,
schemes=['linear', 'nearest'])
]
values = np.arange(1, 9, dtype='float64').reshape(tspace.shape)
for interp_op in interp_ops:
ident_values = coll_op(interp_op(values))
assert all_almost_equal(ident_values, values)
def test_per_axis_interpolation():
"""Test different interpolation schemes per axis."""
rect = odl.IntervalProd([0, 0], [1, 1])
part = odl.uniform_partition_fromintv(rect, [4, 2], nodes_on_bdry=False)
# Coordinate vectors are:
# [0.125, 0.375, 0.625, 0.875], [0.25, 0.75]
fspace = odl.FunctionSpace(rect)
tspace = odl.rn(part.shape)
schemes = ['linear', 'nearest']
variants = [None, 'right']
interp_op = PerAxisInterpolation(fspace,
part,
tspace,
schemes=schemes,
nn_variants=variants)
values = np.arange(1, 9, dtype='float64').reshape(part.shape)
function = interp_op(values)
rvals = values.reshape([4, 2])
# Evaluate at single point
val = function([0.3, 0.5])
l1 = (0.3 - 0.125) / (0.375 - 0.125)
# 0.5 equally far from both neighbors -> 'right' chooses 0.75
true_val = (1 - l1) * rvals[0, 1] + l1 * rvals[1, 1]
assert val == pytest.approx(true_val)
# Input array, with and without output array
pts = np.array([[0.3, 0.6], [0.1, 0.25], [1.0, 1.0]])
l1 = (0.3 - 0.125) / (0.375 - 0.125)
true_val_1 = (1 - l1) * rvals[0, 1] + l1 * rvals[1, 1]
l1 = (0.125 - 0.1) / (0.375 - 0.125)
true_val_2 = (1 - l1) * rvals[0, 0] # only lower left contributes
l1 = (1.0 - 0.875) / (0.875 - 0.625)
true_val_3 = (1 - l1) * rvals[3, 1] # lower left only
true_arr = [true_val_1, true_val_2, true_val_3]
assert all_equal(function(pts.T), true_arr)
out = np.empty(3, dtype='float64')
function(pts.T, out=out)
assert all_equal(out, true_arr)
# Input meshgrid, with and without output array
mg = sparse_meshgrid([0.3, 1.0], [0.4, 0.85])
# Indices: (1, 3) x (0, 1)
lx1 = (0.3 - 0.125) / (0.375 - 0.125)
lx2 = (1.0 - 0.875) / (0.875 - 0.625)
true_val_11 = (1 - lx1) * rvals[0, 0] + lx1 * rvals[1, 0]
true_val_12 = ((1 - lx1) * rvals[0, 1] + lx1 * rvals[1, 1])
true_val_21 = (1 - lx2) * rvals[3, 0]
true_val_22 = (1 - lx2) * rvals[3, 1]
true_mg = [[true_val_11, true_val_12], [true_val_21, true_val_22]]
assert all_equal(function(mg), true_mg)
out = np.empty((2, 2), dtype='float64')
function(mg, out=out)
assert all_equal(out, true_mg)
assert repr(interp_op) != ''