def prepare_coefficient(coefficient, num, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients.
:arg coefficient: UFL Coefficient
:arg num: coefficient index in the original form
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: GEM expression referring to the Coefficient value
"""
varexp = gem.Variable(name, (None, None))
if coefficient.ufl_element().family() == 'Real':
size = numpy.prod(coefficient.ufl_shape, dtype=int)
data = gem.view(varexp, slice(num, num + 1), slice(size))
return gem.reshape(data, (), coefficient.ufl_shape)
element = create_element(coefficient.ufl_element())
size = numpy.prod(element.index_shape, dtype=int)
def expression(data):
result, = prune(
[gem.reshape(gem.view(data, slice(size)), element.index_shape)])
return result
if not interior_facet:
data = gem.view(varexp, slice(num, num + 1), slice(size))
return expression(gem.reshape(data, (), (size, )))
else:
data_p = gem.view(varexp, slice(num, num + 1), slice(size))
data_m = gem.view(varexp, slice(num, num + 1), slice(size, 2 * size))
return (expression(gem.reshape(data_p, (), (size, ))),
expression(gem.reshape(data_m, (), (size, ))))
def prepare_coefficient(coefficient, num, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients.
:arg coefficient: UFL Coefficient
:arg num: coefficient index in the original form
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: GEM expression referring to the Coefficient value
"""
varexp = gem.Variable(name, (None, None))
if coefficient.ufl_element().family() == 'Real':
size = numpy.prod(coefficient.ufl_shape, dtype=int)
data = gem.view(varexp, slice(num, num + 1), slice(size))
return gem.reshape(data, (), coefficient.ufl_shape)
element = create_element(coefficient.ufl_element())
size = numpy.prod(element.index_shape, dtype=int)
def expression(data):
result, = prune([gem.reshape(gem.view(data, slice(size)), element.index_shape)])
return result
if not interior_facet:
data = gem.view(varexp, slice(num, num + 1), slice(size))
return expression(gem.reshape(data, (), (size,)))
else:
data_p = gem.view(varexp, slice(num, num + 1), slice(size))
data_m = gem.view(varexp, slice(num, num + 1), slice(size, 2 * size))
return (expression(gem.reshape(data_p, (), (size,))),
expression(gem.reshape(data_m, (), (size,))))
def test_view_view(matrix):
expression = gem.view(gem.view(matrix, slice(3, 8), slice(5, 12)),
slice(4), slice(3, 6))
assert expression.shape == (4, 3)
actual = [convert(expression, multiindex)
for multiindex in numpy.ndindex(expression.shape)]
assert list(product(range(3, 7), range(8, 11))) == actual
def test_view_view(matrix):
expression = gem.view(gem.view(matrix, slice(3, 8), slice(5, 12)),
slice(4), slice(3, 6))
assert expression.shape == (4, 3)
actual = [convert(expression, multiindex)
for multiindex in numpy.ndindex(expression.shape)]
assert list(product(range(3, 7), range(8, 11))) == actual
def prepare_coefficient(coefficient, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients.
:arg coefficient: UFL Coefficient
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: (funarg, expression)
funarg - :class:`coffee.Decl` function argument
expression - GEM expression referring to the Coefficient
values
"""
assert isinstance(interior_facet, bool)
if coefficient.ufl_element().family() == 'Real':
# Constant
funarg = coffee.Decl(SCALAR_TYPE,
coffee.Symbol(name),
pointers=[("restrict", )],
qualifiers=["const"])
expression = gem.reshape(gem.Variable(name, (None, )),
coefficient.ufl_shape)
return funarg, expression
finat_element = create_element(coefficient.ufl_element())
if isinstance(finat_element, TensorFiniteElement):
scalar_shape = finat_element.base_element.index_shape
tensor_shape = finat_element.index_shape[len(scalar_shape):]
else:
scalar_shape = finat_element.index_shape
tensor_shape = ()
scalar_size = numpy.prod(scalar_shape, dtype=int)
tensor_size = numpy.prod(tensor_shape, dtype=int)
funarg = coffee.Decl(SCALAR_TYPE,
coffee.Symbol(name),
pointers=[("const", "restrict"), ("restrict", )],
qualifiers=["const"])
if not interior_facet:
expression = gem.reshape(
gem.Variable(name, (scalar_size, tensor_size)), scalar_shape,
tensor_shape)
else:
varexp = gem.Variable(name, (2 * scalar_size, tensor_size))
plus = gem.view(varexp, slice(scalar_size), slice(tensor_size))
minus = gem.view(varexp, slice(scalar_size, 2 * scalar_size),
slice(tensor_size))
expression = (gem.reshape(plus, scalar_shape, tensor_shape),
gem.reshape(minus, scalar_shape, tensor_shape))
return funarg, expression
def test_view_reshape(vector):
expression = gem.view(gem.reshape(vector, (3, 4)), slice(2), slice(1, 3))
assert expression.shape == (2, 2)
actual = [convert(expression, multiindex)
for multiindex in numpy.ndindex(expression.shape)]
assert [(1,), (2,), (5,), (6,)] == actual
def test_reshape_shape(vector):
expression = gem.reshape(gem.view(vector, slice(5, 11)), (3, 2))
assert expression.shape == (3, 2)
actual = [convert(expression, multiindex)
for multiindex in numpy.ndindex(expression.shape)]
assert [(i,) for i in range(5, 11)] == actual
def test_view_reshape(vector):
expression = gem.view(gem.reshape(vector, (3, 4)), slice(2), slice(1, 3))
assert expression.shape == (2, 2)
actual = [convert(expression, multiindex)
for multiindex in numpy.ndindex(expression.shape)]
assert [(1,), (2,), (5,), (6,)] == actual
def test_reshape_shape(vector):
expression = gem.reshape(gem.view(vector, slice(5, 11)), (3, 2))
assert expression.shape == (3, 2)
actual = [convert(expression, multiindex)
for multiindex in numpy.ndindex(expression.shape)]
assert [(i,) for i in range(5, 11)] == actual
def prepare_arguments(arguments, multiindices, scalar_type, interior_facet=False, diagonal=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg multiindices: Argument multiindices
:arg interior_facet: interior facet integral?
:arg diagonal: Are we assembling the diagonal of a rank-2 element tensor?
:returns: (funarg, expression)
funarg - :class:`loopy.GlobalArg` function argument
expressions - GEM expressions referring to the argument
tensor
"""
assert isinstance(interior_facet, bool)
if len(arguments) == 0:
# No arguments
funarg = lp.GlobalArg("A", dtype=scalar_type, shape=(1,))
expression = gem.Indexed(gem.Variable("A", (1,)), (0,))
return funarg, [expression]
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
shapes = tuple(element.index_shape for element in elements)
if diagonal:
if len(arguments) != 2:
raise ValueError("Diagonal only for 2-forms")
try:
element, = set(elements)
except ValueError:
raise ValueError("Diagonal only for diagonal blocks (test and trial spaces the same)")
elements = (element, )
shapes = tuple(element.index_shape for element in elements)
multiindices = multiindices[:1]
def expression(restricted):
return gem.Indexed(gem.reshape(restricted, *shapes),
tuple(chain(*multiindices)))
u_shape = numpy.array([numpy.prod(shape, dtype=int) for shape in shapes])
if interior_facet:
c_shape = tuple(2 * u_shape)
slicez = [[slice(r * s, (r + 1) * s)
for r, s in zip(restrictions, u_shape)]
for restrictions in product((0, 1), repeat=len(arguments))]
else:
c_shape = tuple(u_shape)
slicez = [[slice(s) for s in u_shape]]
funarg = lp.GlobalArg("A", dtype=scalar_type, shape=c_shape)
varexp = gem.Variable("A", c_shape)
expressions = [expression(gem.view(varexp, *slices)) for slices in slicez]
return funarg, prune(expressions)
def _slate2gem_block(expr, self):
child, = map(self, expr.children)
child_shapes = expr.children[0].shapes
offsets = tuple(
sum(shape[:idx])
for shape, (idx, *_) in zip(child_shapes.values(), expr._indices))
return view(
child,
*(slice(idx, idx + extent)
for idx, extent in zip(offsets, expr.shape)))
def test_pickle_gem(protocol):
f = gem.VariableIndex(gem.Indexed(gem.Variable('facet', (2,)), (1,)))
q = gem.Index()
r = gem.Index()
_1 = gem.Indexed(gem.Literal(numpy.random.rand(3, 6, 8)), (f, q, r))
_2 = gem.Indexed(gem.view(gem.Variable('w', (None, None)), slice(8), slice(1)), (r, 0))
expr = gem.ComponentTensor(gem.IndexSum(gem.Product(_1, _2), (r,)), (q,))
unpickled = pickle.loads(pickle.dumps(expr, protocol))
assert repr(expr) == repr(unpickled)
def prepare_arguments(arguments,
multiindices,
scalar_type,
interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg multiindices: Argument multiindices
:arg interior_facet: interior facet integral?
:returns: (funarg, prepare, expressions)
funarg - :class:`coffee.Decl` function argument
prepare - list of COFFEE nodes to be prepended to the
kernel body
expressions - GEM expressions referring to the argument
tensor
"""
funarg = coffee.Decl(scalar_type, coffee.Symbol("A"), pointers=[()])
varexp = gem.Variable("A", (None, ))
if len(arguments) == 0:
# No arguments
zero = coffee.FlatBlock("memset({name}, 0, sizeof(*{name}));\n".format(
name=funarg.sym.gencode()))
return funarg, [zero], [gem.reshape(varexp, ())]
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
shapes = [element.index_shape for element in elements]
indices = tuple(chain(*multiindices))
def expression(restricted):
return gem.Indexed(gem.reshape(restricted, *shapes), indices)
u_shape = numpy.array(
[numpy.prod(element.index_shape, dtype=int) for element in elements])
if interior_facet:
c_shape = tuple(2 * u_shape)
slicez = [[
slice(r * s, (r + 1) * s) for r, s in zip(restrictions, u_shape)
] for restrictions in product((0, 1), repeat=len(arguments))]
else:
c_shape = tuple(u_shape)
slicez = [[slice(s) for s in u_shape]]
expressions = [
expression(gem.view(gem.reshape(varexp, c_shape), *slices))
for slices in slicez
]
zero = coffee.FlatBlock(
str.format("memset({name}, 0, {size} * sizeof(*{name}));\n",
name=funarg.sym.gencode(),
size=numpy.product(c_shape, dtype=int)))
return funarg, [zero], prune(expressions)
def prepare_coefficient(coefficient, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients.
:arg coefficient: UFL Coefficient
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: (funarg, expression)
funarg - :class:`coffee.Decl` function argument
expression - GEM expression referring to the Coefficient
values
"""
assert isinstance(interior_facet, bool)
if coefficient.ufl_element().family() == 'Real':
# Constant
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("restrict",)],
qualifiers=["const"])
expression = gem.reshape(gem.Variable(name, (None,)),
coefficient.ufl_shape)
return funarg, expression
finat_element = create_element(coefficient.ufl_element())
shape = finat_element.index_shape
size = numpy.prod(shape, dtype=int)
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("restrict",)],
qualifiers=["const"])
if not interior_facet:
expression = gem.reshape(gem.Variable(name, (size,)), shape)
else:
varexp = gem.Variable(name, (2 * size,))
plus = gem.view(varexp, slice(size))
minus = gem.view(varexp, slice(size, 2 * size))
expression = (gem.reshape(plus, shape),
gem.reshape(minus, shape))
return funarg, expression
def test_pickle_gem(protocol):
f = gem.VariableIndex(gem.Indexed(gem.Variable('facet', (2, )), (1, )))
q = gem.Index()
r = gem.Index()
_1 = gem.Indexed(gem.Literal(numpy.random.rand(3, 6, 8)), (f, q, r))
_2 = gem.Indexed(
gem.view(gem.Variable('w', (None, None)), slice(8), slice(1)), (r, 0))
expr = gem.ComponentTensor(gem.IndexSum(gem.Product(_1, _2), (r, )), (q, ))
unpickled = pickle.loads(pickle.dumps(expr, protocol))
assert repr(expr) == repr(unpickled)
def prepare_coefficient(coefficient, name, scalar_type, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients.
:arg coefficient: UFL Coefficient
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: (funarg, expression)
funarg - :class:`loopy.GlobalArg` function argument
expression - GEM expression referring to the Coefficient
values
"""
assert isinstance(interior_facet, bool)
if coefficient.ufl_element().family() == 'Real':
# Constant
funarg = lp.GlobalArg(name,
dtype=scalar_type,
shape=(coefficient.ufl_element().value_size(), ))
expression = gem.reshape(gem.Variable(name, (None, )),
coefficient.ufl_shape)
return funarg, expression
finat_element = create_element(coefficient.ufl_element())
shape = finat_element.index_shape
size = numpy.prod(shape, dtype=int)
if not interior_facet:
expression = gem.reshape(gem.Variable(name, (size, )), shape)
else:
varexp = gem.Variable(name, (2 * size, ))
plus = gem.view(varexp, slice(size))
minus = gem.view(varexp, slice(size, 2 * size))
expression = (gem.reshape(plus, shape), gem.reshape(minus, shape))
size = size * 2
funarg = lp.GlobalArg(name, dtype=scalar_type, shape=(size, ))
return funarg, expression
def prepare_arguments(arguments, multiindices, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg multiindices: Argument multiindices
:arg interior_facet: interior facet integral?
:returns: (funarg, prepare, expressions)
funarg - :class:`coffee.Decl` function argument
prepare - list of COFFEE nodes to be prepended to the
kernel body
expressions - GEM expressions referring to the argument
tensor
"""
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A"), pointers=[()])
varexp = gem.Variable("A", (None,))
if len(arguments) == 0:
# No arguments
zero = coffee.FlatBlock(
"memset({name}, 0, sizeof(*{name}));\n".format(name=funarg.sym.gencode())
)
return funarg, [zero], [gem.reshape(varexp, ())]
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
shapes = [element.index_shape for element in elements]
indices = tuple(chain(*multiindices))
def expression(restricted):
return gem.Indexed(gem.reshape(restricted, *shapes), indices)
u_shape = numpy.array([numpy.prod(element.index_shape, dtype=int)
for element in elements])
if interior_facet:
c_shape = tuple(2 * u_shape)
slicez = [[slice(r * s, (r + 1) * s)
for r, s in zip(restrictions, u_shape)]
for restrictions in product((0, 1), repeat=len(arguments))]
else:
c_shape = tuple(u_shape)
slicez = [[slice(s) for s in u_shape]]
expressions = [expression(gem.view(gem.reshape(varexp, c_shape), *slices))
for slices in slicez]
zero = coffee.FlatBlock(
str.format("memset({name}, 0, {size} * sizeof(*{name}));\n",
name=funarg.sym.gencode(), size=numpy.product(c_shape, dtype=int))
)
return funarg, [zero], prune(expressions)
def prepare_arguments(arguments,
multiindices,
scalar_type,
interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg multiindices: Argument multiindices
:arg interior_facet: interior facet integral?
:returns: (funarg, expression)
funarg - :class:`coffee.Decl` function argument
expressions - GEM expressions referring to the argument
tensor
"""
assert isinstance(interior_facet, bool)
if len(arguments) == 0:
# No arguments
funarg = coffee.Decl(scalar_type, coffee.Symbol("A", rank=(1, )))
expression = gem.Indexed(gem.Variable("A", (1, )), (0, ))
return funarg, [expression]
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
shapes = tuple(element.index_shape for element in elements)
def expression(restricted):
return gem.Indexed(gem.reshape(restricted, *shapes),
tuple(chain(*multiindices)))
u_shape = numpy.array([numpy.prod(shape, dtype=int) for shape in shapes])
if interior_facet:
c_shape = tuple(2 * u_shape)
slicez = [[
slice(r * s, (r + 1) * s) for r, s in zip(restrictions, u_shape)
] for restrictions in product((0, 1), repeat=len(arguments))]
else:
c_shape = tuple(u_shape)
slicez = [[slice(s) for s in u_shape]]
funarg = coffee.Decl(scalar_type, coffee.Symbol("A", rank=c_shape))
varexp = gem.Variable("A", c_shape)
expressions = [expression(gem.view(varexp, *slices)) for slices in slicez]
return funarg, prune(expressions)
def prepare_arguments(arguments, multiindices, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg multiindices: Argument multiindices
:arg interior_facet: interior facet integral?
:returns: (funarg, expression)
funarg - :class:`coffee.Decl` function argument
expressions - GEM expressions referring to the argument
tensor
"""
assert isinstance(interior_facet, bool)
if len(arguments) == 0:
# No arguments
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=(1,)))
expression = gem.Indexed(gem.Variable("A", (1,)), (0,))
return funarg, [expression]
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
shapes = tuple(element.index_shape for element in elements)
def expression(restricted):
return gem.Indexed(gem.reshape(restricted, *shapes),
tuple(chain(*multiindices)))
u_shape = numpy.array([numpy.prod(shape, dtype=int) for shape in shapes])
if interior_facet:
c_shape = tuple(2 * u_shape)
slicez = [[slice(r * s, (r + 1) * s)
for r, s in zip(restrictions, u_shape)]
for restrictions in product((0, 1), repeat=len(arguments))]
else:
c_shape = tuple(u_shape)
slicez = [[slice(s) for s in u_shape]]
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=c_shape))
varexp = gem.Variable("A", c_shape)
expressions = [expression(gem.view(varexp, *slices)) for slices in slicez]
return funarg, prune(expressions)
def expression(data):
result, = prune([gem.reshape(gem.view(data, slice(size)), element.index_shape)])
return result
def expression(data):
result, = prune(
[gem.reshape(gem.view(data, slice(size)), element.index_shape)])
return result
def expressions(data):
return prune([transpose(gem.reshape(gem.view(data, slice_), shape), rank)
for slice_, shape, rank in zip(slices, transposed_shapes, tensor_ranks)])
def prepare_coefficients(coefficients, num, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients.
:arg coefficients: split UFL Coefficients
:arg num: coefficient index in the original form
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: GEM expression referring to the Coefficient value
"""
varexp = gem.Variable(name, (None, None))
if len(coefficients) == 1 and coefficients[0].ufl_element().family() == 'Real':
coefficient, = coefficients
size = numpy.prod(coefficient.ufl_shape, dtype=int)
data = gem.view(varexp, slice(num, num + 1), slice(size))
expression = gem.reshape(data, (), coefficient.ufl_shape)
return [expression]
elements = [create_element(coeff.ufl_element()) for coeff in coefficients]
space_dimensions = [numpy.prod(element.index_shape, dtype=int)
for element in elements]
ends = list(numpy.cumsum(space_dimensions))
starts = [0] + ends[:-1]
slices = [slice(start, end) for start, end in zip(starts, ends)]
transposed_shapes = []
tensor_ranks = []
for element in elements:
if isinstance(element, TensorFiniteElement):
scalar_shape = element.base_element.index_shape
tensor_shape = element.index_shape[len(scalar_shape):]
else:
scalar_shape = element.index_shape
tensor_shape = ()
transposed_shapes.append(tensor_shape + scalar_shape)
tensor_ranks.append(len(tensor_shape))
def transpose(expr, rank):
assert not expr.free_indices
assert 0 <= rank < len(expr.shape)
if rank == 0:
return expr
else:
indices = tuple(gem.Index(extent=extent) for extent in expr.shape)
transposed_indices = indices[rank:] + indices[:rank]
return gem.ComponentTensor(gem.Indexed(expr, indices),
transposed_indices)
def expressions(data):
return prune([transpose(gem.reshape(gem.view(data, slice_), shape), rank)
for slice_, shape, rank in zip(slices, transposed_shapes, tensor_ranks)])
size = sum(space_dimensions)
if not interior_facet:
data = gem.view(varexp, slice(num, num + 1), slice(size))
return expressions(gem.reshape(data, (), (size,)))
else:
data_p = gem.view(varexp, slice(num, num + 1), slice(size))
data_m = gem.view(varexp, slice(num, num + 1), slice(size, 2 * size))
return list(zip(expressions(gem.reshape(data_p, (), (size,))),
expressions(gem.reshape(data_m, (), (size,)))))