def _bmat(blocks, dtypes):
from pytools import single_valued
from pytential.symbolic.matrix import is_zero
nrows = blocks.shape[0]
ncolumns = blocks.shape[1]
# "block row starts"/"block column starts"
brs = np.cumsum([0] + [
single_valued(blocks[ibrow, ibcol].shape[0]
for ibcol in range(ncolumns)
if not is_zero(blocks[ibrow, ibcol]))
for ibrow in range(nrows)
])
bcs = np.cumsum([0] + [
single_valued(blocks[ibrow, ibcol].shape[1] for ibrow in range(nrows)
if not is_zero(blocks[ibrow, ibcol]))
for ibcol in range(ncolumns)
])
result = np.zeros((brs[-1], bcs[-1]),
dtype=np.find_common_type(dtypes, []))
for ibcol in range(ncolumns):
for ibrow in range(nrows):
result[brs[ibrow]:brs[ibrow + 1], bcs[ibcol]:bcs[ibcol + 1]] = \
blocks[ibrow, ibcol]
return result
def _bmat(blocks, dtypes):
from pytools import single_valued
from pytential.symbolic.matrix import is_zero
nrows = blocks.shape[0]
ncolumns = blocks.shape[1]
# "block row starts"/"block column starts"
brs = np.cumsum([0]
+ [single_valued(blocks[ibrow, ibcol].shape[0]
for ibcol in range(ncolumns)
if not is_zero(blocks[ibrow, ibcol]))
for ibrow in range(nrows)])
bcs = np.cumsum([0]
+ [single_valued(blocks[ibrow, ibcol].shape[1]
for ibrow in range(nrows)
if not is_zero(blocks[ibrow, ibcol]))
for ibcol in range(ncolumns)])
result = np.zeros((brs[-1], bcs[-1]),
dtype=np.find_common_type(dtypes, []))
for ibcol in range(ncolumns):
for ibrow in range(nrows):
result[brs[ibrow]:brs[ibrow + 1], bcs[ibcol]:bcs[ibcol + 1]] = \
blocks[ibrow, ibcol]
return result
def build_matrix(actx,
places,
exprs,
input_exprs,
domains=None,
auto_where=None,
context=None):
"""
:arg actx: a :class:`~meshmode.array_context.ArrayContext`.
:arg places: a :class:`~pytential.symbolic.execution.GeometryCollection`.
Alternatively, any list or mapping that is a valid argument for its
constructor can also be used.
:arg exprs: an array of expressions corresponding to the output block
rows of the matrix. May also be a single expression.
:arg input_exprs: an array of expressions corresponding to the
input block columns of the matrix. May also be a single expression.
:arg domains: a list of discretization identifiers (see 'places') or
*None* values indicating the domains on which each component of the
solution vector lives. *None* values indicate that the component
is a scalar. If *None*, *auto_where* or, if it is not provided,
:class:`~pytential.symbolic.primitives.DEFAULT_SOURCE` is required
to be a key in :attr:`places`.
:arg auto_where: For simple source-to-self or source-to-target
evaluations, find 'where' attributes automatically.
"""
if context is None:
context = {}
from pytential import GeometryCollection
if not isinstance(places, GeometryCollection):
places = GeometryCollection(places, auto_where=auto_where)
exprs = _prepare_expr(places, exprs, auto_where=auto_where)
if not (isinstance(exprs, np.ndarray) and exprs.dtype.char == "O"):
from pytools.obj_array import make_obj_array
exprs = make_obj_array([exprs])
try:
input_exprs = list(input_exprs)
except TypeError:
# not iterable, wrap in a list
input_exprs = [input_exprs]
domains = _prepare_domains(len(input_exprs), places, domains,
places.auto_source)
from pytential.symbolic.matrix import MatrixBuilder, is_zero
nblock_rows = len(exprs)
nblock_columns = len(input_exprs)
blocks = np.zeros((nblock_rows, nblock_columns), dtype=np.object)
dtypes = []
for ibcol in range(nblock_columns):
dep_source = places.get_geometry(domains[ibcol].geometry)
dep_discr = places.get_discretization(domains[ibcol].geometry,
domains[ibcol].discr_stage)
mbuilder = MatrixBuilder(actx,
dep_expr=input_exprs[ibcol],
other_dep_exprs=(input_exprs[:ibcol] +
input_exprs[ibcol + 1:]),
dep_source=dep_source,
dep_discr=dep_discr,
places=places,
context=context)
for ibrow in range(nblock_rows):
block = mbuilder(exprs[ibrow])
assert is_zero(block) or isinstance(block, np.ndarray)
blocks[ibrow, ibcol] = block
if isinstance(block, np.ndarray):
dtypes.append(block.dtype)
return actx.from_numpy(_bmat(blocks, dtypes))
def build_matrix(queue, places, exprs, input_exprs, domains=None,
auto_where=None, context=None):
"""
:arg queue: a :class:`pyopencl.CommandQueue`.
:arg places: a :class:`pytential.symbolic.execution.GeometryCollection`.
Alternatively, any list or mapping that is a valid argument for its
constructor can also be used.
:arg exprs: an array of expressions corresponding to the output block
rows of the matrix. May also be a single expression.
:arg input_exprs: an array of expressions corresponding to the
input block columns of the matrix. May also be a single expression.
:arg domains: a list of discretization identifiers (see 'places') or
*None* values indicating the domains on which each component of the
solution vector lives. *None* values indicate that the component
is a scalar. If *None*, *auto_where* or, if it is not provided,
:class:`~pytential.symbolic.primitives.DEFAULT_SOURCE` is required
to be a key in :attr:`places`.
:arg auto_where: For simple source-to-self or source-to-target
evaluations, find 'where' attributes automatically.
"""
if context is None:
context = {}
from pytools.obj_array import is_obj_array, make_obj_array
if not isinstance(places, GeometryCollection):
places = GeometryCollection(places, auto_where=auto_where)
exprs = _prepare_expr(places, exprs)
if not is_obj_array(exprs):
exprs = make_obj_array([exprs])
try:
input_exprs = list(input_exprs)
except TypeError:
# not iterable, wrap in a list
input_exprs = [input_exprs]
domains = _prepare_domains(len(input_exprs), places, domains,
places._default_source_place)
from pytential.symbolic.matrix import MatrixBuilder, is_zero
nblock_rows = len(exprs)
nblock_columns = len(input_exprs)
blocks = np.zeros((nblock_rows, nblock_columns), dtype=np.object)
dtypes = []
for ibcol in range(nblock_columns):
mbuilder = MatrixBuilder(
queue,
dep_expr=input_exprs[ibcol],
other_dep_exprs=(input_exprs[:ibcol]
+ input_exprs[ibcol + 1:]),
dep_source=places[domains[ibcol]],
dep_discr=places.get_discretization(domains[ibcol]),
places=places,
context=context)
for ibrow in range(nblock_rows):
block = mbuilder(exprs[ibrow])
assert is_zero(block) or isinstance(block, np.ndarray)
blocks[ibrow, ibcol] = block
if isinstance(block, np.ndarray):
dtypes.append(block.dtype)
return cl.array.to_device(queue, _bmat(blocks, dtypes))