FMM driver¶

boxtree.fmm.
drive_fmm
(traversal, expansion_wrangler, src_weights, timing_data=None)¶ Toplevel driver routine for a fast multipole calculation.
In part, this is intended as a template for custom FMMs, in the sense that you may copy and paste its source code as a starting point.
Nonetheless, many common applications (such as pointtopoint FMMs) can be covered by supplying the right expansion_wrangler to this routine.
 Parameters
traversal – A
boxtree.traversal.FMMTraversalInfo
instance.expansion_wrangler – An object exhibiting the
ExpansionWranglerInterface
.src_weights – Source ‘density/weights/charges’. Passed unmodified to expansion_wrangler.
timing_data – Either None, or a
dict
that is populated with timing information for the stages of the algorithm (in the form ofTimingResult
), if such information is available.
Returns the potentials computed by expansion_wrangler.

class
boxtree.fmm.
ExpansionWranglerInterface
¶ Abstract expansion handling interface for use with
drive_fmm()
.See this test code for a very simple sample implementation.
Will usually hold a reference (and thereby be specific to) a
boxtree.Tree
instance.Functions that support returning timing data return a value supporting the
TimingFuture
interface.Changed in version 2018.1: Changed (a subset of) functions to return timing data.

multipole_expansion_zeros
()¶ Return an expansions array (which must support addition) capable of holding one multipole or local expansion for every box in the tree.

local_expansion_zeros
()¶ Return an expansions array (which must support addition) capable of holding one multipole or local expansion for every box in the tree.

output_zeros
()¶ Return a potentials array (which must support addition) capable of holding a potential value for each target in the tree. Note that
drive_fmm()
makes no assumptions about potential other than that it supports addition–it may consist of potentials, gradients of the potential, or arbitrary other pertarget output data.

reorder_sources
(source_array)¶ Return a copy of source_array in tree source order. source_array is in user source order.

reorder_potentials
(potentials)¶ Return a copy of potentials in user target order. source_weights is in tree target order.

form_multipoles
(level_start_source_box_nrs, source_boxes, src_weights)¶ Return an expansions array (compatible with
multipole_expansion_zeros()
) containing multipole expansions in source_boxes due to sources with src_weights. All other expansions must be zero. Returns
A pair (mpoles, timing_future).

coarsen_multipoles
(level_start_source_parent_box_nrs, source_parent_boxes, mpoles)¶ For each box in source_parent_boxes, gather (and translate) the box’s children’s multipole expansions in mpole and add the resulting expansion into the box’s multipole expansion in mpole.
 Returns
A pair (mpoles, timing_future).

eval_direct
(target_boxes, neighbor_sources_starts, neighbor_sources_lists, src_weights)¶ For each box in target_boxes, evaluate the influence of the neighbor sources due to src_weights, which use CSRlike interaction list storage and are indexed like target_boxes.
 Returns
A pair (pot, timing_future), where pot is a a new potential array, see
output_zeros()
.

multipole_to_local
(level_start_target_or_target_parent_box_nrs, target_or_target_parent_boxes, starts, lists, mpole_exps)¶ For each box in target_or_target_parent_boxes, translate and add the influence of the multipole expansion in mpole_exps into a new array of local expansions. starts and lists use CSRlike interaction list storage, and starts is indexed like target_or_target_parent_boxes.
 Returns
A pair (pot, timing_future) where pot is a new (local) expansion array, see
local_expansion_zeros()
.

eval_multipoles
(target_boxes_by_source_level, from_sep_smaller_by_level, mpole_exps)¶ For a level i, each box in target_boxes_by_source_level[i], evaluate the multipole expansion in mpole_exps in the nearby boxes given in from_sep_smaller_by_level, and return a new potential array. starts and lists in from_sep_smaller_by_level[i] use CSRlike interaction list storage and starts is indexed like target_boxes_by_source_level[i].
 Returns
A pair (pot, timing_future) where pot is a new potential array, see
output_zeros()
.

form_locals
(level_start_target_or_target_parent_box_nrs, target_or_target_parent_boxes, starts, lists, src_weights)¶ For each box in target_or_target_parent_boxes, form local expansions due to the sources in the nearby boxes given in starts and lists, and return a new local expansion array. starts and lists use CSRlike interaction list storage and starts is indexed like target_or_target_parent_boxes.
 Returns
A pair (pot, timing_future) where pot is a new local expansion array, see
local_expansion_zeros()
.

refine_locals
(level_start_target_or_target_parent_box_nrs, target_or_target_parent_boxes, local_exps)¶ For each box in child_boxes, translate the box’s parent’s local expansion in local_exps and add the resulting expansion into the box’s local expansion in local_exps.
 Returns
A pair (local_exps, timing_future).

eval_locals
(level_start_target_box_nrs, target_boxes, local_exps)¶ For each box in target_boxes, evaluate the local expansion in local_exps and return a new potential array.
 Returns
A pair (pot, timing_future) where pot is a new potential array, see
output_zeros()
.

finalize_potentials
(potentials)¶ Postprocess the reordered potentials. This is where global scaling factors could be applied. This is distinct from
reorder_potentials()
because some derived FMMs (notably the QBX FMM) do their own reordering.


class
boxtree.fmm.
TimingResult
(*args, **kwargs)¶ Interface for returned timing data.
This supports accessing timing results via a mapping interface, along with combining results via
merge()
.
merge
(other)¶ Merge this result with another by adding together common fields.
See constructor for
dict
.

class
boxtree.fmm.
TimingFuture
¶ Returns timing data for a potentially asynchronous operation.

result
()¶ Return a
TimingResult
. May block.

done
()¶ Return True if the operation is complete.

Integration with PyFMMLib¶
Integrates boxtree
with
pyfmmlib.

class
boxtree.pyfmmlib_integration.
FMMLibRotationDataInterface
¶ Abstract interface for additional, optional data for precomputation of rotation matrices passed to the expansion wrangler.

class
boxtree.pyfmmlib_integration.
FMMLibRotationData
(queue, trav)¶ An implementation of the
FMMLibRotationDataInterface
.

class
boxtree.pyfmmlib_integration.
FMMLibRotationDataNotSuppliedWarning
¶

class
boxtree.pyfmmlib_integration.
FMMLibExpansionWrangler
(tree, helmholtz_k, fmm_level_to_nterms=None, ifgrad=False, dipole_vec=None, dipoles_already_reordered=False, nterms=None, optimized_m2l_precomputation_memory_cutoff_bytes=100000000, rotation_data=None)¶ Implements the
boxtree.fmm.ExpansionWranglerInterface
by using pyfmmlib.Timing results returned by this wrangler contains the values wall_elapsed and (optionally, if supported) process_elapsed, which measure wall time and process time in seconds, respectively.
 Parameters
fmm_level_to_nterms – A callable that, upon being passed the tree and the tree level as an integer, returns the value of nterms for the multipole and local expansions on that level.
rotation_data – Either None or an instance of the
FMMLibRotationDataInterface
. In three dimensions, passing rotation_data enables optimized M2L (List 2) translations. In two dimensions, this does nothing.optimized_m2l_precomputation_memory_cutoff_bytes – When using optimized List 2 translations, an upper bound in bytes on the amount of storage to use for a precomputed rotation matrix.