Direct Solver: Recursive Skeletonization by alexfikl · Pull Request #164 · inducer/pytential

alexfikl · 2022-06-30T07:39:54Z

Attempting to break up the direct solver MR into smaller, more reviewable pieces. As a rundown

[Done] Add proxy generation (already in linalg.proxy).
[Done] Add single-level skeletonization (Direct Solver: Skeletonization #30).
[WIP] Add multi-level skeletonization (Direct Solver: Recursive Skeletonization #164).
[WIP] Add the actual multi-level direct solver (Direct Solver: Multilevel Proxy-based Solver #174).

The code for this is mostly in the deprecated https://gitlab.tiker.net/inducer/pytential/-/merge_requests/137.

alexfikl · 2022-07-14T15:12:05Z

@inducer This should be ready for a look. It doesn't do much:

adds a data structure to hold the hierarchical cluster info from boxtree.Tree and merge cluster indices.
adds some helper functions to do the recursive skeletonization + simple tests.

inducer

Noticed a pending review. Figured it'd be better to submit it. :) Don't quite know how old this is.

inducer · 2022-07-01T15:19:57Z

pytential/linalg/cluster.py

+
+        Current level that is represented.
+
+    .. attribute:: nlevels


Is this avoidable?

Reworked this a while back, so not quite sure if your comment still applies?

pytential/linalg/cluster.py

inducer · 2022-07-01T15:20:42Z

pytential/linalg/cluster.py

+# {{{ cluster tree
+
+@dataclass(frozen=True)
+class ClusterTreeLevel:


Is this two things rather than one?

Yeah, separated into a ClusterTree and ClusterLevel with a ClusterTree.levels() iterator to go through them for the recursive skeletonization.

Naming could still be better probably?

inducer · 2022-07-01T15:21:06Z

test/test_linalg_skeletonization.py

    logger.info("\n%s", case)

-    run_skeletonize_by_proxy(actx, case, case.resolutions[0], visualize=visualize)
+    dd = sym.DOFDescriptor(case.name, discr_stage=case.skel_discr_stage)


Update the test docstring to describe precisely what's being tested here.

Updated the blurb in
https://github.com/inducer/pytential/compare/f71a21b1a54791b02b35712225b9cfaca4be60cf..9a8db7ff410051a6b7d86cd8d5b934d02d094fef

Let me know if it's clear enough!

Copilot

Pull request overview

This PR advances the direct solver work by introducing hierarchical clustering infrastructure and wiring it into proxy-based skeletonization to enable recursive (multi-level) skeletonization, along with the associated test and documentation updates.

Changes:

Add a new pytential.linalg.cluster module providing cluster trees/levels, clustering helpers, and partition_by_nodes.
Extend skeletonization to produce richer results (including diagonal blocks) and add rec_skeletonize_by_proxy for multi-level skeletonization.
Update proxy and skeletonization tests (and docs) to match the new clustering/tree and neighbor-gathering APIs.

Reviewed changes

Copilot reviewed 11 out of 11 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
`pytential/linalg/cluster.py`	New clustering module (cluster tree/levels, partitioning, visualization utilities).
`pytential/linalg/skeletonization.py`	Adds recursive skeletonization and augments skeletonization results/weighting/logging.
`pytential/linalg/proxy.py`	Removes `partition_by_nodes` (moved to cluster module) and updates neighbor gathering API.
`pytential/linalg/utils.py`	Documents/exports helper utilities used by skeletonization (`make_flat_cluster_diag`, `interp_decomp`).
`test/extra_matrix_data.py`	Updates test fixtures to return `(index, tree)` and import partitioning from `linalg.cluster`.
`test/test_linalg_cluster.py`	New tests for cluster tree construction and (un)clustering behavior.
`test/test_linalg_proxy.py`	Adapts tests to updated cluster index return type and neighbor gathering signature.
`test/test_linalg_skeletonization.py`	Updates tests to exercise multilevel skeletonization flow.
`test/test_matrix.py`	Adapts callers to updated `get_cluster_index` / `get_tgt_src_cluster_index` return type.
`doc/linalg.rst`	Includes `pytential.linalg.cluster` in the linalg documentation.
`doc/conf.py`	Adds/adjusts intersphinx mappings for new referenced types.

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Copilot · 2026-02-20T07:41:06Z

pytential/linalg/cluster.py

+    if discr.ambient_dim == 2:
+        _visualize_clusters_2d(actx, generator, discr, srcindex, tree, filename,
+                               dofdesc=dofdesc, overwrite=overwrite)
+    elif discr.ambient_dim == 2:


The 3D branch in visualize_clusters is unreachable because both the if and elif check discr.ambient_dim == 2. This prevents 3D visualization and will raise NotImplementedError for ambient_dim == 3. The elif condition should check for ambient_dim == 3.

Suggested change

elif discr.ambient_dim == 2:

elif discr.ambient_dim == 3:

Copilot · 2026-02-20T07:41:06Z

pytential/linalg/cluster.py

+        ax = fig.gca()
+
+        plotter = TreePlotter(tree._tree)
+        plotter.set_bounding_box()
+        plotter.draw_tree(fill=False, edgecolor="black", zorder=10)


_visualize_clusters_2d unconditionally constructs TreePlotter(tree._tree). When partition_by_nodes(..., tree_kind=None) is used, ClusterTree._tree is None, so visualization will crash. Consider either raising a clearer error if tree._tree is None or skipping tree plotting in that case.

Copilot · 2026-02-20T07:41:06Z

pytential/linalg/skeletonization.py

+    for i, clevel in enumerate(ctree.levels[:-1]):
+        for ibrow, ibcol in product(range(wrangler.nrows), range(wrangler.ncols)):
+            skeleton = _skeletonize_block_by_proxy_with_mats(
+                actx, ibrow, ibcol, proxy.places, proxy, wrangler, tgt_src_index,
+                id_eps=id_eps,
+                # NOTE: we probably never want to set the rank here?
+                id_rank=None,
+                rng=rng,
+                max_particles_in_box=max_particles_in_box)


rec_skeletonize_by_proxy takes places as an argument, but passes proxy.places into _skeletonize_block_by_proxy_with_mats. If a caller supplies _proxy built from a different GeometryCollection than places, the evaluation will use inconsistent geometries. Consider passing places through (and/or asserting proxy.places is places) to avoid subtle mismatches.

Copilot · 2026-02-20T07:41:07Z

pytential/linalg/skeletonization.py

    """Evaluate the proxy to cluster and neighbor to cluster interactions for
    each cluster in *cluster_index*.
    """


Docstring for _evaluate_proxy_skeletonization_interaction still refers to *cluster_index*, but the function now takes source_index/target_index. Updating the wording to match the new parameter names would avoid confusion for future readers.

Copilot · 2026-02-20T07:41:07Z

pytential/linalg/cluster.py

+    assert isinstance(discr, Discretization)
+
+    if tree_kind is not None:
+        setup_actx = lpot_source._setup_actx


In partition_by_nodes, setup_actx is taken from lpot_source._setup_actx, but places.get_geometry(...) can be a plain meshmode.discretization.Discretization (e.g. when GeometryCollection is built from a discretization), which does not provide _setup_actx. gather_cluster_neighbor_points handles this by using discr._setup_actx instead. Consider using discr._setup_actx here (or branching on the type) to avoid an AttributeError when tree_kind is not None.

Suggested change

setup_actx = lpot_source._setup_actx

if hasattr(lpot_source, "_setup_actx"):

setup_actx = lpot_source._setup_actx

else:

setup_actx = discr._setup_actx

alexfikl changed the title ~~Direct Solver:~~ Direct Solver: Recursive Skeletonization Jun 30, 2022

alexfikl force-pushed the direct-solver-recursion branch 5 times, most recently from 39e8347 to 80bb8e1 Compare July 1, 2022 15:00

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alexfikl marked this pull request as ready for review July 14, 2022 12:31

alexfikl requested a review from inducer July 14, 2022 15:12

alexfikl force-pushed the direct-solver-recursion branch 3 times, most recently from 7ed33f4 to ea42c82 Compare August 2, 2022 06:24

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alexfikl mentioned this pull request Aug 4, 2022

Direct Solver: Multilevel Proxy-based Solver #174

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inducer reviewed Aug 23, 2022

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alexfikl mentioned this pull request Aug 12, 2025

Add more types to linalg #271

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alexfikl mentioned this pull request Aug 19, 2025

Improvements to pytential.linalg #272

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add recursive clustering and skeletonization

50b4825

alexfikl force-pushed the direct-solver-recursion branch from 0490e47 to 50b4825 Compare February 13, 2026 12:35

alexfikl requested a review from Copilot February 20, 2026 07:37

Copilot started reviewing on behalf of alexfikl February 20, 2026 07:37 View session

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alexfikl commented Jun 30, 2022 •

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