feat: add Caratheodory and Tree recombination.

Adds a new `recombination.py` module to the solvers subpackage,
providing a generalised `RecombinationSolver`, in addition to the
`CaratheodoryRecombination` and `TreeRecombination` solvers.

A `RecombinationSolverTest` case has been added to `test_solvers.py`,
covering the known degenerate cases that may arise in recombination.

The documentation has been updated where required, but no dedicated
new examples/documentation pages have been created.

Refs: #497

.cspell/custom_misc.txt

@@ -3,6 +3,7 @@ ANNchor
 approximator
 approximators
 archiveprefix
+binom
 cand
 coreax
 coreset
@@ -24,18 +25,23 @@ kdtree
 kernelised
 kernelized
 KSD
+mapsto
 ml.p3.8xlarge
 ndmin
 parsable
 PCIMQ
+phdthesis
 PMLR
 primaryclass
 PRNG
+rcond
+recomb
 refs
 regulariser
 RKHS
 RPCHOLESKY
 sigmas
+subseteq
 supp
 TLDR
 typecheck

.cspell/library_terms.txt

@@ -22,6 +22,7 @@ brightgreen
 bysource
 cmap
 color
+Concretization
 dispname
 dollarmath
 dtype
@@ -30,8 +31,10 @@ dunder
 eigh
 emibcn
 eprint
+errstate
 figsize
 finfo
+flatnonzero
 fori_loop
 fracv
 furo
@@ -112,6 +115,7 @@ sklearn
 softplus
 sphinxcontrib
 sphobjinv
+tensordot
 texttt
 toctree
 tomli
@@ -124,6 +128,7 @@ unsrt
 vars
 viewcode
 vmap
+vmaps
 writebytes
 xlabel
 ylabel

.cspell/people.txt

@@ -1,4 +1,5 @@
 Benard
+Caratheodory
 Chatalic
 Duvenaud
 Epperly
@@ -13,6 +14,8 @@ Jaehoon
 Jiaxin
 Jitkrittum
 Kanagawa
+Litterer
+Lyons
 Martinsson
 Motonobu
 Nystr
@@ -26,6 +29,8 @@ Schreuder
 Smirnov
 Smola
 Staber
+Tchakaloff
+Tchernychova
 Tropp
 Veiga
 Wittawat

coreax/solvers/__init__.py

@@ -32,6 +32,11 @@
     RPCholeskyState,
     SteinThinning,
 )
+from coreax.solvers.recombination import (
+    CaratheodoryRecombination,
+    RecombinationSolver,
+    TreeRecombination,
+)
 
 __all__ = [
     "CompositeSolver",
@@ -49,4 +54,7 @@
     "PaddingInvariantSolver",
     "GreedyKernelPoints",
     "GreedyKernelPointsState",
+    "RecombinationSolver",
+    "CaratheodoryRecombination",
+    "TreeRecombination",
 ]

coreax/solvers/base.py

@@ -112,7 +112,7 @@ class PaddingInvariantSolver(Solver):
     A :class:`Solver` whose results are invariant to zero weighted data.
 
     In some cases, such as in :class:`coreax.solvers.MapReduce`, there is a need to pad
-    data to ensure shape stability. In some cases, we may assign zero weight to the
+    data to ensure shape stability. In these cases, we may assign zero weight to the
     padded data points, which allows certain 'padding invariant' solvers to return the
     same values on a call to :meth:`~coreax.solvers.Solver.reduce` as would have been
     returned if no padding were present.