Sorting & searching: implement partition/argpartition, lexsort, nanargmax/nanargmin, sort_complex

[Nucs]

Overview

NumSharp covers the core of NumPy's Sorting & searching category (sort, argsort, searchsorted, arg*, nonzero, ...) but is missing 6 functions: the partial-sort pair, multi-key sort, NaN-aware argmin/argmax, and complex sort. This tracks adding them.

Problem

Two of the six (partition/argpartition) require a new introselect (quickselect) kernel -- the only genuinely new algorithm here; the other four are compositions over machinery NumSharp already has. argpartition/lexsort are widely used (top-k selection, multi-column sorting) and have no workaround today.

Verified codebase state

• Implemented (np.*): sort, argsort, searchsorted, argmax, argmin, argwhere, nonzero, flatnonzero, count_nonzero, where, extract.
• Missing (6 below): verified absent from np.* and as NDArray methods (reflection + source grep). Note: a Char8.PyBytes.Partition (bytes-string helper) and the internal NDIter engine exist but are unrelated to np.partition.

Proposal

Add under np.*. Implement the shared introselect kernel once (drives both partition and argpartition); the rest compose existing reductions/sorts.

Task checklist (ordered by real-world usage)

• argpartition (20,304) -- new introselect kernel (shared with partition)
• lexsort (13,944) -- stable multi-key argsort
• nanargmax (7,008) -- compose (NumSharp has nan-aware reductions)
• partition (6,612) -- new introselect kernel
• nanargmin (5,920) -- compose
• sort_complex (1,636) -- trivial

Evidence -- GitHub usage ranking

#	Function	GitHub hits	What it does	Effort
1	np.argpartition	20,304	indices that would partition the array (introselect, kth in place)	new introselect kernel (shared with partition)
2	np.lexsort	13,944	indirect stable sort on a sequence of keys (last key is primary)	stable multi-key argsort
3	np.nanargmax	7,008	index of the maximum, ignoring NaN	compose (NumSharp has nan-aware reductions)
4	np.partition	6,612	partial sort -- kth element in its final sorted position, sides unordered	new introselect kernel
5	np.nanargmin	5,920	index of the minimum, ignoring NaN	compose
6	np.sort_complex	1,636	sort a complex array by real part then imaginary part	trivial

Combined usage ~ 55,424 hits. Four of six compose from existing primitives; the two partial-sorts share one new introselect kernel.

_{Usage = GitHub REST code-search total_count in each function's canonical call form (np.<fn>(, or np.<fn>[ for the index-expression objects). It is an approximate estimate (noisy plus/minus ~10% on large sets) and counts only the dominant np. alias. Measured 2026-07-19; treat as relative demand, not exact.}

Scope / Non-goals

• kind= accepted for API parity; introselect is the only partition strategy NumPy actually implements.
• lexsort requires a stable argsort -- verify/extend NumSharp's argsort stability as part of this.
• NaN semantics must match NumPy exactly (all-NaN slice -> ValueError for nanarg*).

Related issues

• Part of the NumPy category-coverage sweep; sibling issues: Set routines: implement np.* set operations (isin, intersect1d, union1d, setdiff1d, setxor1d, unique_*) #622 (set) and Indexing routines: implement the 25 missing np.* indexing functions (diag, nditer, r_/c_, take_along_axis, ...) #624 (indexing). Umbrella / methodology: LinearAlgebra Missing Support #621 (linalg).