Tune MatrixWorkspace LU and QR solve paths

[saschatimme]

Summary

This updates MatrixWorkspace to keep its matrix and factor buffers as plain Matrix{ComplexF64} storage, then routes larger square/rectangular solves through stdlib/LAPACK paths where the benchmarks favor them.

Changes:

• remove StructArray storage from MatrixWorkspace; optimize_data_structure remains accepted as a no-op
• use custom pivoting/lower solve plus stdlib UpperTriangular for the small custom LU/QR solve paths
• cache exact-zero upper diagonal status during custom factorization so repeated workspace solves avoid rescanning the diagonal
• use stdlib LU for square systems with n >= 28
• use stdlib QR for rectangular systems with column count n >= 44
• add breakpoint correctness tests for LU n=27/28, QR n=43/44, plus a rectangular QR case

Validation

• test/linear_algebra_test.jl: 54/54 passing
• targeted surrounding tests:
  • Tracker: 125/125 passing
  • Linear Spaces: 45/45 passing
• upper-solve guard microbenchmark: cached singular flag was faster than per-solve diagonal precheck for 55 / 58 sizes, average cached/precheck ratio 0.984x
• benchmark comparison: clean origin/main at 09484cee versus this branch, single-threaded BLAS, BenchmarkTools.@belapsed, workload is MatrixWorkspace full update! + ldiv!

Benchmark Summary

Shape	Sizes	Wins	Average relative speedup
Square LU n x n	n=3:60	55 / 58	1.339x
Rectangular QR 2n x n	n=3:60	55 / 58	1.100x

Absolute speedup is main_time_ns - branch_time_ns; relative speedup is main_time_ns / branch_time_ns. Negative absolute speedups indicate branch was slower for that size.

n	main ns	branch ns	absolute speedup ns	relative speedup
3	98	118	-20	0.831x
4	132	140	-8	0.943x
5	167	169	-2	0.988x
6	241	230	11	1.048x
7	311	286	25	1.087x
8	377	361	16	1.044x
9	441	413	28	1.068x
10	516	470	46	1.098x
11	645	586	59	1.101x
12	797	719	78	1.108x
13	891	801	90	1.112x
14	1012	917	95	1.104x
15	1217	1083	134	1.124x
16	1375	1233	142	1.115x
17	1617	1425	192	1.135x
18	1854	1633	221	1.135x
19	2009	1883	126	1.067x
20	2269	2093	176	1.084x
21	2565	2384	181	1.076x
22	2907	2736	171	1.062x
23	3240	3094	146	1.047x
24	3620	3338	282	1.084x
25	3979	3703	276	1.075x
26	5028	4131	897	1.217x
27	5840	4696	1144	1.244x
28	6075	4827	1248	1.259x
29	6867	5430	1437	1.265x
30	7469	5826	1643	1.282x
31	7917	6425	1492	1.232x
32	8750	6542	2208	1.338x
33	9250	7417	1833	1.247x
34	9958	7136	2822	1.395x
35	10625	7917	2708	1.342x
36	11875	8180	3695	1.452x
37	12375	9041	3334	1.369x
38	13292	9056	4236	1.468x
39	14042	9959	4083	1.410x
40	15166	10042	5124	1.510x
41	16250	11000	5250	1.477x
42	17208	11583	5625	1.486x
43	18542	12583	5959	1.474x
44	20041	12500	7541	1.603x
45	21417	13833	7584	1.548x
46	23125	14125	9000	1.637x
47	24500	15750	8750	1.556x
48	25833	15375	10458	1.680x
49	27583	16792	10791	1.643x
50	27916	17166	10750	1.626x
51	30083	19125	10958	1.573x
52	31625	18833	12792	1.679x
53	33417	20166	13251	1.657x
54	35667	20917	14750	1.705x
55	38167	22833	15334	1.672x
56	39042	22500	16542	1.735x
57	50250	24125	26125	2.083x
58	43750	24958	18792	1.753x
59	45916	26958	18958	1.703x
60	48291	26417	21874	1.828x

n	m	main ns	branch ns	absolute speedup ns	relative speedup
3	6	144	151	-7	0.954x
4	8	211	213	-2	0.991x
5	10	313	304	9	1.030x
6	12	445	420	25	1.060x
7	14	604	567	37	1.065x
8	16	797	752	45	1.060x
9	18	1033	983	50	1.051x
10	20	1338	1271	67	1.053x
11	22	1692	1600	92	1.058x
12	24	2088	2009	79	1.039x
13	26	2713	2463	250	1.102x
14	28	3271	3042	229	1.075x
15	30	3932	3630	302	1.083x
16	32	4810	4369	441	1.101x
17	34	5583	5201	382	1.073x
18	36	6617	6133	484	1.079x
19	38	7636	7156	480	1.067x
20	40	8750	8278	472	1.057x
21	42	9917	9458	459	1.049x
22	44	11333	10791	542	1.050x
23	46	12833	12291	542	1.044x
24	48	14416	13833	583	1.042x
25	50	16125	15541	584	1.038x
26	52	18042	17333	709	1.041x
27	54	20083	19250	833	1.043x
28	56	22208	21458	750	1.035x
29	58	24417	23625	792	1.034x
30	60	26875	26042	833	1.032x
31	62	29416	28625	791	1.028x
32	64	32250	31375	875	1.028x
33	66	35250	34500	750	1.022x
34	68	38458	37666	792	1.021x
35	70	41833	42041	-208	0.995x
36	72	45542	44541	1001	1.022x
37	74	49875	48583	1292	1.027x
38	76	53667	52375	1292	1.025x
39	78	58083	56166	1917	1.034x
40	80	62500	60875	1625	1.027x
41	82	67500	65250	2250	1.034x
42	84	72375	70000	2375	1.034x
43	86	77084	74833	2251	1.030x
44	88	82542	73708	8834	1.120x
45	90	88083	78709	9374	1.119x
46	92	93750	81709	12041	1.147x
47	94	100167	87792	12375	1.141x
48	96	106208	89375	16833	1.188x
49	98	113000	94833	18167	1.192x
50	100	119667	100084	19583	1.196x
51	102	126792	103916	22876	1.220x
52	104	133916	104250	29666	1.285x
53	106	140917	111125	29792	1.268x
54	108	149833	115959	33874	1.292x
55	110	157666	123334	34332	1.278x
56	112	165958	125250	40708	1.325x
57	114	174792	134666	40126	1.298x
58	116	183459	139541	43918	1.315x
59	118	192875	145542	47333	1.325x
60	120	202417	147250	55167	1.375x