Add TimerOutputs-based timers for internal kernels

[lkdvos]

Instruments the index manipulation, contraction and factorization kernels with @timeit_debug sections, compiled away by default and enabled via TensorKit.enable_timers!().

Section labels carry a category prefix (symmetry: / bookkeeping: / alloc: / dense:), and TensorKit.timer_summary() aggregates exclusive times into per-category totals that sum to the total measured time. The @cached macro times lookups separately from miss-path construction. While timing, get_num_*_threads() return 1 so that the (single-task) timer is never touched concurrently; the guard const-folds away when disabled, leaving production paths unchanged (verified via benchmark against main).

Adds TimerOutputs (1.x, for recursive enable_debug_timings) as a dependency, a "Profiling and timers" manual page, and tests.

🤖 Generated with Claude Code

[lkdvos]

Example output for a single (cold-cache) permute + svd_compact on an SU2Space(0 => 4, 1//2 => 4, 1 => 2) rank-4 tensor:

TensorKit.timer_summary()

    symmetry:  385μs ( 20.6%)   548KiB  39 sections
 bookkeeping:  195μs ( 10.5%)   159KiB  137 sections
       alloc: 25.4μs (  1.4%)   134KiB  3 sections
       dense: 1.19ms ( 63.8%)   228KiB  58 sections
       other: 70.7μs (  3.8%)  25.7KiB  3 sections

TensorKit.print_timers() — full call tree

 Section                                                  ncalls    time    %tot     avg
───────────────────────────────────────────────────────────────────────────────────────────
 svd_compact!                                                  1  1.20ms   64.2%  1.20ms
 ├─ dense: lapack                                              5  1.11ms   59.7%   223μs
 ├─ bookkeeping: cache sectorstructure                        24  19.8μs    1.1%   825ns
 │  └─ bookkeeping: compute sectorstructure                    1  2.15μs    0.1%  2.15μs
 └─ bookkeeping: cache degeneracystructure                    15  7.87μs    0.4%   525ns
 permute!                                                      1   579μs   31.0%   579μs
 └─ braid!                                                     1   579μs   31.0%   579μs
    ├─ bookkeeping: cache treebraider                          1   488μs   26.1%   488μs
    │  └─ symmetry: compute treebraider                        1   481μs   25.8%   481μs
    │     ├─ symmetry: recoupling matrices                     1   420μs   22.5%   420μs
    │     │  ├─ bookkeeping: cache fsbraid                    37   371μs   19.9%  10.0μs
    │     │  │  └─ symmetry: compute fsbraid                  37   347μs   18.6%  9.37μs
    │     │  └─ bookkeeping: repack                           37  16.0μs    0.9%   433ns
    │     ├─ bookkeeping: fusionblocks                         1  37.7μs    2.0%  37.7μs
    │     ├─ bookkeeping: cache sectorstructure                2  7.66μs    0.4%  3.83μs
    │     ├─ bookkeeping: cache degeneracystructure            2  6.41μs    0.3%  3.21μs
    │     └─ bookkeeping: sort                                 1  4.50μs    0.2%  4.50μs
    ├─ dense: tensoradd                                       29  36.9μs    2.0%  1.27μs
    ├─ dense: pack                                             8  21.4μs    1.1%  2.67μs
    ├─ dense: unpack                                           8  12.2μs    0.7%  1.53μs
    ├─ dense: recouple mul!                                    8  6.00μs    0.3%   750ns
    └─ alloc: buffers                                          1   735ns    0.0%   735ns
 alloc: initialize_output                                      1  50.6μs    2.7%  50.6μs
 └─ bookkeeping: cache degeneracystructure                     2  33.6μs    1.8%  16.8μs
 bookkeeping: cache degeneracystructure                        1  29.6μs    1.6%  29.6μs
 alloc: copy_input                                             1  9.30μs    0.5%  9.30μs

(some deeply nested sectorstructure/degeneracystructure sub-branches elided)

[codecov]

Codecov Report

❌ Patch coverage is 98.92857% with 3 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/planar/planaroperations.jl	96.29%	1 Missing ⚠️
src/tensors/indexmanipulations.jl	97.43%	1 Missing ⚠️
src/tensors/treetransformers.jl	92.30%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/TensorKit.jl	17.24% <100.00%> (+3.44%)	⬆️
src/auxiliary/caches.jl	90.10% <100.00%> (+0.57%)	⬆️
src/auxiliary/timers.jl	100.00% <100.00%> (ø)
src/factorizations/factorizations.jl	84.61% <ø> (+15.38%)	⬆️
src/factorizations/matrixalgebrakit.jl	93.83% <100.00%> (+9.15%)	⬆️
src/tensors/linalg.jl	82.93% <100.00%> (+15.35%)	⬆️
src/tensors/tensoroperations.jl	96.53% <100.00%> (+5.95%)	⬆️
src/planar/planaroperations.jl	73.18% <96.29%> (+1.86%)	⬆️
src/tensors/indexmanipulations.jl	89.18% <97.43%> (+12.48%)	⬆️
src/tensors/treetransformers.jl	94.84% <92.30%> (-3.01%)	⬇️

... and 48 files with indirect coverage changes

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[leburgel]

This is pretty amazing.

[Jutho]

Great work. There are quite a few places where I can see it is not entirely straightforward where to put the timer exactly. In particular, for the calls to dense linear algebra blocks/subblocks, do we want one "dense" timer entry around the whole loop over the (sub)blocks (thereby also potentially including other work aside from the dense call) or inside the loop just around the actual dense call.

Anyway, I left some comments, feel free to ignore them.

[lkdvos]

Ok my robot friend accidentally also replied to your comments, please ignore that...

I've integrated most of your suggested changes, in general tried to be reasonable with the granularity of the sections, but I think for detailed information a profiler is probably still the right tool, and this should serve mostly as a generic indication of rough percentages, which is also why there are a number of cases where I think the overhead of the timer would dominate the signal so I left them out deliberately.

[Jutho]

Thanks, this looks very useful and the timer structuring decisions all seem very reasonable to me, and can be finetuned further at some later point if need be.