Build permuted_dense inverse arrays lazily

[Transurgeon]

Motivation

Every permuted_dense (PD) used to build two dense inverse permutations at construction: col_inv (global n ints) and row_inv (global m ints). On the dense left_matmul kron path, the Jacobian is a stacked_pd of p blocks, and every block's column space is the full variable space. That made the index metadata O(p·n_vars + p²·m0), compared with O(nnz) for the values. On CVXPY's OptimalAdvertising benchmark this put the engine's peak at about 6 GB, while the actual nonzeros need about 5 MB.

Change

The inverse arrays are now built lazily, under one rule:

• No constructor builds col_inv / row_inv; they stay NULL.unchanged, and the fills assert the array is present.
• row_gather_pd_alloc is the one exception. Its fill copies rows through bound_iwork, so at alloc it only needs a membership test, which it answers with a binary search (sorted_pos) over row_perm instead of building a global-size table.

Ensure calls were added in BA_pd_csc_alloc, BTA_pd_csc_alloc, BTA_csc_pd_alloc, the coalesce output blocks, BTA_pd_spd_alloc, the kron scratch / BT, and old-code.

An earlier revision added a second "compact" PD mode instead. That needed NULL fallbacks in about six places, and only the kron-csc outputs were made compact. The single lazy rule replaces it with a smaller diff (src+include: +88/−23) and also covers the kron-pd/spd outputs and the ATA raw blocks.

Results

	main	this PR
OptimalAdvertising engine peak (g_peak_bytes)	5973 MB	628 MB
OptimalAdvertising process peak RSS delta	6065 MB	698 MB
OptimalAdvertising get_problem_data (median of 3)	1.06 s	0.62 s
row+col-sum Jacobian init, 128×128 (C test)	1324 B/var	292 B/var
sum(exp(A @ X)) Hessian init, 96×96	94.9 MB	62.8 MB

• OptimalAdvertising P/A/c/b are bit-identical to main.
• CVaRBenchmark and SemidefiniteProgramming peaks are unchanged; they come from a different cause.

Tests

• New test_peak_memory_kron_jacobian, which asserts < 400 B/var. It is guarded by SP_TRACK_MEMORY.
• test_permuted_dense_lazy_inv and test_permuted_dense_times_csc_lazy_inv.
• The full suite passes in Debug, with -DSP_TRACK_MEMORY=ON, and under ASan+UBSan.
• The existing transpose(A @ X) problem-Jacobian test covers the row_gather path: it segfaults if row_gather reads row_inv directly.

🤖 Generated with Claude Code