heuristic for estimating the number of non-zeros in constraint_jacobian

[thowell]

Estimate the number of non-zeros (njmax_nnz) in the sparse constraint Jacobian.

Non-contact constraints (assume all active)

Type	Rows	Non-zeros per row
Connect equality	3	_body_pair_nnz(body1, body2)
Weld equality	6	_body_pair_nnz(body1, body2)
Joint equality	1	1 or 2
Tendon equality	1	merged column union of both tendons
Flex equality	per edge	flexedge_J_rownnz
DOF friction	1	1
Tendon friction	1	ten_J_rownnz
Joint limit	1	1 (slide/hinge) or 3 (ball)
Tendon limit	1	ten_J_rownnz

Contact constraints

1. Enumerate all enabled collision pairs:
   • Contact pairs (pair_geom1/2)
   • Filter geom-geom (filtered by contype/conaffinity, deduplicated by body pair)
   • Flex vertex-to-geom and flex self-collision
2. Compute _body_pair_nnz(body1, body2) for each pair
3. Take the maximum non-zeros across all pairs: max_contact_nnz
4. Contact non-zeros = njmax × max_contact_nnz

Estimate

njmax_nnz = min(non_contact_nnz + njmax × max_contact_nnz, njmax × nv)

Helper: _body_pair_nnz(body1, body2)

Counts unique DOFs in the kinematic tree union of two bodies by walking up
both dof_parentid chains simultaneously (same algorithm as runtime constraint kernels).

Validation for benchmark scenes* with sparse constraint Jacobians

Scene	nv	njmax	nconmax	njmax*nv	heuristic	actual	ratio	savings
aloha_cloth	2716	6300	920	17,110,800	103,710	66,740	1.55	99%
aloha_pot	23	128	24	2,944	1,818	1,414	1.29	38%
apollo_flat	25	64	16	1,600	1,190	405	2.94	26%
apollo_hfield	25	128	32	3,200	2,342	693	3.38	27%
apollo_terrain	25	96	48	2,400	1,766	789	2.24	26%
cloth	2706	3000	200	8,118,000	42,486	22,644	1.88	99%
franka_panda	9	5	1	45	45	4	11.25	0%
humanoid	27	64	24	1,728	1,365	579	2.36	21%
three_humanoids	81	192	100	15,552	5,823	1,674	3.48	63%

*aloha sdf skipped

[erikfrey]

Looks great, just two minor comments