[baggepinnen]

Split out of #5173.

Summary

Two fixes in linearize:

• linearize(sys, [], outputs) failed in ForwardDiff with Invalid Tag object, since the Jacobians with respect to the inputs were prepared and evaluated for an empty, Any-typed input vector. The input vector now has the element type of the state, and the input Jacobians are not evaluated when there are no inputs; B and D then have zero columns. The case without unknowns and inputs, which produced an h_xz of the wrong shape, is handled as well.
• LinearizationFunction stores its input symbols, and the diagnostic for differentiated inputs names them from there. It previously indexed inputs(sys), which is empty when the inputs of a compiled system are parameters that are not marked as inputs, and threw a BoundsError in place of the message.

Tests

The testset "Linearization without inputs" in test/linearize.jl covers both backends and the case without unknowns; it fails on master with the tag error and passes with this change.

🤖 Generated with Claude Code

https://claude.ai/code/session_01QBgBrXDidWG1G2KF64gAte

[github-actions]

Benchmark Results (Julia vlts)

Time benchmarks

	master	796cc48...	master / 796cc48...
ODEProblem	4.54 ± 0.57 ms	4.43 ± 0.14 ms	1.02 ± 0.13
init	0.0837 ± 0.027 ms	0.0608 ± 0.027 ms	1.38 ± 0.76
large_parameter_init/ODEProblem	12.7 ± 0.66 ms	12.9 ± 1.5 ms	0.986 ± 0.13
large_parameter_init/init	0.0795 ± 0.023 ms	0.0791 ± 0.025 ms	1 ± 0.43
mtkcompile	7.95 ± 0.37 ms	7.99 ± 0.34 ms	0.995 ± 0.063
sparse_analytical_jacobian/ODEProblem	16 ± 0.69 ms	15.7 ± 1.2 ms	1.02 ± 0.088
sparse_analytical_jacobian/f_iip	0.06 ± 0 μs	0.06 ± 0 μs	1 ± 0
sparse_analytical_jacobian/f_oop	0.309 ± 0.0071 ms	0.308 ± 0.0068 ms	1 ± 0.032
time_to_load	5.59 ± 0.016 s	5.63 ± 0.06 s	0.993 ± 0.011

Memory benchmarks

	master	796cc48...	master / 796cc48...
ODEProblem	0.0346 M allocs: 1.82 MB	0.0346 M allocs: 1.82 MB	1
init	0.508 k allocs: 0.0846 MB	0.508 k allocs: 0.0846 MB	1
large_parameter_init/ODEProblem	0.147 M allocs: 5.54 MB	0.147 M allocs: 5.54 MB	1
large_parameter_init/init	0.64 k allocs: 0.179 MB	0.64 k allocs: 0.179 MB	1
mtkcompile	0.0594 M allocs: 3.37 MB	0.0594 M allocs: 3.37 MB	1
sparse_analytical_jacobian/ODEProblem	0.106 M allocs: 5.33 MB	0.106 M allocs: 5.33 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.634 k allocs: 19.6 kB	0.634 k allocs: 19.6 kB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	796cc48...	master / 796cc48...
ODEProblem	5.07 ± 0.078 ms	5.03 ± 0.085 ms	1.01 ± 0.023
init	0.0456 ± 0.0066 ms	0.0448 ± 0.0052 ms	1.02 ± 0.19
large_parameter_init/ODEProblem	13.2 ± 0.6 ms	13.3 ± 0.59 ms	0.995 ± 0.063
large_parameter_init/init	0.0661 ± 0.032 ms	0.0655 ± 0.03 ms	1.01 ± 0.68
mtkcompile	8.48 ± 0.93 ms	8.48 ± 0.86 ms	1 ± 0.15
sparse_analytical_jacobian/ODEProblem	16.6 ± 1.7 ms	16.5 ± 1.7 ms	1.01 ± 0.15
sparse_analytical_jacobian/f_iip	0.07 ± 0.01 μs	0.07 ± 0 μs	1 ± 0.14
sparse_analytical_jacobian/f_oop	0.103 ± 0.013 ms	0.103 ± 0.013 ms	1.01 ± 0.18
time_to_load	5.09 ± 0.024 s	5.09 ± 0.025 s	1 ± 0.0068

Memory benchmarks

	master	796cc48...	master / 796cc48...
ODEProblem	0.034 M allocs: 1.61 MB	0.034 M allocs: 1.59 MB	1.01
init	0.475 k allocs: 0.0602 MB	0.475 k allocs: 0.0602 MB	1
large_parameter_init/ODEProblem	0.143 M allocs: 4.85 MB	0.143 M allocs: 4.85 MB	1
large_parameter_init/init	0.757 k allocs: 0.166 MB	0.757 k allocs: 0.166 MB	1
mtkcompile	0.0558 M allocs: 2.63 MB	0.0558 M allocs: 2.63 MB	1
sparse_analytical_jacobian/ODEProblem	0.102 M allocs: 4.24 MB	0.102 M allocs: 4.24 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.848 k allocs: 27 kB	0.848 k allocs: 27 kB	1
time_to_load	0.2 k allocs: 11.7 kB	0.2 k allocs: 11.7 kB	1

[BambOoxX]

It seems this fixes #4886 as well, but I'll let you confirm.