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Use matrix-dependent solver for sparse analytical Jacobian example #3938

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Sep 20, 2025
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Use matrix-dependent solver for sparse analytical Jacobian example #3938

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12 changes: 5 additions & 7 deletions docs/src/examples/sparse_jacobians.md
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Original file line number Diff line number Diff line change
Expand Up @@ -60,7 +60,6 @@ Now let's use `modelingtoolkitize` to generate the symbolic version:

```@example sparsejac
@mtkcompile sys = modelingtoolkitize(prob);
nothing # hide
```

Now we regenerate the problem using `jac=true` for the analytical Jacobian
Expand All @@ -74,21 +73,20 @@ Hard? No! How much did that help?

```@example sparsejac
using BenchmarkTools
@btime solve(prob, save_everystep = false);
@btime solve(prob, FBDF(), save_everystep = false);
return nothing # hide
```

```@example sparsejac
@btime solve(sparseprob, save_everystep = false);
@btime solve(sparseprob, FBDF(), save_everystep = false);
return nothing # hide
```

Notice though that the analytical solution to the Jacobian can be quite expensive.
Thus in some cases we may only want to get the sparsity pattern. In this case,
we can simply do:
It is also possible to use the numerical Jacobian,
but take advantage of the analytical sparsity pattern:

```@example sparsejac
sparsepatternprob = ODEProblem(sys, Pair[], (0.0, 11.5), sparse = true)
@btime solve(sparsepatternprob, save_everystep = false);
@btime solve(sparsepatternprob, FBDF(), save_everystep = false);
return nothing # hide
```
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