# Explicit Jacobian on DAEs?

**URL:** <https://discourse.julialang.org/t/explicit-jacobian-on-daes/21477>\
**Category:** Numerics\
**Tags:** diffeq\
**Created:** [March 4, 2019, 8:26pm UTC](https://discourse.julialang.org/t/explicit-jacobian-on-daes/21477 "2019-03-04T20:26:47Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [March 4, 2019, 10:54pm UTC](https://discourse.julialang.org/t/explicit-jacobian-on-daes/21477/2 "2019-03-04T22:54:32Z")

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Hey,  
So after getting rid of the dispatch and changing back to the default linear solver it works:

```julia
using Sundials

p=[2,1.2,3]

function f(res,du,u,p,t)
  res[1] = du[1] - p[1] * u[1] + p[2] * u[1]*u[2]
  res[2] = du[2] -p[3] * u[2] - u[1]*u[2]
  res[3]= u[2] + u[1] - u[3]
end

function g(J,du,u,p,gamma,t)
  J[1,1] = gamma - p[1] + p[2] * u[2]
  J[1,2] = p[2]* u[1]
  J[1,3] = 0
  J[2,1] = - 1 * u[2]
  J[2,2] = gamma - p[3] - u[1]
  J[2,3] = 0
  J[3,1] = 1
  J[3,2] = 1
  J[3,3] = -1
  nothing
end

fg = DAEFunction(f;jac=g)

dIC=[-0.8,-4]
IC =[1.0,1.0,2.0]
tspan=(0.0,10.0)
diff_vars = [true,true, false]

testProb2 = DAEProblem(fg,dIC,IC,tspan,p,differential_vars=diff_vars)
sol = solve(testProb2,IDA())

```

So that’s using your Jacobian. You can check by putting a print in there. But now you want to scale to a large problem. Instead of going straight to GMRES, if you’re willing to define your Jacobian then it’s usually more efficient to define a sparse Jacobian. You do that by defining `jac_prototype` and pass in a matrix with the right sparsity pattern.  
Then you can directly write the Jacobian pieces in an call a sparse factorization method (`:KLU`). You can then directly loop through `J.data` to speed up the Jacobian updates instead of using Cartesian indexing.

If you are willing to do this work though, sparse factorization with a 5th order Rosenbrock method, writing the DAE in mass matrix form, can be more efficient (it’ll get more miles per factorization!), but of course than can be a pretty substantial rewrite.

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