# Sundials KLU Linear solver
**URL:** https://discourse.julialang.org/t/sundials-klu-linear-solver/112954
**Category:** Modelling & Simulations
**Tags:** ode, sundials
**Created:** [April 15, 2024, 9:57am UTC](https://discourse.julialang.org/t/sundials-klu-linear-solver/112954 "2024-04-15T09:57:53Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@jespfra](https://discourse.julialang.org/u/jespfra)
#### Post date: [April 15, 2024, 9:57am UTC](https://discourse.julialang.org/t/sundials-klu-linear-solver/112954/1 "2024-04-15T09:57:53Z")
Hi everyone,
I am trying to use the KLU method as linear solver for solving an ODE problem using Sundials.
I have tried to apply it to the CVODE\_BDF solver for a simple problem, the rober equation. However, when I provide the sparsity pattern determined from the Jacobian function, that I also provide to the ODEFunction, it says:
> “Sparsity Pattern in receiving SUNMatrix doesn’t match sending SparseMatrix”
The code is:
> using Sundials
> using IncompleteLU
> using SparseArrays
> using Plots
> using LinearAlgebra
>
> ################## Solving ODE ##################
>
> #ode repressentation
> function rober!(du, u, p, t)
> y₁, y₂, y₃ = u
> k₁, k₂, k₃ = p
> du[1] = -k₁ \* y₁ + k₃ \* y₂ \* y₃
> du[2] = k₁ \* y₁ - k₂ \* y₂^2 - k₃ \* y₂ \* y₃
> du[3] = k₂ \* y₂^2
> nothing
> end
>
> u0 = [1.0; 0.0; 0.0]
> tspan = (0.0, 1e4)
> p = [0.04, 3e7, 1e4]
> prob = ODEProblem(rober!, u0, tspan,p)
> sol = solve(prob,CVODE\_BDF())
> p1 = plot();
> plot!(p1,sol,label=“ODE”);
>
> ################## Solving ODE With Jacobian ##################
> #Jacobian
> function rober\_jac!(J, u, p, t)
> y₁, y₂, y₃ = u
> k₁, k₂, k₃ = p
> J[1, 1] = k₁ \* -1
> J[2, 1] = k₁
> J[3, 1] = 0
> J[1, 2] = y₃ \* k₃
> J[2, 2] = y₂ \* k₂ \* -2 + y₃ \* k₃ \* -1
> J[3, 2] = y₂ \* 2 \* k₂
> J[1, 3] = k₃ \* y₂
> J[2, 3] = k₃ \* y₂ \* -1
> J[3, 3] = 0
> nothing
> end
>
> u0 = [1.0, 0, 0]
> tspan = (0.0, 1e4)
> p = [0.04, 3e7, 1e4]
> jac\_proto = zeros(length(u0),length(u0))
> rober\_jac!(jac\_proto, u0 .+ 1e-6, p, 0.0)
> fun = ODEFunction(rober!; jac = rober\_jac!, jac\_prototype = sparse(jac\_proto))
> prob = ODEProblem(fun, u0, tspan,p)
> sol = solve(prob,CVODE\_BDF(; linear\_solver = :KLU))
> p1 = plot();
> plot!(p1,sol,label=“ODE”);
As seen from the ODE definition and the Jacobian, the sparsity patters is indeed:
> x x x
> x x x
> ⋅ x ⋅
However, if I instead set the sparsity patters as a dense 3x3 matrix, it solves the problem without any warning.
> fun = ODEFunction(rober!; jac = rober\_jac!, jac\_prototype = sparse(ones(3,3)))
> prob = ODEProblem(fun, u0, tspan,p)
> sol = solve(prob,CVODE\_BDF(; linear\_solver = :KLU))
> p1 = plot();
> plot!(p1,sol,label=“ODE”);
To me, that seems a bit odd as the elements [3,1] and [3,3] in the jacobian prototype are indeed zeros as also seen from the ODE definition (Rober!) and the Jacobian function (Rober\_jac!).
Did I specify anything incorrectly?
I also looked at the examples from [Sundials.jl/test/common\_interface/jacobians.jl at master · SciML/Sundials.jl (github.com)](https://github.com/SciML/Sundials.jl/blob/master/test/common_interface/jacobians.jl), however, the Jacobian for the Lotka problem is in this case a dense 2x2 matrix.
Did some of you guys try to use the KLU linear solver in a Sundials solver, either ODE or DAE, and specify a sparsity pattern that is not a dense matrix?
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [April 15, 2024, 10:55am UTC](https://discourse.julialang.org/t/sundials-klu-linear-solver/112954/2 "2024-04-15T10:55:33Z")
You have to add the diagonal to it since it’s I - gamma\*J