# Solving DAEs with known sparsity pattern and IDA
**URL:** https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318
**Category:** General Usage
**Tags:** sparse, differentialequation, sundials
**Created:** [May 15, 2024, 6:59pm UTC](https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318 "2024-05-15T18:59:47Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@ataideneto](https://discourse.julialang.org/u/ataideneto)
#### Post date: [May 15, 2024, 6:59pm UTC](https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318/1 "2024-05-15T18:59:47Z")
Hi everyone!
Can someone provide a minimal example of how to use sparsity patterns (jac\_prototype) when solving DAEs with IDA solver? I manage to use sparsity patterns with ODEs and the julia solvers…
Here are some examples that I am trying to solve:
ODE Version
n = 1000
L = 0.5 .+ rand(n)
function odefun(yp, y, p, t)
yp[:] = -L.\*y
end
jac\_pattern = spdiagm(ones(n))
colorvec = matrix\_colors(jac\_pattern)
tspan = (0,2)
y0 = ones(n)
ode = ODEFunction(odefun)
ode\_sparse = ODEFunction(odefun, jac\_prototype=jac\_pattern, colorvec=colorvec)
prob = ODEProblem(ode, y0, tspan)
prob\_sparse = ODEProblem(ode\_sparse, y0, tspan)
@btime solve(prob, TRBDF2()) # solves in 85 ms
@btime solve(prob\_sparse, TRBDF2()) # solves in 1 ms
However the DAE doesn’t work:
n = 1000
L = 0.5 .+ rand(n)
function residuals(res, yp, y, p, t)
res[:] = yp + L.\*y
end
jac\_pattern = spdiagm(ones(n))
colorvec = matrix\_colors(jac\_pattern)
tspan = (0,2)
y0 = ones(n)
yp0 = -L
dae = DAEFunction(residuals)
dae\_sparse = DAEFunction(residuals, jac\_prototype=jac\_pattern, colorvec=colorvec)
prob = DAEProblem(dae, yp0, y0, tspan, differential\_vars=trues(n))
prob\_sparse = DAEProblem(dae\_sparse, yp0, y0, tspan, differential\_vars=trues(n))
@btime solve(prob, IDA()) # solves in 52 ms
@btime solve(prob\_sparse, IDA()) # solves in 49 ms
I would expect that the sparse problem would have a huge decrease in time as in the ODE case.
Thanks for the support!
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### Author:  [@ataideneto](https://discourse.julialang.org/u/ataideneto)
#### Post date: [May 15, 2024, 8:02pm UTC](https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318/2 "2024-05-15T20:02:01Z")
The same problem occurs when using ODE formulation with CVODE\_BDF also from sundials:
n = 1000
L = 0.5 .+ rand(n)
function odefun(yp, y, p, t)
yp[:] = -L.\*y
end
jac\_pattern = spdiagm(ones(n))
colorvec = matrix\_colors(jac\_pattern)
tspan = (0,2)
y0 = ones(n)
ode = ODEFunction(odefun)
ode\_sparse = ODEFunction(odefun, jac\_prototype=jac\_pattern, colorvec=colorvec)
prob = ODEProblem(ode, y0, tspan)
prob\_sparse = ODEProblem(ode\_sparse, y0, tspan)
@btime solve(prob, CVODE\_BDF()) # solves in 27 ms
@btime solve(prob\_sparse, CVODE\_BDF()) # solves in 27ms
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [May 16, 2024, 8:10am UTC](https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318/3 "2024-05-16T08:10:43Z")
With Sundials you have to tell it to use a sparse linear solver, i.e. `CVODE_BDF(linear_solver=:KLU)`
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### Author:  [@ataideneto](https://discourse.julialang.org/u/ataideneto)
#### Post date: [May 16, 2024, 4:16pm UTC](https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318/4 "2024-05-16T16:16:44Z")
Thank you for the answer, Cris!
However, for the KLU you have to pass the actual jacobian…
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### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [May 16, 2024, 10:51pm UTC](https://discourse.julialang.org/t/solving-daes-with-known-sparsity-pattern-and-ida/114318/5 "2024-05-16T22:51:55Z")
Oh yes, Sundials cannot use sparse differentiation.