# How to define ode without mass\_matrix

**URL:** <https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190>\
**Category:** General Usage\
**Tags:** question\
**Created:** [February 14, 2024, 1:18am UTC](https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190 "2024-02-14T01:18:31Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![whucsu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/whucsu/32/207015_2.png) [@whucsu](https://discourse.julialang.org/u/whucsu)\
**Post date:** [February 14, 2024, 1:18am UTC](https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190/1 "2024-02-14T01:18:31Z")

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Dear All,  
I am not so familary with Julia ode.  
Here as to the ode definition using ODEfunction:  
also online:[CMSB-2023/UKF.jl at main · H-Sax/CMSB-2023 · GitHub](https://github.com/H-Sax/CMSB-2023/blob/main/UKF.jl)  
the code as below:  
function NIK!(du, u, p, t)  
pLV, psa, psv, Vlv, Qav, Qmv, Qs = u  
τₑₛ, τₑₚ, Rmv, Zao, Rs, Csa, Csv, Eₘₐₓ, Eₘᵢₙ = p

```
# 1) Left Ventricle
du[1] = (Qmv - Qav) * ShiElastance(t, Eₘᵢₙ, Eₘₐₓ, τ, τₑₛ, τₑₚ, Eshift) + pLV / ShiElastance(t, Eₘᵢₙ, Eₘₐₓ, τ, τₑₛ, τₑₚ, Eshift) * DShiElastance(t, Eₘᵢₙ, Eₘₐₓ, τ, τₑₛ, τₑₚ, Eshift)
# 2) Systemic arteries 
du[2] = (Qav - Qs ) / Csa     
# 3) Venous
du[3] = (Qs - Qmv) / Csv 
# 4) Left Ventricular Volume
du[4] = Qmv - Qav 
# 5) Aortic Valve flow
du[5] = Valve(Zao, (pLV - psa)) - Qav
# 6) Mitral Valve flow
du[6] = Valve(Rmv, (psv - pLV)) - Qmv 
# 7) Systemic flow
du[7] = (du[2] - du[3]) / Rs
nothing 

```

end

## 

M = [1. 0 0 0 0 0 0  
0 1. 0 0 0 0 0  
0 0 1. 0 0 0 0  
0 0 0 1. 0 0 0  
0 0 0 0 0 0 0  
0 0 0 0 0 0 0  
0 0 0 0 0 0 1. ]

Nik\_ODE = ODEFunction(NIK!,mass\_matrix=M)

u0 = [8.0, 8.0, 8.0, 265.0, 0.0, 0.0, 0.0]

p = [0.3, 0.45, 0.06, 0.033, 1.11, 1.13, 11.0, 1.5, 0.03]

tspan = (0, τ \* 30)

prob = ODEProblem(Nik\_ODE, u0, tspan, p)

how to change the ode equation definition without mass matrix :Nik\_ODE = ODEFunction(NIK!,mass\_matrix=M)

thanks.

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<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [February 14, 2024, 1:25am UTC](https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190/2 "2024-02-14T01:25:52Z")

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why don’t you want to use a mass matrix? It does change what the equations mean (specifically this is defining a Differential Algebraic equation in the semi-explicit form).

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**Author:** ![whucsu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/whucsu/32/207015_2.png) [@whucsu](https://discourse.julialang.org/u/whucsu)\
**Post date:** [February 14, 2024, 2:02am UTC](https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190/3 "2024-02-14T02:02:56Z")

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thanks.  
as my next need is to estimate the parameter of p using Optimization.OptimizationProblem with the cost\_function = build\_loss\_objective(prob, Tsit5(), L2Loss(t, data),Optimization.AutoForwardDiff(),maxiters = 10000, verbose = false,save\_idxs = 1)

but the solver is not able to use mass matrices.  
so…

the example is from:[Getting Started with Optimization-Based ODE Parameter Estimation · DiffEqParamEstim.jl](https://docs.sciml.ai/DiffEqParamEstim/stable/getting_started/)

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**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [February 14, 2024, 2:07am UTC](https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190/4 "2024-02-14T02:07:33Z")

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yeah you just need to use a solver that can use mass matrices. I would probably suggest `Rodas5P`, but you might want to try `FBDF` as well. While you’re at it, you might want to rewrite

```julia
using LinearAlgebra
M = Diagonal([1., 1., 1., 0., 0. 1.])

```

which is a little easier to read and write.

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<div class="post-metadata">

**Author:** ![whucsu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/whucsu/32/207015_2.png) [@whucsu](https://discourse.julialang.org/u/whucsu)\
**Post date:** [February 14, 2024, 2:12am UTC](https://discourse.julialang.org/t/how-to-define-ode-without-mass-matrix/110190/5 "2024-02-14T02:12:45Z")

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> [@Oscar\_Smith](#):
>
> Rodas5P

thanks very much, I used Rodas5P according to your suggestion.