# Multiple variable assignment and ODE solution extracting
**URL:** https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647
**Category:** Modelling & Simulations
**Tags:** ode
**Created:** [March 28, 2020, 3:59pm UTC](https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647 "2020-03-28T15:59:45Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@jmaffi](https://discourse.julialang.org/u/jmaffi)
#### Post date: [March 28, 2020, 3:59pm UTC](https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647/1 "2020-03-28T15:59:45Z")
Hi there!
I am quite new to Julia and have read manuals, tutorials, FAQs, and almost all question threads regarding the following, but have not yet found a solution.
I have a system of 17 ordinary differential equations that I can successfully solve with `solve`. However, I need the solutions of each function (the `u`s) to be assinged each to a variable name (say v1, v2, v3, …, v17). So I am expecting them to be arrays of Nx1 (or 1xN).
Do you know a way to do this?
Thank you in advance!
---
### Author:  [@BLI](https://discourse.julialang.org/u/BLI)
#### Post date: [March 28, 2020, 11:45pm UTC](https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647/2 "2020-03-28T23:45:38Z")
Simple example:
```julia
function pendulum!(du,u,p,t)
g = 9.81
L = 2
alpha = u[1]
omega = u[2]
du[1] = omega
du[2] = -g/L*sin(alpha)
end
#
u0 = [pi/4,0.1]
tspan = (0.,5)
prob = ODEProblem(pendulum!,u0,tspan)
sol = solve(prob)
```
Here, `sol` is a fancy data structure that contains the time instances for the solution in field `t`, `sol.t`. It also contains the solution vector of variable `1` in `sol[1,:]`, so I can plot the first variable as follows:
```julia
plot(sol.t,sol[1,:])
```
However, `sol` also contains an interpolation function, and by using function syntax, `sol(0.5)` contains the state vector at time = 0.5. A better way to do the plotting is the following:
```julia
plot(sol,vars=(0,1))
```
which (i) plots variable 1 as a function of variable 0 (= time), and (ii) uses interpolation so the solution looks smoother than if you use `plot(sol.t,sol[1,:])`.
You can extract the solutions as a matrix with variable 1 in row 1, variable 2 in row 2, etc.:
```julia
sol[1:end,:]
```
Here, column `n` corresponds to the time instance `sol.t[n]`.
You can achieve the same by:
```julia
reduce(hcat,sol.(sol.t))
```
Here, `sol.(sol.t))` computes the solution in the points given by time vector `sol.t`, and `reduce(hcat,.)` wraps the result into the same matrix as `sol[1:end,:]`.
Finally, the solver decides at which points you want to compute the solution, i.e., the time instances in `sol.t`. If you, for some reason, want to compute the solution at other time instances, say at regular time intervals `tsamp = tspan[1]:0.1:tspan[2]` for my pendulum, you can create the solution matrix in those points by:
```julia
reduce(hcat,sol.(tsamp))
```
---
### Author:  [@jmaffi](https://discourse.julialang.org/u/jmaffi)
#### Post date: [March 29, 2020, 7:01pm UTC](https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647/3 "2020-03-29T19:01:40Z")
BLI,
Thank you for your reply. I liked the use you gave to `reduce` to build the matrix !
However, I would still need to know how to assign each one of the 17 solutions (say each row of the matrix) to a given variable name. So far the only solution I have is the brute force:
```julia
v1 = M[1,:];
v2 = M[2,:];
...
v17 = M[17,:]
```
with M being the Array that is the result of your `reduce` suggestion.
Any ideas?
Thank you once again.
---
### Author:  [@BLI](https://discourse.julialang.org/u/BLI)
#### Post date: [March 29, 2020, 11:11pm UTC](https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647/4 "2020-03-29T23:11:09Z")
Hm… can you use this? First, I create a dummy `M` matrix just for the illustration.
```julia
julia> M = rand(0:9,5,10)
5×10 Array{Int64,2}:
4 3 5 5 4 0 1 0 5 6
4 3 7 3 5 9 4 0 9 1
1 9 6 3 6 4 2 6 1 8
3 1 8 0 0 4 8 5 7 6
2 6 4 1 0 7 2 4 3 5
```
[5\times 10 matrix of random values taken from the integers from 0, …, 9].
Next, I pick out vectors from the rows of `M` and given them names:
```julia
julia> for i in 1:5
variable_name = Symbol("v$i")
vector = M[i,:]
@eval $variable_name = $vector
end
julia> v1
10-element Array{Int64,1}:
4
3
5
5
4
0
1
0
5
6
```
Is this what you want?
---
### Author:  [@jmaffi](https://discourse.julialang.org/u/jmaffi)
#### Post date: [March 30, 2020, 12:11pm UTC](https://discourse.julialang.org/t/multiple-variable-assignment-and-ode-solution-extracting/36647/5 "2020-03-30T12:11:33Z")
I can work with that! I will need to adapt it since my variables are not actually named vi… each one has a different name since they represent physical variables that are easier to track in named after what they represent.
But this is very good. Thank you!