# Using a modifier function on the output of DifferentialEquation for plotting

**URL:** <https://discourse.julialang.org/t/using-a-modifier-function-on-the-output-of-differentialequation-for-plotting/115669>\
**Category:** General Usage\
**Tags:** plotting, differentialequation\
**Created:** [June 14, 2024, 7:10pm UTC](https://discourse.julialang.org/t/using-a-modifier-function-on-the-output-of-differentialequation-for-plotting/115669 "2024-06-14T19:10:06Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![cmdenis](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cmdenis/32/211517_2.png) [@cmdenis](https://discourse.julialang.org/u/cmdenis)\
**Post date:** [June 14, 2024, 7:10pm UTC](https://discourse.julialang.org/t/using-a-modifier-function-on-the-output-of-differentialequation-for-plotting/115669/1 "2024-06-14T19:10:06Z")

</div>

Hello,

I am using the (fantastic) `DifferentialEquation.jl` package to run some simulation and would like to plot the solution, but after applying a modifying function on the solution.

What I mean is that I would like to apply a function, for instance `sin` on all the solution’s points.

In the past, I would make this work by simply not using the dedicated `Plots` recipes for `DifferentialEquations` and do something like this (I know the following is rather trivial):

```julia
# Define system of equation 
function f(du, u, p, t)
    du[1] = u[1]
end

# Parameter for system (in this case there are none)
p = []

# Initial conditions
u0 = [0.5]

# Time points to integrate
times = 0:0.01:4

# Define ODE problem
prob = ODEProblem(
    f, # system to integrate
    u0, # initial conditions
    (times[1], times[end]), # time bounds to integrate in
    p # parameters for the system
)

# Solve problem
sol = solve(
    prob, # problem to solve for
    saveat = times # times to get an answer for, but shifted by the transient time
    )

# Plot trajectories
modifier_function(x) = sin(x)
newdata = modifier_function.(sol[1, :])
plot(sol.t, newdata)

```

Although this works, I feel like there must be a more systematic way of achieving the same thing. Perhaps, modifying the recipe for `DifferentialEquations`?  
A more “mathy” alternative would be to change the differential equations themselves to obtain the desired output, but systems of nonlinearly coupled equations it becomes a little messy.

Thanks in advance for any help!

---

<div class="post-metadata">

**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:** [June 14, 2024, 7:14pm UTC](https://discourse.julialang.org/t/using-a-modifier-function-on-the-output-of-differentialequation-for-plotting/115669/2 "2024-06-14T19:14:21Z")

</div>

The plotting docs have a few examples [Plot Functions · DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/basics/plot/#Example)

It shows mostly phase plots, but variable 0 is time.

---

<div class="post-metadata">

**Author:** ![cmdenis](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cmdenis/32/211517_2.png) [@cmdenis](https://discourse.julialang.org/u/cmdenis)\
**Post date:** [June 14, 2024, 8:15pm UTC](https://discourse.julialang.org/t/using-a-modifier-function-on-the-output-of-differentialequation-for-plotting/115669/3 "2024-06-14T20:15:22Z")

</div>

Thanks so much, this is perfect! I skimmed over that section to quick, my bad!

This does exactly what I need:

```julia
# Define system of equation 
function f(du, u, p, t)
    du[1] = u[1]
end

# Parameter for system (in this case there are none)
p = []

# Initial conditions
u0 = [0.5]

# Time points to integrate
times = 0:0.01:4

# Define ODE problem
prob = ODEProblem(
    f, # system to integrate
    u0, # initial conditions
    (times[1], times[end]), # time bounds to integrate in
    p # parameters for the system
)

# Solve problem
sol = solve(
    prob, # problem to solve for
    saveat = times # times to get an answer for, but shifted by the transient time
    )

# Plot trajectories
modifier_function(x, t) = (sin(x), t) # returns a tuple

plot(sol, idxs = [(modifier_function, 1, 0)]) # applying the modifier function on the data at index 1, and leaving time at index 0 unchanged

```

---

<div class="post-metadata">

**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:** [June 14, 2024, 9:39pm UTC](https://discourse.julialang.org/t/using-a-modifier-function-on-the-output-of-differentialequation-for-plotting/115669/4 "2024-06-14T21:39:55Z")

</div>

Good to hear.