Streamplot from numerical data

[navdeeprana]

The documentation says that we can create a streamplot for a function that returns dx,dy for a given x,y. Say I have numerical values of the coordinates and the velocities, how can I create a streamplot? Essentially, I want a plotting recipe equivalent to matplotlib streamplot.

[navdeeprana]

@jkrumbiegel, anything on this?

[SimonDanisch]

Do you want https://docs.makie.org/stable/examples/plotting_functions/arrows/index.html#arrows?

[jkrumbiegel]

I think we currently only take a function because you need to be able to evaluate it continuously. But we could (or you could) use an interpolation over the matrix as the function, which should then result in what matplotlib does.

[navdeeprana]

Okay, I will give it a shot.

[navdeeprana]

Okay, this simple snippet works.

using CairoMakie, Interpolations
function splot(u, v)
    nx, ny = size(u)
    x, y = 1:nx, 1:ny
    intu, intv = linear_interpolation((x,y), u), linear_interpolation((x,y), v)
    f(x) = Point2f(intu(x...), intv(x...))
    return streamplot(f, x, y, colormap=:magma)
end

# Streamplot example function
struct FitzhughNagumo{T}
    ϵ::T
    s::T
    γ::T
    β::T
end
P = FitzhughNagumo(0.1, 0.0, 1.5, 0.8)

x = -1.5:0.1:1.5
nx = length(x)
u, v = zeros(nx, nx), zeros(nx, nx)

for (j, xj) in enumerate(x)
    for (i, xi) in enumerate(x)
        u[i, j], v[i, j] = (xi-xj-xi^3+P.s)/P.ϵ, P.γ*xi-xj + P.β
    end
end
fig, ax, pl = splot(u, v)

Output

Can we extend the recipe to support plotting numerical data? If yes, I can improve upon it and open a pull request. Any suggestions on improvements are also welcome.

[NessLange]

@navdeeprana That is a really cool Code! Do you may reveal how you added the arrows inside your plot
and how to extend your example to vector input instead of matrices ?

As I see it u and v are matrices, but what if (like in my case) you got x, y, u, v vectors (same length)

arrows(x,y,u,v) works fine, but I don't figure what to change in your code to accept that input.

[navdeeprana]

@NessLange, thanks. The arrows are added by the streamplot function that is called inside splot. Check it's documentation for more details.

In splot, I assume that the input is matrix. But for 1D data, you can try if the following works

function splot(x, y, u, v)
    intu, intv = linear_interpolation((x,y), u), linear_interpolation((x,y), v)
    f(x) = Point2f(intu(x...), intv(x...))
    return streamplot(f, x, y, colormap=:magma)
end

I am on the phone so can't check it at the moment.

[NessLange]

Thanks for the quick reply. I have checked the nice streamplot documentation and ran the same exact code without having the arrows being drawn in my plot.

Unfortunately I also get an error when running your modified code with vector input.

Here are some data to tinker with

n = 20; x = 0:n; x = x'.*ones(n+1).*2*pi/n; y = 0:n; y = ones(n+1)'.*y.*3*pi/n; u = sin.(x) .* cos.(y) v = -cos.(x) .* sin.(y) x = x[:]; y = y[:]; u = u[:]; v = v[:];

Edit: I do right know, in that case I can just leave the data as matrix and use your original code, but in the case of my real data it is not as easy to transform to a matrix.

[asinghvi17]

Maybe you want an interpolator like https://github.com/DanielVandH/NaturalNeighbours.jl? Or something like this anyway.

You might also want to look at https://github.com/MakieOrg/TopoPlots.jl and see the interpolators used there!

[NessLange]

Awesome, these look like some really fruitful sources! I would never have found that.

[navdeeprana]

About your arrows issue, I do not know, perhaps you have a modified Makie theme or some other custom setting, try updating Makie, running the example code in a clean repl/notebook.

About plotting 1D arrays, Interpolation over a D-tuple requires D dimensional data. For example this snippet

using CairoMakie, Interpolations
function splot(x, y, u, v)
    intu, intv = linear_interpolation((x,y), u), linear_interpolation((x,y), v)
    f(x) = Point2f(intu(x...), intv(x...))
    return streamplot(f, x, y, colormap=:magma)
end

x = 0:0.2:2π
y = 0:0.2:2π
u = @. sin(x) * cos(y')
v = @. cos(x) * sin(y')
splot(x, y, u, v)

yields the following plot

However splot(x,y,vec(u),vec(v)) yields the following error

MethodError: no method matching linear_interpolation(::Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64}}, ::Vector{Float64})

Closest candidates are:
  linear_interpolation(::Tuple{Vararg{AbstractRange, N}}, ::AbstractArray{T, N}; extrapolation_bc) where {N, T}
   @ Interpolations ~/.julia/packages/Interpolations/91PhN/src/convenience-constructors.jl:22
  linear_interpolation(::Tuple{Vararg{AbstractVector, N}}, ::AbstractArray{T, N}; extrapolation_bc) where {N, T}
   @ Interpolations ~/.julia/packages/Interpolations/91PhN/src/convenience-constructors.jl:25
  linear_interpolation(::AbstractRange, ::AbstractVector; extrapolation_bc)
   @ Interpolations ~/.julia/packages/Interpolations/91PhN/src/convenience-constructors.jl:7

Note the function signature linear_interpolation(::Tuple{Vararg{AbstractRange, N}}, ::AbstractArray{T, N}; extrapolation_bc) where {N, T}

So, I think you need to reshape your u, v arrays into matrices and then use splot. Note that matplotlib has similar requirements as mentioned here

[NessLange]

alright, thank you :)