How to plot a time-evolution of 3D Gaussian in Julia? - plot

Question

I want to plot a time-evolution of 3D Gaussian with Makie.jl.
Here is a surface-version code of sin(r)/r.
So I wrote a code in reference to it.
using Makie
using FileIO
using LinearAlgebra
using AbstractPlotting
scene = Scene(backgroundcolor = :black);
f(x,y,z) = exp(-((x)^2 + (y)^2 + (z)^2))
r = LinRange(-5, 5, 50)
vol_func(t) = [Float64(f(x - cos(t),y - sin(t),z - t)) for x = r, y = r,z = r]
vol = volume!(scene,r,r,r,vol_func(20),algorithm = :mip)[end]
scene[Axis].names.textcolor = :gray
N = 20
scene
record(scene, "voloutput.mp4", range(0, stop = 5, length = N)) do t
vol[3] = vol_func(t)
end
But this code does not work.
MethodError: Cannot `convert` an object of type Array{Float64,3} to an object of type LinRange{Float64}
How should I fix the code?
P.S.
The snapshot at initial time is like this.(reference)
using Makie
using FileIO
using LinearAlgebra
using AbstractPlotting
r = LinRange(-20, 20, 500); # our value range
ρ(x, y, z) = exp(-((x-1)^2 + (y)^2 + (z)^2)) # function (charge density)
# create a Scene with the attribute `backgroundcolor = :black`,
# can be any compatible color. Useful for better contrast and not killing your eyes with a white background.
scene = Scene(backgroundcolor = :black)
volume!(
scene,
r, r, r, # coordinates to plot on
ρ, # charge density (functions as colorant)
algorithm = :mip # maximum-intensity-projection
)
scene[Axis].names.textcolor = :gray # let axis labels be seen on dark
background
save("sp.png",scene)
I want to see the yellow region moving as spiral. (2020/08/28)
I just realized not vol[3] but vol[4]. Then, it worked.
But I have a next question. (2020/08/31)
I tried to do the same thing for the matrix-form time-dependent Schrodinger equation with its initial condition being Gaussian.
using LinearAlgebra
using OrdinaryDiffEq
using DifferentialEquations
#Define the underlying equation
function time_evolution(ψdot,ψ,p,t)
ψdot.=-im.*H(Lx,Ly,Lz)*ψ
end
Lx = Ly = Lz = 10
ψ0 = [] # Initial conditions
for iz = 1:Lz
for ix = 1:Lx
for iy = 1:Ly
gauss = exp(-((ix)^2 + (iy)^2 + (iz)^2))
push!(ψ0,gauss)
end
end
end
tspan = (0.,1.0) # Simulation time span
#Pass to Solvers
prob = ODEProblem(time_evolution,ψ0,tspan)
sol = solve(prob)
Here,H(Lx,Ly,Lz) is a N×N matrix parameterized by systemsize Lx,Ly,Lz and N = Lx×Ly×Lz. The sample code of H(Lx,Ly,Lz) is here.
Then,
using Makie
using FileIO
using LinearAlgebra
using AbstractPlotting
using ColorSchemes
x = 1: Lx # our value range
y = 1: Ly
z = 1: Lz
ρ(ix,iy,iz,nt) = abs2.((sol[nt][(iz-1)*Lx*Ly + (ix-1)*Ly + (iy-1)])./norm(sol[nt][(iz-1)*Lx*Ly + (ix-1)*Ly + (iy-1)]))
ψ(nt) = Float64[ρ(ix,iy,iz,nt) for ix in x, iy in y,iz in z]
scene = Scene(backgroundcolor = :white)
c = ψ(length(sol.t))
vol = volume!(
scene,
x, y, z, # coordinates to plot on
c, # charge density (functions as colorant)
algorithm = :mip, # maximum-intensity-projection
colorrange = (0,0.01),
transparency = true,
)[end]
update_cam!(scene, Vec3f0(1,0.5,0.1), Vec3f0(0))
scene[Axis].names.textcolor = :gray # let axis labels be seen on darkbackground
record(scene, "output.mp4", range(0, stop = length(sol.t)-1, length = 1)) do nt
vol[4] = ψ(nt)
end
But this code has an error.
ArgumentError: range(0.0, stop=5.0, length=1): endpoints differ
Where is the mistake?
I found the mistake.(2020/09/02)
sol[nt]→sol(nt)
range(0, stop = length(sol.t)-1, length = 1)→range(0, stop = 1.0, length = 20)
Then, the code passed and a mp4 animation was obtained.
But the plot can't be seen in the mp4 file. Why...