JULIA CODES FOR FLUID FLOW ACROSS CYLINDER

import Pkg; Pkg.add("MAT")
import Pkg; Pkg.add("JuMP")
import Pkg; Pkg.add("Symbolics")
import Pkg; Pkg.add("SymPy")
import Pkg; Pkg.add("PyPlot")

using MAT
using Random
using LinearAlgebra
using JuMP
using Symbolics
using SymPy
using PyPlot

rng = MersenneTwister(1234);
fileIn = matopen("CYLINDER_ALL.mat")
dset = read(fileIn,"UALL")
close(fileIn)

snaps_have=125;
knowpart=dset[:,1:snaps_have];
paddingpart=randn(rng, (89351, 151-snaps_have));
paddingpart_transpose=paddingpart';
pinv_paddingpart_transpose=pinv(paddingpart_transpose);

W=[dset[:,1:snaps_have] pinv_paddingpart_transpose];

TotalSnapshots = size(W,2);
TotalKernels = size(W,2) - 1;
mu = 5.00;

x= Sym("x"); y= Sym("y"); Kernel(x,y)=exp(-1/mu*norm(x-y));

GramMatrix=[Kernel(W[:,i],W[:,j]) for i in 1:TotalKernels, j in 1:TotalKernels];
InteractionMatrix=[Kernel(W[:,i],W[:,j+1]) for i in 1:TotalKernels, j in 1:TotalKernels];

D=eigvals(pinv(GramMatrix)*InteractionMatrix);#eigen-values
D=Diagonal(D);#diagonal matrix of eigen-values
V=eigvecs(pinv(GramMatrix)*InteractionMatrix);#eigen-vectors
V=[V[i,j]/sqrt(V[:,j]'*GramMatrix*V[:,j]) for i in 1:size(V,2), j in 1:size(V,2)]; #normalization

KoopmanModes = pinv(GramMatrix*V)*W[:,1:end-1]';
KoopmanModes = KoopmanModes';#Koopman-Modes

img=imshow(real(reshape(KoopmanModes[:,61],(199,:))))
colorbar()
title("Koopman Mode(s)-150 with 151 snaps")

colormap=(:gnuplot)
img=matplotlib.pyplot.imshow(imag(reshape(KoopmanModes[:,61],(199,:))),colormap)
colorbar()
title("Koopman Mode(s)-61 with 3 snaps")