using LinearAlgebra using Plots using Printf  function solve(f; x1=0, x2=1) 	N = length(f) 	x = Array(range(x1, x2, length=N)) 	h = x[2] - x[1] 	diag = fill(+2/h^2, N-2) 	semidiag = fill(-1/h^2, N-3) 	L = Tridiagonal(semidiag, diag, semidiag) 	u = L \ f[2:end-1] 	u = cat([0], u, [0], dims=1) 	return x, u end  function animate() 	# Store all Green's function solutions 	N = 101 	U = zeros(N, N) 	p = plot() 	for i in 1:N 		f = [i == j ? 1 : 0 for j in 1:N] 		x, u = solve(f) 		U[i,:] = u 		plot!(p, u) 	end  	# Solve a real problem 	f1 = exp.(-(x.-0.5).^2 / (2*0.01)) 	x, u1 = solve(f1) 	u = zeros(N)  	barw = x[2]-x[1] # plot bars with no gap between them  	anim = @animate for i in 1:N 	    y = @sprintf("%.2f", (i-1) / (N-1)) # as string 		f2 = [i == j ? 1 : 0 for j in 1:N] 		x, u2 = solve(f2) 		u += u2 * f1[i]  		colors = [i == j ? :black : :red for j in 1:N]  		# for some reason, only (1599, 1600) gives a height that is divisible by 2 during mp4 generation 		plot(layout=(2, 2), size=(1599, 1600), xlims=(0,1), xticks=([0, 0.5, 1], ["\$0\$", "\$x\$", "\$1\$"]), yticks=nothing, bar_width=barw, titlefontsize=40, tickfontsize=40, framestyle=:box, grid=false, legend=nothing, margin=10Plots.mm, top_margin=0Plots.mm)  		# Plot point-source and Green's function solution 		bar!(subplot=1, x[i:i], f2[i:i],         color=:green,      linecolor=:green,     bar_width=barw, ylims=(0, 1.10), title="\$\\delta(x-$y)\$") 		bar!(subplot=2, x,      u2,              color=:darkgreen,  linecolor=:darkgreen, bar_width=barw, ylims=(0, 0.02), title="\$G(x,$y)\$")  		# Plot full source and full solution 		bar!(subplot=3, x[1:i],     f1[1:i],     color=:blue,      linecolor=:blue,       bar_width=barw, ylims=(0, 1.10), title="\$ \\hat{L}\\,(x) u(x) = f(x < $y) \$") 		bar!(subplot=3, x[i+1:end], f1[i+1:end], color=:lightgrey, linecolor=:lightgrey,  bar_width=barw, ylims=(0, 1.10)) 		bar!(subplot=4, x,          u1,          color=:lightgrey, linecolor=:lightgrey,  bar_width=barw, ylims=(0, 0.06)) 		bar!(subplot=4, x,          u,           color=:darkblue,  linecolor=:darkblue,   bar_width=barw, ylims=(0, 0.06), title="\$ u(x) = {\\int}_{0}^{$y} \\! f(x') \\, G(x,x') \\, \\mathrm{d} x' \$") 	end  	mp4(anim, "green.mp4", fps=5) 	run(`ffmpeg -i green.mp4 -vf "fps=10,scale=640:640:flags=lanczos,split[s0][s1];[s0]palettegen[p];[s1][p]paletteuse" -loop 0 green.gif`) end  animate() 

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