@@ -107,7 +107,7 @@ svdval_w = svdvals(snapshot_w)
107107svdval_fv = svdvals(snapshot_fv)
108108using Plots, LaTeXStrings
109109svd_plt = plot(yscale = :log10, xticks = eachindex(svdval_v), titlefont = 11,
110- legendfont = 10, title = "Singular values of the snapshots")
110+ legendfont = 10, title = "Singular values of the snapshots")
111111plot!(svd_plt, svdval_v, markershape = :circle, label = L"Singular Val of $v$")
112112plot!(svd_plt, svdval_w, markershape = :circle, label = L"Singular Val of $w$")
113113plot!(svd_plt, svdval_fv, markershape = :circle, label = L"Singular Val of $f(v)$")
@@ -118,9 +118,9 @@ points ``x`` from the full-order system.
118118
119119``` @example deim_FitzHugh_Nagumo
120120full_plt = plot(xlabel = L"v(x,t)", ylabel = L"x", zlabel = L"w(x,t)", xlims = (-0.5, 2.0),
121- ylims = (0.0, L), zlims = (0.0, 0.25), legend = false, xflip = true,
122- camera = (50, 30), titlefont = 10,
123- title = "Phase−Space diagram of full $(nameof(pde_sys)) system")
121+ ylims = (0.0, L), zlims = (0.0, 0.25), legend = false, xflip = true,
122+ camera = (50, 30), titlefont = 10,
123+ title = "Phase−Space diagram of full $(nameof(pde_sys)) system")
124124@views for i in 1:nₓ
125125 plot!(full_plt, snapshot_v[i, :], _ -> sol_x[i], snapshot_w[i, :])
126126end
@@ -149,9 +149,9 @@ And plot the result from the POD-DEIM reduced system.
149149
150150``` @example deim_FitzHugh_Nagumo
151151deim_plt = plot(xlabel = L"v(x,t)", ylabel = L"x", zlabel = L"w(x,t)", xlims = (-0.5, 2.0),
152- ylims = (0.0, L), zlims = (0.0, 0.25), legend = false, xflip = true,
153- camera = (50, 30), titlefont = 10,
154- title = "Phase−Space diagram of reduced $(nameof(pde_sys)) system")
152+ ylims = (0.0, L), zlims = (0.0, 0.25), legend = false, xflip = true,
153+ camera = (50, 30), titlefont = 10,
154+ title = "Phase−Space diagram of reduced $(nameof(pde_sys)) system")
155155@views for i in 1:nₓ
156156 plot!(deim_plt, sol_deim_v[i, :], _ -> sol_deim_x[i], sol_deim_w[i, :])
157157end
@@ -178,12 +178,12 @@ function unconnected(v::AbstractVector, nₜ::Integer)
178178 vec(data)
179179end
180180plt_2 = plot(xlabel = L"v(x,t)", ylabel = L"x", zlabel = L"w(x,t)", xlims = (-0.5, 2.0),
181- ylims = (0.0, L), zlims = (0.0, 0.25), xflip = true, camera = (50, 30),
182- titlefont = 10, title = "Comparison of full and reduced systems")
181+ ylims = (0.0, L), zlims = (0.0, 0.25), xflip = true, camera = (50, 30),
182+ titlefont = 10, title = "Comparison of full and reduced systems")
183183plot!(plt_2, unconnected(snapshot_v), unconnected(sol_x, nₜ), unconnected(snapshot_w),
184- label = "Full$(length(ode_sys.eqs))")
184+ label = "Full$(length(ode_sys.eqs))")
185185plot!(plt_2, unconnected(sol_deim_v), unconnected(sol_deim_x, nₜ_deim),
186- unconnected(sol_deim_w), label = "POD$(pod_dim)/DEIM$(deim_dim)")
186+ unconnected(sol_deim_w), label = "POD$(pod_dim)/DEIM$(deim_dim)")
187187```
188188
189189As we can see, the reduced-order system captures the limit cycle of the original full-order
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