From 0182e0ad8924ea3e3ace630877dba74afb938137 Mon Sep 17 00:00:00 2001
From: Joshua Lampert <51029046+JoshuaLampert@users.noreply.github.com>
Date: Mon, 20 Nov 2023 17:42:33 +0100
Subject: [PATCH] Interpolate x value for plotting (#64)

* interpolate x value for plotting

* format

* add compat for Interpolations
---
 Project.toml                  | 2 ++
 src/DispersiveShallowWater.jl | 1 +
 src/visualization.jl          | 8 +++++---
 3 files changed, 8 insertions(+), 3 deletions(-)

diff --git a/Project.toml b/Project.toml
index 2ca57501..060118ea 100644
--- a/Project.toml
+++ b/Project.toml
@@ -5,6 +5,7 @@ version = "0.1.2-pre"
 
 [deps]
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
+Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PolynomialBases = "c74db56a-226d-5e98-8bb0-a6049094aeea"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -19,6 +20,7 @@ SummationByPartsOperators = "9f78cca6-572e-554e-b819-917d2f1cf240"
 
 [compat]
 DiffEqBase = "6.121"
+Interpolations = "0.14"
 LinearAlgebra = "1"
 PolynomialBases = "0.4.15"
 Printf = "1"
diff --git a/src/DispersiveShallowWater.jl b/src/DispersiveShallowWater.jl
index d866f52f..77b98726 100644
--- a/src/DispersiveShallowWater.jl
+++ b/src/DispersiveShallowWater.jl
@@ -1,6 +1,7 @@
 module DispersiveShallowWater
 
 using DiffEqBase
+using Interpolations
 using LinearAlgebra: mul!, ldiv!, factorize, I, Diagonal
 using PolynomialBases
 using Printf: @printf, @sprintf
diff --git a/src/visualization.jl b/src/visualization.jl
index f80ade23..4d72c9a8 100644
--- a/src/visualization.jl
+++ b/src/visualization.jl
@@ -105,12 +105,14 @@ end
         nsubplots -= 1
     end
 
-    index = argmin(abs.(grid(semi) .- x))
     solution = zeros(nvariables(semi), length(sol.t))
     data = zeros(nvars, length(sol.t))
     for i in 1:nvariables(semi)
         for k in 1:length(sol.t)
-            solution[i, k] = wrap_array(sol.u[k], semi)[i, index]
+            # Allow that the spatial value `x` is not on the grid. Thus, interpolate the given values to the provided `x`
+            # with a linear spline.
+            solution[i, k] = linear_interpolation(grid(semi),
+                                                  view(wrap_array(sol.u[k], semi), i, :))(x)
         end
     end
 
@@ -120,7 +122,7 @@ end
 
     names = varnames(conversion, equations)
     plot_title -->
-    "$(get_name(semi.equations)) at x = $(round(grid(semi)[index], digits=5))"
+    "$(get_name(semi.equations)) at x = $(round(x, digits=5))"
     layout --> nsubplots
 
     for i in 1:nsubplots