add plots to least squares

Author: MaxenceGollier

docs/Project.toml

@@ -5,6 +5,7 @@ DocumenterCitations = "daee34ce-89f3-4625-b898-19384cb65244"
 LLSModels = "39f5bc3e-5160-4bf8-ac48-504fd2534d24"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NLPModelsModifiers = "e01155f1-5c6f-4375-a9d8-616dd036575f"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 ProximalOperators = "a725b495-10eb-56fe-b38b-717eba820537"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RegularizedProblems = "ea076b23-609f-44d2-bb12-a4ae45328278"

docs/src/examples/ls.md

@@ -50,7 +50,7 @@ end
 f_model = ADNLSModel(F, x0, m, name = "nonlinear LS model of f")
 
 # Get the regularizer from ProximalOperators
-λ  = 1.0   
+λ  = 0.01
 h = NormL0(λ)
 
 # Wrap into a RegularizedNLPModel
@@ -69,9 +69,41 @@ out = LM(regularized_pb, verbose = 1, atol = 1e-4)
 println("LM converged after $(out.iter) iterations.")
 ```
 
+We can visualize the solution with plots,
+```@example ls
+using Plots
+
+# Extract estimated parameters
+a_est, b_est = out.solution
+
+# True curve
+y_true = [a_true * exp(b_true * ti) for ti in t]
+
+# Estimated curve
+y_est = [a_est * exp(b_est * ti) for ti in t]
+
+# Plot
+scatter(t, y, label="Noisy data", legend=:bottomleft)
+plot!(t, y_true, label="True model", lw=2)
+plot!(t, y_est, label="Fitted model", lw=2, ls=:dash) 
+```
+
 ```@example ls
 #We can choose LMTR instead which is a trust-region method
 out = LMTR(regularized_pb, verbose = 1, atol = 1e-4)
 println("LMTR converged after $(out.iter) iterations.")
+```
+
+```@example ls
+# Extract estimated parameters
+a_est, b_est = out.solution
+
+# Estimated curve
+y_est = [a_est * exp(b_est * ti) for ti in t]
+
+# Plot
+scatter(t, y, label="Noisy data", legend=:bottomleft)
+plot!(t, y_true, label="True model", lw=2)
+plot!(t, y_est, label="Fitted model", lw=2, ls=:dash) 
 
 ```