Merge be9078a into dbcd827

docs/make.jl

@@ -17,6 +17,9 @@ makedocs(
         "LinearSurrogate" => "LinearSurrogate.md",
         "InverseDistance" => "InverseDistance.md"
         ]
+    "Benchmarks" => [
+        "Sphere function" => "sphere_function.md"
+    ]
     "Contributing" => "contributing.md"
     ]
 )

docs/src/contributing.md

@@ -12,5 +12,7 @@ You can also contact me on the Julia slack channel at @ludoro.
 # List of contributors
 
 - Ludovico Bessi (@ludoro)
-- Chris Rackauckas
+- Chris Rackauckas (@ChrisRackauckas)
 - Rohit Singh Rathaur (@TeAmp0is0N)
+- Andrea Cognolato (@mrandri19)
+- Kanav Gupta (@kanav99)

docs/src/sphere_function.md

@@ -0,0 +1,55 @@
+# Sphere function
+
+The sphere function of dimension d is defined as:
+$$ f(x) = \sum_{i=1}^d x_i $$
+with lower bound -10 and upper bound 10.
+
+Let's import Surrogates and Plots:
+```@example sphere_function
+using Surrogates
+using Plots
+default()
+```
+
+Define the objective function:
+```@example sphere_function
+function sphere_function(x)
+    return sum(x.^2)
+end
+```
+
+The 1D case is just a simple parabola, let's plot it:
+```@example sphere_function
+n = 100
+lb = -10
+ub = 10
+x = sample(n,lb,ub,SobolSample())
+y = sphere_function.(x)
+xs = lb:0.001:ub
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lb, ub), ylims=(-2, 120))
+plot!(xs,sphere_function.(xs), label="True function")
+```
+
+Fitting RadialSurrogate with different radial basis:
+```@example sphere_function
+rad_1d_linear = RadialBasis(x,y,lb,ub)
+rad_1d_cubic = RadialBasis(x,y,lb,ub,rad = cubicRadial)
+rad_1d_multiquadric = RadialBasis(x,y,lb,ub, rad = multiquadricRadial)
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lb, ub), ylims=(-2, 120))
+plot!(xs,sphere_function.(xs), label="True function")
+plot!(xs, rad_1d_linear.(xs), label="Radial surrogate with linear")
+plot!(xs, rad_1d_cubic.(xs), label="Radial surrogate with cubic")
+plot!(xs, rad_1d_multiquadric.(xs), label="Radial surrogate with multiquadric")
+```
+
+Fitting Lobachesky Surrogate with different values of hyperparameters alpha:
+```@example sphere_function
+loba_1 = LobacheskySurrogate(x,y,lb,ub)
+loba_2 = LobacheskySurrogate(x,y,lb,ub,alpha = 1.5, n = 6)
+loba_3 = LobacheskySurrogate(x,y,lb,ub,alpha = 0.3, n = 6)
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lb, ub), ylims=(-2, 120))
+plot!(xs,sphere_function.(xs), label="True function")
+plot!(xs, loba_1.(xs), label="Lobachesky surrogate 1")
+plot!(xs, loba_2.(xs), label="Lobachesky surrogate 2")
+plot!(xs, loba_3.(xs), label="Lobachesky surrogate 3")
+```