Merge branch 'master' of https://github.com/SciML/Surrogates.jl

Project.toml

@@ -29,10 +29,11 @@ GLM = "1.3"
 GaussianMixtures = "0.3"
 IterativeSolvers = "0.8"
 LatinHypercubeSampling = "1.2"
+PolyChaos = "0.2"
 Requires = "0.5, 1.0"
 Sobol = "1.3"
 Stheno = "0.6"
-XGBoost = "0.4"
+XGBoost = "0.4, 1.1"
 julia = "1"
 
 [extras]

docs/make.jl

@@ -12,6 +12,7 @@ makedocs(
         "Basics" => "tutorials.md",
         "RandomForestSurrogate" => "randomforest.md",
         "Radials" => "radials.md",
+        "LinearSurrogate" => "LinearSurrogate.md",
         "Kriging" => "kriging.md"
         ]
     "Contributing" => "contributing.md"

docs/src/LinearSurrogate.md

@@ -0,0 +1,67 @@
+## Linear Surrogate
+Linear Surrogate is a linear approach to modeling the relationship between a scalar response or dependent variable and one or more explanatory variables. We will use Linear Surrogate to optimize **Eggholder Function**.
+
+$f(x) = - x_{1} \sin\left(\sqrt{\lvert{x_{1} - x_{2} -47}\rvert}\right) - \left(x_{2} + 47\right) \sin\left(\sqrt{\left|{\frac{1}{2} x_{1} + x_{2} + 47}\right|}\right)$.
+
+First of all we have to import these two packages: `Surrogates` and `Plots`.
+
+```@example linear_surrogate1D
+using Surrogates
+using Plots
+default()
+```
+
+### Sampling
+
+We choose to sample f in 6 points between 0 and 10 using the `sample` function. The sampling points are chosen using a Sobol sequence, this can be done by passing `SobolSample()` to the `sample` function.
+
+```@example linear_surrogate1D
+# http://infinity77.net/global_optimization/test_functions.html#test-functions-index.
+x_1 = 1
+x_2 = 2
+
+term1 = -(x_2+47) * sin(sqrt(abs(x_2+x_1/2+47)))
+term2 = -x_1 * sin(sqrt(abs(x_1-(x_2+47))))
+f(x) = term1 + term2
+n_samples = 6
+lower_bound = 5.2
+upper_bound = 12.5
+x = sample(n_samples, lower_bound, upper_bound, sobolSample())
+y = f.(x)
+scatter(x, y, label="Sampled points", xlims=(lower_bound, upper_bound))
+plot!(f, label="True function", xlims=(lower_bound, upper_bound))
+```
+
+## Building a Surrogate
+
+With our sampled points we can build the **Linear Surrogate** using the `LinearSurrogate` function.
+
+We can simply calculate `linear_surrogate` for any value.
+
+```@example linear_surrogate1D
+my_linear_surr_1D = LinearSurrogate(x, y, lower_bound, upper_bound)
+add_point!(my_linear_surr_1D,4.0,7.2)
+add_point!(my_linear_surr_1D,[5.0,6.0],[8.3,9.7])
+val = my_linear_surr_1D(5.0)
+```
+
+Now, we will simply plot `linear_surrogate`:
+
+```@example linear_surrogate1D
+plot(x, y, seriestype=:scatter, label="Sampled points", xlims=(lower_bound, upper_bound))
+plot!(f, label="True function",  xlims=(lower_bound, upper_bound))
+plot!(my_linear_surr_1D, label="Surrogate function",  xlims=(lower_bound, upper_bound))
+```
+
+## Optimizing
+
+Having built a surrogate, we can now use it to search for minimas in our original function `f`.
+
+To optimize using our surrogate we call `surrogate_optimize` method. We choose to use Stochastic RBF as optimization technique and again Sobol sampling as sampling technique.
+
+```@example linear_surrogate1D
+@show surrogate_optimize(f, SRBF(), lower_bound, upper_bound, my_linear_surr_1D, SobolSample())
+scatter(x, y, label="Sampled points")
+plot!(f, label="True function",  xlims=(lower_bound, upper_bound))
+plot!(my_linear_surr_1D, label="Surrogate function",  xlims=(lower_bound, upper_bound))
+```

src/Radials.jl

@@ -32,7 +32,7 @@ end)
 Constructor for RadialBasis surrogate.
 """
 function RadialBasis(x, y, lb::Number, ub::Number; rad::RadialFunction=linearRadial, scale_factor::Real=1.0, sparse = false)
-    q = rad.q
+    q = rad.q + 1
     phi = rad.phi
     coeff = _calc_coeffs(x, y, lb, ub, phi, q,scale_factor, sparse)
     return RadialBasis(phi, q, x, y, lb, ub, coeff,scale_factor,sparse)
@@ -44,7 +44,7 @@ RadialBasis(x,y,lb,ub,rad::RadialFunction, scale_factor::Float = 1.0)
 Constructor for RadialBasis surrogate
 """
 function RadialBasis(x, y, lb, ub; rad::RadialFunction = linearRadial, scale_factor::Real=1.0, sparse = false)
-    q = rad.q
+    q = rad.q + 1
     phi = rad.phi
     coeff = _calc_coeffs(x, y, lb, ub, phi, q, scale_factor, sparse)
     return RadialBasis(phi, q, x, y, lb, ub, coeff,scale_factor, sparse)