add brent, deckkers-aarts fns, refactor

plots/plots.jl

@@ -0,0 +1,53 @@
+using BenchmarkFunctions
+using Plots
+pyplot()
+
+## plot 1D functions
+plot("gramacy_lee",   -0.5:0.001:2.5)
+savefig("./plots/1d_gramacy_lee.svg")
+
+## plot 2D functions
+plot("adjiman",       -4:0.1:4, -4:0.1:4)
+savefig("./plots/2d_adjiman.svg")
+plot("ackley_2",      -4:0.1:4, -4:0.1:4)
+savefig("./plots/2d_ackley_2.svg")
+plot("ackley_3",      -4:0.1:4, -4:0.1:4)
+savefig("./plots/2d_ackley_3.svg")
+plot("bartels_conn",  -4:0.1:4, -4:0.1:4)
+savefig("./plots/2d_bartels_conn.svg")
+plot("beale",         -4:0.1:4, -4:0.1:4)
+savefig("./plots/2d_beale.svg")
+plot("bird",          -2π:0.1:2π, -2π:0.1:2π)
+savefig("./plots/2d_bird.svg")
+plot("bohachevsky_1", -100:1:100, -100:1:100)
+savefig("./plots/2d_bohachevsky_1.svg")
+plot("bohachevsky_2", -2:0.1:2, -2:0.1:2)
+savefig("./plots/2d_bohachevsky_2.svg")
+plot("bohachevsky_3", -2:0.1:2, -2:0.1:2)
+savefig("./plots/2d_bohachevsky_3.svg")
+plot("brent",         -15:0.1:-5, -15:0.1:-5)
+savefig("./plots/2d_brent.svg")
+plot("deckkers_aarts",-20:0.2:20, -20:0.2:20)
+savefig("./plots/2d_deckkers_aarts.svg")
+plot("himmelblau",    -5:0.1:5, -5:0.1:5)
+savefig("./plots/2d_himmelblau.svg")
+plot("mccormick",     -1.5:0.1:4, -3:0.1:3)
+savefig("./plots/2d_mccormick.svg")
+
+## plot nD functions
+plot("ackley_1",      -10:0.01:10)
+savefig("./plots/nd_ackley_1_1d.svg")
+plot("ackley_1",      -10:0.1:10, -10:0.1:10)
+savefig("./plots/nd_ackley_1_2d.svg")
+plot("ackley_4",      -5:0.1:5, -5:0.1:5)
+savefig("./plots/nd_ackley_4_2d.svg")
+plot("alpine_1",      -10:0.01:10)
+savefig("./plots/nd_alpine_1_1d.svg")
+plot("alpine_1",      -10:0.1:10, -10:0.1:10)
+savefig("./plots/nd_alpine_1_2d.svg")
+plot("alpine_2",       0:0.01:10)
+savefig("./plots/nd_alpine_2_1d.svg")
+plot("alpine_2",       0:0.1:10, 0:0.1:10)
+savefig("./plots/nd_alpine_2_2d.svg")
+plot("rosenbrock",    -2:0.1:2, -2:0.1:2)
+savefig("./plots/nd_rosenbrock_2d.svg")

src/BenchmarkFunctions.jl

@@ -5,36 +5,9 @@ using Plots
 using LaTeXStrings
 
 # utils
-include("attributes.jl")
-include("ndgrid.jl")
-include("plot.jl")
-export attributes, ndgrid, plot
+include("utils/utils.jl")
 
-# 1-dimensional
-include("gramacy_lee.jl")
-export gramacy_lee
-
-# 2-dimensional
-include("adjiman.jl")
-include("ackley_2.jl")
-include("ackley_3.jl")
-include("bartels_conn.jl")
-include("beale.jl")
-include("bird.jl")
-include("bohachevsky_1.jl")
-include("bohachevsky_2.jl")
-include("bohachevsky_3.jl")
-include("himmelblau.jl")
-include("mccormick.jl")
-export adjiman, ackley_2, ackley_3, bartels_conn, beale, bird, bohachevsky_1,
-        bohachevsky_2, bohachevsky_3, himmelblau, mccormick
-
-# n-dimensional
-include("ackley_1.jl")
-include("ackley_4.jl")
-include("alpine_1.jl")
-include("alpine_2.jl")
-include("rosenbrock.jl")
-export ackley_1, ackley_4, alpine_1, alpine_2, rosenbrock
+# functions
+include("functions/functions.jl")
 
 end

src/functions/brent.jl

@@ -0,0 +1,16 @@
+"""
+    brent(X)
+
+Compute the 2-dimensional Brent function on sample vector `X`.
+
+The function is usually evaluated on `xᵢ` ∈ [-10, 10] for i = 1, 2.
+"""
+function brent(X)
+
+    @assert all(length.(X) .== 2) "Sample vector tuples must be length 2."
+
+    y = [Tuple( (x[1]+10)^2 + (x[2]+10)^2 + exp(-x[1]^2 - x[2]^2) ) for x in X]
+
+    return y
+
+end

src/functions/deckkers_aarts.jl

@@ -0,0 +1,17 @@
+"""
+    deckkers_aarts(X)
+
+Compute the 2-dimensional Deckkers-Aarts function on sample vector `X`.
+
+The function is usually evaluated on `xᵢ` ∈ [-20, 20] for i = 1, 2.
+"""
+function deckkers_aarts(X)
+
+    @assert all(length.(X) .== 2) "Sample vector tuples must be length 2."
+
+    y = [Tuple( 1e5*x[1]^2 + x[2]^2 - (x[1]^2+x[2]^2)^2 +
+                1e-5*(x[1]^2+x[2]^2)^4 ) for x in X]
+
+    return y
+
+end

src/functions/functions.jl

@@ -0,0 +1,29 @@
+# 1-dimensional
+include("gramacy_lee.jl")
+export gramacy_lee
+
+# 2-dimensional
+include("adjiman.jl")
+include("ackley_2.jl")
+include("ackley_3.jl")
+include("bartels_conn.jl")
+include("beale.jl")
+include("bird.jl")
+include("bohachevsky_1.jl")
+include("bohachevsky_2.jl")
+include("bohachevsky_3.jl")
+include("brent.jl")
+include("deckkers_aarts.jl")
+include("himmelblau.jl")
+include("mccormick.jl")
+export adjiman, ackley_2, ackley_3, bartels_conn, beale, bird, bohachevsky_1,
+        bohachevsky_2, bohachevsky_3, brent, deckkers_aarts, himmelblau,
+        mccormick
+
+# n-dimensional
+include("ackley_1.jl")
+include("ackley_4.jl")
+include("alpine_1.jl")
+include("alpine_2.jl")
+include("rosenbrock.jl")
+export ackley_1, ackley_4, alpine_1, alpine_2, rosenbrock

src/attributes.jl → src/utils/attributes.jl

@@ -34,6 +34,8 @@ functionDict = Dict("gramacy_lee"   => Set(["1d", "continuous", "differentiable"
                     "bohachevsky_1" => Set(["2d", "continuous", "differentiable",     "convex",     "unimodal",   "separable"]),
                     "bohachevsky_2" => Set(["2d", "continuous", "differentiable",     "non-convex", "multimodal", "non-separable"]),
                     "bohachevsky_3" => Set(["2d", "continuous", "differentiable",     "non-convex", "multimodal", "non-separable"]),
+                    "brent"         => Set(["2d", "continuous", "differentiable",     "convex",     "unimodal",   "non-separable"]),
+                    "deckkers_aarts"=> Set(["2d", "continuous", "differentiable",     "non-convex", "multimodal", "non-separable"]),
                     "himmelblau"    => Set(["2d", "continuous", "differentiable",     "non-convex", "multimodal", "separable"]),
                     "mccormick"     => Set(["2d", "continuous", "differentiable",     "convex",     "multimodal", "separable"]),
                     "ackley_1"      => Set(["nd", "continuous", "differentiable",     "non-convex", "multimodal", "separable"]),

src/utils/utils.jl

@@ -0,0 +1,4 @@
+include("attributes.jl")
+include("ndgrid.jl")
+include("plot.jl")
+export attributes, ndgrid, plot

test/runtests.jl

@@ -2,33 +2,35 @@ using BenchmarkFunctions
 using Test
 
 @testset "1-dimensional function minima" begin
-    @test isapprox(minimum(gramacy_lee(  ndgrid(-0.5:0.01:2.5)))[1],          -2.84962, atol=0.1)
+    @test isapprox(minimum(gramacy_lee(   ndgrid(-0.5:0.01:2.5)))[1],          -2.84962, atol=0.1)
 end
 
 @testset "2-dimensional function minima" begin
-    @test isapprox(minimum(ackley_2(     ndgrid(-5  :0.1:5 ,-5 :0.1:5 )))[1], -200.,    atol=0.1)
-    @test isapprox(minimum(ackley_3(     ndgrid(-5  :0.1:5 ,-5 :0.1:5 )))[1], -195.629, atol=0.1)
-    @test isapprox(minimum(adjiman(      ndgrid(-1  :0.1:2 ,-1 :0.1:1 )))[1], -2.02181, atol=0.1)
-    @test isapprox(minimum(bartels_conn( ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  1,       atol=0.1)
-    @test isapprox(minimum(beale(        ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
-    @test isapprox(minimum(bird(         ndgrid(-2π :0.05:2π,-2π:0.05:2π)))[1],-106.764, atol=0.1)
-    @test isapprox(minimum(bohachevsky_1(ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
-    @test isapprox(minimum(bohachevsky_2(ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
-    @test isapprox(minimum(bohachevsky_3(ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
-    @test isapprox(minimum(himmelblau(   ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
-    @test isapprox(minimum(mccormick(    ndgrid(-1.5:0.1:4 ,-3 :0.1:3 )))[1], -1.9133,  atol=0.1)
+    @test isapprox(minimum(ackley_2(      ndgrid(-5  :0.1:5 ,-5 :0.1:5 )))[1], -200.,    atol=0.1)
+    @test isapprox(minimum(ackley_3(      ndgrid(-5  :0.1:5 ,-5 :0.1:5 )))[1], -195.629, atol=0.1)
+    @test isapprox(minimum(adjiman(       ndgrid(-1  :0.1:2 ,-1 :0.1:1 )))[1], -2.02181, atol=0.1)
+    @test isapprox(minimum(bartels_conn(  ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  1,       atol=0.1)
+    @test isapprox(minimum(beale(         ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
+    @test isapprox(minimum(bird(          ndgrid(-2π :0.05:2π,-2π:0.05:2π)))[1],-106.764,atol=0.1)
+    @test isapprox(minimum(bohachevsky_1( ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
+    @test isapprox(minimum(bohachevsky_2( ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
+    @test isapprox(minimum(bohachevsky_3( ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
+    @test isapprox(minimum(brent(         ndgrid(-15 :0.1:-5,-15:0.1:-5)))[1], exp(-200),atol=0.1)
+    @test isapprox(minimum(deckkers_aarts(ndgrid(-20 :0.4:20,-20:0.4:20)))[1], -24771,   atol=1e2)
+    @test isapprox(minimum(himmelblau(    ndgrid(-4  :0.1:4 ,-4 :0.1:4 )))[1],  0.,      atol=0.1)
+    @test isapprox(minimum(mccormick(     ndgrid(-1.5:0.1:4 ,-3 :0.1:3 )))[1], -1.9133,  atol=0.1)
 end
 
 @testset "n-dimensional function minima" begin
-    @test isapprox(minimum(ackley_1(     ndgrid( -5:0.1: 5), n=1))[1],        0.,       atol=0.1)
-    @test isapprox(minimum(ackley_1(     ndgrid( -5:0.1: 5, -5:0.1: 5)))[1],  0.,       atol=0.1)
-    @test isapprox(minimum(ackley_4(     ndgrid( -5:0.1: 5, -5:0.1: 5)))[1], -4.590101, atol=0.1)
-    @test isapprox(minimum(alpine_1(     ndgrid(-10:0.1:10), n=1))[1],        0.,       atol=0.1)
-    @test isapprox(minimum(alpine_1(     ndgrid(-10:0.1:10,-10:0.1:10)))[1],  0.,       atol=0.1)
-    @test isapprox(minimum(alpine_2(     ndgrid(  0:0.1:10), n=1))[1],       -2.808^1,  atol=0.1)
-    @test isapprox(minimum(alpine_2(     ndgrid(  0:0.1:10,  0:0.1:10)))[1], -2.808^2,  atol=0.1)
-    @test isapprox(minimum(rosenbrock(   ndgrid( -2:0.1: 2, -2:0.1: 2)))[1],  0.,       atol=0.1)
-    @test isapprox(minimum(rosenbrock(   ndgrid( -2:0.1: 2, -2:0.1: 2,-2:0.1:2), n=3))[1], 0., atol=0.1)
+    @test isapprox(minimum(ackley_1(      ndgrid( -5:0.1: 5), n=1))[1],        0.,       atol=0.1)
+    @test isapprox(minimum(ackley_1(      ndgrid( -5:0.1: 5, -5:0.1: 5)))[1],  0.,       atol=0.1)
+    @test isapprox(minimum(ackley_4(      ndgrid( -5:0.1: 5, -5:0.1: 5)))[1], -4.590101, atol=0.1)
+    @test isapprox(minimum(alpine_1(      ndgrid(-10:0.1:10), n=1))[1],        0.,       atol=0.1)
+    @test isapprox(minimum(alpine_1(      ndgrid(-10:0.1:10,-10:0.1:10)))[1],  0.,       atol=0.1)
+    @test isapprox(minimum(alpine_2(      ndgrid(  0:0.1:10), n=1))[1],       -2.808^1,  atol=0.1)
+    @test isapprox(minimum(alpine_2(      ndgrid(  0:0.1:10,  0:0.1:10)))[1], -2.808^2,  atol=0.1)
+    @test isapprox(minimum(rosenbrock(    ndgrid( -2:0.1: 2, -2:0.1: 2)))[1],  0.,       atol=0.1)
+    @test isapprox(minimum(rosenbrock(    ndgrid( -2:0.1: 2, -2:0.1: 2,-2:0.1:2), n=3))[1], 0., atol=0.1)
 end
 
 @testset "Attribute output" begin