Performance improvements for simpsons_rule and simpsons38_rule

Improving performance of simpsons_rule and simpsons38_rule
fusion809 · Jul 9, 2020 · cdd820f · cdd820f
1 parent 1271feb
commit cdd820f
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Showing 3 changed files with 51 additions and 31 deletions.
diff --git a/desktop.ini b/desktop.ini
@@ -0,0 +1,4 @@
+[ViewState]
+Mode=
+Vid=
+FolderType=Documents
diff --git a/src/Simpson.jl b/src/Simpson.jl
@@ -1,23 +1,22 @@
-function stepwise_simpsons(f::Function, h::Number, x::Number, i::Integer, N::Number, k::Integer)
-    if k==1
-        if i == 1 || i == N + 1
-            return h / 3 * f(x)
-        elseif (i % 2) == 1
-            return 2 * h / 3 * f(x)
-        else
-            return 4 * h / 3 * f(x)
-        end
-    elseif k==2
-        if i==1 || i == N + 1
-            return (3*h/8)*f(x)
-        elseif ((i-1) % 3) == 0
-            return (3*h/4)*f(x)
-        else
-            return (9*h/8)*f(x)
-        end
+function stepwise_simpsons(f::Function, h::Number, x::Number, i::Integer, N::Number)
+    if i == 1 || i == N + 1
+        return h / 3 * f(x)
+    elseif (i % 2) == 1
+        return 2 * h / 3 * f(x)
+    else
+        return 4 * h / 3 * f(x)
     end
 end
 
+function stepwise_simpsons38(f::Function, h::Number, x::Number, i::Integer, N::Number)
+    if i==1 || i == N + 1
+        return (3*h/8)*f(x)
+    elseif ((i-1) % 3) == 0
+        return (3*h/4)*f(x)
+    else
+        return (9*h/8)*f(x)
+    end
+end
 """
     simpsons_rule(f::Function, N::Number, a::Number, b::Number)
 
@@ -34,7 +33,7 @@ function simpsons_rule(f::Function, N::Number, a::Number, b::Number)
     y = 0;
     x = a;
     for i=1:N+1
-        y = y + stepwise_simpsons(f, h, x, i, N, 1);
+        y = y + stepwise_simpsons(f, h, x, i, N);
         if i < N+1
             x = x + h;
         end
@@ -58,7 +57,7 @@ function simpsons38_rule(f::Function, N::Number, a::Number, b::Number)
     y = 0;
     x = a;
     for i=1:N+1
-        y = y + stepwise_simpsons(f, h, x, i, N, 2);
+        y = y + stepwise_simpsons38(f, h, x, i, N);
         if i < N+1
             x = x + h;
         end

diff --git a/test/Computation_times_Travis_80.2.jl → test/Computation_times_Travis_92.2.jl b/test/Computation_times_Travis_80.2.jl → test/Computation_times_Travis_92.2.jl
@@ -1,16 +1,33 @@
-# Taken from https://travis-ci.com/github/fusion809/FunctionIntegrator.jl/jobs/355708079
+# Taken from https://travis-ci.com/github/fusion809/FunctionIntegrator.jl/jobs/358878829
 # 10th entry is simppen
-L_chebyshev1=[1.435044; 0.307644; 0.045131; 0.104719; 0.116603; 0.090129; 0.088141; 0.114219; 0.162800; 0.441775; 0.102337; 0.050055; 0.048896];
-L_chebyshev2=[0.197077; 0.068784; 0.043831; 0.099813; 0.111966; 0.125740; 0.103428; 0.098729; 0.064575; 8.991385; 0.096214; 0.052295; 0.049748];
-L_chebyshev3 = [0.155732; 0.072039; 0.049798; 0.111535; 0.099392; 0.101607; 0.111045; 0.111373; 0.070177; 3.208550; 0.092763; 0.057960; 0.055562];
-L_chebyshev4 = [0.146024; 0.070966; 0.049619; 0.092735; 0.098091; 0.100671; 0.099425; 0.099531; 0.070195; 4.146543; 0.094798; 0.056763; 0.053876];
-L_jacobi = [21.200547; 0.741378; 0.079454; 0.468545; 0.220772; 2.786482; 0.531896; 0.446746; 0.479568; 22.058539; 0.242638; 1.933591; 0.694156];
-L_legendre=[0.105352; 0.076702; 0.030384; 0.071562; 0.078758; 0.078509; 0.088236; 0.090079; 0.043331; 4.383104; 0.059413; 0.036632; 0.033564];
-L_lobatto=[0.192820; 0.012460; 0.000103; 0.080504; 0.143451; 0.117507; 0.086438; 0.091315; 0.000142; 21.927058; 0.025977; 0.000409; 0.000141];
-L_radau = [0.138636; 0.012143; 0.000040; 0.094062; 0.129707; 0.104701; 0.086289; 0.087083; 0.000057; 22.282400; 0.025089; 0.000345; 0.000109];
-L_rectangle_midpoint = [0.073889; 0.000017; 0.000330; 0.019159; 0.022585; 0.030032; 0.018576; 0.021532; 0.000027; 1.863286; 0.035673; 0.000545; 0.000903];
-L_simpsons=[0.060178; 0.040657; 0.000012; 0.023218; 0.041971; 0.028887; 0.025965; 0.031452; 0.018607; 13.831230; 0.047495; 0.000064; 0.000078];
-L_trapezoidal=[0.161483; 0.034553; 0.000577; 0.017627; 0.032416; 0.022288; 0.019312; 0.023317; 0.013583; 13.361007; 0.077226; 0.001042; 0.001420];
+L_adaptive_simpsons = [0.153903;
+0.045990;
+0.000090;
+
+L_chebyshev1=[1.493455; # AiryAi(x)
+0.291795; # besselj
+0.041686; # cos_cot
+0.104719; #
+0.116603;
+0.090129;
+0.088141;
+0.114219;
+0.162800;
+0.441775;
+0.102337;
+0.050055;
+0.048896];
+L_chebyshev2=[0.176496; 0.060008; 0.041355; 0.099813; 0.111966; 0.125740; 0.103428; 0.098729; 0.064575; 8.991385; 0.096214; 0.052295; 0.049748];
+L_chebyshev3 = [0.150834; 0.072039; 0.049798; 0.111535; 0.099392; 0.101607; 0.111045; 0.111373; 0.070177; 3.208550; 0.092763; 0.057960; 0.055562];
+L_chebyshev4 = [0.125087; 0.070966; 0.049619; 0.092735; 0.098091; 0.100671; 0.099425; 0.099531; 0.070195; 4.146543; 0.094798; 0.056763; 0.053876];
+L_jacobi = [20.655073; 0.741378; 0.079454; 0.468545; 0.220772; 2.786482; 0.531896; 0.446746; 0.479568; 22.058539; 0.242638; 1.933591; 0.694156];
+L_legendre=[0.122725; 0.076702; 0.030384; 0.071562; 0.078758; 0.078509; 0.088236; 0.090079; 0.043331; 4.383104; 0.059413; 0.036632; 0.033564];
+L_lobatto=[0.169799; 0.012460; 0.000103; 0.080504; 0.143451; 0.117507; 0.086438; 0.091315; 0.000142; 21.927058; 0.025977; 0.000409; 0.000141];
+L_radau = [0.151726; 0.012143; 0.000040; 0.094062; 0.129707; 0.104701; 0.086289; 0.087083; 0.000057; 22.282400; 0.025089; 0.000345; 0.000109];
+L_rectangle_midpoint = [0.073208; 0.000017; 0.000330; 0.019159; 0.022585; 0.030032; 0.018576; 0.021532; 0.000027; 1.863286; 0.035673; 0.000545; 0.000903];
+L_simpsons=[0.080275; 0.040657; 0.000012; 0.023218; 0.041971; 0.028887; 0.025965; 0.031452; 0.018607; 13.831230; 0.047495; 0.000064; 0.000078];
+L_simpsons38=[0.068510; ]
+L_trapezoidal=[0.149524; 0.034553; 0.000577; 0.017627; 0.032416; 0.022288; 0.019312; 0.023317; 0.013583; 13.361007; 0.077226; 0.001042; 0.001420];
 
 N = length(L_simpsons);