June 2018 Update

Task/Numerical-integration/Julia/numerical-integration.julia

@@ -1,8 +1,16 @@
-function simpson(f, a,b, n)
-    h = (b-a)/n
-    s = f(a + h/2)
+function simpson(f::Function, a::Number, b::Number, n::Integer)
+    h = (b - a) / n
+    s = f(a + h / 2)
     for i in 1:(n-1)
-        s += f(a + h*i + h/2) + 0.5 * f(a + h*i)
+        s += f(a + h * i + h / 2) + f(a + h * i) / 2
     end
-    h/6 * (f(a) + f(b) + 4*s)
+    return h/6 * (f(a) + f(b) + 4*s)
 end
+
+rst =
+    simpson(x -> x ^ 3, 0, 1, 100),
+    simpson(x -> 1 / x, 1, 100, 1000),
+    simpson(x -> x, 0, 5000, 5_000_000),
+    simpson(x -> x, 0, 6000, 6_000_000)
+
+@show rst

Task/Numerical-integration/Ring/numerical-integration.ring

@@ -0,0 +1,88 @@
+# Project : Numerical integration
+# Date    : 2018/04/087
+# Author : Gal Zsolt (~ CalmoSoft ~)
+# Email   : <calmosoft@gmail.com>
+
+decimals(8)
+data = [["pow(x,3)",0,1,100], ["1/x",1, 100,1000], ["x",0,5000,5000000], ["x",0,6000,6000000]]
+see "Function   Range   L-Rect   R-Rect   M-Rect   Trapeze   Simpson" + nl
+for p = 1 to 4
+     d1 = data[p][1]
+     d2 = data[p][2]
+     d3 = data[p][3]
+     d4 = data[p][4]
+     see "" + d1 + "   " + d2  + " - " + d3  + "   " + lrect(d1, d2, d3, d4) + "   " + rrect(d1, d2, d3, d4)
+     see "  " + mrect(d1, d2, d3, d4) + "   " + trapeze(d1, d2, d3, d4) + "   " + simpson(d1, d2, d3, d4) + nl
+next
+
+func lrect(x2, a, b, n)
+       s = 0
+       d = (b - a) / n
+       x = a
+       for i = 1 to n
+       eval("result = " + x2)
+            s = s + d * result
+            x = x + d
+       next
+       return s
+
+func rrect(x2, a, b, n)
+       s = 0
+       d = (b - a) / n
+       x = a
+       for i = 1 to n
+            x = x + d
+            eval("result = " + x2)
+            s = s + d *result
+       next
+       return s
+
+func mrect(x2, a, b, n)
+       s = 0
+       d = (b - a) / n
+       x = a
+       for i = 1 to n
+            x = x + d/2
+            eval("result = " + x2)
+            s = s + d * result
+            x =  x +d/2
+       next
+       return s
+
+func trapeze(x2, a, b, n)
+       s = 0
+       d = (b - a) / n
+       x = b
+       eval("result = " + x2)
+       f = result
+       x = a
+       eval("result = " + x2)
+       s = d * (f + result) / 2
+       for i = 1 to n-1
+            x = x + d
+           eval("result = " + x2)
+            s = s + d * result
+       next
+       return s
+
+func simpson(x2, a, b, n)
+        s1 = 0
+        s = 0
+        d = (b - a) / n
+        x = b
+        eval("result = " + x2)
+        f = result
+        x = a + d/2
+       eval("result = " + x2)
+        s1 = result
+        for i = 1 to n-1
+            x = x + d/2
+            eval("result = " + x2)
+            s = s + result
+            x = x + d/2
+            eval("result = " + x2)
+            s1 = s1 + result
+        next
+        x = a
+        eval("result = " + x2)
+        return (d / 6) * (f + result + 4 * s1 + 2 * s)

Task/Numerical-integration/Stata/numerical-integration.stata

@@ -0,0 +1,41 @@
+mata
+function integrate(f,a,b,n,u,v) {
+	s = 0
+	h = (b-a)/n
+	m = length(u)
+	for (i=0; i<n; i++) {
+		x = a+i*h
+		for (j=1; j<=m; j++) s = s+v[j]*(*f)(x+h*u[j])
+	}
+	return(s*h)
+}
+
+function log_(x) {
+	return(log(x))
+}
+
+function id(x) {
+	return(x)
+}
+
+function cube(x) {
+	return(x*x*x)
+}
+
+function inv(x) {
+	return(1/x)
+}
+
+function test(f,a,b,n) {
+	return(integrate(f,a,b,n,(0,1),(1,0)),
+	       integrate(f,a,b,n,(0,1),(0,1)),
+	       integrate(f,a,b,n,(0.5),(1)),
+	       integrate(f,a,b,n,(0,1),(0.5,0.5)),
+	       integrate(f,a,b,n,(0,1/2,1),(1/6,4/6,1/6)))
+}
+
+test(&cube(),0,1,100)
+test(&inv(),1,100,1000)
+test(&id(),0,5000,5000000)
+test(&id(),0,6000,6000000)
+end