June 2018 Update

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