tasks a-s

Task/Numerical-integration/AutoHotkey/numerical-integration.ahk

@@ -0,0 +1,35 @@
+MsgBox % Rect("fun", 0, 1, 10,-1) ; 0.45 left
+MsgBox % Rect("fun", 0, 1, 10)    ; 0.50 mid
+MsgBox % Rect("fun", 0, 1, 10, 1) ; 0.55 right
+MsgBox % Trapez("fun", 0, 1, 10)  ; 0.50
+MsgBox % Simpson("fun", 0, 1, 10) ; 0.50
+
+Rect(f,a,b,n,side=0) { ; side: -1=left, 0=midpoint, 1=right
+   h := (b - a) / n
+   sum := 0, a += (side-1)*h/2
+   Loop %n%
+      sum += %f%(a + h*A_Index)
+   Return h*sum
+}
+
+Trapez(f,a,b,n) {
+   h := (b - a) / n
+   sum := 0
+   Loop % n-1
+      sum += %f%(a + h*A_Index)
+   Return h/2 * (%f%(a) + %f%(b) + 2*sum)
+}
+
+Simpson(f,a,b,n) {
+   h := (b - a) / n
+   sum1 := sum2 := 0, ah := a - h/2
+   Loop %n%
+      sum1 += %f%(ah + h*A_Index)
+   Loop % n-1
+      sum2 += %f%(a + h*A_Index)
+   Return h/6 * (%f%(a) + %f%(b) + 4*sum1 + 2*sum2)
+}
+
+fun(x) { ; linear test function
+   Return x
+}