tasks a-s

Task/Roots-of-a-function/DWScript/roots-of-a-function.dwscript

@@ -0,0 +1,51 @@
+type TFunc = function (x : Float) : Float;
+
+function f(x : Float) : Float;
+begin
+   Result := x*x*x-3.0*x*x +2.0*x;
+end;
+
+const e = 1.0e-12;
+
+function Secant(xA, xB : Float; f : TFunc) : Float;
+const
+   limit = 50;
+var
+   fA, fB : Float;
+   d : Float;
+   i : Integer;
+begin
+   fA := f(xA);
+   for i := 0 to limit do begin
+      fB := f(xB);
+      d := (xB-xA)/(fB-fA)*fB;
+      if Abs(d) < e then
+         Exit(xB);
+      xA := xB;
+      fA := fB;
+      xB -= d;
+   end;
+   PrintLn(Format('Function is not converging near (%7.4f,%7.4f).', [xA, xB]));
+   Result := -99.0;
+end;
+
+const fstep = 1.0e-2;
+
+var x := -1.032;		// just so we use secant method
+var xx, value : Float;
+var s := f(x)>0.0;
+
+while (x < 3.0) do begin
+   value := f(x);
+   if Abs(value)<e then begin
+      PrintLn(Format("Root found at x= %12.9f", [x]));
+      s := (f(x+0.0001)>0.0);
+   end else if (value>0.0) <> s then begin
+      xx := Secant(x-fstep, x, f);
+      if xx <> -99.0 then   // -99 meaning secand method failed
+         PrintLn(Format('Root found at x = %12.9f', [xx]))
+      else PrintLn(Format('Root found near x= %7.4f', [xx]));
+      s := (f(x+0.0001)>0.0);
+   end;
+   x += fstep;
+end;