Initial data commit

Task/Steffensens-method/RATFOR/steffensens-method.ratfor

@@ -0,0 +1,106 @@
+function aitken (f, p0)
+  implicit none
+
+  double precision f, p0, aitken
+  external f
+
+  double precision p1, p2
+
+  p1 = f(p0)
+  p2 = f(p1)
+  aitken = p0 - (p1 - p0)**2 / (p2 - (2.0d0 * p1) + p0)
+end
+
+subroutine steff (f, pinit, tol, mxiter, ierr, pfinal)
+  implicit none
+
+  double precision f, pinit, tol, pfinal
+  integer mxiter, ierr
+  external f
+
+  double precision p0, p, aitken
+  integer iter
+  external aitken
+
+  p0 = pinit
+  p = aitken (f, p0)
+  iter = 1
+  while (abs (p - p0) > tol && iter < mxiter)
+    {
+      p0 = p
+      p = aitken (f, p0)
+      iter = iter + 1
+    }
+  if (abs (p - p0) > tol)
+    ierr = -1
+  else
+    {
+      ierr = 0
+      pfinal = p
+    }
+end
+
+function dcstlj (c0, c1, c2, t)
+  implicit none
+
+  double precision c0, c1, c2, t, dcstlj
+
+  double precision s, c01, c12, c012
+
+  s = 1.0d0 - t
+  c01 = (s * c0) + (t * c1)
+  c12 = (s * c1) + (t * c2)
+  c012 = (s * c01) + (t * c12)
+  dcstlj = c012
+end
+
+function x (t)
+  implicit none
+  double precision x, t, dcstlj
+  external dcstlj
+  x = dcstlj (2.0d0, -8.0d0, 2.0d0, t)
+end
+
+function y (t)
+  implicit none
+  double precision y, t, dcstlj
+  external dcstlj
+  y = dcstlj (1.0d0, 2.0d0, 3.0d0, t)
+end
+
+function impleq (x, y)
+  implicit none
+  double precision x, y, impleq
+  impleq = (5.0d0 * x * x) + y - 5.0d0
+end
+
+function f (t)
+  implicit none
+  double precision f, t, x, y, impleq
+  external x, y, impleq
+  f = impleq (x(t), y(t)) + t
+end
+
+program RCstef
+  implicit none
+
+  double precision x, y, impleq, f
+  external x, y, impleq, f, steff
+
+  double precision t0, t
+  integer i, ierr
+
+  t0 = 0.0d0
+  for (i = 0; i != 11; i = i + 1)
+    {
+      call steff (f, t0, 0.00000001d0, 1000, ierr, t)
+      if (ierr < 0)
+        write (*,*) "t0 = ", t0, " : no answer"
+      else if (abs (impleq (x(t), y(t))) <= 0.000001)
+        write (*,*) "t0 = ", t0, " : intersection at (", _
+                    x(t), ", ", y(t), ")"
+      else
+        write (*,*) "t0 = ", t0, " : spurious solution"
+      t0 = t0 + 0.1d0
+    }
+end