CFD Utilities Files

MAXMIN DESCIPTION:

   MAXMIN drives a selection of methods of estimating derivative
   information for one or more 1-D datasets ("curves").   It was
   originally intended to test an algorithm for locating all  of
   the maxima and minima contained in experimental measurements.
   This searching for turning points is now optional  -  looking
   at derivatives has become the main purpose, either to examine
   algorithm behavior or to use the values elsewhere.

   Results are presented in QPLOTable form.

   This version concerns itself with 1st and 2nd derivatives.

METHOD:

   MAXMIN is basically SMOOTH (which fits curves to data points)
   adapted to look at 1st and 2nd derivatives, with an option to
   calculate the locations of turning points by  locating  zeros
   in the 1st derivatives.

   Dataset format:

      TITLE        <Default for plot frame titles>
      N            <No. of pts. for first curve>
      X    F       <Coordinates for first curve;
      X    F        X ought to be monotonically increasing,
      X    F        even though some methods don't require this;
      :    :        distinctions could be made if necessary.>
      :    :
      N            <No. of pts. for next curve>
      X    F
      X    F
      :    :
      :    :       <and so on>


   Plotting considerations:

      Plotting function values, derivatives, and locations of turning
      points is problematic because of possible scaling conflicts.
      Any of these may be suppressed in the saved results.  (The data
      points and fitted function values are linked - either both are
      shown or neither is shown.)  All quantities show up on the same
      frame (with a new frame for each method, and results for all
      curves in the dataset on the same frame).

   Method outline:

      Prompt for dataset and plot title.
      Prompt for suppressing the turning-point estimations (meaning
         look at derivatives only).
      Prompt for choice of smoothing routine.
      WHILE <valid method selected> DO
         Prompt for such things as smoothing parameters.
         Initialize QPLOT file.
         Read no. of data points in first dataset (curve).
         WHILE <not EOF> DO
            Read a dataset.
            Fit requested smoothing curve.
            Generate uniformly-spaced abscissas in data range.
            Evaluate curve at each of these.
            Also evaluate first derivative of curve at each of these.
            Write QPLOT info for up to five curves (data, smoothed curve,
               first derivative curve, plus, if requested, any maxima
               as one curve, and any minima as another).
            Read no. of points for next dataset.
         END WHILE
         Rewind data file.
         Prompt for another method.
      END WHILE

HISTORY:

   D.A.Saunders  06/27/83  Added max/min code to SMOOTH
   D.A.S.        07/09/83  Replaced FSCALC with FSCOEF
   C.L.Hooper    08/15/83  Added FSARBU and FSARBE
   D.A.S.        08/19/83  Added FSARBN
   C.L.H.        08/24/83  Added IQHSCU
   D.A.S.        06/10/87  Generalized for looking at derivatives (with
                           max/mins optional)
     "           06/12/87  Installed finite difference derivative option
     "           06/16/87  Installed FSCALC and provided for 2nd derivs.
     "           11/05/87  Installed MSFIT/CSDVAL
     "           11/24/87  Installed LSFIT1/CSDVAL
     "           08/26/88  Bug fix involving NFPP=0.  Linked display of
                           data with display of fit so that both may be
                           suppressed if f' and f" are the main interest.
     "           07/12/89  FSARBE call needs B(0), not B(1) now.
     "           03/13/90  Installed LCSFIT (no 2nd derivatives though).
     "           03/06/17  Dinesh wanted to try locating maxima and
                           minima within a very large radiation dataset.
     "           02/12/23  Minor edits after a cfdtools module version
                           was found to misbehave.


AUTHOR:  David Saunders, NASA Ames/Sterling Software, June/July 1983.