CFD Utilities Files

PURPOSE:

   SMOOTH drives a variety of 1-D smoothing/interpolating algorithms,
   either for evaluating or comparing them, or for generating quanti-
   ties that may be used elsewhere.   It applies the chosen method(s)
   to one or more "curves" read from a single file, and saves results
   in a form suited to plotting by some other program.   On VAXes and
   IRISes at NASA Ames,  plottable results are tailored to the  QPLOT
   package.   A Macintosh derivative known as QuickFit is also avail-
   able for which QuickPlot is appropriate. Results may also be saved
   in the format used for the input data.

   This version permits repeating the above with further input files.
   Plots of curves from any one input file will appear on one frame -
   a new plot frame for a new input file.

   This version also allows selection of X and Y from multiple-column
   files (same columns for all curves assumed),  and two data formats
   are supported (the original "NPTS" form and an "indefinite" form).

   Input data file format:

      [TITLE]         <Optional title, up to 80 characters.>
      [N1]            <# pts. in 1st curve: not needed if "END"
      X (1)  Y (1)        is present; both are redundant if
      X (2)  Y (2)        there is only one curve.>
      X (3)  Y (3)
      X (4)  Y (4)    <X and Y may be extracted from specified
      :      :            columns if there are more than two.>
      :      :
      ! X     Y       <"!" suppresses points or adds comments.>
      X (N1) Y (N1)
                      <Blank lines are ignored.>
      N2  or  END     <Repeat for more curves, omitting title.>
      X (1)  Y (1)
      :      :
      :      :

   Normally,  uniformly-spaced abscissas are generated for evaluating
   fitted curves in order to plot them, but these may be suppressed.

   Evaluating fitted curves at further abscissas read from  (column 1
   of) a file is also provided for, with these abscissas being in the
   same format as above - any further columns are ignored.

   The original data,  the fitted curve,  and any further evaluations
   are written to a file of plottable results, named "smooth.plt." In
   the case of least squares methods, plots of deviations may also be
   obtained via a separate plot file, "smooth.dev."   (Its scaling is
   unlikely to be the same as for the original data.)  This file con-
   tains  X (data), Y (fit), and Y (fit) - Y (data)  in three columns
   with columns 1 and 3 set ready to plot (but column 2 there in case
   it is needed).

   Evaluated results may also be saved in "SMOOTH" format as the file
   "smooth.out" if requested.

   Any coefficients computed by a smoothing/fitting method are  saved
   separately in "smooth.log."


METHOD:  <Outline>

   Open files for plottable and/or reusable results.

   NEW FILE:
      Prompt for and open an input data file.
      Read the input data title.
      Prompt for whether to normalize the data to [0,1].
      Prompt for plot title and axis labels, and initialize plot frame.
      Prompt for the number of uniformly-spaced abscissas to be used in
         evaluating and plotting each fitted curve (may be suppressed).
      Prompt for the filename of optional user-supplied abscissas for
         an additional fit evaluation and plot, and for possible reuse.
      If <user-supplied abscissas> open and read this file.
      Initialize the tabulated output.

   NEW CURVE FIT:
      Rewind data file.
      Select a smoothing routine (else GO TO NEXT).
      Skip the data file title.
      Read NX, number of data points in the first dataset (curve).

      WHILE <not EOF> DO
         Read one dataset (curve).
         If <first selection>
            Write plot info for this dataset.
            If <normalizing> normalize X (*) and Y (*) to [0, 1].
         If <fit to be plotted> generate uniformly-spaced abscissas
            in the data range.
         Prompt for smoothing parameters (if applicable).
         Perform requested curve fit.
         If <fit to be plotted> evaluate curve at generated abscissas.
         If <user-supplied abscissas> evaluate curve at these.
         If <normalizing> denormalize results.
         Read NX for next curve.
      END WHILE

      GO TO NEW CURVE FIT

   NEXT:

      Close input data file for possible reuse of logical unit.
      If <new file desired> then
         Output "end-frame" to plottable data file.
         GO TO NEW FILE
      Else
         Close plottable and printable files.
         Done.

HISTORY:

  DAS   06/10/83   Initial design and code (ICSSCU, PNFIT; new frame
                   for each method - multiple curves per frame).
  CLH   06/16/83   Added ICSFKU option.
  DAS   06/20/83   Added FSFIT  option for periodic data.
  DAS   06/22/83   Added FSCOEF option for periodic data.
  CLH   07/07/83   Added ICSVKU option.
  CLH   10/11/83   Added ICSMOU option.
  CLH   12/12/83   Added IQHSCU option.
  RGL   04/25/84   Updated line type for compatibility with current
                   QPLOT conventions; added legend for each curve;
                   installed prompting utility READER.
  DAS   06/29/84   All curves on a single frame now; QPLOT namelist
                   introduced; data may be in columns or rows.
  RGL   07/17/84   Added CSFIT option.
  RGL   02/15/85   Added option for a file of abscissas to be used
                   in smoothed curve evaluation and plotting;
                   reverted to restricting data format to columns;
                   included on-line description of available methods
                   and of spline end conditions possible with CSFIT;
                   incorporated QPLDAT to write the plot file.
  DAS   03/05/85   Added WAGFIT option.
  RGL   05/14/85   Added TABLE1 option.
  RGL   05/23/85   Added printing of calculated coefficients.
  RGL   07/13/85   Evaluations at uniformly-spaced abscissas (for
                   probable plotting purposes) may be suppressed now.
  DAS   12/20/85   Streamlined the terminal I/O.
  RGL   03/27/86   Suppressed unnecessary output of IMSL error codes.
  DAS   04/21/86   Removed DO WHILEs and END DOs and use of MAX in
                   parameter statement in anticipation of move to PC;
                   added PSFIT option (PSTVAL only - not PSEVAL).
  DAS   05/27/86   Added VECFIT option.
  DAS   06/12/86   Added option to scale/unscale data for the case
                   of polynomial fits (to handle large numbers).
  DAS   06/16/86   Provided for simple shift of data by the mean,
                   for polynomial fits.  (These last two are for
                   comparison purposes; full scaling is probably
                   unnecessary.)  [P.S.: Introduction of a normalizing
                   option used by all methods meant giving up the
                   shift-by-the-mean option for PNFIT later - see 7/89.]
  DAS   07/17/86   WAGFIT was simplified - needed to handle "ramp"
                   function differently here.
  DAS   08/14/86   Installed tension spline (CURV1, CURV2).
  DAS   12/10/86   Refinements prompted by QuickFit version on Mac:
                   > go back for another input data file;
                   > arbitrary units for Fourier methods;
                   > smarter handling of closed case for PSFIT
                     (insert a point at I=NX+1 if necessary).
  DAS   12/23/86   Added MSFIT/CSEVAL combination; made use of SELECT.
  DAS   01/15/87   PSFIT can now choose MSFIT, which now has optional
                   periodic boundary conditions.
  RAK   02/17/87   Installed PLSFIT for testing (the TIGHT option
                   should give the same answers as MSFIT under PSFIT).
  DAS   02/20/87   > Installed LINE1D in parallel with TABLE1. (Both
                     are retained because SMOOTH serves to test them.)
                   > Provided for plotting the deviations for least
                     squares methods by setting XEVAL (*) = X (*).
                   > SELECT now permits no default - handy at "done"
                     time, when CR = CTRL Z = quit.
                   > Echoed RMS and maximum deviations to the screen
                     as well as to the log file.
  DAS/RAK 3/3/87   > Straightened out some logic errors in the above.
                   > Added Y (fit) as third column in smooth.dev.
                   > Introduced PROTECT for checking monotonicity, etc.
                   > FSFIT now works for N=0.
  DAS   10/20/87   > Provided for timing (fit + evaluation) for each curve
                     of each file more precisely.  (Total CPU time is also
                     measured, but it includes the I/O.)
                   > CSFIT and MSFIT can handle decreasing abscissas now
                     because of revised search used by CSEVAL.
                   > Upped MXPTS to 1001 (but PSFIT/PSEVAL retain internal
                     COMMON block limit of 500).
  DAS   11/20/87   Installed LSFIT1 to test it.
  DAS   06/10/88   Safeguarded Fourier methods better; upped MXFCOF to 180.
  DAS   10/22/88   Wagner function option now handles arbitrary units,
                   including descending abscissas.
  DAS   02/17/89   Handled LSFIT1's option to suppress spline step.
  DAS   03/30/89   Added prompt for a subtitle on the plot.
  DAS   05/08/89   LSFIT1 should have NEARPTS >= DEGREE + 2, not + 1.
  DAS   07/09/89   Introduced GETSCALE/USESCALE for all methods.  This was
                   prompted by a wind tunnel data case that worked fine in
                   QPLOT, which normalizes before applying PLSFIT, but was
                   poorly handled by SMOOTH's PLSFIT option.  (Only PNFIT
                   had been given scaling/shifting options; now it is clear
                   that ALL methods are best applied to normalized data.)
  DAS   07/15/89   Installed FSERIES/FSSUM/FSEVAL2 (mainly to test
                   Macintosh versions).
  DAS   08/31/89   Installed LCSFIT.  Small fix to blank out legends after
                   the first dataset.
  DAS   09/09/89   EPS needed for WAGFIT [0,1] test; YPLOT(*) was not being
                   vertically shifted; legend text for LSFIT1 was being
                   clobbered by deviations info.; shortened it.
  DAS   05/29/90   "No. of uniform abscissas" prompt was imprecise for
                   parametric fits.  Normalizing prompt also needs a
                   warning.
  DAS   07/30/90   Installed RDXYZ which became available from program
                   PROFILE, allowing commented-out points in the input
                   files and eliminating list-directed I/O and some error
                   handling.
  DAS   01/17/91   Replaced XFORMX with GETXFORM/USESCALE.  MXPTS & MXPLOT
                   raised to 1500.
  DAS   05/27/91   Results may now be saved in SMOOTH format if desired (as
                   well as or instead of QPLOT format).  Also handled the
                   NX=0 dataset case.  [D. Serafini request in both cases.]
  DAS   06/07/91   Replaced IMSL's IQHSCU with QHSFIT (same algorithm).
  DAS   06/17/91   Added date/time stamp as caption in the QPLOTable file.
  DAS   06/20/91   LCSFIT now has a periodic end-condition option.
  DAS   10/16/91   PSFIT and PSTVAL usage changed.
  DAS   12/11/91   Introduced multi-column capability plus an alternative
                   "indefinite-number-of-points-per-curve" data format, as
                   both supported by a revised form of RDXYZ.  The upward
                   compatibility with SMOOTH's original "NPTS" data format
                   was achieved at some cost in complexity, and not all
                   cases of mismatched NPTS values are trapped gracefully.
                   The alternative data format is now preferred.
  DAS   12/31/91   Made TITLE optional for data files and target X file.
  DAS   02/12/92   TITLE was being skipped at the top of the loop over
                   datasets, even when none was present.  And the test for
                   an empty file shouldn't have decremented DATASET if
                   the (previous) value of NX was not zero.
  DAS   08/16/97   CSEVAL needs NDATA = -NX for the periodic case now.
  DAS   10/14/99   Fortran 90 translation (mainly to eliminate 0 carriage
                   control).  Always display sum of squares & RMS deviation
                   whether deviations are being plotted or not.
  DAS   07/07/00   Added QINTERP.
  DAS   09/27/00   Plugged SMOOTHXYZ into the defunct ICSMOU slot.
  DAS   01/28/04   Increased LSFIT1 limit to 100 neighboring pts., not 10.
  DAS   06/14/04   For FSFIT, the transformation to [0, 2pi] was using
                   X(1) and X(NX) but the abscissas need not be ordered.
  DAS   11/19/10   Added exponential curve fits AEBXPLUSC and ABXECX.
  DAS   11/23/10   Added power law curve fit AXBPLUSC.
  DAS   12/28/10   Exponential & power law fits need not trap unordered data.
  DAS   06/17/16   Printed coefficients have more digits showing now.
                   No more use of 1P: ES formatting is preferable.
  DAS   11/23/16   Make the comment character # instead of !, for Tecplot
                   compatibility.  This required RDXYZ2 variant with COMMENT
                   as an argument.  Suppress output of deviations by default.
  DAS   07/01/20   Added LEGENDRE option.
  DAS   12/29/22   Added RADIAL_BASIS_1D_WEIGHTS & RADIAL_BASIS_1D_EVAL.
  DAS   05/20/24   Added the BERNSTEIN linear least squares option.
  DAS   10/08/24-  Revised smooth.f as smooth.f90.  Some F77isms remain.
        10/10/24   Replacing plottable outputs intended for the (defunct)
                   QPLOT with Tecplotable output appears more trouble than
                   it's worth.  Some editing to suit Tecplot can be expected.

AUTHOR:  David Saunders, Sterling Software/NASA Ames, Moffett Field, CA
         Now with AMA, Inc. at NASA ARC.