CFD Utilities Files

PURPOSE:

   GEN1D is intended to generate data that can be used for evaluating 1-D
   interpolation/smoothing routines. It provides a menu of likely functions
   of one variable (easily modified as necessary).  It also provides the
   option to evaluate the specified function at a self-generated set of
   grid points or at a set read from a file.  Results are written to
   'gen1d.dat' in the following (Tecplotable) format:

                    # Title with function details
                    # NPTS
                    X(1)     Y(1)
                    X(2)     Y(2)
                     :        :
                    X(NPTS)  Y(NPTS)

   If a grid is read from a file, its format is the same except that it has
   1 column, not 2.  (Columns after the first will be ignored.)

   Provision is made for parametric functions in the form X = X(T),
   Y = Y(T).  Here, reading a T distribution is an unlikely requirement
   and is NOT provided for.

   An option for applying noise to the Y values (or to both X and Y for the
   parametric functions) is also provided.

METHOD:

      Select function of X from menu.
      Prompt for type of grid to use:
      IF <self-generated> THEN
         Prompt for XMIN, XMAX, DX.
         Generate points X(*).
      ELSE
         Prompt for grid file name and read X(*).
      END IF
      Prompt for additional constants and evaluate function at all pts.
      Write them to the output file.

HISTORY:

  DAS   10/17/86   Adapted from GEN2D
  DAS   02/18/87   Provided for X=X(T), Y=Y(T) parametric functions
  DAS   11/20/87   Installed option to apply noise to the data
  DAS   06/05/91   Added sin(x)/x and sinh(x)/x options.
  DAS   03/21/92   Added parametric form of the parabola.
  DAS   01/09/93   Made the cubic a quartic.
  DAS   08/22/97   Added Hermite cubic on [0, 1]
  DAS   09/27/00   Replaced IMSL's GGNML with GAUSS/RAN3 found on the web.
  DAS   10/26/01   Added QUINTIC.
  DAS   10/29/03   Slight changes for 64-bit version.
  DAS   07/19/04   Use of $ carriage control was obsolete.
  DAS   10/27/10   Added f(x) = Aexp(Bx) + C option; Fortran 90 upgrades.
  DAS   11/15/10   Generalized previous option to handle Aexp(B/x) + C too.
  DAS   11/22/10   Added Ax**n*exp(Bx) and power law option:  Ax**B + C.
  DAS   05/24/11   Outputs are 64-bit precision now, not single precision.
  DAS   10/06/11   Added sin**n(x.pi/2) (x in [0, 1]) & 2 catenary options.
  DAS   10/13/11   Replaced explicit discretization of a cosh (x/a) - a
                   with a call to catenary grid (left|right|both halves)
                   unless a desired parameter a is input.
  DAS   05/16/14   Added Gaussian and normal distribution options, along
                   with the error function-related options.
  DAS   06/13/24   Added evaluation of Bernstein polynomials.
  DAS   07/23/24   Made use of bernstein_polynomial, which was belatedly
                   added to numodules as a level above bernstein_basis.


AUTHOR:  David Saunders, Sterling Software/ELORET/ERC at NASA Ames.