CFD Utilities Files

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!
   program zeromin2
!
!     This is a Fortran 90 update of the FORTRAN 77 original, from which
!     most of the following description is retained.
!
!  Description and usage:
!
!     ZEROMIN2 is an adaptation of ZEROMIN for driving the reverse-
!     communication versions of FMIN and ZEROIN.
!
!     Like ZEROMIN, it finds (within a user specified interval) either a root
!     of a function of one variable or a minimum of a function of one variable.
!     It also provides for displaying the function via Tecplot if requested.
!
!     The underlying algorithms are both due to Richard Brent (Stanford Uni-
!     versity, c. 1970) and described in Forsythe, Malcolm, and Moler (1977).
!     FMINRC is actually a revision of FMIN77, itself a subroutine version by
!     Robert Kennelly of the original FMIN.
!
!     Note that compilation is expected to use -r8 or equivalent in order to
!     perform 64-bit arithmetic.
!
!     To utilize the program without changes, the user must supply the one-
!     dimensional function of interest in the form of a real function FUNC1D
!     with a single input argument that is the independent variable.
!
!     A sample FUNC1D routine might be:
!
!        real function func1d (x)
!        real, intent (in) :: x
!        func1d = tan (x) - 1./x    ! The search interval is assumed to
!        end function func1d        ! exclude x = 0.
!
!     For more elaborate functions, ZEROMIN2 could be modified to evaluate the
!     function in any way necessary.  The function form of FUNC1D has been
!     retained in the initial version to enable simple testing of FMINRC against
!     the original FMIN77.
!
!     A second routine may be provided by the user.  Appropriately enough,
!     this subroutine must be titled USER.  It allows the user to perform
!     operations that ZEROMIN2 and FUNC1D do not already perform.  It should
!     have the form
!
!         subroutine user (luncrt, lunkbd, lunout, lunplt, first)
!
!     For example, if more than one variable is used to compute the
!     quantity returned by FUNC1D, then the user must supply a USER
!     routine to prompt for or set up values for the other variables.
!     USER and FUNC1D must communicate through COMMON variables unless
!     ZEROMIN2 is modified to change FUNC1D's argument list.
!
!     Note that USER is called within the retry loop over different
!     search intervals.  This may require distinguishing (within USER)
!     its first call from subsequent calls.
!
!     Even if no extra computation outside FUNC1D is required, a dummy USER is
!     still needed, and one such is supplied as part of the ZEROMIN2 package.
!     FUNC1D must be relinked with ZEROMIN2 for each new application.
!
!     At the start of a run, the user is prompted for the operation to be
!     performed and the number of coordinate points wanted in the plot, which
!     may also be suppressed.  The search interval and length of the interval
!     of uncertainty for the search convergence are also prompted for.  If it
!     appears that the interval does not contain a zero or a minimum, retries
!     are permitted.
!
!     Two files may be produced by ZEROMIN2.  The first file will have either
!     the abscissa value for the root or the abscissa value for the minimum
!     and the minimum ordinate value.  Also output in the same file are the
!     interval boundaries.  This file is named zeromin2.out.  The second file
!     is Tecplotable and is optional.  It will include the title and the
!     specified number of coordinate points that are calculated by the program
!     to display the function.  The root or minimum will also be plotted as a
!     single symbol.  This file name is zeromin2.dat.
!
!
!  External references:
!
!     Name      Description
!
!     FUNC1D    One-dimensional function for which a minimum or root is sought.
!     FMINRC    Seeks a local minimum of a 1-D function in a specified interval.
!!!!! QPLDAT    ENTRY points QPLFRM, QPLCRV write plot data in QPLOT format.
!!!!!           No longer used because QPLOT is history now.
!     READER    Prompting utility, with ENTRY points READD, READI, etc.
!     SELECT    Menu utility.
!     USER      Subroutine provided by the user to do any operations
!               not already provided by ZEROMIN2 and FUNC1D.  May be 
!               defaulted if no other input or computations are needed.
!     ZERORC    Finds a root of a 1-D function within a specified interval.
!
!
!  History:
!
!     23 Oct. 1987   PTS   Initial implementation of ZEROMIN (along the
!                          lines of NLSQ).
!     10 Apr. 1992   DAS   ZEROMIN2 adapted from ZEROMIN in order to
!                          test FMINRC and ZERORC.
!     19 Oct. 2023   DAS   F90 translation during a slow patch.
!
!  Authors:  Phillip T. Snyder, Sterling Software/NASA Ames Research Center, CA
!            David A. Saunders, AMA, Inc. at NASA ARC.
!
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