SORT_RC
Sort Using Reverse Communication

SORT_RC is a FORTRAN77 library which can sort a list of any kind of objects, using reverse communication (RC).

The program works by repeatedly asking the user to compare two items on the list. The user is free to carry out the comparison in the calling program, in any desired way.

A typical usage, to sort an array of 100 items, might look something like this:

        n = 100
        indx = 0   -- Indicates the beginning of a sort
 
        begin loop

          sort_rc ( n, indx, i, j, isgn )

          if ( indx < 0 )   (Compare items I and J)

            if ( a(i) <= a(j) )
              isgn = -1
            else
              isgn = +1
 
           else if ( 0 < indx )  (Swap items I and J)
  
             k    = a(i)
             a(i) = a(j)
             a(j) = k
 
           else
 
             exit loop

        end loop
      

The original version of sort_rc() requires the use of several variables declared internally to the function, whose values must be preserved between calls. The conventions for such computations vary from language to language; moreover, this kind of approach means that a single copy of the function cannot handle multiple requests for computation that might arise, especially in parallel computations. For that reason, a revised function, called sort_safe_rc(), is available, which does not rely on hidden internal variables and may safely be used to manage multiple simultaneous sorts.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

SORT_RC is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BACKTRACK_BINARY_RC, a FORTRAN77 library which carries out a backtrack search for a set of binary decisions, using reverse communication.

BISECTION_RC, a FORTRAN77 library which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication.

CG_RC, a FORTRAN77 library which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).

SUBSET, a FORTRAN77 library which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems.

ZERO_RC, a FORTRAN77 library which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication.

Reference:

1. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.

Source Code:

• sort_rc.f, the source code;
• sort_rc.sh, commands to compile the source code;

Examples and Tests:

• sort_rc_prb.f, the calling program;
• sort_rc_prb.sh, commands to compile, link and run the calling program;
• sort_rc_prb_output.txt, the output file.

List of Routines:

• I4VEC_PRINT prints an I4VEC.
• I4VEC_UNIFORM_AB returns a scaled pseudorandom I4VEC.
• SORT_RC externally sorts a list of items into ascending order.
• SORT_SAFE_RC externally sorts a list of items into ascending order.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.