NAME

       slacn2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slacn2 (N, V, X, ISGN, EST, KASE, ISAVE)
           SLACN2 estimates the 1-norm of a square matrix, using reverse communication for
           evaluating matrix-vector products.

Function/Subroutine Documentation

   subroutine slacn2 (integer N, real, dimension( * ) V, real, dimension( * ) X, integer,
       dimension( * ) ISGN, real EST, integer KASE, integer, dimension( 3 ) ISAVE)
       SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating
       matrix-vector products.

       Purpose:

            SLACN2 estimates the 1-norm of a square, real matrix A.
            Reverse communication is used for evaluating matrix-vector products.

       Parameters:
           N

                     N is INTEGER
                    The order of the matrix.  N >= 1.

           V

                     V is REAL array, dimension (N)
                    On the final return, V = A*W,  where  EST = norm(V)/norm(W)
                    (W is not returned).

           X

                     X is REAL array, dimension (N)
                    On an intermediate return, X should be overwritten by
                          A * X,   if KASE=1,
                          A**T * X,  if KASE=2,
                    and SLACN2 must be re-called with all the other parameters
                    unchanged.

           ISGN

                     ISGN is INTEGER array, dimension (N)

           EST

                     EST is REAL
                    On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
                    unchanged from the previous call to SLACN2.
                    On exit, EST is an estimate (a lower bound) for norm(A).

           KASE

                     KASE is INTEGER
                    On the initial call to SLACN2, KASE should be 0.
                    On an intermediate return, KASE will be 1 or 2, indicating
                    whether X should be overwritten by A * X  or A**T * X.
                    On the final return from SLACN2, KASE will again be 0.

           ISAVE

                     ISAVE is INTEGER array, dimension (3)
                    ISAVE is used to save variables between calls to SLACN2

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Further Details:

             Originally named SONEST, dated March 16, 1988.

             This is a thread safe version of SLACON, which uses the array ISAVE
             in place of a SAVE statement, as follows:

                SLACON     SLACN2
                 JUMP     ISAVE(1)
                 J        ISAVE(2)
                 ITER     ISAVE(3)

       Contributors:
           Nick Higham, University of Manchester

       References:
           N.J. Higham, 'FORTRAN codes for estimating the one-norm of
             a real or complex matrix, with applications to condition estimation', ACM Trans.
           Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Author

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