NAME

       dlacn2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlacn2 (N, V, X, ISGN, EST, KASE, ISAVE)
           DLACN2 estimates the 1-norm of a square matrix, using reverse communication for
           evaluating matrix-vector products.

Function/Subroutine Documentation

   subroutine dlacn2 (integer N, double precision, dimension( * ) V, double precision, dimension(
       * ) X, integer, dimension( * ) ISGN, double precision EST, integer KASE, integer,
       dimension( 3 ) ISAVE)
       DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating
       matrix-vector products.

       Purpose:

            DLACN2 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 DOUBLE PRECISION array, dimension (N)
                    On the final return, V = A*W,  where  EST = norm(V)/norm(W)
                    (W is not returned).

           X

                     X is DOUBLE PRECISION array, dimension (N)
                    On an intermediate return, X should be overwritten by
                          A * X,   if KASE=1,
                          A**T * X,  if KASE=2,
                    and DLACN2 must be re-called with all the other parameters
                    unchanged.

           ISGN

                     ISGN is INTEGER array, dimension (N)

           EST

                     EST is DOUBLE PRECISION
                    On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
                    unchanged from the previous call to DLACN2.
                    On exit, EST is an estimate (a lower bound) for norm(A).

           KASE

                     KASE is INTEGER
                    On the initial call to DLACN2, 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 DLACN2, KASE will again be 0.

           ISAVE

                     ISAVE is INTEGER array, dimension (3)
                    ISAVE is used to save variables between calls to DLACN2

       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 DLACON, which uses the array ISAVE
             in place of a SAVE statement, as follows:

                DLACON     DLACN2
                 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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