slacon(3S)

NAME
     SLACON - estimate the 1-norm of a square, real matrix A

SYNOPSIS
     SUBROUTINE SLACON( N, V, X, ISGN, EST, KASE )

         INTEGER        KASE, N

         REAL           EST

         INTEGER        ISGN( * )

         REAL           V( * ), X( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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


ARGUMENTS
     N      (input) INTEGER
            The order of the matrix.  N >= 1.

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

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

     ISGN   (workspace) INTEGER array, dimension (N)

     EST    (output) REAL
            An estimate (a lower bound) for norm(A).
     KASE   (input/output) INTEGER
            On the initial call to SLACON, 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' * X.  On the final return
            from SLACON, KASE will again be 0.

FURTHER DETAILS
     Contributed by Nick Higham, University of Manchester.
     Originally named SONEST, dated March 16, 1988.

     Reference: 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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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