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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( * )



     #include <sunperf.h>

     void slacon(int n, float *v, float  *sx,  int  *isgn,  float
               *est, int *kase) ;

PURPOSE
     SLACON estimates the 1-norm of  a  square,  real  matrix  A.
     Reverse  communication  is used for evaluating matrix-vector
     products.  If the initial call is made with  KASE  equal  to
     -255 and subsequent intermediate calls are made as described
     below then this subroutine is MT-safe, otherwise it  is  not
     MT-safe.


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 MT-unsafe 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.  On an MT-safe intermediate
               return, X should be overwritten by A * X  if  bits
               8-11  of  KASE=0001,  A'  *  X  if  bits  8-11  of
               KASE=0010, and SLACON must be re-called  with  all
               the  other parameters unchanged.  The MT-safe mode
               is described below in the description of the  KASE
               argument.

     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 or
               -255.   If  KASE  was supplied as 0 on the initial
               call then on an intermediate return, KASE will  be
               1 or 2, indicating whether X should be overwritten
               by A * X  or A' * X.  If KASE was supplied as -255
               on the initial call then on an intermediate return
               the low 8 bits of KASE will be 0 and  the  next  4
               bits  will  contain  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.
               If the initial call is made  with  KASE  equal  to
               -255  then this subroutine is MT-safe but does not
               conform to the standard LAPACK  calling  sequence.
               If  the  initial call is made with KASE equal to 0
               then it is not MT-safe, but  it  conforms  to  the
               standard LAPACK calling sequence.

FURTHER DETAILS
     Contributed by Nick Higham, University of Manchester.
     Originally named SONEST, dated 27 Jun 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.

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