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NAME
     slaqtr - solve the real quasi-triangular system   op(T)*p  =
     scale*c, if LREAL = .TRUE

SYNOPSIS
     SUBROUTINE SLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE,  X,
               WORK, INFO )

     LOGICAL LREAL, LTRAN

     INTEGER INFO, LDT, N

     REAL SCALE, W

     REAL B( * ), T( LDT, * ), WORK( * ), X( * )



     #include <sunperf.h>

     void slaqtr(int ltran, int lfloat, int n, float *t, int ldt,
               float  *sb, float w, float *sscale, float *sx, int
               *info) ;

PURPOSE
     SLAQTR solves the real quasi-triangular system

     or the complex quasi-triangular systems

                op(T + iB)*(p+iq) =  scale*(c+id),   if  LREAL  =
     .FALSE.

     in real arithmetic, where T is upper quasi-triangular.
     If LREAL = .FALSE., then the first diagonal block of T  must
     be 1 by 1, B is the specially structured matrix

                    B = [ b(1) b(2) ... b(n) ]
                        [       w            ]
                        [           w        ]
                        [              .     ]
                        [                 w  ]

     op(A) = A or A', A' denotes the conjugate transpose of
     matrix A.

     On input, X = [ c ].  On output, X = [ p ].
                   [ d ]                  [ q ]

     This subroutine is designed for the condition number estima-
     tion in routine STRSNA.


ARGUMENTS
     LTRAN     (input) LOGICAL
               On entry, LTRAN specifies the option of  conjugate
               transpose:   =  .FALSE.,     op(T+i*B)  = T+i*B, =
               .TRUE.,     op(T+i*B) = (T+i*B)'.

     LREAL     (input) LOGICAL
               On entry, LREAL specifies the input matrix  struc-
               ture:   =  .FALSE.,     the  input  is  complex  =
               .TRUE.,     the input is real

     N         (input) INTEGER
               On entry, N specifies the order of T+i*B. N >= 0.

     T         (input) REAL array, dimension (LDT,N)
               On entry, T contains a matrix in  Schur  canonical
               form.  If LREAL = .FALSE., then the first diagonal
               block of T must be 1 by 1.

     LDT       (input) INTEGER
               The leading dimension of  the  matrix  T.  LDT  >=
               max(1,N).

     B         (input) REAL array, dimension (N)
               On entry, B contains  the  elements  to  form  the
               matrix B as described above.  If LREAL = .TRUE., B
               is not referenced.

     W         (input) REAL
               On entry, W is the diagonal element of the  matrix
               B.  If LREAL = .TRUE., W is not referenced.

     SCALE     (output) REAL
               On exit, SCALE is the scale factor.

     X         (input/output) REAL array, dimension (2*N)
               On entry, X contains the right hand  side  of  the
               system.   On  exit,  X is overwritten by the solu-
               tion.

     WORK      (workspace) REAL array, dimension (N)

     INFO      (output) INTEGER
               On exit, INFO is set to 0: successful exit.
               1: the some diagonal 1 by 1 block  has  been  per-
               turbed by a small number SMIN to keep nonsingular-
               ity.  2: the some diagonal 2 by 2 block  has  been
               perturbed by a small number in SLALN2 to keep non-
               singularity.  NOTE: In  the  interests  of  speed,
               this routine does not check the inputs for errors.

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