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SLAQTR(3F)							    SLAQTR(3F)

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( * )

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 estimation 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 structure:  = .FALSE.,
	     the input is complex = .TRUE.,	the input is real

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SLAQTR(3F)							    SLAQTR(3F)

     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 solution.

     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 perturbed by a small
	     number SMIN to keep nonsingularity.  2: the some diagonal 2 by 2
	     block has been perturbed by a small number in SLALN2 to keep
	     nonsingularity.  NOTE: In the interests of speed, this routine
	     does not check the inputs for errors.

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