SLAQTR(l)								 )								 SLAQTR(l)

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 op(T)*p = scale*c, if LREAL = .TRUE.  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

       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.

LAPACK version 3.0						   15 June 2000 							 SLAQTR(l)