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LAPACK version 3.0
slaqtr(3)

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

SYNTAX
  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( * )

DESCRIPTION
  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.