DLAQTR (3lapack)

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

SYNOPSIS

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

      LOGICAL        LREAL, LTRAN

      INTEGER        INFO, LDT, N

      DOUBLE         PRECISION SCALE, W

      DOUBLE         PRECISION B( * ), T( LDT, * ), WORK( * ), X( * )

PURPOSE

  DLAQTR 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
  DTRSNA.

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

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

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

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

  X       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DLALN2 to keep
          nonsingularity.  NOTE: In the interests of speed, this routine does
          not check the inputs for errors.