DLAQTR 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**T, A**T denotes the 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.

LTRAN

          LTRAN is 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)**T.

LREAL

          LREAL is LOGICAL


          On entry, LREAL specifies the input matrix structure:


             = .FALSE.,    the input is complex


             = .TRUE.,     the input is real

N

          N is INTEGER


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

T

          T is 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

          LDT is INTEGER


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

B

          B is 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

          W is DOUBLE PRECISION


          On entry, W is the diagonal element of the matrix B.


          If LREAL = .TRUE., W is not referenced.

SCALE

          SCALE is DOUBLE PRECISION


          On exit, SCALE is the scale factor.

X

          X is 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

          WORK is DOUBLE PRECISION array, dimension (N)

INFO

          INFO is 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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016