SLAQTR(3)      LAPACK routine of NEC Numeric Library Collection      SLAQTR(3)



NAME
       SLAQTR

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



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**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 STRSNA.




ARGUMENTS
           LTRAN     (input)
                     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     (input)
                     LREAL is LOGICAL
                     On entry, LREAL specifies the input matrix structure:
                        = .FALSE.,    the input is complex
                        = .TRUE.,     the input is real

           N         (input)
                     N is INTEGER
                     On entry, N specifies the order of T+i*B. N >= 0.

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

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

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

           X         (input/output)
                     X is 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      (output)
                     WORK is REAL array, dimension (N)

           INFO      (output)
                     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 SLALN2 to keep nonsingularity.
                     NOTE: In the interests of speed, this routine does not
                           check the inputs for errors.



LAPACK routine                  31 October 2017                      SLAQTR(3)