SRC/slaqtr.f(3)            Library Functions Manual            SRC/slaqtr.f(3)

NAME
       SRC/slaqtr.f

SYNOPSIS
   Functions/Subroutines
       subroutine slaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
           SLAQTR solves a real quasi-triangular system of equations, or a
           complex quasi-triangular system of special form, in real
           arithmetic.

Function/Subroutine Documentation
   subroutine slaqtr (logical ltran, logical lreal, integer n, real,
       dimension( ldt, * ) t, integer ldt, real, dimension( * ) b, real w,
       real scale, real, dimension( * ) x, real, dimension( * ) work, integer
       info)
       SLAQTR solves a real quasi-triangular system of equations, or a complex
       quasi-triangular system of special form, in real arithmetic.

       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.

       Parameters
           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 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

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

           B

                     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

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

           SCALE

                     SCALE is REAL
                     On exit, SCALE is the scale factor.

           X

                     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

                     WORK is REAL 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 SLALN2 to keep nonsingularity.
                     NOTE: In the interests of speed, this routine does not
                           check the inputs for errors.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 163 of file slaqtr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/slaqtr.f(3)