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

NAME
       SRC/dlaqtr.f

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

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

       Purpose:


            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.

       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 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 163 of file dlaqtr.f.

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

LAPACK                          Version 3.12.0                 SRC/dlaqtr.f(3)