slaqtr(3S)

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

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

         LOGICAL        LREAL, LTRAN

         INTEGER        INFO, LDT, N

         REAL           SCALE, W

         REAL           B( * ), T( LDT, * ), WORK( * ), X( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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', 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 STRSNA.
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) 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) INTEGER
             The leading dimension of the matrix T. LDT >= max(1,N).

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

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

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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.