slaqtr.f(3)

NAME
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 (logicalLTRAN, logicalLREAL, integerN, real, dimension( ldt, * )T, integerLDT, real, dimension( * )B, realW, realSCALE, real, dimension( * )X, real, dimension( * )WORK, integerINFO)

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.

Date:
    September 2012

Definition at line 165 of file slaqtr.f.

Author

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