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dlaqtr.f File Reference

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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. More...
 

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.

Download DLAQTR + dependencies [TGZ] [ZIP] [TXT]

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
[in]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.
[in]LREAL
          LREAL is LOGICAL
          On entry, LREAL specifies the input matrix structure:
             = .FALSE.,    the input is complex
             = .TRUE.,     the input is real
[in]N
          N is INTEGER
          On entry, N specifies the order of T+i*B. N >= 0.
[in]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.
[in]LDT
          LDT is INTEGER
          The leading dimension of the matrix T. LDT >= max(1,N).
[in]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.
[in]W
          W is DOUBLE PRECISION
          On entry, W is the diagonal element of the matrix B.
          If LREAL = .TRUE., W is not referenced.
[out]SCALE
          SCALE is DOUBLE PRECISION
          On exit, SCALE is the scale factor.
[in,out]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.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]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.
Date
September 2012

Definition at line 165 of file dlaqtr.f.

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