SYNOPSIS

SUBROUTINE DLAQTR(

LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )

    

LOGICAL LREAL, LTRAN

    

INTEGER INFO, LDT, N

    

DOUBLE PRECISION SCALE, W

    

DOUBLE PRECISION B( * ), T( LDT, * ), WORK( * ), X( * )

PURPOSE

DLAQTR solves the real quasi-triangular system 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 DTRSNA.

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) 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 (input) INTEGER

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

B (input) 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 (input) DOUBLE PRECISION

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

SCALE (output) DOUBLE PRECISION

On exit, SCALE is the scale factor.

X (input/output) 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 (workspace) DOUBLE PRECISION 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 DLALN2 to keep nonsingularity. NOTE: In the interests of speed, this routine does not check the inputs for errors.