NAME

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

SYNOPSIS

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

void dlaqtr(long ltran, long ldouble, long int n, double
∗t, long int ldt, double ∗db, double w, double ∗dscale, double ∗dx, long int ∗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.

Sun, Inc.  —  Last change: 20 Sep 1996