Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3 - solves 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( * )

```

#### PURPOSE

```       SLAQTR 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**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.

```

#### 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)**T.

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.

LAPACK auxiliary routine (version 3.3.1)   April 2011                            SLAQTR(3lapack)
```