# slaqtr (l) - Linux Man Pages

## NAME

SLAQTR - 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(1) b(2) ... b(n) ]

]

]

]

]
op(A) = A or Aaq, Aaq denotes the conjugate transpose of
matrix A.
On input, X = [ c ]. On output, X = [ p ].

]
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)aq.
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.