slaqtr(3)

NAME

SLAQTR - solve 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 op(T)*p =

scale*c, if LREAL = .TRUE. or the complex quasi-triangular sys

tems

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 esti

mation 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)'.

LREAL (input) LOGICAL

On entry, LREAL specifies the input matrix struc

ture: = .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 ma

trix B as described above. If LREAL = .TRUE., B is not refer

enced.

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 per

turbed 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 version 3.0 15 June 2000

SLAQTR(3)