1SLAQTR(1)           LAPACK auxiliary routine (version 3.1)           SLAQTR(1)
2
3
4

NAME

6       SLAQTR - the real quasi-triangular system   op(T)*p = scale*c, if LREAL
7       = .TRUE
8

SYNOPSIS

10       SUBROUTINE SLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK,  INFO
11                          )
12
13           LOGICAL        LREAL, LTRAN
14
15           INTEGER        INFO, LDT, N
16
17           REAL           SCALE, W
18
19           REAL           B( * ), T( LDT, * ), WORK( * ), X( * )
20

PURPOSE

22       SLAQTR solves the real quasi-triangular system
23
24       or the complex quasi-triangular systems
25
26                  op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.
27
28       in real arithmetic, where T is upper quasi-triangular.
29       If  LREAL = .FALSE., then the first diagonal block of T must be 1 by 1,
30       B is the specially structured matrix
31
32                      B = [ b(1) b(2) ... b(n) ]
33                          [       w            ]
34                          [           w        ]
35                          [              .     ]
36                          [                 w  ]
37
38       op(A) = A or A', A' denotes the conjugate transpose of
39       matrix A.
40
41       On input, X = [ c ].  On output, X = [ p ].
42                     [ d ]                  [ q ]
43
44       This subroutine is designed for the condition number estimation in rou‐
45       tine STRSNA.
46
47

ARGUMENTS

49       LTRAN   (input) LOGICAL
50               On  entry, LTRAN specifies the option of conjugate transpose: =
51               .FALSE.,     op(T+i*B)  =  T+i*B,  =  .TRUE.,      op(T+i*B)  =
52               (T+i*B)'.
53
54       LREAL   (input) LOGICAL
55               On  entry,  LREAL  specifies  the  input  matrix  structure:  =
56               .FALSE.,    the input is complex =  .TRUE.,      the  input  is
57               real
58
59       N       (input) INTEGER
60               On entry, N specifies the order of T+i*B. N >= 0.
61
62       T       (input) REAL array, dimension (LDT,N)
63               On  entry,  T  contains  a  matrix in Schur canonical form.  If
64               LREAL = .FALSE., then the first diagonal block of T must  be  1
65               by 1.
66
67       LDT     (input) INTEGER
68               The leading dimension of the matrix T. LDT >= max(1,N).
69
70       B       (input) REAL array, dimension (N)
71               On  entry,  B  contains  the  elements  to form the matrix B as
72               described above.  If LREAL = .TRUE., B is not referenced.
73
74       W       (input) REAL
75               On entry, W is the diagonal element of the matrix B.  If  LREAL
76               = .TRUE., W is not referenced.
77
78       SCALE   (output) REAL
79               On exit, SCALE is the scale factor.
80
81       X       (input/output) REAL array, dimension (2*N)
82               On  entry,  X  contains  the right hand side of the system.  On
83               exit, X is overwritten by the solution.
84
85       WORK    (workspace) REAL array, dimension (N)
86
87       INFO    (output) INTEGER
88               On exit, INFO is set to 0: successful exit.
89               1: the some diagonal 1 by 1 block has been perturbed by a small
90               number  SMIN to keep nonsingularity.  2: the some diagonal 2 by
91               2 block has been perturbed by a small number in SLALN2 to  keep
92               nonsingularity.   NOTE: In the interests of speed, this routine
93               does not check the inputs for errors.
94
95
96
97 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLAQTR(1)