1SLAQTR(1)           LAPACK auxiliary routine (version 3.2)           SLAQTR(1)
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NAME

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

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

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

41       LTRAN   (input) LOGICAL
42               On  entry, LTRAN specifies the option of conjugate transpose: =
43               .FALSE.,     op(T+i*B)  =  T+i*B,  =  .TRUE.,      op(T+i*B)  =
44               (T+i*B)'.
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46       LREAL   (input) LOGICAL
47               On  entry,  LREAL  specifies  the  input  matrix  structure:  =
48               .FALSE.,    the input is complex =  .TRUE.,      the  input  is
49               real
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51       N       (input) INTEGER
52               On entry, N specifies the order of T+i*B. N >= 0.
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54       T       (input) REAL array, dimension (LDT,N)
55               On  entry,  T  contains  a  matrix in Schur canonical form.  If
56               LREAL = .FALSE., then the first diagonal block of T must  be  1
57               by 1.
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59       LDT     (input) INTEGER
60               The leading dimension of the matrix T. LDT >= max(1,N).
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62       B       (input) REAL array, dimension (N)
63               On  entry,  B  contains  the  elements  to form the matrix B as
64               described above.  If LREAL = .TRUE., B is not referenced.
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66       W       (input) REAL
67               On entry, W is the diagonal element of the matrix B.  If  LREAL
68               = .TRUE., W is not referenced.
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70       SCALE   (output) REAL
71               On exit, SCALE is the scale factor.
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73       X       (input/output) REAL array, dimension (2*N)
74               On  entry,  X  contains  the right hand side of the system.  On
75               exit, X is overwritten by the solution.
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77       WORK    (workspace) REAL array, dimension (N)
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79       INFO    (output) INTEGER
80               On exit, INFO is set to 0: successful exit.
81               1: the some diagonal 1 by 1 block has been perturbed by a small
82               number  SMIN to keep nonsingularity.  2: the some diagonal 2 by
83               2 block has been perturbed by a small number in SLALN2 to  keep
84               nonsingularity.   NOTE: In the interests of speed, this routine
85               does not check the inputs for errors.
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89 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLAQTR(1)