1DLAQTR(1)           LAPACK auxiliary routine (version 3.1)           DLAQTR(1)
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NAME

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

10       SUBROUTINE DLAQTR( 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           DOUBLE         PRECISION SCALE, W
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19           DOUBLE         PRECISION B( * ), T( LDT, * ), WORK( * ), X( * )
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PURPOSE

22       DLAQTR solves the real quasi-triangular system
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24       or the complex quasi-triangular systems
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26                  op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.
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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
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32                      B = [ b(1) b(2) ... b(n) ]
33                          [       w            ]
34                          [           w        ]
35                          [              .     ]
36                          [                 w  ]
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38       op(A) = A or A', A' denotes the conjugate transpose of
39       matrix A.
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41       On input, X = [ c ].  On output, X = [ p ].
42                     [ d ]                  [ q ]
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44       This subroutine is designed for the condition number estimation in rou‐
45       tine DTRSNA.
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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)'.
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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
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59       N       (input) INTEGER
60               On entry, N specifies the order of T+i*B. N >= 0.
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62       T       (input) DOUBLE PRECISION 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 mu be 1  by
65               1.
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67       LDT     (input) INTEGER
68               The leading dimension of the matrix T. LDT >= max(1,N).
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70       B       (input) DOUBLE PRECISION 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.
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74       W       (input) DOUBLE PRECISION
75               On entry, W is the diagonal element of the matrix B.  If  LREAL
76               = .TRUE., W is not referenced.
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78       SCALE   (output) DOUBLE PRECISION
79               On exit, SCALE is the scale factor.
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81       X       (input/output) DOUBLE PRECISION 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.
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85       WORK    (workspace) DOUBLE PRECISION array, dimension (N)
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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 DLALN2 to  keep
92               nonsingularity.   NOTE: In the interests of speed, this routine
93               does not check the inputs for errors.
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97 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLAQTR(1)