1DORGHR(1)                LAPACK routine (version 3.1)                DORGHR(1)
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NAME

6       DORGHR  - a real orthogonal matrix Q which is defined as the product of
7       IHI-ILO elementary reflectors of order N, as returned by DGEHRD
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SYNOPSIS

10       SUBROUTINE DORGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
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12           INTEGER        IHI, ILO, INFO, LDA, LWORK, N
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14           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

17       DORGHR generates a real orthogonal matrix Q which  is  defined  as  the
18       product  of  IHI-ILO  elementary  reflectors of order N, as returned by
19       DGEHRD:
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21       Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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ARGUMENTS

25       N       (input) INTEGER
26               The order of the matrix Q. N >= 0.
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28       ILO     (input) INTEGER
29               IHI     (input) INTEGER ILO and IHI must have the  same  values
30               as  in  the  previous  call  of  DGEHRD. Q is equal to the unit
31               matrix except in the submatrix  Q(ilo+1:ihi,ilo+1:ihi).   1  <=
32               ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
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34       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
35               On  entry,  the vectors which define the elementary reflectors,
36               as returned by DGEHRD.  On exit, the N-by-N  orthogonal  matrix
37               Q.
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39       LDA     (input) INTEGER
40               The leading dimension of the array A. LDA >= max(1,N).
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42       TAU     (input) DOUBLE PRECISION array, dimension (N-1)
43               TAU(i) must contain the scalar factor of the elementary reflec‐
44               tor H(i), as returned by DGEHRD.
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46       WORK      (workspace/output)   DOUBLE   PRECISION   array,    dimension
47       (MAX(1,LWORK))
48               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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50       LWORK   (input) INTEGER
51               The dimension of the array WORK. LWORK >= IHI-ILO.  For optimum
52               performance LWORK >= (IHI-ILO)*NB,  where  NB  is  the  optimal
53               blocksize.
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55               If  LWORK  = -1, then a workspace query is assumed; the routine
56               only calculates the optimal size of  the  WORK  array,  returns
57               this  value  as the first entry of the WORK array, and no error
58               message related to LWORK is issued by XERBLA.
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60       INFO    (output) INTEGER
61               = 0:  successful exit
62               < 0:  if INFO = -i, the i-th argument had an illegal value
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66 LAPACK routine (version 3.1)    November 2006                       DORGHR(1)