1DORGRQ(1)                LAPACK routine (version 3.2)                DORGRQ(1)
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NAME

6       DORGRQ - generates an M-by-N real matrix Q with orthonormal rows,
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SYNOPSIS

9       SUBROUTINE DORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, K, LDA, LWORK, M, N
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13           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       DORGRQ  generates  an M-by-N real matrix Q with orthonormal rows, which
17       is defined as the last M rows of a product of K  elementary  reflectors
18       of order N
19             Q  =  H(1) H(2) . . . H(k)
20       as returned by DGERQF.
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ARGUMENTS

23       M       (input) INTEGER
24               The number of rows of the matrix Q. M >= 0.
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26       N       (input) INTEGER
27               The number of columns of the matrix Q. N >= M.
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29       K       (input) INTEGER
30               The  number  of elementary reflectors whose product defines the
31               matrix Q. M >= K >= 0.
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33       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
34               On entry, the (m-k+i)-th row  must  contain  the  vector  which
35               defines  the  elementary  reflector H(i), for i = 1,2,...,k, as
36               returned by DGERQF in the last k rows of its array argument  A.
37               On exit, the M-by-N matrix Q.
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39       LDA     (input) INTEGER
40               The first dimension of the array A. LDA >= max(1,M).
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42       TAU     (input) DOUBLE PRECISION array, dimension (K)
43               TAU(i) must contain the scalar factor of the elementary reflec‐
44               tor H(i), as returned by DGERQF.
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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 >= max(1,M).  For opti‐
52               mum performance LWORK >= M*NB, where NB is the  optimal  block‐
53               size.   If  LWORK  = -1, then a workspace query is assumed; the
54               routine only calculates the optimal size  of  the  WORK  array,
55               returns this value as the first entry of the WORK array, and no
56               error message related to LWORK is issued by XERBLA.
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58       INFO    (output) INTEGER
59               = 0:  successful exit
60               < 0:  if INFO = -i, the i-th argument has an illegal value
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64 LAPACK routine (version 3.2)    November 2008                       DORGRQ(1)