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

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

9       SUBROUTINE SORGRQ( 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           REAL           A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       SORGRQ  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
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20             Q  =  H(1) H(2) . . . H(k)
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22       as returned by SGERQF.
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ARGUMENTS

26       M       (input) INTEGER
27               The number of rows of the matrix Q. M >= 0.
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29       N       (input) INTEGER
30               The number of columns of the matrix Q. N >= M.
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32       K       (input) INTEGER
33               The  number  of elementary reflectors whose product defines the
34               matrix Q. M >= K >= 0.
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36       A       (input/output) REAL array, dimension (LDA,N)
37               On entry, the (m-k+i)-th row  must  contain  the  vector  which
38               defines  the  elementary  reflector H(i), for i = 1,2,...,k, as
39               returned by SGERQF in the last k rows of its array argument  A.
40               On exit, the M-by-N matrix Q.
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42       LDA     (input) INTEGER
43               The first dimension of the array A. LDA >= max(1,M).
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45       TAU     (input) REAL array, dimension (K)
46               TAU(i) must contain the scalar factor of the elementary reflec‐
47               tor H(i), as returned by SGERQF.
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49       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
50               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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52       LWORK   (input) INTEGER
53               The dimension of the array WORK. LWORK >= max(1,M).  For  opti‐
54               mum  performance  LWORK >= M*NB, where NB is the optimal block‐
55               size.
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57               If LWORK = -1, then a workspace query is assumed;  the  routine
58               only  calculates  the  optimal  size of the WORK array, returns
59               this value as the first entry of the WORK array, and  no  error
60               message related to LWORK is issued by XERBLA.
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62       INFO    (output) INTEGER
63               = 0:  successful exit
64               < 0:  if INFO = -i, the i-th argument has an illegal value
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68 LAPACK routine (version 3.1)    November 2006                       SORGRQ(1)