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

6       SORGRQ - generates 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
19             Q  =  H(1) H(2) . . . H(k)
20       as returned by SGERQF.
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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) REAL 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 SGERQF 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) REAL array, dimension (K)
43               TAU(i) must contain the scalar factor of the elementary reflec‐
44               tor H(i), as returned by SGERQF.
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46       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
47               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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49       LWORK   (input) INTEGER
50               The dimension of the array WORK. LWORK >= max(1,M).  For  opti‐
51               mum  performance  LWORK >= M*NB, where NB is the optimal block‐
52               size.  If LWORK = -1, then a workspace query  is  assumed;  the
53               routine  only  calculates  the  optimal size of the WORK array,
54               returns this value as the first entry of the WORK array, and no
55               error message related to LWORK is issued by XERBLA.
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57       INFO    (output) INTEGER
58               = 0:  successful exit
59               < 0:  if INFO = -i, the i-th argument has an illegal value
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63 LAPACK routine (version 3.2)    November 2008                       SORGRQ(1)