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

6       CUNGRQ - an M-by-N complex matrix Q with orthonormal rows,
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SYNOPSIS

9       SUBROUTINE CUNGRQ( 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           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       CUNGRQ  generates  an  M-by-N  complex  matrix Q with orthonormal rows,
17       which is defined as the last M  rows  of  a  product  of  K  elementary
18       reflectors of order N
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20             Q  =  H(1)' H(2)' . . . H(k)'
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22       as returned by CGERQF.
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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) COMPLEX 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 CGERQF 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) COMPLEX array, dimension (K)
46               TAU(i) must contain the scalar factor of the elementary reflec‐
47               tor H(i), as returned by CGERQF.
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49       WORK    (workspace/output) COMPLEX 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                       CUNGRQ(1)