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

6       ZGERQF - an RQ factorization of a complex M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE ZGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       ZGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R
17       * Q.
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ARGUMENTS

21       M       (input) INTEGER
22               The number of rows of the matrix A.  M >= 0.
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24       N       (input) INTEGER
25               The number of columns of the matrix A.  N >= 0.
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27       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
28               On entry, the M-by-N matrix A.  On exit, if m <= n,  the  upper
29               triangle  of  the  subarray  A(1:m,n-m+1:n) contains the M-by-M
30               upper triangular matrix R; if m >= n, the elements on and above
31               the  (m-n)-th  subdiagonal contain the M-by-N upper trapezoidal
32               matrix R; the remaining elements, with the array TAU, represent
33               the  unitary  matrix  Q  as  a  product  of min(m,n) elementary
34               reflectors (see Further Details).  LDA     (input) INTEGER  The
35               leading dimension of the array A.  LDA >= max(1,M).
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37       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
38               The  scalar  factors  of the elementary reflectors (see Further
39               Details).
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41       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
42               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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44       LWORK   (input) INTEGER
45               The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
46               mum  performance  LWORK >= M*NB, where NB is the optimal block‐
47               size.
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49               If LWORK = -1, then a workspace query is assumed;  the  routine
50               only  calculates  the  optimal  size of the WORK array, returns
51               this value as the first entry of the WORK array, and  no  error
52               message related to LWORK is issued by XERBLA.
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54       INFO    (output) INTEGER
55               = 0:  successful exit
56               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

59       The matrix Q is represented as a product of elementary reflectors
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61          Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
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63       Each H(i) has the form
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65          H(i) = I - tau * v * v'
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67       where  tau  is  a  complex  scalar, and v is a complex vector with v(n-
68       k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
69       A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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74 LAPACK routine (version 3.1)    November 2006                       ZGERQF(1)