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

6       ZGERQF - computes 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

20       M       (input) INTEGER
21               The number of rows of the matrix A.  M >= 0.
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23       N       (input) INTEGER
24               The number of columns of the matrix A.  N >= 0.
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26       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
27               On entry, the M-by-N matrix A.  On exit, if m <= n,  the  upper
28               triangle  of  the  subarray  A(1:m,n-m+1:n) contains the M-by-M
29               upper triangular matrix R; if m >= n, the elements on and above
30               the  (m-n)-th  subdiagonal contain the M-by-N upper trapezoidal
31               matrix R; the remaining elements, with the array TAU, represent
32               the  unitary  matrix  Q  as  a  product  of min(m,n) elementary
33               reflectors (see Further Details).  LDA     (input) INTEGER  The
34               leading dimension of the array A.  LDA >= max(1,M).
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36       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
37               The  scalar  factors  of the elementary reflectors (see Further
38               Details).
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40       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
41               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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43       LWORK   (input) INTEGER
44               The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
45               mum  performance  LWORK >= M*NB, where NB is the optimal block‐
46               size.  If LWORK = -1, then a workspace query  is  assumed;  the
47               routine  only  calculates  the  optimal size of the WORK array,
48               returns this value as the first entry of the WORK array, and no
49               error message related to LWORK is issued by XERBLA.
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51       INFO    (output) INTEGER
52               = 0:  successful exit
53               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

56       The matrix Q is represented as a product of elementary reflectors
57          Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
58       Each H(i) has the form
59          H(i) = I - tau * v * v'
60       where  tau  is  a  complex  scalar, and v is a complex vector with v(n-
61       k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in
62       A(m-k+i,1:n-k+i-1), and tau in TAU(i).
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66 LAPACK routine (version 3.2)    November 2008                       ZGERQF(1)