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

6       ZGELQF - computes an LQ factorization of a complex M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE ZGELQF( 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       ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L
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, the  elements  on  and
28               below the diagonal of the array contain the m-by-min(m,n) lower
29               trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
30               elements  above the diagonal, with the array TAU, represent the
31               unitary matrix Q as a product  of  elementary  reflectors  (see
32               Further  Details).   LDA     (input) INTEGER The leading dimen‐
33               sion of the array A.  LDA >= max(1,M).
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35       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
36               The scalar factors of the elementary  reflectors  (see  Further
37               Details).
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39       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
40               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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42       LWORK   (input) INTEGER
43               The dimension of the array WORK.  LWORK >= max(1,M).  For opti‐
44               mum performance LWORK >= M*NB, where NB is the  optimal  block‐
45               size.   If  LWORK  = -1, then a workspace query is assumed; the
46               routine only calculates the optimal size  of  the  WORK  array,
47               returns this value as the first entry of the WORK array, and no
48               error message related to LWORK is issued by XERBLA.
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50       INFO    (output) INTEGER
51               = 0:  successful exit
52               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

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