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

6       DGELQF - computes an LQ factorization of a real M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       DGELQF  computes an LQ factorization of a real 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) DOUBLE PRECISION 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               orthogonal 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) DOUBLE PRECISION 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)   DOUBLE   PRECISION   array,   dimension
40       (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(k) . . . H(2) H(1), where k = min(m,n).
58       Each H(i) has the form
59          H(i) = I - tau * v * v'
60       where tau is a real scalar, and v is a real vector with
61       v(1:i-1)  =  0  and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
62       and tau in TAU(i).
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66 LAPACK routine (version 3.2)    November 2008                       DGELQF(1)