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

6       DGELQF - 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

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) DOUBLE PRECISION array, dimension (LDA,N)
28               On entry, the M-by-N matrix A.  On exit, the  elements  on  and
29               below the diagonal of the array contain the m-by-min(m,n) lower
30               trapezoidal matrix L (L is lower triangular if  m  <=  n);  the
31               elements  above the diagonal, with the array TAU, represent the
32               orthogonal matrix Q as a product of elementary reflectors  (see
33               Further  Details).   LDA     (input) INTEGER The leading dimen‐
34               sion of the array A.  LDA >= max(1,M).
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36       TAU     (output) DOUBLE PRECISION 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)   DOUBLE   PRECISION   array,   dimension
41       (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(k) . . . H(2) H(1), 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 real scalar, and v is a real vector with
68       v(1:i-1)  =  0  and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
69       and tau in TAU(i).
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74 LAPACK routine (version 3.1)    November 2006                       DGELQF(1)