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

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

9       SUBROUTINE SGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           REAL           A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       SGELQF  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) REAL 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) REAL 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) REAL 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.
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48               If  LWORK  = -1, then a workspace query is assumed; the routine
49               only calculates the optimal size of  the  WORK  array,  returns
50               this  value  as the first entry of the WORK array, and no error
51               message related to LWORK is issued by XERBLA.
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53       INFO    (output) INTEGER
54               = 0:  successful exit
55               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

58       The matrix Q is represented as a product of elementary reflectors
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60          Q = H(k) . . . H(2) H(1), where k = min(m,n).
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62       Each H(i) has the form
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64          H(i) = I - tau * v * v'
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66       where tau is a real scalar, and v is a real vector with
67       v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on  exit  in  A(i,i+1:n),
68       and tau in TAU(i).
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73 LAPACK routine (version 3.1)    November 2006                       SGELQF(1)