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

6       DGEQRF - computes a QR factorization of a real M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE DGEQRF( 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       DGEQRF  computes  a QR factorization of a real M-by-N matrix A: A = Q *
17       R.
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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               above the diagonal of the array contain the min(M,N)-by-N upper
29               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
30               elements  below the diagonal, with the array TAU, represent the
31               orthogonal matrix Q as a product of min(m,n) elementary reflec‐
32               tors (see Further Details).
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34       LDA     (input) INTEGER
35               The leading dimension of the array A.  LDA >= max(1,M).
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37       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
38               The  scalar  factors  of the elementary reflectors (see Further
39               Details).
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41       WORK      (workspace/output)   DOUBLE   PRECISION   array,    dimension
42       (MAX(1,LWORK))
43               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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45       LWORK   (input) INTEGER
46               The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
47               mum performance LWORK >= N*NB, where NB is the  optimal  block‐
48               size.   If  LWORK  = -1, then a workspace query is assumed; the
49               routine only calculates the optimal size  of  the  WORK  array,
50               returns this value as the first entry of the WORK array, and no
51               error 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
59          Q = H(1) H(2) . . . H(k), where k = min(m,n).
60       Each H(i) has the form
61          H(i) = I - tau * v * v'
62       where tau is a real scalar, and v is a real vector with
63       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on  exit  in  A(i+1:m,i),
64       and tau in TAU(i).
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68 LAPACK routine (version 3.2)    November 2008                       DGEQRF(1)