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

6       DGEQRF - 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

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               above the diagonal of the array contain the min(M,N)-by-N upper
30               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
31               elements  below the diagonal, with the array TAU, represent the
32               orthogonal matrix Q as a product of min(m,n) elementary reflec‐
33               tors (see Further Details).
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35       LDA     (input) INTEGER
36               The leading dimension of the array A.  LDA >= max(1,M).
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38       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
39               The  scalar  factors  of the elementary reflectors (see Further
40               Details).
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42       WORK      (workspace/output)   DOUBLE   PRECISION   array,    dimension
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44               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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46       LWORK   (input) INTEGER
47               The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
48               mum performance LWORK >= N*NB, where NB is the  optimal  block‐
49               size.
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51               If  LWORK  = -1, then a workspace query is assumed; the routine
52               only calculates the optimal size of  the  WORK  array,  returns
53               this  value  as the first entry of the WORK array, and no error
54               message related to LWORK is issued by XERBLA.
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56       INFO    (output) INTEGER
57               = 0:  successful exit
58               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

61       The matrix Q is represented as a product of elementary reflectors
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63          Q = H(1) H(2) . . . H(k), where k = min(m,n).
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65       Each H(i) has the form
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67          H(i) = I - tau * v * v'
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69       where tau is a real scalar, and v is a real vector with
70       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on  exit  in  A(i+1:m,i),
71       and tau in TAU(i).
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76 LAPACK routine (version 3.1)    November 2006                       DGEQRF(1)