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dgeqrf examples
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Man Page Details
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NAME
       DGEQRF - a QR factorization of a real M-by-N matrix A

SYNOPSIS
       SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

           INTEGER        INFO, LDA, LWORK, M, N

           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       DGEQRF  computes  a QR factorization of a real M-by-N matrix A: A = Q *
       R.


ARGUMENTS
       M       (input) INTEGER
               The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
               The number of columns of the matrix A.  N >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
               On entry, the M-by-N matrix A.  On exit, the  elements  on  and
               above the diagonal of the array contain the min(M,N)-by-N upper
               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
               elements  below the diagonal, with the array TAU, represent the
               orthogonal matrix Q as a product of min(m,n) elementary reflec-
               tors (see Further Details).

       LDA     (input) INTEGER
               The leading dimension of the array A.  LDA >= max(1,M).

       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
               The  scalar  factors  of the elementary reflectors (see Further
               Details).

       WORK      (workspace/output)   DOUBLE   PRECISION   array,    dimension
       (MAX(1,LWORK))
               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
               The dimension of the array WORK.  LWORK >= max(1,N).  For opti-
               mum  performance  LWORK >= N*NB, where NB is the optimal block-
               size.

               If LWORK = -1, then a workspace query is assumed;  the  routine
               only  calculates  the  optimal  size of the WORK array, returns
               this value as the first entry of the WORK array, and  no  error
               message related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
       The matrix Q is represented as a product of elementary reflectors

          Q = H(1) H(2) . . . H(k), where k = min(m,n).

       Each H(i) has the form

          H(i) = I - tau * v * v'

       where tau is a real scalar, and v is a real vector with
       v(1:i-1)  =  0  and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
       and tau in TAU(i).

