File: dgeqr2

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--- 
:name: dgeqr2
:md5sum: fb9ab1f2a4dd3ec44720edcbe890256c
:category: :subroutine
:arguments: 
- m: 
    :type: integer
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- tau: 
    :type: doublereal
    :intent: output
    :dims: 
    - MIN(m,n)
- work: 
    :type: doublereal
    :intent: workspace
    :dims: 
    - n
- info: 
    :type: integer
    :intent: output
:substitutions: {}

:fortran_help: "      SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  DGEQR2 computes a QR factorization of a real m by n matrix A:\n\
  *  A = Q * R.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  M       (input) INTEGER\n\
  *          The number of rows of the matrix A.  M >= 0.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The number of columns of the matrix A.  N >= 0.\n\
  *\n\
  *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
  *          On entry, the m by n matrix A.\n\
  *          On exit, the elements on and above the diagonal of the array\n\
  *          contain the min(m,n) by n upper trapezoidal matrix R (R is\n\
  *          upper triangular if m >= n); the elements below the diagonal,\n\
  *          with the array TAU, represent the orthogonal matrix Q as a\n\
  *          product of elementary reflectors (see Further Details).\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A.  LDA >= max(1,M).\n\
  *\n\
  *  TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))\n\
  *          The scalar factors of the elementary reflectors (see Further\n\
  *          Details).\n\
  *\n\
  *  WORK    (workspace) DOUBLE PRECISION array, dimension (N)\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0: successful exit\n\
  *          < 0: if INFO = -i, the i-th argument had an illegal value\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  The matrix Q is represented as a product of elementary reflectors\n\
  *\n\
  *     Q = H(1) H(2) . . . H(k), where k = min(m,n).\n\
  *\n\
  *  Each H(i) has the form\n\
  *\n\
  *     H(i) = I - tau * v * v'\n\
  *\n\
  *  where tau is a real scalar, and v is a real vector with\n\
  *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),\n\
  *  and tau in TAU(i).\n\
  *\n\
  *  =====================================================================\n\
  *\n"