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## sgerq2()

subroutine sgerq2 | ( | integer | m,
|  | integer | n,
|  | real, dimension( lda, * ) | a,
|  | integer | lda,
|  | real, dimension( * ) | tau,
|  | real, dimension( * ) | work,
|  | integer | info )

SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Download SGERQ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> SGERQ2 computes an RQ factorization of a real m by n matrix A:
      !> A = R * Q.
      !>

Parameters

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix A.  M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix A.  N >= 0.
      !>

  [in,out]

  A

      !>          A is REAL array, dimension (LDA,N)
      !>          On entry, the m by n matrix A.
      !>          On exit, if m <= n, the upper triangle of the subarray
      !>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
      !>          if m >= n, the elements on and above the (m-n)-th subdiagonal
      !>          contain the m by n upper trapezoidal matrix R; the remaining
      !>          elements, with the array TAU, represent the orthogonal matrix
      !>          Q as a product of elementary reflectors (see Further
      !>          Details).
      !>

  [in]

  LDA

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

  [out]

  TAU

      !>          TAU is REAL array, dimension (min(M,N))
      !>          The scalar factors of the elementary reflectors (see Further
      !>          Details).
      !>

  [out]

  WORK

      !>          WORK is REAL array, dimension (M)
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0: successful exit
      !>          < 0: if INFO = -i, the i-th argument had an illegal value
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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