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## zgeqr2()

subroutine zgeqr2 | ( | integer | m,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex*16, dimension( * ) | tau,
|  | complex*16, dimension( * ) | work,
|  | integer | info )

ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Download ZGEQR2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZGEQR2 computes a QR factorization of a complex m-by-n matrix A:
      !>
      !>    A = Q * ( R ),
      !>            ( 0 )
      !>
      !> where:
      !>
      !>    Q is a m-by-m orthogonal matrix;
      !>    R is an upper-triangular n-by-n matrix;
      !>    0 is a (m-n)-by-n zero matrix, if m > n.
      !>
      !>

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 COMPLEX*16 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 unitary 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 COMPLEX*16 array, dimension (min(M,N))
      !>          The scalar factors of the elementary reflectors (see Further
      !>          Details).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX*16 array, dimension (N)
      !>

  [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**H
      !>
      !>  where tau is a complex scalar, and v is a complex 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).
      !>