GEQR2 - 5.2 English - 68552

QR factorization of a real m-by-n matrix a.

Purpose:

    QR factorization of a real m-by-n matrix a
    The factorization has the form
        A = Q * R

Parameters:

• m – [in]

  m is integer*

  The number of rows of the matrix a. m >= 0.

• n – [in]

  n is integer*

  The number of columns of the matrix a. n >= 0.

• a – [inout]

  a is float/double/COMPLEX/COMPLEX*16 array, dimension (lda,n)

  On entry, the m-by-n matrix to be factored.

  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 elementary reflectors (see Further Details).

• lda – [in]

  lda is integer*

  The leading dimension of the matrix a, lda >= fla_max(1,m)

• tau – [out]

  tau is float/double/COMPLEX/COMPLEX*16 array, dimension (min(m,n))

  The scalar factors of the elementary reflectors (see Further Details).

  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(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).
  

• WORK – [out] WORK is COMPLEX array, dimension (N)

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

  < 0: if INFO = -i, the i-th argument had an illegal value