SGEQL2 computes a QL factorization of a real m by n matrix A:


 A = Q * L.

M

          M is INTEGER


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

N

          N is INTEGER


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

A

          A is REAL array, dimension (LDA,N)


          On entry, the m by n matrix A.


          On exit, if m >= n, the lower triangle of the subarray


          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;


          if m <= n, the elements on and below the (n-m)-th


          superdiagonal contain the m by n lower trapezoidal matrix L;


          the remaining elements, with the array TAU, represent the


          orthogonal matrix Q as a product of elementary reflectors


          (see Further Details).

LDA

          LDA is INTEGER


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

TAU

          TAU is REAL array, dimension (min(M,N))


          The scalar factors of the elementary reflectors (see Further


          Details).

WORK

          WORK is REAL array, dimension (N)

INFO

          INFO is INTEGER


          = 0: successful exit


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  The matrix Q is represented as a product of elementary reflectors


     Q = H(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in


  A(1:m-k+i-1,n-k+i), and tau in TAU(i).