ZGELQT3 recursively computes a LQ factorization of a complex M-by-N
 matrix A, using the compact WY representation of Q.
 Based on the algorithm of Elmroth and Gustavson,
 IBM J. Res. Develop. Vol 44 No. 4 July 2000.

M

          M is INTEGER
          The number of rows of the matrix A.  M =< N.

N

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the complex M-by-N matrix A.  On exit, the elements on and
          below the diagonal contain the N-by-N lower triangular matrix L; the
          elements above the diagonal are the rows of V.  See below for
          further details.

LDA

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

T

          T is COMPLEX*16 array, dimension (LDT,N)
          The N-by-N upper triangular factor of the block reflector.
          The elements on and above the diagonal contain the block
          reflector T; the elements below the diagonal are not used.
          See below for further details.

LDT

          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N).

INFO

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

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  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is
               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (     1  v3 v3 v3 )
  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
  block reflector H is then given by
               H = I - V * T * V**T
  where V**T is the transpose of V.
  For details of the algorithm, see Elmroth and Gustavson (cited above).