DGEQRT3 recursively computes a QR factorization of a real 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 DOUBLE PRECISION array, dimension (LDA,N)


          On entry, the real M-by-N matrix A.  On exit, the elements on and


          above the diagonal contain the N-by-N upper triangular matrix R; the


          elements below the diagonal are the columns 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 DOUBLE PRECISION 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 column


  below the diagonal. For example, if M=5 and N=3, the matrix V is


               V = (  1       )


                   ( v1  1    )


                   ( v1 v2  1 )


                   ( v1 v2 v3 )


                   ( v1 v2 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).