DGELQT computes a blocked LQ factorization of a real M-by-N matrix A


 using the compact WY representation of Q.

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.

MB

          MB is INTEGER


          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)


          On entry, the M-by-N matrix A.


          On exit, the elements on and below the diagonal of the array


          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is


          lower triangular if M <= N); the elements above the diagonal


          are the rows of V.

LDA

          LDA is INTEGER


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

T

          T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))


          The upper triangular block reflectors stored in compact form


          as a sequence of upper triangular blocks.  See below


          for further details.

LDT

          LDT is INTEGER


          The leading dimension of the array T.  LDT >= MB.

WORK

          WORK is DOUBLE PRECISION array, dimension (MB*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.

November 2017

  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 )


  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.


  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each


  block is of order MB except for the last block, which is of order


  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block


  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB


  for the last block) T's are stored in the MB-by-K matrix T as


               T = (T1 T2 ... TB).