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. M >= N >= 0.

MB

          MB is INTEGER


          The row block size to be used in the blocked QR.


          MB > N.

NB

          NB is INTEGER


          The column block size to be used in the blocked QR.


          N >= NB >= 1.

A

          A is COMPLEX array, dimension (LDA,N)


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


          On exit, the elements on and above the diagonal


          of the array contain the N-by-N upper triangular matrix R;


          the elements below the diagonal represent Q by the columns


          of blocked V (see Further Details).

LDA

          LDA is INTEGER


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

T

          T is COMPLEX array,


          dimension (LDT, N * Number_of_row_blocks)


          where Number_of_row_blocks = CEIL((M-N)/(MB-N))


          The blocked upper triangular block reflectors stored in compact form


          as a sequence of upper triangular blocks.


          See Further Details below.

LDT

          LDT is INTEGER


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

WORK

         (workspace) COMPLEX array, dimension (MAX(1,LWORK))

LWORK

          The dimension of the array WORK.  LWORK >= NB*N.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal size of the WORK array, returns


          this value as the first entry of the WORK array, and no error


          message related to LWORK is issued by XERBLA.

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.

Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations, representing Q as a product of other orthogonal matrices Q = Q(1) * Q(2) * . . . * Q(k) where each Q(i) zeros out subdiagonal entries of a block of MB rows of A: Q(1) zeros out the subdiagonal entries of rows 1:MB of A Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A . . .