SIDE

          SIDE is CHARACTER*1


          = 'L': apply Q or Q**T from the Left;


          = 'R': apply Q or Q**T from the Right.

TRANS

          TRANS is CHARACTER*1


          = 'N':  No transpose, apply Q;


          = 'T':  Transpose, apply Q**T.

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 C. M >= N >= 0.

K

          K is INTEGER


          The number of elementary reflectors whose product defines


          the matrix Q.


          N >= K >= 0;

MB

          MB is INTEGER


          The block size to be used in the blocked QR.


          MB > N. (must be the same as DLATSQR)

NB

          NB is INTEGER


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


          N >= NB >= 1.

A

          A is REAL array, dimension (LDA,K)


          The i-th column must contain the vector which defines the


          blockedelementary reflector H(i), for i = 1,2,...,k, as


          returned by DLATSQR in the first k columns of


          its array argument A.

LDA

          LDA is INTEGER


          The leading dimension of the array A.


          If SIDE = 'L', LDA >= max(1,M);


          if SIDE = 'R', LDA >= max(1,N).

T

          T is REAL array, dimension


          ( N * Number of blocks(CEIL(M-K/MB-K)),


          The blocked 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 >= NB.

C

          C is REAL array, dimension (LDC,N)


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


          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

LDC

          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M).

WORK

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

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.


          If SIDE = 'L', LWORK >= max(1,N)*NB;


          if SIDE = 'R', LWORK >= max(1,MB)*NB.


          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 . . .