SLAMTSQR overwrites the general real M-by-N matrix C with


                 SIDE = 'L'     SIDE = 'R'


 TRANS = 'N':      Q * C          C * Q


 TRANS = 'T':      Q**T * C       C * Q**T


      where Q is a real orthogonal matrix defined as the product


      of blocked elementary reflectors computed by tall skinny


      QR factorization (SLATSQR)

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. N >= 0.

K

          K is INTEGER


          The number of elementary reflectors whose product defines


          the matrix Q. M >= K >= 0;

MB

          MB is INTEGER


          The block size to be used in the blocked QR.


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

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 SLATSQR 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


   . . .


 Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors


 stored under the diagonal of rows 1:MB of A, and by upper triangular


 block reflectors, stored in array T(1:LDT,1:N).


 For more information see Further Details in GEQRT.


 Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors


 stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular


 block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).


 The last Q(k) may use fewer rows.


 For more information see Further Details in TPQRT.


 For more details of the overall algorithm, see the description of


 Sequential TSQR in Section 2.2 of [1].


 [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”


     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,


     SIAM J. Sci. Comput, vol. 34, no. 1, 2012