SRC/zlamtsqr.f(3)          Library Functions Manual          SRC/zlamtsqr.f(3)

NAME
       SRC/zlamtsqr.f

SYNOPSIS
   Functions/Subroutines
       subroutine zlamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c,
           ldc, work, lwork, info)
           ZLAMTSQR

Function/Subroutine Documentation
   subroutine zlamtsqr (character side, character trans, integer m, integer n,
       integer k, integer mb, integer nb, complex*16, dimension( lda, * ) a,
       integer lda, complex*16, dimension( ldt, * ) t, integer ldt,
       complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension(
       * ) work, integer lwork, integer info)
       ZLAMTSQR

       Purpose:


           !>
           !>      ZLAMTSQR overwrites the general complex M-by-N matrix C with
           !>
           !>
           !>                 SIDE = 'L'     SIDE = 'R'
           !> TRANS = 'N':      Q * C          C * Q
           !> TRANS = 'C':      Q**H * C       C * Q**H
           !>      where Q is a complex unitary matrix defined as the product
           !>      of blocked elementary reflectors computed by tall skinny
           !>      QR factorization (ZLATSQR)
           !>

       Parameters
           SIDE

           !>          SIDE is CHARACTER*1
           !>          = 'L': apply Q or Q**H from the Left;
           !>          = 'R': apply Q or Q**H from the Right.
           !>

           TRANS

           !>          TRANS is CHARACTER*1
           !>          = 'N':  No transpose, apply Q;
           !>          = 'C':  Conjugate Transpose, apply Q**H.
           !>

           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 ZLATSQR)
           !>

           NB

           !>          NB is INTEGER
           !>          The column block size to be used in the blocked QR.
           !>          N >= NB >= 1.
           !>

           A

           !>          A is COMPLEX*16 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 ZLATSQR 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDC,N)
           !>          On entry, the M-by-N matrix C.
           !>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
           !>

           LDC

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

           WORK

           !>          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
           !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
           !>

           LWORK

           !>          LWORK is INTEGER
           !>          The dimension of the array WORK.
           !>          If MIN(M,N,K) = 0, LWORK >= 1.
           !>          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 minimal 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
           !>

       Author
           Univ. of Tennessee


           Univ. of California Berkeley


           Univ. of Colorado Denver


           NAG Ltd.

       Further Details:


           !> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
           !> representing Q as a product of other unitary 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
           !>

       Definition at line 199 of file zlamtsqr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0               SRC/zlamtsqr.f(3)