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))

           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

       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 197 of file zlamtsqr.f.

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

LAPACK                          Version 3.12.0               SRC/zlamtsqr.f(3)