.TH "SRC/zlamtsqr.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zlamtsqr.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlamtsqr\fP (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)"
.br
.RI "\fBZLAMTSQR\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBZLAMTSQR\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!>      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)
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right\&.
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate Transpose, apply Q**H\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >=0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q\&. M >= K >= 0;
!>
!> 
.fi
.PP
.br
\fIMB\fP 
.PP
.nf
!>          MB is INTEGER
!>          The block size to be used in the blocked QR\&.
!>          MB > N\&. (must be the same as ZLATSQR)
!> 
.fi
.PP
.br
\fINB\fP 
.PP
.nf
!>          NB is INTEGER
!>          The column block size to be used in the blocked QR\&.
!>          N >= NB >= 1\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
!>          LDC is INTEGER
!>          The leading dimension of the array C\&. LDC >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

.PP
.nf
!> 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
!> 
.fi
.PP
 
.RE
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Definition at line \fB199\fP of file \fBzlamtsqr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.