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

.in +1c
.ti -1c
.RI "subroutine \fBzlatsqr\fP (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)"
.br
.RI "\fBZLATSQR\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlatsqr (integer m, integer n, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(ldt, *) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 ZLATSQR computes a blocked Tall-Skinny QR factorization of
 a complex M-by-N matrix A for M >= N:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix, stored on exit in an implicit
    form in the elements below the diagonal of the array A and in
    the elements of the array T;

    R is an upper-triangular N-by-N matrix, stored on exit in
    the elements on and above the diagonal of the array A\&.

    0 is a (M-N)-by-N zero matrix, and is not stored\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\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 A\&. M >= N >= 0\&.
.fi
.PP
.br
\fIMB\fP 
.PP
.nf
          MB is INTEGER
          The row block size to be used in the blocked QR\&.
          MB > N\&.
.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,N)
          On entry, the M-by-N matrix A\&.
          On exit, the elements on and above the diagonal
          of the array contain the N-by-N upper triangular matrix R;
          the elements below the diagonal represent Q by the columns
          of blocked V (see Further Details)\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
.fi
.PP
.br
\fIT\fP 
.PP
.nf
          T is COMPLEX*16 array,
          dimension (LDT, N * Number_of_row_blocks)
          where Number_of_row_blocks = CEIL((M-N)/(MB-N))
          The blocked upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks\&.
          See Further Details below\&.
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
          LDT is INTEGER
          The leading dimension of the array T\&.  LDT >= NB\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
         (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.  LWORK >= NB*N\&.
          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\&.
.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
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 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
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB167\fP of file \fBzlatsqr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.