.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 
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\fBPurpose:\fP
.RS 4

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.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 
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.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 
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.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))
!>          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\&.
!>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= NB*N, otherwise\&.
!>
!>          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 

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Univ\&. of Colorado Denver 

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

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.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
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.RE
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Definition at line \fB170\fP of file \fBzlatsqr\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.