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

.in +1c
.ti -1c
.RI "subroutine \fBzgetsqrhrt\fP (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)"
.br
.RI "\fBZGETSQRHRT\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgetsqrhrt (integer m, integer n, integer mb1, integer nb1, integer nb2, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
!>
!> ZGETSQRHRT computes a NB2-sized column blocked QR-factorization
!> of a complex M-by-N matrix A with M >= N,
!>
!>    A = Q * R\&.
!>
!> The routine uses internally a NB1-sized column blocked and MB1-sized
!> row blocked TSQR-factorization and perfors the reconstruction
!> of the Householder vectors from the TSQR output\&. The routine also
!> converts the R_tsqr factor from the TSQR-factorization output into
!> the R factor that corresponds to the Householder QR-factorization,
!>
!>    A = Q_tsqr * R_tsqr = Q * R\&.
!>
!> The output Q and R factors are stored in the same format as in ZGEQRT
!> (Q is in blocked compact WY-representation)\&. See the documentation
!> of ZGEQRT for more details on the format\&.
!> 
.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
\fIMB1\fP 
.PP
.nf
!>          MB1 is INTEGER
!>          The row block size to be used in the blocked TSQR\&.
!>          MB1 > N\&.
!> 
.fi
.PP
.br
\fINB1\fP 
.PP
.nf
!>          NB1 is INTEGER
!>          The column block size to be used in the blocked TSQR\&.
!>          N >= NB1 >= 1\&.
!> 
.fi
.PP
.br
\fINB2\fP 
.PP
.nf
!>          NB2 is INTEGER
!>          The block size to be used in the blocked QR that is
!>          output\&. NB2 >= 1\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>
!>          On entry: an M-by-N matrix A\&.
!>
!>          On exit:
!>           a) the elements on and above the diagonal
!>              of the array contain the N-by-N upper-triangular
!>              matrix R corresponding to the Householder QR;
!>           b) the elements below the diagonal represent Q by
!>              the columns of blocked V (compact WY-representation)\&.
!> 
.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))
!>          The upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB2\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&.
!>          If MIN(M,N) = 0, LWORK >= 1, else
!>          LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
!>          where
!>             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
!>             NB1LOCAL = MIN(NB1,N)\&.
!>             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
!>             LW1 = NB1LOCAL * N,
!>             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) )\&.
!>
!>          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
\fBContributors:\fP
.RS 4

.PP
.nf
!>
!> November 2020, Igor Kozachenko,
!>                Computer Science Division,
!>                University of California, Berkeley
!>
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB180\fP of file \fBzgetsqrhrt\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.