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

.in +1c
.ti -1c
.RI "subroutine \fBzlarzt\fP (direct, storev, n, k, v, ldv, tau, t, ldt)"
.br
.RI "\fBZLARZT\fP forms the triangular factor T of a block reflector H = I - vtvH\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlarzt (character direct, character storev, integer n, integer k, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( * ) tau, complex*16, dimension( ldt, * ) t, integer ldt)"

.PP
\fBZLARZT\fP forms the triangular factor T of a block reflector H = I - vtvH\&.  
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\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZLARZT forms the triangular factor T of a complex block reflector
!> H of order > n, which is defined as a product of k elementary
!> reflectors\&.
!>
!> If DIRECT = 'F', H = H(1) H(2) \&. \&. \&. H(k) and T is upper triangular;
!>
!> If DIRECT = 'B', H = H(k) \&. \&. \&. H(2) H(1) and T is lower triangular\&.
!>
!> If STOREV = 'C', the vector which defines the elementary reflector
!> H(i) is stored in the i-th column of the array V, and
!>
!>    H  =  I - V * T * V**H
!>
!> If STOREV = 'R', the vector which defines the elementary reflector
!> H(i) is stored in the i-th row of the array V, and
!>
!>    H  =  I - V**H * T * V
!>
!> Currently, only STOREV = 'R' and DIRECT = 'B' are supported\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Specifies the order in which the elementary reflectors are
!>          multiplied to form the block reflector:
!>          = 'F': H = H(1) H(2) \&. \&. \&. H(k) (Forward, not supported yet)
!>          = 'B': H = H(k) \&. \&. \&. H(2) H(1) (Backward)
!> 
.fi
.PP
.br
\fISTOREV\fP 
.PP
.nf
!>          STOREV is CHARACTER*1
!>          Specifies how the vectors which define the elementary
!>          reflectors are stored (see also Further Details):
!>          = 'C': columnwise                        (not supported yet)
!>          = 'R': rowwise
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the block reflector H\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The order of the triangular factor T (= the number of
!>          elementary reflectors)\&. K >= 1\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX*16 array, dimension
!>                               (LDV,K) if STOREV = 'C'
!>                               (LDV,N) if STOREV = 'R'
!>          The matrix V\&. See further details\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX*16 array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX*16 array, dimension (LDT,K)
!>          The k by k triangular factor T of the block reflector\&.
!>          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
!>          lower triangular\&. The rest of the array is not used\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= K\&.
!> 
.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
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  The shape of the matrix V and the storage of the vectors which define
!>  the H(i) is best illustrated by the following example with n = 5 and
!>  k = 3\&. The elements equal to 1 are not stored; the corresponding
!>  array elements are modified but restored on exit\&. The rest of the
!>  array is not used\&.
!>
!>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
!>
!>                                              ______V_____
!>         ( v1 v2 v3 )                        /            \\
!>         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 \&. \&. \&. \&. 1 )
!>     V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 \&. \&. \&. 1   )
!>         ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 \&. \&. 1     )
!>         ( v1 v2 v3 )
!>            \&.  \&.  \&.
!>            \&.  \&.  \&.
!>            1  \&.  \&.
!>               1  \&.
!>                  1
!>
!>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
!>
!>                                                        ______V_____
!>            1                                          /            \\
!>            \&.  1                           ( 1 \&. \&. \&. \&. v1 v1 v1 v1 v1 )
!>            \&.  \&.  1                        ( \&. 1 \&. \&. \&. v2 v2 v2 v2 v2 )
!>            \&.  \&.  \&.                        ( \&. \&. 1 \&. \&. v3 v3 v3 v3 v3 )
!>            \&.  \&.  \&.
!>         ( v1 v2 v3 )
!>         ( v1 v2 v3 )
!>     V = ( v1 v2 v3 )
!>         ( v1 v2 v3 )
!>         ( v1 v2 v3 )
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB184\fP of file \fBzlarzt\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.