.TH "dlarzt.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
dlarzt.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlarzt\fP (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)"
.br
.RI "\fI\fBDLARZT\fP forms the triangular factor T of a block reflector H = I - vtvH\&. \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlarzt (characterDIRECT, characterSTOREV, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( * )TAU, double precision, dimension( ldt, * )T, integerLDT)"

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

.PP
.nf
 DLARZT forms the triangular factor T of a real 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**T

 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**T * 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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
\fBDate:\fP
.RS 4
September 2012 
.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 186 of file dlarzt\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.