LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
dlarzt.f File Reference

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## Functions/Subroutines

subroutine dlarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
DLARZT forms the triangular factor T of a block reflector H = I - vtvH.

## Function/Subroutine Documentation

 subroutine dlarzt ( character DIRECT, character STOREV, integer N, integer K, double precision, dimension( ldv, * ) V, integer LDV, double precision, dimension( * ) TAU, double precision, dimension( ldt, * ) T, integer LDT )

DLARZT forms the triangular factor T of a block reflector H = I - vtvH.

Purpose:
``` 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.```
Parameters:
 [in] DIRECT ``` 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)``` [in] STOREV ``` 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``` [in] N ``` N is INTEGER The order of the block reflector H. N >= 0.``` [in] K ``` K is INTEGER The order of the triangular factor T (= the number of elementary reflectors). K >= 1.``` [in,out] V ``` V is DOUBLE PRECISION array, dimension (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V. See further details.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i).``` [out] T ``` 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.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= K.```
Date:
September 2012
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
```  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 )```

Definition at line 186 of file dlarzt.f.

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