# clarzt.f - Man Page

SRC/clarzt.f

## Synopsis

### Functions/Subroutines

subroutine clarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
CLARZT forms the triangular factor T of a block reflector H = I - vtvH.

## Function/Subroutine Documentation

### subroutine clarzt (character direct, character storev, integer n, integer k, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( * ) tau, complex, dimension( ldt, * ) t, integer ldt)

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

Purpose:

``` CLARZT 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.```
Parameters

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)```

STOREV

```          STOREV is CHARACTER*1
Specifies how the vectors which define the elementary
= 'C': columnwise                        (not supported yet)
= 'R': rowwise```

N

```          N is INTEGER
The order of the block reflector H. N >= 0.```

K

```          K is INTEGER
The order of the triangular factor T (= the number of
elementary reflectors). K >= 1.```

V

```          V is COMPLEX array, dimension
(LDV,K) if STOREV = 'C'
(LDV,N) if STOREV = 'R'
The matrix V. See further details.```

LDV

```          LDV is INTEGER
The leading dimension of the array V.
If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.```

TAU

```          TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).```

T

```          T is COMPLEX 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.```

LDT

```          LDT is INTEGER
The leading dimension of the array T. LDT >= K.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

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 184 of file clarzt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clarzt(3) is an alias of clarzt.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK