# zlarzt.f - Man Page

SRC/zlarzt.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### 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)

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

**Purpose:**

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.

**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 reflectors are stored (see also Further Details): = '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*16 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*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i).

*T*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.

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

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

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 **zlarzt.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK