# clarzt.f - Man Page

## 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 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 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**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 187 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 14 2017 Version 3.8.0 LAPACK