zlarzt.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzlarzt.f
SYNOPSIS
Functions/Subroutinessubroutine 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​. 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 zlarzt​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
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