ZLARZT(3S)ZLARZT(3S)NAMEZLARZT - form the triangular factor T of a complex block reflector H of
order > n, which is defined as a product of k elementary reflectors
SYNOPSIS
SUBROUTINE ZLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
CHARACTER DIRECT, STOREV
INTEGER K, LDT, LDV, N
COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSEZLARZT 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'
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 * V
Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
ARGUMENTS
DIRECT (input) 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)
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ZLARZT(3S)ZLARZT(3S)
STOREV (input) CHARACTER*1
Specifies how the vectors which define the elementary reflectors
are stored (see also Further Details):
= 'R': rowwise
N (input) INTEGER
The order of the block reflector H. N >= 0.
K (input) INTEGER
The order of the triangular factor T (= the number of elementary
reflectors). K >= 1.
V (input/output) COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V. See
further details.
LDV (input) INTEGER
The leading dimension of the array V. If STOREV = 'C', LDV >=
max(1,N); if STOREV = 'R', LDV >= K.
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector
H(i).
T (output) 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 (input) INTEGER
The leading dimension of the array T. LDT >= K.
FURTHER DETAILS
Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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 . .
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ZLARZT(3S)ZLARZT(3S)
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 )
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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