Contents
clarzt - form the triangular factor T of a complex block
reflector H of order > n, which is defined as a product of k
elementary reflectors
SUBROUTINE CLARZT(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
CHARACTER * 1 DIRECT, STOREV
COMPLEX V(LDV,*), TAU(*), T(LDT,*)
INTEGER N, K, LDV, LDT
SUBROUTINE CLARZT_64(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
CHARACTER * 1 DIRECT, STOREV
COMPLEX V(LDV,*), TAU(*), T(LDT,*)
INTEGER*8 N, K, LDV, LDT
F95 INTERFACE
SUBROUTINE LARZT(DIRECT, STOREV, N, K, V, [LDV], TAU, T, [LDT])
CHARACTER(LEN=1) :: DIRECT, STOREV
COMPLEX, DIMENSION(:) :: TAU
COMPLEX, DIMENSION(:,:) :: V, T
INTEGER :: N, K, LDV, LDT
SUBROUTINE LARZT_64(DIRECT, STOREV, N, K, V, [LDV], TAU, T, [LDT])
CHARACTER(LEN=1) :: DIRECT, STOREV
COMPLEX, DIMENSION(:) :: TAU
COMPLEX, DIMENSION(:,:) :: V, T
INTEGER(8) :: N, K, LDV, LDT
C INTERFACE
#include <sunperf.h>
void clarzt(char direct, char storev, int n, int k, complex
*v, int ldv, complex *tau, complex *t, int ldt);
void clarzt_64(char direct, char storev, long n, long k,
complex *v, long ldv, complex *tau, complex *t,
long ldt);
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'
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.
DIRECT (input)
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 sup-
ported yet)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (input)
Specifies how the vectors which define the elemen-
tary reflectors are stored (see also Further
Details):
= 'R': rowwise
N (input) The order of the block reflector H. N >= 0.
K (input) The order of the triangular factor T (= the number
of elementary reflectors). K >= 1.
V (input) (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R'
The matrix V. See further details.
LDV (input)
The leading dimension of the array V. If STOREV =
'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
TAU (input)
TAU(i) must contain the scalar factor of the ele-
mentary reflector H(i).
T (input) The k by k triangular factor T of the block
reflector. If DIRECT = 'F', T is upper triangu-
lar; if DIRECT = 'B', T is lower triangular. The
rest of the array is not used.
LDT (input)
The leading dimension of the array T. LDT >= K.
Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knox-
ville, 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 . .
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 )
V = ( v1 v2 v3 )
( v1 v2 v3 )