|
Unix VPS
Support
FAQ
Network
Miscellaneous
|
| larft(3) | LAPACK | larft(3) |
NAME
larft - larft: generate T matrix
SYNOPSIS
Functions
subroutine clarft (direct, storev, n, k, v, ldv, tau, t,
ldt)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
subroutine dlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH
subroutine slarft (direct, storev, n, k, v, ldv, tau, t, ldt)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
subroutine zlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
ZLARFT forms the triangular factor T of a block reflector H = I - vtvH
Detailed Description
Function Documentation
subroutine clarft (character direct, character storev, integer n, integer k, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( * ) tau, complex, dimension( ldt, * ) t, integer ldt)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
Purpose:
CLARFT 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
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)
= '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
= '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.
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.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )
Definition at line 162 of file clarft.f.
subroutine dlarft (character direct, character storev, integer n, integer k, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( * ) tau, double precision, dimension( ldt, * ) t, integer ldt)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH
Purpose:
DLARFT forms the triangular factor T of a real 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**T
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 * T * V
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)
= '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
= '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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).
T
T is DOUBLE PRECISION 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.
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.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )
Definition at line 162 of file dlarft.f.
subroutine slarft (character direct, character storev, integer n, integer k, real, dimension( ldv, * ) v, integer ldv, real, dimension( * ) tau, real, dimension( ldt, * ) t, integer ldt)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
Purpose:
SLARFT forms the triangular factor T of a real 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**T
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 * T * V
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)
= '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
= '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 REAL 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 REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).
T
T is REAL 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.
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.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )
Definition at line 162 of file slarft.f.
subroutine zlarft (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)
ZLARFT forms the triangular factor T of a block reflector H = I - vtvH
Purpose:
ZLARFT 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
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)
= '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
= '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.
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.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )
Definition at line 162 of file zlarft.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
| Sun Jan 12 2025 15:13:37 | Version 3.12.1 |
Visit the GSP FreeBSD Man Page Interface.
Output converted with ManDoc.