table of contents
| larfb(3) | LAPACK | larfb(3) |
NAME¶
larfb - larfb: apply block Householder reflector
SYNOPSIS¶
Functions¶
subroutine clarfb (side, trans, direct, storev, m, n, k, v,
ldv, t, ldt, c, ldc, work, ldwork)
CLARFB applies a block reflector or its conjugate-transpose to a
general rectangular matrix. subroutine dlarfb (side, trans, direct,
storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
DLARFB applies a block reflector or its transpose to a general
rectangular matrix. subroutine slarfb (side, trans, direct, storev,
m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
SLARFB applies a block reflector or its transpose to a general
rectangular matrix. subroutine zlarfb (side, trans, direct, storev,
m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
ZLARFB applies a block reflector or its conjugate-transpose to a
general rectangular matrix.
Detailed Description¶
Function Documentation¶
subroutine clarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldwork, * ) work, integer ldwork)¶
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Purpose:
CLARFB applies a complex block reflector H or its transpose H**H to a
complex M-by-N matrix C, from either the left or the right.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply H or H**H from the Left
= 'R': apply H or H**H from the Right
TRANS
TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H**H (Conjugate transpose)
DIRECT
DIRECT is CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV
STOREV is CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise
M
M is INTEGER
The number of rows of the matrix C.
N
N is INTEGER
The number of columns of the matrix C.
K
K is INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
V
V is COMPLEX array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The matrix V. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
if STOREV = 'R', LDV >= K.
T
T is COMPLEX array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= K.
C
C is COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is COMPLEX array, dimension (LDWORK,K)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).
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; 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 = ( 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 )
subroutine dlarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( ldwork, * ) work, integer ldwork)¶
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Purpose:
DLARFB applies a real block reflector H or its transpose H**T to a
real m by n matrix C, from either the left or the right.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply H or H**T from the Left
= 'R': apply H or H**T from the Right
TRANS
TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'T': apply H**T (Transpose)
DIRECT
DIRECT is CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV
STOREV is CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise
M
M is INTEGER
The number of rows of the matrix C.
N
N is INTEGER
The number of columns of the matrix C.
K
K is INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
V
V is DOUBLE PRECISION array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The matrix V. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
if STOREV = 'R', LDV >= K.
T
T is DOUBLE PRECISION array, dimension (LDT,K)
The triangular k by k matrix T in the representation of the
block reflector.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= K.
C
C is DOUBLE PRECISION array, dimension (LDC,N)
On entry, the m by n matrix C.
On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is DOUBLE PRECISION array, dimension (LDWORK,K)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).
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; 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 = ( 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 )
subroutine slarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( ldwork, * ) work, integer ldwork)¶
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Purpose:
SLARFB applies a real block reflector H or its transpose H**T to a
real m by n matrix C, from either the left or the right.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply H or H**T from the Left
= 'R': apply H or H**T from the Right
TRANS
TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'T': apply H**T (Transpose)
DIRECT
DIRECT is CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV
STOREV is CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise
M
M is INTEGER
The number of rows of the matrix C.
N
N is INTEGER
The number of columns of the matrix C.
K
K is INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
V
V is REAL array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The matrix V. See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
if STOREV = 'R', LDV >= K.
T
T is REAL array, dimension (LDT,K)
The triangular k by k matrix T in the representation of the
block reflector.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= K.
C
C is REAL array, dimension (LDC,N)
On entry, the m by n matrix C.
On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is REAL array, dimension (LDWORK,K)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).
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; 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 = ( 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 )
subroutine zlarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( ldwork, * ) work, integer ldwork)¶
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Purpose:
ZLARFB applies a complex block reflector H or its transpose H**H to a
complex M-by-N matrix C, from either the left or the right.
Parameters
SIDE
SIDE is CHARACTER*1
= 'L': apply H or H**H from the Left
= 'R': apply H or H**H from the Right
TRANS
TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H**H (Conjugate transpose)
DIRECT
DIRECT is CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV
STOREV is CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise
M
M is INTEGER
The number of rows of the matrix C.
N
N is INTEGER
The number of columns of the matrix C.
K
K is INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
V
V is COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
See Further Details.
LDV
LDV is INTEGER
The leading dimension of the array V.
If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
if STOREV = 'R', LDV >= K.
T
T is COMPLEX*16 array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= K.
C
C is COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is COMPLEX*16 array, dimension (LDWORK,K)
LDWORK
LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).
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; 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 = ( 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 )
Author¶
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