slarfb.f - Man Page
SRC/slarfb.f
Synopsis
Functions/Subroutines
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.
Function/Subroutine Documentation
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 )
Definition at line 195 of file slarfb.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Referenced By
The man page slarfb(3) is an alias of slarfb.f(3).
Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK