![]() |
![]()
| ![]() |
![]()
NAMEzlarfb.f -SYNOPSISFunctions/Subroutinessubroutine zlarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK) Function/Subroutine Documentationsubroutine zlarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( ldt, * )T, integerLDT, complex*16, dimension( ldc, * )C, integerLDC, complex*16, dimension( ldwork, * )WORK, integerLDWORK)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. SIDE
Author:
SIDE is CHARACTER*1 = 'L': apply H or H**H from the Left = 'R': apply H or H**H from the RightTRANS 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': RowwiseM 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).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). Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
June 2013
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 ) AuthorGenerated automatically by Doxygen for LAPACK from the source code.
|