clarfb (3)  Linux Man Pages
NAME
clarfb.f 
SYNOPSIS
Functions/Subroutines
subroutine clarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugatetranspose to a general rectangular matrix.
Function/Subroutine Documentation
subroutine clarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldt, * )T, integerLDT, complex, dimension( ldc, * )C, integerLDC, complex, dimension( ldwork, * )WORK, integerLDWORK)
CLARFB applies a block reflector or its conjugatetranspose to a general rectangular matrix.
Purpose:

CLARFB applies a complex block reflector H or its transpose H**H to a complex MbyN 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
TRANSTRANS is CHARACTER*1 = 'N': apply H (No transpose) = 'C': apply H**H (Conjugate transpose)
DIRECTDIRECT 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)
STOREVSTOREV is CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columnwise = 'R': Rowwise
MM is INTEGER The number of rows of the matrix C.
NN is INTEGER The number of columns of the matrix C.
KK is INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
VV 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.
LDVLDV 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.
TT is COMPLEX array, dimension (LDT,K) The triangular KbyK matrix T in the representation of the block reflector.
LDTLDT is INTEGER The leading dimension of the array T. LDT >= K.
CC is COMPLEX array, dimension (LDC,N) On entry, the MbyN matrix C. On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
LDCLDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
WORKWORK is COMPLEX array, dimension (LDWORK,K)
LDWORKLDWORK 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.
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 )
Definition at line 195 of file clarfb.f.
Author
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