.TH SLARFB 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME SLARFB - a real block reflector H or its transpose H\(aq to a real m by n matrix C, from either the left or the right .SH SYNOPSIS .TP 19 SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK ) .TP 19 .ti +4 CHARACTER DIRECT, SIDE, STOREV, TRANS .TP 19 .ti +4 INTEGER K, LDC, LDT, LDV, LDWORK, M, N .TP 19 .ti +4 REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), WORK( LDWORK, * ) .SH PURPOSE SLARFB applies a real block reflector H or its transpose H\(aq to a real m by n matrix C, from either the left or the right. .SH ARGUMENTS .TP 8 SIDE (input) CHARACTER*1 = \(aqL\(aq: apply H or H\(aq from the Left .br = \(aqR\(aq: apply H or H\(aq from the Right .TP 8 TRANS (input) CHARACTER*1 .br = \(aqN\(aq: apply H (No transpose) .br = \(aqT\(aq: apply H\(aq (Transpose) .TP 8 DIRECT (input) CHARACTER*1 Indicates how H is formed from a product of elementary reflectors = \(aqF\(aq: H = H(1) H(2) . . . H(k) (Forward) .br = \(aqB\(aq: H = H(k) . . . H(2) H(1) (Backward) .TP 8 STOREV (input) CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: .br = \(aqC\(aq: Columnwise .br = \(aqR\(aq: Rowwise .TP 8 M (input) INTEGER The number of rows of the matrix C. .TP 8 N (input) INTEGER The number of columns of the matrix C. .TP 8 K (input) INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). .TP 8 V (input) REAL array, dimension (LDV,K) if STOREV = \(aqC\(aq (LDV,M) if STOREV = \(aqR\(aq and SIDE = \(aqL\(aq (LDV,N) if STOREV = \(aqR\(aq and SIDE = \(aqR\(aq The matrix V. See further details. .TP 8 LDV (input) INTEGER The leading dimension of the array V. If STOREV = \(aqC\(aq and SIDE = \(aqL\(aq, LDV >= max(1,M); if STOREV = \(aqC\(aq and SIDE = \(aqR\(aq, LDV >= max(1,N); if STOREV = \(aqR\(aq, LDV >= K. .TP 8 T (input) REAL array, dimension (LDT,K) The triangular k by k matrix T in the representation of the block reflector. .TP 8 LDT (input) INTEGER The leading dimension of the array T. LDT >= K. .TP 8 C (input/output) REAL array, dimension (LDC,N) On entry, the m by n matrix C. On exit, C is overwritten by H*C or H\(aq*C or C*H or C*H\(aq. .TP 8 LDC (input) INTEGER The leading dimension of the array C. LDA >= max(1,M). .TP 8 WORK (workspace) REAL array, dimension (LDWORK,K) .TP 8 LDWORK (input) INTEGER The leading dimension of the array WORK. If SIDE = \(aqL\(aq, LDWORK >= max(1,N); if SIDE = \(aqR\(aq, LDWORK >= max(1,M).