Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - 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

**SYNOPSIS**

SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK ) IMPLICIT NONE CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), WORK( LDWORK, * )

**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.

**ARGUMENTS**

SIDE (input) CHARACTER*1 = 'L': apply H or H**T from the Left = 'R': apply H or H**T from the Right TRANS (input) CHARACTER*1 = 'N': apply H (No transpose) = 'T': apply H**T (Transpose) DIRECT (input) 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 (input) CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columnwise = 'R': Rowwise M (input) INTEGER The number of rows of the matrix C. N (input) INTEGER The number of columns of the matrix C. K (input) INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). V (input) 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 (input) 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 (input) DOUBLE PRECISION array, dimension (LDT,K) The triangular k by k matrix T in the representation of the block reflector. LDT (input) INTEGER The leading dimension of the array T. LDT >= K. C (input/output) 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 (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,K) LDWORK (input) INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M).

**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 ) LAPACK auxiliary routine (version 3.3.1) April 2011 DLARFB(3lapack)