# clarfb.f - Man Page

## 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 conjugate-transpose to a general rectangular matrix.

## Function/Subroutine Documentation

### subroutine clarfb (character SIDE, character TRANS, character DIRECT, character STOREV, integer M, integer N, integer K, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( ldwork, * ) WORK, integer LDWORK)

**CLARFB** applies a block reflector or its conjugate-transpose to a general rectangular matrix.

**Purpose:**

CLARFB 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.

**Parameters:***SIDE*SIDE is CHARACTER*1 = 'L': apply H or H**H from the Left = 'R': apply H or H**H from the Right

*TRANS*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': 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).

*V*V 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.

*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 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 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 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.

**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 197 of file clarfb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clarfb(3) is an alias of clarfb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK