Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

SYNOPSIS

       SUBROUTINE CLARFB( 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

           COMPLEX        C( LDC, * ), T( LDT, * ), V( LDV, * ), WORK( LDWORK, * )

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.

ARGUMENTS

        SIDE    (input) CHARACTER*1
                = 'L': apply H or H**H from the Left
                = 'R': apply H or H**H from the Right

        TRANS   (input) CHARACTER*1
                = 'N': apply H (No transpose)
                = 'C': apply H**H (Conjugate 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) 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     (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) COMPLEX 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) 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     (input) INTEGER
                The leading dimension of the array C. LDC >= max(1,M).

        WORK    (workspace) COMPLEX 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                            CLARFB(3lapack)