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 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 )

Author

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