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.

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).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

  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 )