NAME

       ztprfb.f -

SYNOPSIS

   Functions/Subroutines
       subroutine ztprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B,
           LDB, WORK, LDWORK)
           ZTPRFB applies a real or complex 'triangular-pentagonal' blocked reflector to a real
           or complex matrix, which is composed of two blocks.

Function/Subroutine Documentation

   subroutine ztprfb (character SIDE, character TRANS, character DIRECT, character STOREV,
       integer M, integer N, integer K, integer L, complex*16, dimension( ldv, * ) V, integer
       LDV, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension( lda, * ) A,
       integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension(
       ldwork, * ) WORK, integer LDWORK)
       ZTPRFB applies a real or complex 'triangular-pentagonal' blocked reflector to a real or
       complex matrix, which is composed of two blocks.

       Purpose:

            ZTPRFB applies a complex "triangular-pentagonal" block reflector H or its
            conjugate transpose H**H to a complex matrix C, which is composed of two
            blocks A and B, either from the left or 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': Columns
                     = 'R': Rows

           M

                     M is INTEGER
                     The number of rows of the matrix B.
                     M >= 0.

           N

                     N is INTEGER
                     The number of columns of the matrix B.
                     N >= 0.

           K

                     K is INTEGER
                     The order of the matrix T, i.e. the number of elementary
                     reflectors whose product defines the block reflector.
                     K >= 0.

           L

                     L is INTEGER
                     The order of the trapezoidal part of V.
                     K >= L >= 0.  See Further Details.

           V

                     V is COMPLEX*16 array, dimension
                                           (LDV,K) if STOREV = 'C'
                                           (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                           (LDV,N) if STOREV = 'R' and SIDE = 'R'
                     The pentagonal matrix V, which contains the elementary reflectors
                     H(1), H(2), ..., H(K).  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*16 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.

           A

                     A is COMPLEX*16 array, dimension
                     (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'
                     On entry, the K-by-N or M-by-K matrix A.
                     On exit, A is overwritten by the corresponding block of
                     H*C or H**H*C or C*H or C*H**H.  See Futher Details.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.
                     If SIDE = 'L', LDC >= max(1,K);
                     If SIDE = 'R', LDC >= max(1,M).

           B

                     B is COMPLEX*16 array, dimension (LDB,N)
                     On entry, the M-by-N matrix B.
                     On exit, B is overwritten by the corresponding block of
                     H*C or H**H*C or C*H or C*H**H.  See Further Details.

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B.
                     LDB >= max(1,M).

           WORK

                     WORK is COMPLEX*16 array, dimension
                     (LDWORK,N) if SIDE = 'L',
                     (LDWORK,K) if SIDE = 'R'.

           LDWORK

                     LDWORK is INTEGER
                     The leading dimension of the array WORK.
                     If SIDE = 'L', LDWORK >= K;
                     if SIDE = 'R', LDWORK >= M.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Further Details:

             The matrix C is a composite matrix formed from blocks A and B.
             The block B is of size M-by-N; if SIDE = 'R', A is of size M-by-K,
             and if SIDE = 'L', A is of size K-by-N.

             If SIDE = 'R' and DIRECT = 'F', C = [A B].

             If SIDE = 'L' and DIRECT = 'F', C = [A]
                                                 [B].

             If SIDE = 'R' and DIRECT = 'B', C = [B A].

             If SIDE = 'L' and DIRECT = 'B', C = [B]
                                                 [A].

             The pentagonal matrix V is composed of a rectangular block V1 and a
             trapezoidal block V2.  The size of the trapezoidal block is determined by
             the parameter L, where 0<=L<=K.  If L=K, the V2 block of V is triangular;
             if L=0, there is no trapezoidal block, thus V = V1 is rectangular.

             If DIRECT = 'F' and STOREV = 'C':  V = [V1]
                                                    [V2]
                - V2 is upper trapezoidal (first L rows of K-by-K upper triangular)

             If DIRECT = 'F' and STOREV = 'R':  V = [V1 V2]

                - V2 is lower trapezoidal (first L columns of K-by-K lower triangular)

             If DIRECT = 'B' and STOREV = 'C':  V = [V2]
                                                    [V1]
                - V2 is lower trapezoidal (last L rows of K-by-K lower triangular)

             If DIRECT = 'B' and STOREV = 'R':  V = [V2 V1]

                - V2 is upper trapezoidal (last L columns of K-by-K upper triangular)

             If STOREV = 'C' and SIDE = 'L', V is M-by-K with V2 L-by-K.

             If STOREV = 'C' and SIDE = 'R', V is N-by-K with V2 L-by-K.

             If STOREV = 'R' and SIDE = 'L', V is K-by-M with V2 K-by-L.

             If STOREV = 'R' and SIDE = 'R', V is K-by-N with V2 K-by-L.

Author

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