SRC/stprfb.f(3)            Library Functions Manual            SRC/stprfb.f(3)

NAME
       SRC/stprfb.f

SYNOPSIS
   Functions/Subroutines
       subroutine stprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t,
           ldt, a, lda, b, ldb, work, ldwork)
           STPRFB applies a real 'triangular-pentagonal' block reflector to a
           real matrix, which is composed of two blocks.

Function/Subroutine Documentation
   subroutine stprfb (character side, character trans, character direct,
       character storev, integer m, integer n, integer k, integer l, real,
       dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t,
       integer ldt, real, dimension( lda, * ) a, integer lda, real, dimension(
       ldb, * ) b, integer ldb, real, dimension( ldwork, * ) work, integer
       ldwork)
       STPRFB applies a real 'triangular-pentagonal' block reflector to a real
       matrix, which is composed of two blocks.

       Purpose:


            STPRFB applies a real 'triangular-pentagonal' block reflector H or its
            transpose H**T to a real 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**T from the Left
                     = 'R': apply H or H**T from the Right

           TRANS

                     TRANS is CHARACTER*1
                     = 'N': apply H (No transpose)
                     = 'T': apply H**T (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 REAL 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 REAL 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 REAL 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**T*C or C*H or C*H**T.  See Further Details.

           LDA

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

           B

                     B is REAL 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**T*C or C*H or C*H**T.  See Further Details.

           LDB

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

           WORK

                     WORK is REAL 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.

       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.

       Definition at line 249 of file stprfb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/stprfb.f(3)