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"blockreflectortoarealmatrix,whichiscomposedoftwoblocks.

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  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
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LAPACK                          Version 3.12.0                 SRC/stprfb.f(3)