dtprfb.f(3)

NAME
dtprfb.f -

SYNOPSIS

  Functions/Subroutines
subroutine DTPRFB (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
DTPRFB

Function/Subroutine Documentation

  subroutine DTPRFB (CHARACTERSIDE, CHARACTERTRANS, CHARACTERDIRECT, CHARACTERSTOREV, INTEGERM, INTEGERN, INTEGERK, INTEGERL, DOUBLE PRECISION, dimension( ldv, * )V, INTEGERLDV, DOUBLE PRECISION, dimension( ldt, * )T, INTEGERLDT, DOUBLE PRECISION, dimension( lda, * )A, INTEGERLDA, DOUBLE PRECISION, dimension( ldb, * )B, INTEGERLDB, DOUBLE PRECISION, dimension( ldwork, * )WORK, INTEGERLDWORK)

DTPRFB

Purpose:

     DTPRFB 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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:
    November 2011

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 251 of file dtprfb.f'.

Author

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