SRC/dtprfb.f(3)

NAME
SRC/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 applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

Function/Subroutine Documentation

  subroutine dtprfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldwork, * ) work, integer ldwork)

DTPRFB applies a real 'triangular-pentagonal' block reflector to a real matrix, which is composed of two blocks.

Purpose:

    !>
    !> DTPRFB 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 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 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 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.

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 dtprfb.f.

Author

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