SRC/dormbr.f(3)

NAME
SRC/dormbr.f

SYNOPSIS

  Functions/Subroutines
subroutine dormbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMBR

Function/Subroutine Documentation

  subroutine dormbr (character vect, character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DORMBR

Purpose:

    !>
    !> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
    !> with
    !>                 SIDE = 'L'     SIDE = 'R'
    !> TRANS = 'N':      Q * C          C * Q
    !> TRANS = 'T':      Q**T * C       C * Q**T
    !>
    !> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
    !> with
    !>                 SIDE = 'L'     SIDE = 'R'
    !> TRANS = 'N':      P * C          C * P
    !> TRANS = 'T':      P**T * C       C * P**T
    !>
    !> Here Q and P**T are the orthogonal matrices determined by DGEBRD when
    !> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
    !> P**T are defined as products of elementary reflectors H(i) and G(i)
    !> respectively.
    !>
    !> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
    !> order of the orthogonal matrix Q or P**T that is applied.
    !>
    !> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
    !> if nq >= k, Q = H(1) H(2) . . . H(k);
    !> if nq < k, Q = H(1) H(2) . . . H(nq-1).
    !>
    !> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
    !> if k < nq, P = G(1) G(2) . . . G(k);
    !> if k >= nq, P = G(1) G(2) . . . G(nq-1).
    !>

Parameters
    VECT

    !>          VECT is CHARACTER*1
    !>          = 'Q': apply Q or Q**T;
    !>          = 'P': apply P or P**T.
    !>

    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q, Q**T, P or P**T from the Left;
    !>          = 'R': apply Q, Q**T, P or P**T from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q  or P;
    !>          = 'T':  Transpose, apply Q**T or P**T.
    !>

    M

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

    N

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

    K

    !>          K is INTEGER
    !>          If VECT = 'Q', the number of columns in the original
    !>          matrix reduced by DGEBRD.
    !>          If VECT = 'P', the number of rows in the original
    !>          matrix reduced by DGEBRD.
    !>          K >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension
    !>                                (LDA,min(nq,K)) if VECT = 'Q'
    !>                                (LDA,nq)        if VECT = 'P'
    !>          The vectors which define the elementary reflectors H(i) and
    !>          G(i), whose products determine the matrices Q and P, as
    !>          returned by DGEBRD.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.
    !>          If VECT = 'Q', LDA >= max(1,nq);
    !>          if VECT = 'P', LDA >= max(1,min(nq,K)).
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (min(nq,K))
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i) or G(i) which determines Q or P, as returned
    !>          by DGEBRD in the array argument TAUQ or TAUP.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
    !>          or P*C or P**T*C or C*P or C*P**T.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If SIDE = 'L', LWORK >= max(1,N);
    !>          if SIDE = 'R', LWORK >= max(1,M).
    !>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
    !>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
    !>          blocksize.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 193 of file dormbr.f.

Author

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