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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