SRC/sormbr.f(3)

NAME
SRC/sormbr.f

SYNOPSIS

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

Function/Subroutine Documentation

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

SORMBR

Purpose:

    !>
    !> If VECT = 'Q', SORMBR 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', SORMBR 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 SGEBRD 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 SGEBRD.
    !>          If VECT = 'P', the number of rows in the original
    !>          matrix reduced by SGEBRD.
    !>          K >= 0.
    !>

    A

    !>          A is REAL 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 SGEBRD.
    !>

    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 REAL 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 SGEBRD in the array argument TAUQ or TAUP.
    !>

    C

    !>          C is REAL 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 REAL 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 194 of file sormbr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.