Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with  SIDE = 'L'
       SIDE = 'R' TRANS = 'N'

SYNOPSIS

       SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

           CHARACTER      SIDE, TRANS, VECT

           INTEGER        INFO, K, LDA, LDC, LWORK, M, N

           DOUBLE         PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

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).

ARGUMENTS

        VECT    (input) CHARACTER*1
                = 'Q': apply Q or Q**T;
                = 'P': apply P or P**T.

        SIDE    (input) 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   (input) CHARACTER*1
                = 'N':  No transpose, apply Q  or P;
                = 'T':  Transpose, apply Q**T or P**T.

        M       (input) INTEGER
                The number of rows of the matrix C. M >= 0.

        N       (input) INTEGER
                The number of columns of the matrix C. N >= 0.

        K       (input) 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       (input) 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     (input) 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     (input) 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       (input/output) 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     (input) INTEGER
                The leading dimension of the array C. LDC >= max(1,M).

        WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) 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    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value

 LAPACK routine (version 3.2)               April 2011                            DORMBR(3lapack)