DORMBR(3f)

NAME
DORMBR - = '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