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

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( * )

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).

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 (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