dormbr (l)  Linux Manuals
dormbr: VECT = aqQaq, DORMBR overwrites the general real MbyN matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq
NAME
DORMBR  VECT = aqQaq, DORMBR overwrites the general real MbyN matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaqSYNOPSIS
 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 = aqQaq, DORMBR overwrites the general real MbyN matrix C withIf VECT = aqPaq, DORMBR overwrites the general real MbyN matrix C with
TRANS = aqNaq: P * C C * P
TRANS = aqTaq: 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 = aqLaq and nq = n if SIDE = aqRaq. Thus nq is the order of the orthogonal matrix Q or P**T that is applied. If VECT = aqQaq, A is assumed to have been an NQbyK matrix: if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq1).
If VECT = aqPaq, A is assumed to have been a KbyNQ matrix: if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq1).
ARGUMENTS
 VECT (input) CHARACTER*1

= aqQaq: apply Q or Q**T;
= aqPaq: apply P or P**T.  SIDE (input) CHARACTER*1

= aqLaq: apply Q, Q**T, P or P**T from the Left;
= aqRaq: apply Q, Q**T, P or P**T from the Right.  TRANS (input) CHARACTER*1

= aqNaq: No transpose, apply Q or P;
= aqTaq: 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 = aqQaq, the number of columns in the original matrix reduced by DGEBRD. If VECT = aqPaq, 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 = aqQaq (LDA,nq) if VECT = aqPaq 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 = aqQaq, LDA >= max(1,nq); if VECT = aqPaq, 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 MbyN 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 = aqLaq, LWORK >= max(1,N); if SIDE = aqRaq, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = aqLaq, and LWORK >= M*NB if SIDE = aqRaq, 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 ith argument had an illegal value