sormbr (l)  Linux Manuals
sormbr: VECT = aqQaq, SORMBR overwrites the general real MbyN matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq
NAME
SORMBR  VECT = aqQaq, SORMBR overwrites the general real MbyN matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaqSYNOPSIS
 SUBROUTINE SORMBR(
 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
 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
PURPOSE
If VECT = aqQaq, SORMBR overwrites the general real MbyN matrix C withIf VECT = aqPaq, SORMBR 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 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 = 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 SGEBRD. If VECT = aqPaq, the number of rows in the original matrix reduced by SGEBRD. K >= 0.
 A (input) REAL 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 SGEBRD.
 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) 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 (input/output) REAL 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) REAL 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