LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
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Go to the source code of this file.
Functions/Subroutines | |
subroutine | sormbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO) |
SORMBR |
subroutine sormbr | ( | character | VECT, |
character | SIDE, | ||
character | TRANS, | ||
integer | M, | ||
integer | N, | ||
integer | K, | ||
real, dimension( lda, * ) | A, | ||
integer | LDA, | ||
real, dimension( * ) | TAU, | ||
real, dimension( ldc, * ) | C, | ||
integer | LDC, | ||
real, dimension( * ) | WORK, | ||
integer | LWORK, | ||
integer | INFO | ||
) |
SORMBR
Download SORMBR + dependencies [TGZ] [ZIP] [TXT]If VECT = 'Q', SORMBR 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', SORMBR 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 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 = '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).
[in] | VECT | VECT is CHARACTER*1 = 'Q': apply Q or Q**T; = 'P': apply P or P**T. |
[in] | SIDE | SIDE is 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. |
[in] | TRANS | TRANS is CHARACTER*1 = 'N': No transpose, apply Q or P; = 'T': Transpose, apply Q**T or P**T. |
[in] | M | M is INTEGER The number of rows of the matrix C. M >= 0. |
[in] | N | N is INTEGER The number of columns of the matrix C. N >= 0. |
[in] | K | K is INTEGER If VECT = 'Q', the number of columns in the original matrix reduced by SGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by SGEBRD. K >= 0. |
[in] | A | A is REAL 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 SGEBRD. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)). |
[in] | TAU | TAU is 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. |
[in,out] | C | C is REAL 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. |
[in] | LDC | LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). |
[out] | WORK | WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
[in] | LWORK | LWORK is 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. |
[out] | INFO | INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value |
Definition at line 196 of file sormbr.f.