*> \brief \b SORMBR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SORMBR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, * LDC, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS, VECT * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * REAL A( LDA, * ), C( LDC, * ), TAU( * ), * \$ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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). *> \endverbatim * * Arguments: * ========== * *> \param[in] VECT *> \verbatim *> VECT is CHARACTER*1 *> = 'Q': apply Q or Q**T; *> = 'P': apply P or P**T. *> \endverbatim *> *> \param[in] SIDE *> \verbatim *> 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. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q or P; *> = 'T': Transpose, apply Q**T or P**T. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> 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. *> \endverbatim *> *> \param[in] A *> \verbatim *> 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. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> 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)). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> 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. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> 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. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> 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. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup realOTHERcomputational * * ===================================================================== SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, \$ LDC, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, VECT INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), C( LDC, * ), TAU( * ), \$ WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL ILAENV, LSAME * .. * .. External Subroutines .. EXTERNAL SORMLQ, SORMQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 APPLYQ = LSAME( VECT, 'Q' ) LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q or P and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = MAX( 1, N ) ELSE NQ = N NW = MAX( 1, M ) END IF IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( K.LT.0 ) THEN INFO = -6 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. \$ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) \$ THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN IF( APPLYQ ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M-1, N, M-1, \$ -1 ) ELSE NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, N-1, N-1, \$ -1 ) END IF ELSE IF( LEFT ) THEN NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M-1, N, M-1, \$ -1 ) ELSE NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M, N-1, N-1, \$ -1 ) END IF END IF LWKOPT = NW*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SORMBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * WORK( 1 ) = 1 IF( M.EQ.0 .OR. N.EQ.0 ) \$ RETURN * IF( APPLYQ ) THEN * * Apply Q * IF( NQ.GE.K ) THEN * * Q was determined by a call to SGEBRD with nq >= k * CALL SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, \$ WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * Q was determined by a call to SGEBRD with nq < k * IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL SORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, \$ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF ELSE * * Apply P * IF( NOTRAN ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF IF( NQ.GT.K ) THEN * * P was determined by a call to SGEBRD with nq > k * CALL SORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, \$ WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * P was determined by a call to SGEBRD with nq <= k * IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL SORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, \$ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of SORMBR * END