*> \brief \b STPMLQT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download STPMLQT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE STPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, * A, LDA, B, LDB, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT * .. * .. Array Arguments .. * REAL V( LDV, * ), A( LDA, * ), B( LDB, * ), * \$ T( LDT, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STPMLQT applies a real orthogonal matrix Q obtained from a *> "triangular-pentagonal" real block reflector H to a general *> real matrix C, which consists of two blocks A and B. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left; *> = 'R': apply Q or Q**T from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'T': Transpose, apply Q**T. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix B. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix B. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> \endverbatim *> *> \param[in] L *> \verbatim *> L is INTEGER *> The order of the trapezoidal part of V. *> K >= L >= 0. See Further Details. *> \endverbatim *> *> \param[in] MB *> \verbatim *> MB is INTEGER *> The block size used for the storage of T. K >= MB >= 1. *> This must be the same value of MB used to generate T *> in STPLQT. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is REAL array, dimension (LDV,K) *> The i-th row must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> STPLQT in B. See Further Details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. LDV >= K. *> \endverbatim *> *> \param[in] T *> \verbatim *> T is REAL array, dimension (LDT,K) *> The upper triangular factors of the block reflectors *> as returned by STPLQT, stored as a MB-by-K matrix. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= MB. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is REAL array, dimension *> (LDA,N) if SIDE = 'L' or *> (LDA,K) if SIDE = 'R' *> On entry, the K-by-N or M-by-K matrix A. *> On exit, A is overwritten by the corresponding block of *> Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,K); *> If SIDE = 'R', LDA >= max(1,M). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is REAL array, dimension (LDB,N) *> On entry, the M-by-N matrix B. *> On exit, B is overwritten by the corresponding block of *> Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. *> LDB >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array. The dimension of WORK is *> N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. *> \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 doubleOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The columns of the pentagonal matrix V contain the elementary reflectors *> H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a *> trapezoidal block V2: *> *> V = [V1] [V2]. *> *> *> The size of the trapezoidal block V2 is determined by the parameter L, *> where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L *> rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; *> if L=0, there is no trapezoidal block, hence V = V1 is rectangular. *> *> If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M. *> [B] *> *> If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N. *> *> The real orthogonal matrix Q is formed from V and T. *> *> If TRANS='N' and SIDE='L', C is on exit replaced with Q * C. *> *> If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C. *> *> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q. *> *> If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T. *> \endverbatim *> * ===================================================================== SUBROUTINE STPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, \$ A, LDA, B, LDB, WORK, 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 INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT * .. * .. Array Arguments .. REAL V( LDV, * ), A( LDA, * ), B( LDB, * ), \$ T( LDT, * ), WORK( * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. LOGICAL LEFT, RIGHT, TRAN, NOTRAN INTEGER I, IB, NB, LB, KF, LDAQ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, STPRFB * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * .. Test the input arguments .. * INFO = 0 LEFT = LSAME( SIDE, 'L' ) RIGHT = LSAME( SIDE, 'R' ) TRAN = LSAME( TRANS, 'T' ) NOTRAN = LSAME( TRANS, 'N' ) * IF ( LEFT ) THEN LDAQ = MAX( 1, K ) ELSE IF ( RIGHT ) THEN LDAQ = MAX( 1, M ) END IF IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN INFO = -1 ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 ) THEN INFO = -5 ELSE IF( L.LT.0 .OR. L.GT.K ) THEN INFO = -6 ELSE IF( MB.LT.1 .OR. (MB.GT.K .AND. K.GT.0) ) THEN INFO = -7 ELSE IF( LDV.LT.K ) THEN INFO = -9 ELSE IF( LDT.LT.MB ) THEN INFO = -11 ELSE IF( LDA.LT.LDAQ ) THEN INFO = -13 ELSE IF( LDB.LT.MAX( 1, M ) ) THEN INFO = -15 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'STPMLQT', -INFO ) RETURN END IF * * .. Quick return if possible .. * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN * IF( LEFT .AND. NOTRAN ) THEN * DO I = 1, K, MB IB = MIN( MB, K-I+1 ) NB = MIN( M-L+I+IB-1, M ) IF( I.GE.L ) THEN LB = 0 ELSE LB = 0 END IF CALL STPRFB( 'L', 'T', 'F', 'R', NB, N, IB, LB, \$ V( I, 1 ), LDV, T( 1, I ), LDT, \$ A( I, 1 ), LDA, B, LDB, WORK, IB ) END DO * ELSE IF( RIGHT .AND. TRAN ) THEN * DO I = 1, K, MB IB = MIN( MB, K-I+1 ) NB = MIN( N-L+I+IB-1, N ) IF( I.GE.L ) THEN LB = 0 ELSE LB = NB-N+L-I+1 END IF CALL STPRFB( 'R', 'N', 'F', 'R', M, NB, IB, LB, \$ V( I, 1 ), LDV, T( 1, I ), LDT, \$ A( 1, I ), LDA, B, LDB, WORK, M ) END DO * ELSE IF( LEFT .AND. TRAN ) THEN * KF = ((K-1)/MB)*MB+1 DO I = KF, 1, -MB IB = MIN( MB, K-I+1 ) NB = MIN( M-L+I+IB-1, M ) IF( I.GE.L ) THEN LB = 0 ELSE LB = 0 END IF CALL STPRFB( 'L', 'N', 'F', 'R', NB, N, IB, LB, \$ V( I, 1 ), LDV, T( 1, I ), LDT, \$ A( I, 1 ), LDA, B, LDB, WORK, IB ) END DO * ELSE IF( RIGHT .AND. NOTRAN ) THEN * KF = ((K-1)/MB)*MB+1 DO I = KF, 1, -MB IB = MIN( MB, K-I+1 ) NB = MIN( N-L+I+IB-1, N ) IF( I.GE.L ) THEN LB = 0 ELSE LB = NB-N+L-I+1 END IF CALL STPRFB( 'R', 'T', 'F', 'R', M, NB, IB, LB, \$ V( I, 1 ), LDV, T( 1, I ), LDT, \$ A( 1, I ), LDA, B, LDB, WORK, M ) END DO * END IF * RETURN * * End of STPMLQT * END