*> \brief \b STPMQRT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download STPMQRT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE STPMQRT( SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, * A, LDA, B, LDB, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDV, LDA, LDB, M, N, L, NB, LDT * .. * .. Array Arguments .. * REAL V( LDV, * ), A( LDA, * ), B( LDB, * ), T( LDT, * ), * \$ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STPMQRT 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] NB *> \verbatim *> NB is INTEGER *> The block size used for the storage of T. K >= NB >= 1. *> This must be the same value of NB used to generate T *> in CTPQRT. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is REAL array, dimension (LDV,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> CTPQRT in B. See Further Details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. *> If SIDE = 'L', LDV >= max(1,M); *> if SIDE = 'R', LDV >= max(1,N). *> \endverbatim *> *> \param[in] T *> \verbatim *> T is REAL array, dimension (LDT,K) *> The upper triangular factors of the block reflectors *> as returned by CTPQRT, stored as a NB-by-K matrix. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= NB. *> \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', LDC >= max(1,K); *> If SIDE = 'R', LDC >= 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*NB if SIDE = 'L', or M*NB 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 realOTHERcomputational * *> \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 upper trapezoidal, consisting of the first L *> rows of a K-by-K upper triangular matrix. If L=K, V2 is upper 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 M-by-K. *> [B] *> *> If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is N-by-K. *> *> 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 STPMQRT( SIDE, TRANS, M, N, K, L, NB, 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, NB, LDT * .. * .. Array Arguments .. REAL V( LDV, * ), A( LDA, * ), B( LDB, * ), T( LDT, * ), \$ WORK( * ) * .. * * ===================================================================== * * .. * .. Local Scalars .. LOGICAL LEFT, RIGHT, TRAN, NOTRAN INTEGER I, IB, MB, LB, KF, LDAQ, LDVQ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL STPRFB, XERBLA * .. * .. 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 LDVQ = MAX( 1, M ) LDAQ = MAX( 1, K ) ELSE IF ( RIGHT ) THEN LDVQ = MAX( 1, N ) 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( NB.LT.1 .OR. (NB.GT.K .AND. K.GT.0) ) THEN INFO = -7 ELSE IF( LDV.LT.LDVQ ) THEN INFO = -9 ELSE IF( LDT.LT.NB ) 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( 'STPMQRT', -INFO ) RETURN END IF * * .. Quick return if possible .. * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN * IF( LEFT .AND. TRAN ) THEN * DO I = 1, K, NB IB = MIN( NB, K-I+1 ) MB = MIN( M-L+I+IB-1, M ) IF( I.GE.L ) THEN LB = 0 ELSE LB = MB-M+L-I+1 END IF CALL STPRFB( 'L', 'T', 'F', 'C', MB, N, IB, LB, \$ V( 1, I ), LDV, T( 1, I ), LDT, \$ A( I, 1 ), LDA, B, LDB, WORK, IB ) END DO * ELSE IF( RIGHT .AND. NOTRAN ) THEN * DO I = 1, K, NB IB = MIN( NB, K-I+1 ) MB = MIN( N-L+I+IB-1, N ) IF( I.GE.L ) THEN LB = 0 ELSE LB = MB-N+L-I+1 END IF CALL STPRFB( 'R', 'N', 'F', 'C', M, MB, IB, LB, \$ V( 1, I ), LDV, T( 1, I ), LDT, \$ A( 1, I ), LDA, B, LDB, WORK, M ) END DO * ELSE IF( LEFT .AND. NOTRAN ) THEN * KF = ((K-1)/NB)*NB+1 DO I = KF, 1, -NB IB = MIN( NB, K-I+1 ) MB = MIN( M-L+I+IB-1, M ) IF( I.GE.L ) THEN LB = 0 ELSE LB = MB-M+L-I+1 END IF CALL STPRFB( 'L', 'N', 'F', 'C', MB, N, IB, LB, \$ V( 1, I ), LDV, T( 1, I ), LDT, \$ A( I, 1 ), LDA, B, LDB, WORK, IB ) END DO * ELSE IF( RIGHT .AND. TRAN ) THEN * KF = ((K-1)/NB)*NB+1 DO I = KF, 1, -NB IB = MIN( NB, K-I+1 ) MB = MIN( N-L+I+IB-1, N ) IF( I.GE.L ) THEN LB = 0 ELSE LB = MB-N+L-I+1 END IF CALL STPRFB( 'R', 'T', 'F', 'C', M, MB, IB, LB, \$ V( 1, I ), LDV, T( 1, I ), LDT, \$ A( 1, I ), LDA, B, LDB, WORK, M ) END DO * END IF * RETURN * * End of STPMQRT * END