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347 lines
9.4 KiB
347 lines
9.4 KiB
2 years ago
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*> \brief \b CTPMLQT
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CTPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
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* A, LDA, B, LDB, WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER SIDE, TRANS
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* INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
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* ..
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* .. Array Arguments ..
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* COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
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* $ T( LDT, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CTPMLQT applies a complex unitary matrix Q obtained from a
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*> "triangular-pentagonal" complex block reflector H to a general
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*> complex matrix C, which consists of two blocks A and B.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> = 'L': apply Q or Q**H from the Left;
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*> = 'R': apply Q or Q**H from the Right.
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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> = 'N': No transpose, apply Q;
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*> = 'C': Conjugate transpose, apply Q**H.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix B. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix B. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of elementary reflectors whose product defines
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*> the matrix Q.
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*> \endverbatim
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*>
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*> \param[in] L
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*> \verbatim
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*> L is INTEGER
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*> The order of the trapezoidal part of V.
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*> K >= L >= 0. See Further Details.
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*> \endverbatim
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*>
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*> \param[in] MB
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*> \verbatim
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*> MB is INTEGER
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*> The block size used for the storage of T. K >= MB >= 1.
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*> This must be the same value of MB used to generate T
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*> in CTPLQT.
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*> \endverbatim
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*>
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*> \param[in] V
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*> \verbatim
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*> V is COMPLEX array, dimension (LDV,K)
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*> The i-th row must contain the vector which defines the
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*> elementary reflector H(i), for i = 1,2,...,k, as returned by
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*> CTPLQT in B. See Further Details.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of the array V. LDV >= K.
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*> \endverbatim
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*>
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*> \param[in] T
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*> \verbatim
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*> T is COMPLEX array, dimension (LDT,K)
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*> The upper triangular factors of the block reflectors
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*> as returned by CTPLQT, stored as a MB-by-K matrix.
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*> \endverbatim
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*>
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*> \param[in] LDT
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*> \verbatim
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*> LDT is INTEGER
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*> The leading dimension of the array T. LDT >= MB.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is COMPLEX array, dimension
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*> (LDA,N) if SIDE = 'L' or
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*> (LDA,K) if SIDE = 'R'
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*> On entry, the K-by-N or M-by-K matrix A.
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*> On exit, A is overwritten by the corresponding block of
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*> Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A.
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*> If SIDE = 'L', LDA >= max(1,K);
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*> If SIDE = 'R', LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX array, dimension (LDB,N)
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*> On entry, the M-by-N matrix B.
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*> On exit, B is overwritten by the corresponding block of
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*> Q*C or Q**H*C or C*Q or C*Q**H. See Further Details.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B.
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*> LDB >= max(1,M).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array. The dimension of WORK is
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*> N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doubleOTHERcomputational
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The columns of the pentagonal matrix V contain the elementary reflectors
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*> H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
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*> trapezoidal block V2:
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*>
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*> V = [V1] [V2].
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*>
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*>
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*> The size of the trapezoidal block V2 is determined by the parameter L,
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*> where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L
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*> rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular;
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*> if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
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*>
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*> If SIDE = 'L': C = [A] where A is K-by-N, B is M-by-N and V is K-by-M.
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*> [B]
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*>
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*> If SIDE = 'R': C = [A B] where A is M-by-K, B is M-by-N and V is K-by-N.
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*>
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*> The complex unitary matrix Q is formed from V and T.
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*>
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*> If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
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*>
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*> If TRANS='C' and SIDE='L', C is on exit replaced with Q**H * C.
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*>
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*> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
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*>
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*> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE CTPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
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$ A, LDA, B, LDB, WORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE, TRANS
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INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
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* ..
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* .. Array Arguments ..
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COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
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$ T( LDT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* ..
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* .. Local Scalars ..
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LOGICAL LEFT, RIGHT, TRAN, NOTRAN
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INTEGER I, IB, NB, LB, KF, LDAQ
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, CTPRFB
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* .. Test the input arguments ..
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*
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INFO = 0
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LEFT = LSAME( SIDE, 'L' )
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RIGHT = LSAME( SIDE, 'R' )
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TRAN = LSAME( TRANS, 'C' )
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NOTRAN = LSAME( TRANS, 'N' )
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*
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IF ( LEFT ) THEN
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LDAQ = MAX( 1, K )
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ELSE IF ( RIGHT ) THEN
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LDAQ = MAX( 1, M )
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END IF
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IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
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INFO = -1
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ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
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INFO = -2
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ELSE IF( M.LT.0 ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( K.LT.0 ) THEN
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INFO = -5
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ELSE IF( L.LT.0 .OR. L.GT.K ) THEN
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INFO = -6
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ELSE IF( MB.LT.1 .OR. (MB.GT.K .AND. K.GT.0) ) THEN
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INFO = -7
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ELSE IF( LDV.LT.K ) THEN
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INFO = -9
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ELSE IF( LDT.LT.MB ) THEN
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INFO = -11
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ELSE IF( LDA.LT.LDAQ ) THEN
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INFO = -13
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ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
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INFO = -15
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CTPMLQT', -INFO )
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RETURN
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END IF
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*
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* .. Quick return if possible ..
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*
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IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) RETURN
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*
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IF( LEFT .AND. NOTRAN ) THEN
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*
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DO I = 1, K, MB
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IB = MIN( MB, K-I+1 )
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NB = MIN( M-L+I+IB-1, M )
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IF( I.GE.L ) THEN
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LB = 0
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ELSE
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LB = 0
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END IF
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CALL CTPRFB( 'L', 'C', 'F', 'R', NB, N, IB, LB,
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$ V( I, 1 ), LDV, T( 1, I ), LDT,
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$ A( I, 1 ), LDA, B, LDB, WORK, IB )
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END DO
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*
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ELSE IF( RIGHT .AND. TRAN ) THEN
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*
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DO I = 1, K, MB
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IB = MIN( MB, K-I+1 )
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NB = MIN( N-L+I+IB-1, N )
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IF( I.GE.L ) THEN
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LB = 0
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ELSE
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LB = NB-N+L-I+1
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END IF
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CALL CTPRFB( 'R', 'N', 'F', 'R', M, NB, IB, LB,
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$ V( I, 1 ), LDV, T( 1, I ), LDT,
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$ A( 1, I ), LDA, B, LDB, WORK, M )
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END DO
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*
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ELSE IF( LEFT .AND. TRAN ) THEN
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*
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KF = ((K-1)/MB)*MB+1
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DO I = KF, 1, -MB
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IB = MIN( MB, K-I+1 )
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NB = MIN( M-L+I+IB-1, M )
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IF( I.GE.L ) THEN
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LB = 0
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ELSE
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LB = 0
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END IF
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CALL CTPRFB( 'L', 'N', 'F', 'R', NB, N, IB, LB,
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$ V( I, 1 ), LDV, T( 1, I ), LDT,
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$ A( I, 1 ), LDA, B, LDB, WORK, IB )
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END DO
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*
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ELSE IF( RIGHT .AND. NOTRAN ) THEN
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*
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KF = ((K-1)/MB)*MB+1
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DO I = KF, 1, -MB
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IB = MIN( MB, K-I+1 )
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NB = MIN( N-L+I+IB-1, N )
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IF( I.GE.L ) THEN
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LB = 0
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ELSE
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LB = NB-N+L-I+1
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END IF
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CALL CTPRFB( 'R', 'C', 'F', 'R', M, NB, IB, LB,
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$ V( I, 1 ), LDV, T( 1, I ), LDT,
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$ A( 1, I ), LDA, B, LDB, WORK, M )
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END DO
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*
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END IF
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*
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RETURN
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*
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* End of CTPMLQT
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*
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END
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