* Definition:
* ===========
*
* SUBROUTINE CTPMLQT( 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 ..
* COMPLEX V( LDV, * ), A( LDA, * ), B( LDB, * ),
* $ T( LDT, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTPMLQT applies a complex orthogonal matrix Q obtained from a
*> "triangular-pentagonal" complex block reflector H to a general
*> complex 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**H from the Left;
*> = 'R': apply Q or Q**H from the Right.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> = 'N': No transpose, apply Q;
*> = 'C': Transpose, apply Q**H.
*> \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 DTPLQT.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is COMPLEX array, dimension (LDA,K)
*> The i-th row must contain the vector which defines the
*> elementary reflector H(i), for i = 1,2,...,k, as returned by
*> DTPLQT 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 COMPLEX array, dimension (LDT,K)
*> The upper triangular factors of the block reflectors
*> as returned by DTPLQT, 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 COMPLEX 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**H*C or C*Q or C*Q**H. 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 COMPLEX 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**H*C or C*Q or C*Q**H. 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 COMPLEX 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.
*
*> \date June 2017
*
*> \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='C' and SIDE='L', C is on exit replaced with Q**H * C.
*>
*> If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
*>
*> If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE CTPMLQT( SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT,
$ A, LDA, B, LDB, WORK, INFO )
*
* -- LAPACK computational routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS
INTEGER INFO, K, LDV, LDA, LDB, M, N, L, MB, LDT
* ..
* .. Array Arguments ..
COMPLEX 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, CTPRFB
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* .. Test the input arguments ..
*
INFO = 0
LEFT = LSAME( SIDE, 'L' )
RIGHT = LSAME( SIDE, 'R' )
TRAN = LSAME( TRANS, 'C' )
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( 'CTPMLQT', -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 CTPRFB( 'L', 'C', '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 CTPRFB( '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 CTPRFB( '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 CTPRFB( 'R', 'C', '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 CTPMLQT
*
END