*> \brief \b CUPMTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CUPMTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS, UPLO * INTEGER INFO, LDC, M, N * .. * .. Array Arguments .. * COMPLEX AP( * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CUPMTR overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix of order nq, with nq = m if *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of *> nq-1 elementary reflectors, as returned by CHPTRD using packed *> storage: *> *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). *> \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] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangular packed storage used in previous *> call to CHPTRD; *> = 'L': Lower triangular packed storage used in previous *> call to CHPTRD. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'C': Conjugate transpose, apply Q**H. *> \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] AP *> \verbatim *> AP is COMPLEX array, dimension *> (M*(M+1)/2) if SIDE = 'L' *> (N*(N+1)/2) if SIDE = 'R' *> The vectors which define the elementary reflectors, as *> returned by CHPTRD. AP is modified by the routine but *> restored on exit. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX array, dimension (M-1) if SIDE = 'L' *> or (N-1) if SIDE = 'R' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by CHPTRD. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \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 COMPLEX array, dimension *> (N) if SIDE = 'L' *> (M) 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 December 2016 * *> \ingroup complexOTHERcomputational * * ===================================================================== SUBROUTINE CUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, \$ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO INTEGER INFO, LDC, M, N * .. * .. Array Arguments .. COMPLEX AP( * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL FORWRD, LEFT, NOTRAN, UPPER INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ COMPLEX AII, TAUI * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CLARF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) UPPER = LSAME( UPLO, 'U' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CUPMTR', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) \$ RETURN * IF( UPPER ) THEN * * Q was determined by a call to CHPTRD with UPLO = 'U' * FORWRD = ( LEFT .AND. NOTRAN ) .OR. \$ ( .NOT.LEFT .AND. .NOT.NOTRAN ) * IF( FORWRD ) THEN I1 = 1 I2 = NQ - 1 I3 = 1 II = 2 ELSE I1 = NQ - 1 I2 = 1 I3 = -1 II = NQ*( NQ+1 ) / 2 - 1 END IF * IF( LEFT ) THEN NI = N ELSE MI = M END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(1:i,1:n) * MI = I ELSE * * H(i) or H(i)**H is applied to C(1:m,1:i) * NI = I END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = TAU( I ) ELSE TAUI = CONJG( TAU( I ) ) END IF AII = AP( II ) AP( II ) = ONE CALL CLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAUI, C, LDC, \$ WORK ) AP( II ) = AII * IF( FORWRD ) THEN II = II + I + 2 ELSE II = II - I - 1 END IF 10 CONTINUE ELSE * * Q was determined by a call to CHPTRD with UPLO = 'L'. * FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR. \$ ( .NOT.LEFT .AND. NOTRAN ) * IF( FORWRD ) THEN I1 = 1 I2 = NQ - 1 I3 = 1 II = 2 ELSE I1 = NQ - 1 I2 = 1 I3 = -1 II = NQ*( NQ+1 ) / 2 - 1 END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 20 I = I1, I2, I3 AII = AP( II ) AP( II ) = ONE IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(i+1:m,1:n) * MI = M - I IC = I + 1 ELSE * * H(i) or H(i)**H is applied to C(1:m,i+1:n) * NI = N - I JC = I + 1 END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = TAU( I ) ELSE TAUI = CONJG( TAU( I ) ) END IF CALL CLARF( SIDE, MI, NI, AP( II ), 1, TAUI, C( IC, JC ), \$ LDC, WORK ) AP( II ) = AII * IF( FORWRD ) THEN II = II + NQ - I + 1 ELSE II = II - NQ + I - 2 END IF 20 CONTINUE END IF RETURN * * End of CUPMTR * END