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303 lines
7.8 KiB
303 lines
7.8 KiB
2 years ago
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*> \brief \b ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZUNMR3 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunmr3.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunmr3.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunmr3.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
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* 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, L, LDA, LDC, M, N
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), 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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*> ZUNMR3 overwrites the general complex m by n matrix C with
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*>
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*> Q * C if SIDE = 'L' and TRANS = 'N', or
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*>
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*> Q**H* C if SIDE = 'L' and TRANS = 'C', or
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*>
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*> C * Q if SIDE = 'R' and TRANS = 'N', or
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*>
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*> C * Q**H if SIDE = 'R' and TRANS = 'C',
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*>
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*> where Q is a complex unitary matrix defined as the product of k
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*> elementary reflectors
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*>
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*> Q = H(1) H(2) . . . H(k)
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*>
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*> as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n
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*> if SIDE = 'R'.
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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': apply Q (No transpose)
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*> = 'C': apply Q**H (Conjugate transpose)
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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 C. 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 C. 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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*> If SIDE = 'L', M >= K >= 0;
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*> if SIDE = 'R', N >= K >= 0.
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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 number of columns of the matrix A containing
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*> the meaningful part of the Householder reflectors.
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*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension
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*> (LDA,M) if SIDE = 'L',
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*> (LDA,N) if SIDE = 'R'
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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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*> ZTZRZF in the last k rows of its array argument A.
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*> A is modified by the routine but restored on exit.
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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. LDA >= max(1,K).
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is COMPLEX*16 array, dimension (K)
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i), as returned by ZTZRZF.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is COMPLEX*16 array, dimension (LDC,N)
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*> On entry, the m-by-n matrix C.
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*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= 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*16 array, dimension
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*> (N) if SIDE = 'L',
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*> (M) 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 complex16OTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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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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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
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$ 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, L, LDA, LDC, M, N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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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, NOTRAN
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INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
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COMPLEX*16 TAUI
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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, ZLARZ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG, MAX
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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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NOTRAN = LSAME( TRANS, 'N' )
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*
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* NQ is the order of Q
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*
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IF( LEFT ) THEN
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NQ = M
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ELSE
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NQ = N
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END IF
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IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) 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 .OR. K.GT.NQ ) THEN
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INFO = -5
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ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
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$ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
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INFO = -6
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ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
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INFO = -8
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -11
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZUNMR3', -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 )
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$ RETURN
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*
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IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN
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I1 = 1
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I2 = K
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I3 = 1
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ELSE
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I1 = K
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I2 = 1
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I3 = -1
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END IF
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*
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IF( LEFT ) THEN
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NI = N
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JA = M - L + 1
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JC = 1
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ELSE
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MI = M
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JA = N - L + 1
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IC = 1
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END IF
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*
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DO 10 I = I1, I2, I3
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IF( LEFT ) THEN
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*
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* H(i) or H(i)**H is applied to C(i:m,1:n)
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*
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MI = M - I + 1
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IC = I
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ELSE
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*
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* H(i) or H(i)**H is applied to C(1:m,i:n)
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*
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NI = N - I + 1
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JC = I
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END IF
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*
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* Apply H(i) or H(i)**H
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*
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IF( NOTRAN ) THEN
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TAUI = TAU( I )
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ELSE
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TAUI = DCONJG( TAU( I ) )
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END IF
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CALL ZLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAUI,
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$ C( IC, JC ), LDC, WORK )
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*
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10 CONTINUE
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*
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RETURN
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*
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* End of ZUNMR3
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*
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END
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