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372 lines
11 KiB
372 lines
11 KiB
2 years ago
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*> \brief \b SORMBR
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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 SORMBR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormbr.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/sormbr.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/sormbr.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 SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
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* LDC, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER SIDE, TRANS, VECT
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* INTEGER INFO, K, LDA, LDC, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), C( LDC, * ), TAU( * ),
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* $ 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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*> If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
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*> with
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*> SIDE = 'L' SIDE = 'R'
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*> TRANS = 'N': Q * C C * Q
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*> TRANS = 'T': Q**T * C C * Q**T
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*>
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*> If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C
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*> with
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*> SIDE = 'L' SIDE = 'R'
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*> TRANS = 'N': P * C C * P
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*> TRANS = 'T': P**T * C C * P**T
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*>
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*> Here Q and P**T are the orthogonal matrices determined by SGEBRD when
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*> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
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*> P**T are defined as products of elementary reflectors H(i) and G(i)
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*> respectively.
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*>
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*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
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*> order of the orthogonal matrix Q or P**T that is applied.
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*>
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*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
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*> if nq >= k, Q = H(1) H(2) . . . H(k);
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*> if nq < k, Q = H(1) H(2) . . . H(nq-1).
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*>
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*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
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*> if k < nq, P = G(1) G(2) . . . G(k);
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*> if k >= nq, P = G(1) G(2) . . . G(nq-1).
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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] VECT
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*> \verbatim
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*> VECT is CHARACTER*1
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*> = 'Q': apply Q or Q**T;
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*> = 'P': apply P or P**T.
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*> \endverbatim
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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, Q**T, P or P**T from the Left;
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*> = 'R': apply Q, Q**T, P or P**T 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 or P;
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*> = 'T': Transpose, apply Q**T or P**T.
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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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*> If VECT = 'Q', the number of columns in the original
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*> matrix reduced by SGEBRD.
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*> If VECT = 'P', the number of rows in the original
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*> matrix reduced by SGEBRD.
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*> K >= 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 REAL array, dimension
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*> (LDA,min(nq,K)) if VECT = 'Q'
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*> (LDA,nq) if VECT = 'P'
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*> The vectors which define the elementary reflectors H(i) and
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*> G(i), whose products determine the matrices Q and P, as
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*> returned by SGEBRD.
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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 VECT = 'Q', LDA >= max(1,nq);
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*> if VECT = 'P', LDA >= max(1,min(nq,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 REAL array, dimension (min(nq,K))
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i) or G(i) which determines Q or P, as returned
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*> by SGEBRD in the array argument TAUQ or TAUP.
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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 REAL 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**T*C or C*Q**T or C*Q
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*> or P*C or P**T*C or C*P or C*P**T.
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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 REAL array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK.
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*> If SIDE = 'L', LWORK >= max(1,N);
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*> if SIDE = 'R', LWORK >= max(1,M).
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*> For optimum performance LWORK >= N*NB if SIDE = 'L', and
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*> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
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*> blocksize.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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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 realOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
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$ LDC, WORK, LWORK, 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, VECT
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INTEGER INFO, K, LDA, LDC, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), C( LDC, * ), TAU( * ),
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$ 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 APPLYQ, LEFT, LQUERY, NOTRAN
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CHARACTER TRANST
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INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL ILAENV, LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SORMLQ, SORMQR, XERBLA
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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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APPLYQ = LSAME( VECT, 'Q' )
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LEFT = LSAME( SIDE, 'L' )
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NOTRAN = LSAME( TRANS, 'N' )
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LQUERY = ( LWORK.EQ.-1 )
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*
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* NQ is the order of Q or P and NW is the minimum dimension of WORK
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*
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IF( LEFT ) THEN
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NQ = M
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NW = MAX( 1, N )
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ELSE
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NQ = N
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NW = MAX( 1, M )
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END IF
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IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
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INFO = -3
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ELSE IF( M.LT.0 ) THEN
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INFO = -4
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ELSE IF( N.LT.0 ) THEN
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INFO = -5
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ELSE IF( K.LT.0 ) THEN
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INFO = -6
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ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
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$ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
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$ 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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ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
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INFO = -13
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( APPLYQ ) THEN
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IF( LEFT ) THEN
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NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M-1, N, M-1,
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$ -1 )
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ELSE
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NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, N-1, N-1,
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$ -1 )
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END IF
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ELSE
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IF( LEFT ) THEN
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NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M-1, N, M-1,
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$ -1 )
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ELSE
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NB = ILAENV( 1, 'SORMLQ', SIDE // TRANS, M, N-1, N-1,
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$ -1 )
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END IF
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END IF
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LWKOPT = NW*NB
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WORK( 1 ) = LWKOPT
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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( 'SORMBR', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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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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WORK( 1 ) = 1
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IF( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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IF( APPLYQ ) THEN
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*
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* Apply Q
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*
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IF( NQ.GE.K ) THEN
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*
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* Q was determined by a call to SGEBRD with nq >= k
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*
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CALL SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
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$ WORK, LWORK, IINFO )
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ELSE IF( NQ.GT.1 ) THEN
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*
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* Q was determined by a call to SGEBRD with nq < k
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*
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IF( LEFT ) THEN
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MI = M - 1
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NI = N
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I1 = 2
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I2 = 1
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ELSE
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MI = M
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NI = N - 1
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I1 = 1
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I2 = 2
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END IF
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CALL SORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
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$ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
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END IF
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ELSE
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*
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* Apply P
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*
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IF( NOTRAN ) THEN
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TRANST = 'T'
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ELSE
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TRANST = 'N'
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END IF
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IF( NQ.GT.K ) THEN
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*
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* P was determined by a call to SGEBRD with nq > k
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*
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CALL SORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
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$ WORK, LWORK, IINFO )
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ELSE IF( NQ.GT.1 ) THEN
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*
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* P was determined by a call to SGEBRD with nq <= k
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*
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IF( LEFT ) THEN
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MI = M - 1
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NI = N
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I1 = 2
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I2 = 1
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ELSE
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MI = M
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NI = N - 1
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I1 = 1
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I2 = 2
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||
|
|
END IF
|
||
|
|
CALL SORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
|
||
|
|
$ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
WORK( 1 ) = LWKOPT
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SORMBR
|
||
|
|
*
|
||
|
|
END
|