forked from lijiext/lammps
435 lines
14 KiB
FortranFixed
435 lines
14 KiB
FortranFixed
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*> \brief \b DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
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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 DLAED0 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed0.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/dlaed0.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/dlaed0.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 DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
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* WORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
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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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*> DLAED0 computes all eigenvalues and corresponding eigenvectors of a
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*> symmetric tridiagonal matrix using the divide and conquer method.
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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] ICOMPQ
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*> \verbatim
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*> ICOMPQ is INTEGER
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*> = 0: Compute eigenvalues only.
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*> = 1: Compute eigenvectors of original dense symmetric matrix
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*> also. On entry, Q contains the orthogonal matrix used
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*> to reduce the original matrix to tridiagonal form.
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*> = 2: Compute eigenvalues and eigenvectors of tridiagonal
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*> matrix.
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*> \endverbatim
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*>
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*> \param[in] QSIZ
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*> \verbatim
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*> QSIZ is INTEGER
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*> The dimension of the orthogonal matrix used to reduce
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*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
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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 dimension of the symmetric tridiagonal matrix. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (N)
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*> On entry, the main diagonal of the tridiagonal matrix.
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*> On exit, its eigenvalues.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is DOUBLE PRECISION array, dimension (N-1)
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*> The off-diagonal elements of the tridiagonal matrix.
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*> On exit, E has been destroyed.
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*> \endverbatim
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*>
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*> \param[in,out] Q
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*> \verbatim
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*> Q is DOUBLE PRECISION array, dimension (LDQ, N)
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*> On entry, Q must contain an N-by-N orthogonal matrix.
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*> If ICOMPQ = 0 Q is not referenced.
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*> If ICOMPQ = 1 On entry, Q is a subset of the columns of the
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*> orthogonal matrix used to reduce the full
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*> matrix to tridiagonal form corresponding to
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*> the subset of the full matrix which is being
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*> decomposed at this time.
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*> If ICOMPQ = 2 On entry, Q will be the identity matrix.
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*> On exit, Q contains the eigenvectors of the
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*> tridiagonal matrix.
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*> \endverbatim
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*>
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*> \param[in] LDQ
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*> \verbatim
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*> LDQ is INTEGER
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*> The leading dimension of the array Q. If eigenvectors are
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*> desired, then LDQ >= max(1,N). In any case, LDQ >= 1.
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*> \endverbatim
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*>
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*> \param[out] QSTORE
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*> \verbatim
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*> QSTORE is DOUBLE PRECISION array, dimension (LDQS, N)
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*> Referenced only when ICOMPQ = 1. Used to store parts of
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*> the eigenvector matrix when the updating matrix multiplies
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*> take place.
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*> \endverbatim
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*>
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*> \param[in] LDQS
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*> \verbatim
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*> LDQS is INTEGER
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*> The leading dimension of the array QSTORE. If ICOMPQ = 1,
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*> then LDQS >= max(1,N). In any case, LDQS >= 1.
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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 DOUBLE PRECISION array,
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*> If ICOMPQ = 0 or 1, the dimension of WORK must be at least
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*> 1 + 3*N + 2*N*lg N + 3*N**2
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*> ( lg( N ) = smallest integer k
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*> such that 2^k >= N )
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*> If ICOMPQ = 2, the dimension of WORK must be at least
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*> 4*N + N**2.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array,
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*> If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
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*> 6 + 6*N + 5*N*lg N.
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*> ( lg( N ) = smallest integer k
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*> such that 2^k >= N )
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*> If ICOMPQ = 2, the dimension of IWORK must be at least
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*> 3 + 5*N.
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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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*> > 0: The algorithm failed to compute an eigenvalue while
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*> working on the submatrix lying in rows and columns
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*> INFO/(N+1) through mod(INFO,N+1).
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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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*> \date September 2012
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*
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*> \ingroup auxOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> Jeff Rutter, Computer Science Division, University of California
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*> at Berkeley, USA
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*
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* =====================================================================
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SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
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$ WORK, IWORK, INFO )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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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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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
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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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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.D0, ONE = 1.D0, TWO = 2.D0 )
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* ..
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* .. Local Scalars ..
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INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
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$ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
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$ J, K, LGN, MATSIZ, MSD2, SMLSIZ, SMM1, SPM1,
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$ SPM2, SUBMAT, SUBPBS, TLVLS
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DOUBLE PRECISION TEMP
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* ..
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* .. External Subroutines ..
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EXTERNAL DCOPY, DGEMM, DLACPY, DLAED1, DLAED7, DSTEQR,
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$ XERBLA
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, INT, LOG, MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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*
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IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.2 ) THEN
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INFO = -1
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ELSE IF( ( ICOMPQ.EQ.1 ) .AND. ( QSIZ.LT.MAX( 0, N ) ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
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INFO = -7
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ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DLAED0', -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( N.EQ.0 )
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$ RETURN
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*
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SMLSIZ = ILAENV( 9, 'DLAED0', ' ', 0, 0, 0, 0 )
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*
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* Determine the size and placement of the submatrices, and save in
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* the leading elements of IWORK.
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*
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IWORK( 1 ) = N
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SUBPBS = 1
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TLVLS = 0
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10 CONTINUE
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IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN
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DO 20 J = SUBPBS, 1, -1
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IWORK( 2*J ) = ( IWORK( J )+1 ) / 2
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IWORK( 2*J-1 ) = IWORK( J ) / 2
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20 CONTINUE
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TLVLS = TLVLS + 1
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SUBPBS = 2*SUBPBS
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GO TO 10
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END IF
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DO 30 J = 2, SUBPBS
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IWORK( J ) = IWORK( J ) + IWORK( J-1 )
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30 CONTINUE
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*
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* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
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* using rank-1 modifications (cuts).
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*
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SPM1 = SUBPBS - 1
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DO 40 I = 1, SPM1
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SUBMAT = IWORK( I ) + 1
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SMM1 = SUBMAT - 1
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D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) )
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D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) )
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40 CONTINUE
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*
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INDXQ = 4*N + 3
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IF( ICOMPQ.NE.2 ) THEN
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*
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* Set up workspaces for eigenvalues only/accumulate new vectors
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* routine
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*
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TEMP = LOG( DBLE( N ) ) / LOG( TWO )
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LGN = INT( TEMP )
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IF( 2**LGN.LT.N )
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$ LGN = LGN + 1
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IF( 2**LGN.LT.N )
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$ LGN = LGN + 1
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IPRMPT = INDXQ + N + 1
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IPERM = IPRMPT + N*LGN
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IQPTR = IPERM + N*LGN
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IGIVPT = IQPTR + N + 2
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IGIVCL = IGIVPT + N*LGN
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*
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IGIVNM = 1
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IQ = IGIVNM + 2*N*LGN
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IWREM = IQ + N**2 + 1
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*
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* Initialize pointers
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*
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DO 50 I = 0, SUBPBS
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IWORK( IPRMPT+I ) = 1
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IWORK( IGIVPT+I ) = 1
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50 CONTINUE
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IWORK( IQPTR ) = 1
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END IF
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*
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* Solve each submatrix eigenproblem at the bottom of the divide and
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* conquer tree.
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*
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CURR = 0
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DO 70 I = 0, SPM1
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IF( I.EQ.0 ) THEN
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SUBMAT = 1
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MATSIZ = IWORK( 1 )
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ELSE
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SUBMAT = IWORK( I ) + 1
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MATSIZ = IWORK( I+1 ) - IWORK( I )
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END IF
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IF( ICOMPQ.EQ.2 ) THEN
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CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
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$ Q( SUBMAT, SUBMAT ), LDQ, WORK, INFO )
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IF( INFO.NE.0 )
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$ GO TO 130
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ELSE
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CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ),
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$ WORK( IQ-1+IWORK( IQPTR+CURR ) ), MATSIZ, WORK,
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$ INFO )
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IF( INFO.NE.0 )
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$ GO TO 130
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IF( ICOMPQ.EQ.1 ) THEN
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CALL DGEMM( 'N', 'N', QSIZ, MATSIZ, MATSIZ, ONE,
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$ Q( 1, SUBMAT ), LDQ, WORK( IQ-1+IWORK( IQPTR+
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$ CURR ) ), MATSIZ, ZERO, QSTORE( 1, SUBMAT ),
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$ LDQS )
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END IF
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IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2
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CURR = CURR + 1
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END IF
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K = 1
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DO 60 J = SUBMAT, IWORK( I+1 )
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IWORK( INDXQ+J ) = K
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K = K + 1
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60 CONTINUE
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70 CONTINUE
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*
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* Successively merge eigensystems of adjacent submatrices
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* into eigensystem for the corresponding larger matrix.
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*
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* while ( SUBPBS > 1 )
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*
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CURLVL = 1
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80 CONTINUE
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IF( SUBPBS.GT.1 ) THEN
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SPM2 = SUBPBS - 2
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DO 90 I = 0, SPM2, 2
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IF( I.EQ.0 ) THEN
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SUBMAT = 1
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MATSIZ = IWORK( 2 )
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MSD2 = IWORK( 1 )
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CURPRB = 0
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ELSE
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SUBMAT = IWORK( I ) + 1
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MATSIZ = IWORK( I+2 ) - IWORK( I )
|
||
|
|
MSD2 = MATSIZ / 2
|
||
|
|
CURPRB = CURPRB + 1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
|
||
|
|
* into an eigensystem of size MATSIZ.
|
||
|
|
* DLAED1 is used only for the full eigensystem of a tridiagonal
|
||
|
|
* matrix.
|
||
|
|
* DLAED7 handles the cases in which eigenvalues only or eigenvalues
|
||
|
|
* and eigenvectors of a full symmetric matrix (which was reduced to
|
||
|
|
* tridiagonal form) are desired.
|
||
|
|
*
|
||
|
|
IF( ICOMPQ.EQ.2 ) THEN
|
||
|
|
CALL DLAED1( MATSIZ, D( SUBMAT ), Q( SUBMAT, SUBMAT ),
|
||
|
|
$ LDQ, IWORK( INDXQ+SUBMAT ),
|
||
|
|
$ E( SUBMAT+MSD2-1 ), MSD2, WORK,
|
||
|
|
$ IWORK( SUBPBS+1 ), INFO )
|
||
|
|
ELSE
|
||
|
|
CALL DLAED7( ICOMPQ, MATSIZ, QSIZ, TLVLS, CURLVL, CURPRB,
|
||
|
|
$ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS,
|
||
|
|
$ IWORK( INDXQ+SUBMAT ), E( SUBMAT+MSD2-1 ),
|
||
|
|
$ MSD2, WORK( IQ ), IWORK( IQPTR ),
|
||
|
|
$ IWORK( IPRMPT ), IWORK( IPERM ),
|
||
|
|
$ IWORK( IGIVPT ), IWORK( IGIVCL ),
|
||
|
|
$ WORK( IGIVNM ), WORK( IWREM ),
|
||
|
|
$ IWORK( SUBPBS+1 ), INFO )
|
||
|
|
END IF
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ GO TO 130
|
||
|
|
IWORK( I / 2+1 ) = IWORK( I+2 )
|
||
|
|
90 CONTINUE
|
||
|
|
SUBPBS = SUBPBS / 2
|
||
|
|
CURLVL = CURLVL + 1
|
||
|
|
GO TO 80
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* end while
|
||
|
|
*
|
||
|
|
* Re-merge the eigenvalues/vectors which were deflated at the final
|
||
|
|
* merge step.
|
||
|
|
*
|
||
|
|
IF( ICOMPQ.EQ.1 ) THEN
|
||
|
|
DO 100 I = 1, N
|
||
|
|
J = IWORK( INDXQ+I )
|
||
|
|
WORK( I ) = D( J )
|
||
|
|
CALL DCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 )
|
||
|
|
100 CONTINUE
|
||
|
|
CALL DCOPY( N, WORK, 1, D, 1 )
|
||
|
|
ELSE IF( ICOMPQ.EQ.2 ) THEN
|
||
|
|
DO 110 I = 1, N
|
||
|
|
J = IWORK( INDXQ+I )
|
||
|
|
WORK( I ) = D( J )
|
||
|
|
CALL DCOPY( N, Q( 1, J ), 1, WORK( N*I+1 ), 1 )
|
||
|
|
110 CONTINUE
|
||
|
|
CALL DCOPY( N, WORK, 1, D, 1 )
|
||
|
|
CALL DLACPY( 'A', N, N, WORK( N+1 ), N, Q, LDQ )
|
||
|
|
ELSE
|
||
|
|
DO 120 I = 1, N
|
||
|
|
J = IWORK( INDXQ+I )
|
||
|
|
WORK( I ) = D( J )
|
||
|
|
120 CONTINUE
|
||
|
|
CALL DCOPY( N, WORK, 1, D, 1 )
|
||
|
|
END IF
|
||
|
|
GO TO 140
|
||
|
|
*
|
||
|
|
130 CONTINUE
|
||
|
|
INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1
|
||
|
|
*
|
||
|
|
140 CONTINUE
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DLAED0
|
||
|
|
*
|
||
|
|
END
|