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294 lines
8.4 KiB
294 lines
8.4 KiB
2 years ago
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*> \brief <b> DSTEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
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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 DSTEVD + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstevd.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/dstevd.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/dstevd.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 DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
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* LIWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBZ
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* INTEGER INFO, LDZ, LIWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
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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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*> DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
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*> real symmetric tridiagonal matrix. If eigenvectors are desired, it
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*> uses a divide and conquer algorithm.
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*>
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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] JOBZ
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*> \verbatim
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*> JOBZ is CHARACTER*1
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*> = 'N': Compute eigenvalues only;
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*> = 'V': Compute eigenvalues and eigenvectors.
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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 order of the 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 n diagonal elements of the tridiagonal matrix
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*> A.
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*> On exit, if INFO = 0, the eigenvalues in ascending order.
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*> \endverbatim
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*>
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*> \param[in,out] E
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*> \verbatim
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*> E is DOUBLE PRECISION array, dimension (N-1)
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*> On entry, the (n-1) subdiagonal elements of the tridiagonal
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*> matrix A, stored in elements 1 to N-1 of E.
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*> On exit, the contents of E are destroyed.
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*> \endverbatim
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*>
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*> \param[out] Z
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*> \verbatim
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*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
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*> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
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*> eigenvectors of the matrix A, with the i-th column of Z
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*> holding the eigenvector associated with D(i).
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*> If JOBZ = 'N', then Z is not referenced.
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*> \endverbatim
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*>
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*> \param[in] LDZ
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*> \verbatim
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*> LDZ is INTEGER
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*> The leading dimension of the array Z. LDZ >= 1, and if
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*> JOBZ = 'V', LDZ >= max(1,N).
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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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*> dimension (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 JOBZ = 'N' or N <= 1 then LWORK must be at least 1.
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*> If JOBZ = 'V' and N > 1 then LWORK must be at least
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*> ( 1 + 4*N + N**2 ).
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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 sizes of the WORK and IWORK
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*> arrays, returns these values as the first entries of the WORK
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*> and IWORK arrays, and no error message related to LWORK or
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*> LIWORK is issued by XERBLA.
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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, dimension (MAX(1,LIWORK))
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*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
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*> \endverbatim
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*>
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*> \param[in] LIWORK
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*> \verbatim
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*> LIWORK is INTEGER
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*> The dimension of the array IWORK.
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*> If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1.
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*> If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N.
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*>
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*> If LIWORK = -1, then a workspace query is assumed; the
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*> routine only calculates the optimal sizes of the WORK and
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*> IWORK arrays, returns these values as the first entries of
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*> the WORK and IWORK arrays, and no error message related to
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*> LWORK or LIWORK 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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*> > 0: if INFO = i, the algorithm failed to converge; i
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*> off-diagonal elements of E did not converge to zero.
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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 doubleOTHEReigen
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*
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* =====================================================================
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SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
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$ LIWORK, INFO )
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*
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* -- LAPACK driver 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 JOBZ
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INTEGER INFO, LDZ, LIWORK, LWORK, N
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
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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
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, WANTZ
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INTEGER ISCALE, LIWMIN, LWMIN
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DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
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$ TNRM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, DLANST
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EXTERNAL LSAME, DLAMCH, DLANST
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* ..
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* .. External Subroutines ..
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EXTERNAL DSCAL, DSTEDC, DSTERF, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC SQRT
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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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WANTZ = LSAME( JOBZ, 'V' )
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LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
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*
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INFO = 0
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LIWMIN = 1
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LWMIN = 1
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IF( N.GT.1 .AND. WANTZ ) THEN
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LWMIN = 1 + 4*N + N**2
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LIWMIN = 3 + 5*N
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END IF
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*
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IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
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INFO = -6
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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WORK( 1 ) = LWMIN
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IWORK( 1 ) = LIWMIN
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*
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -8
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ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -10
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END IF
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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( 'DSTEVD', -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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IF( N.EQ.0 )
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$ RETURN
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*
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IF( N.EQ.1 ) THEN
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IF( WANTZ )
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$ Z( 1, 1 ) = ONE
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RETURN
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END IF
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*
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* Get machine constants.
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*
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SAFMIN = DLAMCH( 'Safe minimum' )
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EPS = DLAMCH( 'Precision' )
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SMLNUM = SAFMIN / EPS
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BIGNUM = ONE / SMLNUM
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RMIN = SQRT( SMLNUM )
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RMAX = SQRT( BIGNUM )
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*
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* Scale matrix to allowable range, if necessary.
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*
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ISCALE = 0
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TNRM = DLANST( 'M', N, D, E )
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IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
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ISCALE = 1
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SIGMA = RMIN / TNRM
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ELSE IF( TNRM.GT.RMAX ) THEN
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ISCALE = 1
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SIGMA = RMAX / TNRM
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END IF
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IF( ISCALE.EQ.1 ) THEN
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CALL DSCAL( N, SIGMA, D, 1 )
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CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
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END IF
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*
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* For eigenvalues only, call DSTERF. For eigenvalues and
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* eigenvectors, call DSTEDC.
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*
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IF( .NOT.WANTZ ) THEN
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CALL DSTERF( N, D, E, INFO )
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ELSE
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CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
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$ INFO )
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END IF
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*
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* If matrix was scaled, then rescale eigenvalues appropriately.
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*
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IF( ISCALE.EQ.1 )
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$ CALL DSCAL( N, ONE / SIGMA, D, 1 )
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*
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WORK( 1 ) = LWMIN
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IWORK( 1 ) = LIWMIN
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*
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RETURN
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*
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* End of DSTEVD
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*
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END
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