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329 lines
10 KiB
329 lines
10 KiB
2 years ago
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*> \brief <b> DSPEVD 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 DSPEVD + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspevd.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/dspevd.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/dspevd.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 DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
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* IWORK, LIWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBZ, UPLO
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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 AP( * ), W( * ), 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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*> DSPEVD computes all the eigenvalues and, optionally, eigenvectors
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*> of a real symmetric matrix A in packed storage. If eigenvectors are
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*> desired, it 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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': Upper triangle of A is stored;
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*> = 'L': Lower triangle of A is stored.
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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 A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] AP
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*> \verbatim
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*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
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*> On entry, the upper or lower triangle of the symmetric matrix
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*> A, packed columnwise in a linear array. The j-th column of A
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*> is stored in the array AP as follows:
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
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*>
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*> On exit, AP is overwritten by values generated during the
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*> reduction to tridiagonal form. If UPLO = 'U', the diagonal
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*> and first superdiagonal of the tridiagonal matrix T overwrite
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*> the corresponding elements of A, and if UPLO = 'L', the
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*> diagonal and first subdiagonal of T overwrite the
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*> corresponding elements of A.
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*> \endverbatim
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*>
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*> \param[out] W
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*> \verbatim
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*> W is DOUBLE PRECISION array, dimension (N)
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*> If INFO = 0, the eigenvalues in ascending order.
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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 W(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, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the required 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 N <= 1, LWORK must be at least 1.
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*> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
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*> If JOBZ = 'V' and N > 1, LWORK must be at least
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*> 1 + 6*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 required 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 required 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, LIWORK must be at least 1.
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*> If JOBZ = 'V' and N > 1, 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 required 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 an intermediate tridiagonal
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*> form 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 DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
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$ IWORK, 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, UPLO
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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 AP( * ), W( * ), 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 = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, WANTZ
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INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
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$ LLWORK, LWMIN
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DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
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$ SMLNUM
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, DLANSP
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EXTERNAL LSAME, DLAMCH, DLANSP
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* ..
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* .. External Subroutines ..
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EXTERNAL DOPMTR, DSCAL, DSPTRD, 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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IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -1
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ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
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$ 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( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
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INFO = -7
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( N.LE.1 ) THEN
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LIWMIN = 1
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LWMIN = 1
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ELSE
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IF( WANTZ ) THEN
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LIWMIN = 3 + 5*N
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LWMIN = 1 + 6*N + N**2
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ELSE
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LIWMIN = 1
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LWMIN = 2*N
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END IF
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END IF
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IWORK( 1 ) = LIWMIN
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WORK( 1 ) = LWMIN
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*
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IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -9
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ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
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INFO = -11
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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( 'DSPEVD', -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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W( 1 ) = AP( 1 )
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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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ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
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ISCALE = 0
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IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
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ISCALE = 1
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SIGMA = RMIN / ANRM
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ELSE IF( ANRM.GT.RMAX ) THEN
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ISCALE = 1
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SIGMA = RMAX / ANRM
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END IF
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IF( ISCALE.EQ.1 ) THEN
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CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
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END IF
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*
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* Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
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*
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INDE = 1
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INDTAU = INDE + N
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CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
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*
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* For eigenvalues only, call DSTERF. For eigenvectors, first call
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* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
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* tridiagonal matrix, then call DOPMTR to multiply it by the
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* Householder transformations represented in AP.
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*
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IF( .NOT.WANTZ ) THEN
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CALL DSTERF( N, W, WORK( INDE ), INFO )
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ELSE
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INDWRK = INDTAU + N
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LLWORK = LWORK - INDWRK + 1
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CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
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$ LLWORK, IWORK, LIWORK, INFO )
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CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
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$ WORK( INDWRK ), IINFO )
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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, W, 1 )
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*
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WORK( 1 ) = LWMIN
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IWORK( 1 ) = LIWMIN
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RETURN
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*
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* End of DSPEVD
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*
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END
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