*> \brief DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSPEVD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, * IWORK, LIWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, LDZ, LIWORK, LWORK, N * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSPEVD computes all the eigenvalues and, optionally, eigenvectors *> of a real symmetric matrix A in packed storage. If eigenvectors are *> desired, it uses a divide and conquer algorithm. *> *> The divide and conquer algorithm makes very mild assumptions about *> floating point arithmetic. It will work on machines with a guard *> digit in add/subtract, or on those binary machines without guard *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or *> Cray-2. It could conceivably fail on hexadecimal or decimal machines *> without guard digits, but we know of none. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the symmetric matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. *> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite *> the corresponding elements of A, and if UPLO = 'L', the *> diagonal and first subdiagonal of T overwrite the *> corresponding elements of A. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ, N) *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal *> eigenvectors of the matrix A, with the i-th column of Z *> holding the eigenvector associated with W(i). *> If JOBZ = 'N', then Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the required LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N. *> If JOBZ = 'V' and N > 1, LWORK must be at least *> 1 + 6*N + N**2. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK *> and IWORK arrays, and no error message related to LWORK or *> LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK. *> \endverbatim *> *> \param[in] LIWORK *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. *> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK and *> IWORK arrays, returns these values as the first entries of *> the WORK and IWORK arrays, and no error message related to *> LWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = i, the algorithm failed to converge; i *> off-diagonal elements of an intermediate tridiagonal *> form did not converge to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup doubleOTHEReigen * * ===================================================================== SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, \$ IWORK, LIWORK, INFO ) * * -- LAPACK driver routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDZ, LIWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, WANTZ INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN, \$ LLWORK, LWMIN DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANSP EXTERNAL LSAME, DLAMCH, DLANSP * .. * .. External Subroutines .. EXTERNAL DOPMTR, DSCAL, DSPTRD, DSTEDC, DSTERF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) \$ THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -7 END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LIWMIN = 1 LWMIN = 1 ELSE IF( WANTZ ) THEN LIWMIN = 3 + 5*N LWMIN = 1 + 6*N + N**2 ELSE LIWMIN = 1 LWMIN = 2*N END IF END IF IWORK( 1 ) = LIWMIN WORK( 1 ) = LWMIN * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -9 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -11 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSPEVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( N.EQ.1 ) THEN W( 1 ) = AP( 1 ) IF( WANTZ ) \$ Z( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = DLANSP( 'M', UPLO, N, AP, WORK ) ISCALE = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 ) END IF * * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form. * INDE = 1 INDTAU = INDE + N CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO ) * * For eigenvalues only, call DSTERF. For eigenvectors, first call * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the * tridiagonal matrix, then call DOPMTR to multiply it by the * Householder transformations represented in AP. * IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, WORK( INDE ), INFO ) ELSE INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ), \$ LLWORK, IWORK, LIWORK, INFO ) CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ, \$ WORK( INDWRK ), IINFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) \$ CALL DSCAL( N, ONE / SIGMA, W, 1 ) * WORK( 1 ) = LWMIN IWORK( 1 ) = LIWMIN RETURN * * End of DSPEVD * END