*> \brief SSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SSYEV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * REAL A( LDA, * ), W( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSYEV computes all eigenvalues and, optionally, eigenvectors of a *> real symmetric matrix A. *> \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] A *> \verbatim *> A is REAL array, dimension (LDA, N) *> On entry, the symmetric matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> orthonormal eigenvectors of the matrix A. *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') *> or the upper triangle (if UPLO='U') of A, including the *> diagonal, is destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is REAL array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,3*N-1). *> For optimal efficiency, LWORK >= (NB+2)*N, *> where NB is the blocksize for SSYTRD returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK 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. * *> \ingroup realSYeigen * * ===================================================================== SUBROUTINE SSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) * * -- LAPACK driver routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. REAL A( LDA, * ), W( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. LOGICAL LOWER, LQUERY, WANTZ INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, \$ LLWORK, LWKOPT, NB REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV REAL SLAMCH, SLANSY EXTERNAL ILAENV, LSAME, SLAMCH, SLANSY * .. * .. External Subroutines .. EXTERNAL SLASCL, SORGTR, SSCAL, SSTEQR, SSTERF, SSYTRD, \$ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( 1, ( NB+2 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY ) \$ INFO = -8 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SSYEV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN RETURN END IF * IF( N.EQ.1 ) THEN W( 1 ) = A( 1, 1 ) WORK( 1 ) = 2 IF( WANTZ ) \$ A( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = SLAMCH( 'Safe minimum' ) EPS = SLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = SLANSY( 'M', UPLO, N, A, LDA, 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 ) \$ CALL SLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) * * Call SSYTRD to reduce symmetric matrix to tridiagonal form. * INDE = 1 INDTAU = INDE + N INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 CALL SSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), \$ WORK( INDWRK ), LLWORK, IINFO ) * * For eigenvalues only, call SSTERF. For eigenvectors, first call * SORGTR to generate the orthogonal matrix, then call SSTEQR. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, WORK( INDE ), INFO ) ELSE CALL SORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), \$ LLWORK, IINFO ) CALL SSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ), \$ INFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * Set WORK(1) to optimal workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of SSYEV * END