*> \brief SSTEV 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 SSTEV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ * INTEGER INFO, LDZ, N * .. * .. Array Arguments .. * REAL D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSTEV computes all eigenvalues and, optionally, eigenvectors of a *> real symmetric tridiagonal matrix A. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is REAL array, dimension (N) *> On entry, the n diagonal elements of the tridiagonal matrix *> A. *> On exit, if INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is REAL array, dimension (N-1) *> On entry, the (n-1) subdiagonal elements of the tridiagonal *> matrix A, stored in elements 1 to N-1 of E. *> On exit, the contents of E are destroyed. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is REAL 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 D(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 REAL array, dimension (max(1,2*N-2)) *> If JOBZ = 'N', WORK is not referenced. *> \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 E 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 December 2016 * *> \ingroup realOTHEReigen * * ===================================================================== SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOBZ INTEGER INFO, LDZ, N * .. * .. Array Arguments .. REAL D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. LOGICAL WANTZ INTEGER IMAX, ISCALE REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM, $ TNRM * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANST EXTERNAL LSAME, SLAMCH, SLANST * .. * .. External Subroutines .. EXTERNAL SSCAL, SSTEQR, SSTERF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -6 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SSTEV ', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( N.EQ.1 ) THEN IF( WANTZ ) $ Z( 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. * ISCALE = 0 TNRM = SLANST( 'M', N, D, E ) IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / TNRM ELSE IF( TNRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / TNRM END IF IF( ISCALE.EQ.1 ) THEN CALL SSCAL( N, SIGMA, D, 1 ) CALL SSCAL( N-1, SIGMA, E( 1 ), 1 ) END IF * * For eigenvalues only, call SSTERF. For eigenvalues and * eigenvectors, call SSTEQR. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, D, E, INFO ) ELSE CALL SSTEQR( 'I', N, D, E, Z, LDZ, WORK, 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, D, 1 ) END IF * RETURN * * End of SSTEV * END