LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sstev.f
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00001 *> \brief <b> SSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SSTEV + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sstev.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstev.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstev.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          JOBZ
00025 *       INTEGER            INFO, LDZ, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               D( * ), E( * ), WORK( * ), Z( LDZ, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> SSTEV computes all eigenvalues and, optionally, eigenvectors of a
00038 *> real symmetric tridiagonal matrix A.
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] JOBZ
00045 *> \verbatim
00046 *>          JOBZ is CHARACTER*1
00047 *>          = 'N':  Compute eigenvalues only;
00048 *>          = 'V':  Compute eigenvalues and eigenvectors.
00049 *> \endverbatim
00050 *>
00051 *> \param[in] N
00052 *> \verbatim
00053 *>          N is INTEGER
00054 *>          The order of the matrix.  N >= 0.
00055 *> \endverbatim
00056 *>
00057 *> \param[in,out] D
00058 *> \verbatim
00059 *>          D is REAL array, dimension (N)
00060 *>          On entry, the n diagonal elements of the tridiagonal matrix
00061 *>          A.
00062 *>          On exit, if INFO = 0, the eigenvalues in ascending order.
00063 *> \endverbatim
00064 *>
00065 *> \param[in,out] E
00066 *> \verbatim
00067 *>          E is REAL array, dimension (N-1)
00068 *>          On entry, the (n-1) subdiagonal elements of the tridiagonal
00069 *>          matrix A, stored in elements 1 to N-1 of E.
00070 *>          On exit, the contents of E are destroyed.
00071 *> \endverbatim
00072 *>
00073 *> \param[out] Z
00074 *> \verbatim
00075 *>          Z is REAL array, dimension (LDZ, N)
00076 *>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
00077 *>          eigenvectors of the matrix A, with the i-th column of Z
00078 *>          holding the eigenvector associated with D(i).
00079 *>          If JOBZ = 'N', then Z is not referenced.
00080 *> \endverbatim
00081 *>
00082 *> \param[in] LDZ
00083 *> \verbatim
00084 *>          LDZ is INTEGER
00085 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00086 *>          JOBZ = 'V', LDZ >= max(1,N).
00087 *> \endverbatim
00088 *>
00089 *> \param[out] WORK
00090 *> \verbatim
00091 *>          WORK is REAL array, dimension (max(1,2*N-2))
00092 *>          If JOBZ = 'N', WORK is not referenced.
00093 *> \endverbatim
00094 *>
00095 *> \param[out] INFO
00096 *> \verbatim
00097 *>          INFO is INTEGER
00098 *>          = 0:  successful exit
00099 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00100 *>          > 0:  if INFO = i, the algorithm failed to converge; i
00101 *>                off-diagonal elements of E did not converge to zero.
00102 *> \endverbatim
00103 *
00104 *  Authors:
00105 *  ========
00106 *
00107 *> \author Univ. of Tennessee 
00108 *> \author Univ. of California Berkeley 
00109 *> \author Univ. of Colorado Denver 
00110 *> \author NAG Ltd. 
00111 *
00112 *> \date November 2011
00113 *
00114 *> \ingroup realOTHEReigen
00115 *
00116 *  =====================================================================
00117       SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
00118 *
00119 *  -- LAPACK driver routine (version 3.4.0) --
00120 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00121 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00122 *     November 2011
00123 *
00124 *     .. Scalar Arguments ..
00125       CHARACTER          JOBZ
00126       INTEGER            INFO, LDZ, N
00127 *     ..
00128 *     .. Array Arguments ..
00129       REAL               D( * ), E( * ), WORK( * ), Z( LDZ, * )
00130 *     ..
00131 *
00132 *  =====================================================================
00133 *
00134 *     .. Parameters ..
00135       REAL               ZERO, ONE
00136       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
00137 *     ..
00138 *     .. Local Scalars ..
00139       LOGICAL            WANTZ
00140       INTEGER            IMAX, ISCALE
00141       REAL               BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
00142      $                   TNRM
00143 *     ..
00144 *     .. External Functions ..
00145       LOGICAL            LSAME
00146       REAL               SLAMCH, SLANST
00147       EXTERNAL           LSAME, SLAMCH, SLANST
00148 *     ..
00149 *     .. External Subroutines ..
00150       EXTERNAL           SSCAL, SSTEQR, SSTERF, XERBLA
00151 *     ..
00152 *     .. Intrinsic Functions ..
00153       INTRINSIC          SQRT
00154 *     ..
00155 *     .. Executable Statements ..
00156 *
00157 *     Test the input parameters.
00158 *
00159       WANTZ = LSAME( JOBZ, 'V' )
00160 *
00161       INFO = 0
00162       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00163          INFO = -1
00164       ELSE IF( N.LT.0 ) THEN
00165          INFO = -2
00166       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00167          INFO = -6
00168       END IF
00169 *
00170       IF( INFO.NE.0 ) THEN
00171          CALL XERBLA( 'SSTEV ', -INFO )
00172          RETURN
00173       END IF
00174 *
00175 *     Quick return if possible
00176 *
00177       IF( N.EQ.0 )
00178      $   RETURN
00179 *
00180       IF( N.EQ.1 ) THEN
00181          IF( WANTZ )
00182      $      Z( 1, 1 ) = ONE
00183          RETURN
00184       END IF
00185 *
00186 *     Get machine constants.
00187 *
00188       SAFMIN = SLAMCH( 'Safe minimum' )
00189       EPS = SLAMCH( 'Precision' )
00190       SMLNUM = SAFMIN / EPS
00191       BIGNUM = ONE / SMLNUM
00192       RMIN = SQRT( SMLNUM )
00193       RMAX = SQRT( BIGNUM )
00194 *
00195 *     Scale matrix to allowable range, if necessary.
00196 *
00197       ISCALE = 0
00198       TNRM = SLANST( 'M', N, D, E )
00199       IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
00200          ISCALE = 1
00201          SIGMA = RMIN / TNRM
00202       ELSE IF( TNRM.GT.RMAX ) THEN
00203          ISCALE = 1
00204          SIGMA = RMAX / TNRM
00205       END IF
00206       IF( ISCALE.EQ.1 ) THEN
00207          CALL SSCAL( N, SIGMA, D, 1 )
00208          CALL SSCAL( N-1, SIGMA, E( 1 ), 1 )
00209       END IF
00210 *
00211 *     For eigenvalues only, call SSTERF.  For eigenvalues and
00212 *     eigenvectors, call SSTEQR.
00213 *
00214       IF( .NOT.WANTZ ) THEN
00215          CALL SSTERF( N, D, E, INFO )
00216       ELSE
00217          CALL SSTEQR( 'I', N, D, E, Z, LDZ, WORK, INFO )
00218       END IF
00219 *
00220 *     If matrix was scaled, then rescale eigenvalues appropriately.
00221 *
00222       IF( ISCALE.EQ.1 ) THEN
00223          IF( INFO.EQ.0 ) THEN
00224             IMAX = N
00225          ELSE
00226             IMAX = INFO - 1
00227          END IF
00228          CALL SSCAL( IMAX, ONE / SIGMA, D, 1 )
00229       END IF
00230 *
00231       RETURN
00232 *
00233 *     End of SSTEV
00234 *
00235       END
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