LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cstegr.f
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00001 *> \brief \b CSTEGR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CSTEGR + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cstegr.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cstegr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
00022 *                  ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
00023 *                  LIWORK, INFO )
00024 * 
00025 *       .. Scalar Arguments ..
00026 *       CHARACTER          JOBZ, RANGE
00027 *       INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
00028 *       REAL             ABSTOL, VL, VU
00029 *       ..
00030 *       .. Array Arguments ..
00031 *       INTEGER            ISUPPZ( * ), IWORK( * )
00032 *       REAL               D( * ), E( * ), W( * ), WORK( * )
00033 *       COMPLEX            Z( LDZ, * )
00034 *       ..
00035 *  
00036 *
00037 *> \par Purpose:
00038 *  =============
00039 *>
00040 *> \verbatim
00041 *>
00042 *> CSTEGR computes selected eigenvalues and, optionally, eigenvectors
00043 *> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
00044 *> a well defined set of pairwise different real eigenvalues, the corresponding
00045 *> real eigenvectors are pairwise orthogonal.
00046 *>
00047 *> The spectrum may be computed either completely or partially by specifying
00048 *> either an interval (VL,VU] or a range of indices IL:IU for the desired
00049 *> eigenvalues.
00050 *>
00051 *> CSTEGR is a compatability wrapper around the improved CSTEMR routine.
00052 *> See SSTEMR for further details.
00053 *>
00054 *> One important change is that the ABSTOL parameter no longer provides any
00055 *> benefit and hence is no longer used.
00056 *>
00057 *> Note : CSTEGR and CSTEMR work only on machines which follow
00058 *> IEEE-754 floating-point standard in their handling of infinities and
00059 *> NaNs.  Normal execution may create these exceptiona values and hence
00060 *> may abort due to a floating point exception in environments which
00061 *> do not conform to the IEEE-754 standard.
00062 *> \endverbatim
00063 *
00064 *  Arguments:
00065 *  ==========
00066 *
00067 *> \param[in] JOBZ
00068 *> \verbatim
00069 *>          JOBZ is CHARACTER*1
00070 *>          = 'N':  Compute eigenvalues only;
00071 *>          = 'V':  Compute eigenvalues and eigenvectors.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] RANGE
00075 *> \verbatim
00076 *>          RANGE is CHARACTER*1
00077 *>          = 'A': all eigenvalues will be found.
00078 *>          = 'V': all eigenvalues in the half-open interval (VL,VU]
00079 *>                 will be found.
00080 *>          = 'I': the IL-th through IU-th eigenvalues will be found.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] N
00084 *> \verbatim
00085 *>          N is INTEGER
00086 *>          The order of the matrix.  N >= 0.
00087 *> \endverbatim
00088 *>
00089 *> \param[in,out] D
00090 *> \verbatim
00091 *>          D is REAL array, dimension (N)
00092 *>          On entry, the N diagonal elements of the tridiagonal matrix
00093 *>          T. On exit, D is overwritten.
00094 *> \endverbatim
00095 *>
00096 *> \param[in,out] E
00097 *> \verbatim
00098 *>          E is REAL array, dimension (N)
00099 *>          On entry, the (N-1) subdiagonal elements of the tridiagonal
00100 *>          matrix T in elements 1 to N-1 of E. E(N) need not be set on
00101 *>          input, but is used internally as workspace.
00102 *>          On exit, E is overwritten.
00103 *> \endverbatim
00104 *>
00105 *> \param[in] VL
00106 *> \verbatim
00107 *>          VL is REAL
00108 *> \endverbatim
00109 *>
00110 *> \param[in] VU
00111 *> \verbatim
00112 *>          VU is REAL
00113 *>
00114 *>          If RANGE='V', the lower and upper bounds of the interval to
00115 *>          be searched for eigenvalues. VL < VU.
00116 *>          Not referenced if RANGE = 'A' or 'I'.
00117 *> \endverbatim
00118 *>
00119 *> \param[in] IL
00120 *> \verbatim
00121 *>          IL is INTEGER
00122 *> \endverbatim
00123 *>
00124 *> \param[in] IU
00125 *> \verbatim
00126 *>          IU is INTEGER
00127 *>
00128 *>          If RANGE='I', the indices (in ascending order) of the
00129 *>          smallest and largest eigenvalues to be returned.
00130 *>          1 <= IL <= IU <= N, if N > 0.
00131 *>          Not referenced if RANGE = 'A' or 'V'.
00132 *> \endverbatim
00133 *>
00134 *> \param[in] ABSTOL
00135 *> \verbatim
00136 *>          ABSTOL is REAL
00137 *>          Unused.  Was the absolute error tolerance for the
00138 *>          eigenvalues/eigenvectors in previous versions.
00139 *> \endverbatim
00140 *>
00141 *> \param[out] M
00142 *> \verbatim
00143 *>          M is INTEGER
00144 *>          The total number of eigenvalues found.  0 <= M <= N.
00145 *>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
00146 *> \endverbatim
00147 *>
00148 *> \param[out] W
00149 *> \verbatim
00150 *>          W is REAL array, dimension (N)
00151 *>          The first M elements contain the selected eigenvalues in
00152 *>          ascending order.
00153 *> \endverbatim
00154 *>
00155 *> \param[out] Z
00156 *> \verbatim
00157 *>          Z is COMPLEX array, dimension (LDZ, max(1,M) )
00158 *>          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
00159 *>          contain the orthonormal eigenvectors of the matrix T
00160 *>          corresponding to the selected eigenvalues, with the i-th
00161 *>          column of Z holding the eigenvector associated with W(i).
00162 *>          If JOBZ = 'N', then Z is not referenced.
00163 *>          Note: the user must ensure that at least max(1,M) columns are
00164 *>          supplied in the array Z; if RANGE = 'V', the exact value of M
00165 *>          is not known in advance and an upper bound must be used.
00166 *>          Supplying N columns is always safe.
00167 *> \endverbatim
00168 *>
00169 *> \param[in] LDZ
00170 *> \verbatim
00171 *>          LDZ is INTEGER
00172 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00173 *>          JOBZ = 'V', then LDZ >= max(1,N).
00174 *> \endverbatim
00175 *>
00176 *> \param[out] ISUPPZ
00177 *> \verbatim
00178 *>          ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
00179 *>          The support of the eigenvectors in Z, i.e., the indices
00180 *>          indicating the nonzero elements in Z. The i-th computed eigenvector
00181 *>          is nonzero only in elements ISUPPZ( 2*i-1 ) through
00182 *>          ISUPPZ( 2*i ). This is relevant in the case when the matrix
00183 *>          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
00184 *> \endverbatim
00185 *>
00186 *> \param[out] WORK
00187 *> \verbatim
00188 *>          WORK is REAL array, dimension (LWORK)
00189 *>          On exit, if INFO = 0, WORK(1) returns the optimal
00190 *>          (and minimal) LWORK.
00191 *> \endverbatim
00192 *>
00193 *> \param[in] LWORK
00194 *> \verbatim
00195 *>          LWORK is INTEGER
00196 *>          The dimension of the array WORK. LWORK >= max(1,18*N)
00197 *>          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
00198 *>          If LWORK = -1, then a workspace query is assumed; the routine
00199 *>          only calculates the optimal size of the WORK array, returns
00200 *>          this value as the first entry of the WORK array, and no error
00201 *>          message related to LWORK is issued by XERBLA.
00202 *> \endverbatim
00203 *>
00204 *> \param[out] IWORK
00205 *> \verbatim
00206 *>          IWORK is INTEGER array, dimension (LIWORK)
00207 *>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
00208 *> \endverbatim
00209 *>
00210 *> \param[in] LIWORK
00211 *> \verbatim
00212 *>          LIWORK is INTEGER
00213 *>          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
00214 *>          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
00215 *>          if only the eigenvalues are to be computed.
00216 *>          If LIWORK = -1, then a workspace query is assumed; the
00217 *>          routine only calculates the optimal size of the IWORK array,
00218 *>          returns this value as the first entry of the IWORK array, and
00219 *>          no error message related to LIWORK is issued by XERBLA.
00220 *> \endverbatim
00221 *>
00222 *> \param[out] INFO
00223 *> \verbatim
00224 *>          INFO is INTEGER
00225 *>          On exit, INFO
00226 *>          = 0:  successful exit
00227 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00228 *>          > 0:  if INFO = 1X, internal error in SLARRE,
00229 *>                if INFO = 2X, internal error in CLARRV.
00230 *>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
00231 *>                the nonzero error code returned by SLARRE or
00232 *>                CLARRV, respectively.
00233 *> \endverbatim
00234 *
00235 *  Authors:
00236 *  ========
00237 *
00238 *> \author Univ. of Tennessee 
00239 *> \author Univ. of California Berkeley 
00240 *> \author Univ. of Colorado Denver 
00241 *> \author NAG Ltd. 
00242 *
00243 *> \date November 2011
00244 *
00245 *> \ingroup complexOTHERcomputational
00246 *
00247 *> \par Contributors:
00248 *  ==================
00249 *>
00250 *> Inderjit Dhillon, IBM Almaden, USA \n
00251 *> Osni Marques, LBNL/NERSC, USA \n
00252 *> Christof Voemel, LBNL/NERSC, USA \n
00253 *
00254 *  =====================================================================
00255       SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
00256      $           ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
00257      $           LIWORK, INFO )
00258 *
00259 *  -- LAPACK computational routine (version 3.4.0) --
00260 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00261 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00262 *     November 2011
00263 *
00264 *     .. Scalar Arguments ..
00265       CHARACTER          JOBZ, RANGE
00266       INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
00267       REAL             ABSTOL, VL, VU
00268 *     ..
00269 *     .. Array Arguments ..
00270       INTEGER            ISUPPZ( * ), IWORK( * )
00271       REAL               D( * ), E( * ), W( * ), WORK( * )
00272       COMPLEX            Z( LDZ, * )
00273 *     ..
00274 *
00275 *  =====================================================================
00276 *
00277 *     .. Local Scalars ..
00278       LOGICAL TRYRAC
00279 *     ..
00280 *     .. External Subroutines ..
00281       EXTERNAL CSTEMR
00282 *     ..
00283 *     .. Executable Statements ..
00284       INFO = 0
00285       TRYRAC = .FALSE.
00286 
00287       CALL CSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
00288      $                   M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
00289      $                   IWORK, LIWORK, INFO )
00290 *
00291 *     End of CSTEGR
00292 *
00293       END
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