LAPACK 3.3.0

zstegr.f

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00001       SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
00002      $           ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
00003      $           LIWORK, INFO )
00004 
00005       IMPLICIT NONE
00006 *
00007 *
00008 *  -- LAPACK computational routine (version 3.2) --
00009 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00010 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00011 *     November 2006
00012 *
00013 *     .. Scalar Arguments ..
00014       CHARACTER          JOBZ, RANGE
00015       INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
00016       DOUBLE PRECISION ABSTOL, VL, VU
00017 *     ..
00018 *     .. Array Arguments ..
00019       INTEGER            ISUPPZ( * ), IWORK( * )
00020       DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * )
00021       COMPLEX*16         Z( LDZ, * )
00022 *     ..
00023 *
00024 *  Purpose
00025 *  =======
00026 *
00027 *  ZSTEGR computes selected eigenvalues and, optionally, eigenvectors
00028 *  of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
00029 *  a well defined set of pairwise different real eigenvalues, the corresponding
00030 *  real eigenvectors are pairwise orthogonal.
00031 *
00032 *  The spectrum may be computed either completely or partially by specifying
00033 *  either an interval (VL,VU] or a range of indices IL:IU for the desired
00034 *  eigenvalues.
00035 *
00036 *  ZSTEGR is a compatability wrapper around the improved ZSTEMR routine.
00037 *  See DSTEMR for further details.
00038 *
00039 *  One important change is that the ABSTOL parameter no longer provides any
00040 *  benefit and hence is no longer used.
00041 *
00042 *  Note : ZSTEGR and ZSTEMR work only on machines which follow
00043 *  IEEE-754 floating-point standard in their handling of infinities and
00044 *  NaNs.  Normal execution may create these exceptiona values and hence
00045 *  may abort due to a floating point exception in environments which
00046 *  do not conform to the IEEE-754 standard.
00047 *
00048 *  Arguments
00049 *  =========
00050 *
00051 *  JOBZ    (input) CHARACTER*1
00052 *          = 'N':  Compute eigenvalues only;
00053 *          = 'V':  Compute eigenvalues and eigenvectors.
00054 *
00055 *  RANGE   (input) CHARACTER*1
00056 *          = 'A': all eigenvalues will be found.
00057 *          = 'V': all eigenvalues in the half-open interval (VL,VU]
00058 *                 will be found.
00059 *          = 'I': the IL-th through IU-th eigenvalues will be found.
00060 *
00061 *  N       (input) INTEGER
00062 *          The order of the matrix.  N >= 0.
00063 *
00064 *  D       (input/output) DOUBLE PRECISION array, dimension (N)
00065 *          On entry, the N diagonal elements of the tridiagonal matrix
00066 *          T. On exit, D is overwritten.
00067 *
00068 *  E       (input/output) DOUBLE PRECISION array, dimension (N)
00069 *          On entry, the (N-1) subdiagonal elements of the tridiagonal
00070 *          matrix T in elements 1 to N-1 of E. E(N) need not be set on
00071 *          input, but is used internally as workspace.
00072 *          On exit, E is overwritten.
00073 *
00074 *  VL      (input) DOUBLE PRECISION
00075 *  VU      (input) DOUBLE PRECISION
00076 *          If RANGE='V', the lower and upper bounds of the interval to
00077 *          be searched for eigenvalues. VL < VU.
00078 *          Not referenced if RANGE = 'A' or 'I'.
00079 *
00080 *  IL      (input) INTEGER
00081 *  IU      (input) INTEGER
00082 *          If RANGE='I', the indices (in ascending order) of the
00083 *          smallest and largest eigenvalues to be returned.
00084 *          1 <= IL <= IU <= N, if N > 0.
00085 *          Not referenced if RANGE = 'A' or 'V'.
00086 *
00087 *  ABSTOL  (input) DOUBLE PRECISION
00088 *          Unused.  Was the absolute error tolerance for the
00089 *          eigenvalues/eigenvectors in previous versions.
00090 *
00091 *  M       (output) INTEGER
00092 *          The total number of eigenvalues found.  0 <= M <= N.
00093 *          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
00094 *
00095 *  W       (output) DOUBLE PRECISION array, dimension (N)
00096 *          The first M elements contain the selected eigenvalues in
00097 *          ascending order.
00098 *
00099 *  Z       (output) COMPLEX*16 array, dimension (LDZ, max(1,M) )
00100 *          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
00101 *          contain the orthonormal eigenvectors of the matrix T
00102 *          corresponding to the selected eigenvalues, with the i-th
00103 *          column of Z holding the eigenvector associated with W(i).
00104 *          If JOBZ = 'N', then Z is not referenced.
00105 *          Note: the user must ensure that at least max(1,M) columns are
00106 *          supplied in the array Z; if RANGE = 'V', the exact value of M
00107 *          is not known in advance and an upper bound must be used.
00108 *          Supplying N columns is always safe.
00109 *
00110 *  LDZ     (input) INTEGER
00111 *          The leading dimension of the array Z.  LDZ >= 1, and if
00112 *          JOBZ = 'V', then LDZ >= max(1,N).
00113 *
00114 *  ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
00115 *          The support of the eigenvectors in Z, i.e., the indices
00116 *          indicating the nonzero elements in Z. The i-th computed eigenvector
00117 *          is nonzero only in elements ISUPPZ( 2*i-1 ) through
00118 *          ISUPPZ( 2*i ). This is relevant in the case when the matrix
00119 *          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
00120 *
00121 *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
00122 *          On exit, if INFO = 0, WORK(1) returns the optimal
00123 *          (and minimal) LWORK.
00124 *
00125 *  LWORK   (input) INTEGER
00126 *          The dimension of the array WORK. LWORK >= max(1,18*N)
00127 *          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
00128 *          If LWORK = -1, then a workspace query is assumed; the routine
00129 *          only calculates the optimal size of the WORK array, returns
00130 *          this value as the first entry of the WORK array, and no error
00131 *          message related to LWORK is issued by XERBLA.
00132 *
00133 *  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
00134 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
00135 *
00136 *  LIWORK  (input) INTEGER
00137 *          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
00138 *          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
00139 *          if only the eigenvalues are to be computed.
00140 *          If LIWORK = -1, then a workspace query is assumed; the
00141 *          routine only calculates the optimal size of the IWORK array,
00142 *          returns this value as the first entry of the IWORK array, and
00143 *          no error message related to LIWORK is issued by XERBLA.
00144 *
00145 *  INFO    (output) INTEGER
00146 *          On exit, INFO
00147 *          = 0:  successful exit
00148 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00149 *          > 0:  if INFO = 1X, internal error in DLARRE,
00150 *                if INFO = 2X, internal error in ZLARRV.
00151 *                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
00152 *                the nonzero error code returned by DLARRE or
00153 *                ZLARRV, respectively.
00154 *
00155 *  Further Details
00156 *  ===============
00157 *
00158 *  Based on contributions by
00159 *     Inderjit Dhillon, IBM Almaden, USA
00160 *     Osni Marques, LBNL/NERSC, USA
00161 *     Christof Voemel, LBNL/NERSC, USA
00162 *
00163 *  =====================================================================
00164 *
00165 *     .. Local Scalars ..
00166       LOGICAL TRYRAC
00167 *     ..
00168 *     .. External Subroutines ..
00169       EXTERNAL ZSTEMR
00170 *     ..
00171 *     .. Executable Statements ..
00172       INFO = 0
00173       TRYRAC = .FALSE.
00174 
00175       CALL ZSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
00176      $                   M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
00177      $                   IWORK, LIWORK, INFO )
00178 *
00179 *     End of ZSTEGR
00180 *
00181       END
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