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    1: *> \brief <b> DSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DSTEV + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstev.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstev.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstev.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          JOBZ
   25: *       INTEGER            INFO, LDZ, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DSTEV computes all eigenvalues and, optionally, eigenvectors of a
   38: *> real symmetric tridiagonal matrix A.
   39: *> \endverbatim
   40: *
   41: *  Arguments:
   42: *  ==========
   43: *
   44: *> \param[in] JOBZ
   45: *> \verbatim
   46: *>          JOBZ is CHARACTER*1
   47: *>          = 'N':  Compute eigenvalues only;
   48: *>          = 'V':  Compute eigenvalues and eigenvectors.
   49: *> \endverbatim
   50: *>
   51: *> \param[in] N
   52: *> \verbatim
   53: *>          N is INTEGER
   54: *>          The order of the matrix.  N >= 0.
   55: *> \endverbatim
   56: *>
   57: *> \param[in,out] D
   58: *> \verbatim
   59: *>          D is DOUBLE PRECISION array, dimension (N)
   60: *>          On entry, the n diagonal elements of the tridiagonal matrix
   61: *>          A.
   62: *>          On exit, if INFO = 0, the eigenvalues in ascending order.
   63: *> \endverbatim
   64: *>
   65: *> \param[in,out] E
   66: *> \verbatim
   67: *>          E is DOUBLE PRECISION array, dimension (N-1)
   68: *>          On entry, the (n-1) subdiagonal elements of the tridiagonal
   69: *>          matrix A, stored in elements 1 to N-1 of E.
   70: *>          On exit, the contents of E are destroyed.
   71: *> \endverbatim
   72: *>
   73: *> \param[out] Z
   74: *> \verbatim
   75: *>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
   76: *>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
   77: *>          eigenvectors of the matrix A, with the i-th column of Z
   78: *>          holding the eigenvector associated with D(i).
   79: *>          If JOBZ = 'N', then Z is not referenced.
   80: *> \endverbatim
   81: *>
   82: *> \param[in] LDZ
   83: *> \verbatim
   84: *>          LDZ is INTEGER
   85: *>          The leading dimension of the array Z.  LDZ >= 1, and if
   86: *>          JOBZ = 'V', LDZ >= max(1,N).
   87: *> \endverbatim
   88: *>
   89: *> \param[out] WORK
   90: *> \verbatim
   91: *>          WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2))
   92: *>          If JOBZ = 'N', WORK is not referenced.
   93: *> \endverbatim
   94: *>
   95: *> \param[out] INFO
   96: *> \verbatim
   97: *>          INFO is INTEGER
   98: *>          = 0:  successful exit
   99: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  100: *>          > 0:  if INFO = i, the algorithm failed to converge; i
  101: *>                off-diagonal elements of E did not converge to zero.
  102: *> \endverbatim
  103: *
  104: *  Authors:
  105: *  ========
  106: *
  107: *> \author Univ. of Tennessee
  108: *> \author Univ. of California Berkeley
  109: *> \author Univ. of Colorado Denver
  110: *> \author NAG Ltd.
  111: *
  112: *> \ingroup doubleOTHEReigen
  113: *
  114: *  =====================================================================
  115:       SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
  116: *
  117: *  -- LAPACK driver routine --
  118: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  119: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  120: *
  121: *     .. Scalar Arguments ..
  122:       CHARACTER          JOBZ
  123:       INTEGER            INFO, LDZ, N
  124: *     ..
  125: *     .. Array Arguments ..
  126:       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
  127: *     ..
  128: *
  129: *  =====================================================================
  130: *
  131: *     .. Parameters ..
  132:       DOUBLE PRECISION   ZERO, ONE
  133:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
  134: *     ..
  135: *     .. Local Scalars ..
  136:       LOGICAL            WANTZ
  137:       INTEGER            IMAX, ISCALE
  138:       DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
  139:      $                   TNRM
  140: *     ..
  141: *     .. External Functions ..
  142:       LOGICAL            LSAME
  143:       DOUBLE PRECISION   DLAMCH, DLANST
  144:       EXTERNAL           LSAME, DLAMCH, DLANST
  145: *     ..
  146: *     .. External Subroutines ..
  147:       EXTERNAL           DSCAL, DSTEQR, DSTERF, XERBLA
  148: *     ..
  149: *     .. Intrinsic Functions ..
  150:       INTRINSIC          SQRT
  151: *     ..
  152: *     .. Executable Statements ..
  153: *
  154: *     Test the input parameters.
  155: *
  156:       WANTZ = LSAME( JOBZ, 'V' )
  157: *
  158:       INFO = 0
  159:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  160:          INFO = -1
  161:       ELSE IF( N.LT.0 ) THEN
  162:          INFO = -2
  163:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  164:          INFO = -6
  165:       END IF
  166: *
  167:       IF( INFO.NE.0 ) THEN
  168:          CALL XERBLA( 'DSTEV ', -INFO )
  169:          RETURN
  170:       END IF
  171: *
  172: *     Quick return if possible
  173: *
  174:       IF( N.EQ.0 )
  175:      $   RETURN
  176: *
  177:       IF( N.EQ.1 ) THEN
  178:          IF( WANTZ )
  179:      $      Z( 1, 1 ) = ONE
  180:          RETURN
  181:       END IF
  182: *
  183: *     Get machine constants.
  184: *
  185:       SAFMIN = DLAMCH( 'Safe minimum' )
  186:       EPS = DLAMCH( 'Precision' )
  187:       SMLNUM = SAFMIN / EPS
  188:       BIGNUM = ONE / SMLNUM
  189:       RMIN = SQRT( SMLNUM )
  190:       RMAX = SQRT( BIGNUM )
  191: *
  192: *     Scale matrix to allowable range, if necessary.
  193: *
  194:       ISCALE = 0
  195:       TNRM = DLANST( 'M', N, D, E )
  196:       IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
  197:          ISCALE = 1
  198:          SIGMA = RMIN / TNRM
  199:       ELSE IF( TNRM.GT.RMAX ) THEN
  200:          ISCALE = 1
  201:          SIGMA = RMAX / TNRM
  202:       END IF
  203:       IF( ISCALE.EQ.1 ) THEN
  204:          CALL DSCAL( N, SIGMA, D, 1 )
  205:          CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
  206:       END IF
  207: *
  208: *     For eigenvalues only, call DSTERF.  For eigenvalues and
  209: *     eigenvectors, call DSTEQR.
  210: *
  211:       IF( .NOT.WANTZ ) THEN
  212:          CALL DSTERF( N, D, E, INFO )
  213:       ELSE
  214:          CALL DSTEQR( 'I', N, D, E, Z, LDZ, WORK, INFO )
  215:       END IF
  216: *
  217: *     If matrix was scaled, then rescale eigenvalues appropriately.
  218: *
  219:       IF( ISCALE.EQ.1 ) THEN
  220:          IF( INFO.EQ.0 ) THEN
  221:             IMAX = N
  222:          ELSE
  223:             IMAX = INFO - 1
  224:          END IF
  225:          CALL DSCAL( IMAX, ONE / SIGMA, D, 1 )
  226:       END IF
  227: *
  228:       RETURN
  229: *
  230: *     End of DSTEV
  231: *
  232:       END