dstevr.f

famous linear algebra library (LAPACK) ports to windows

      SUBROUTINE DSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
     $                   M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
     $                   LIWORK, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE
      INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
      DOUBLE PRECISION   ABSTOL, VL, VU
*     ..
*     .. Array Arguments ..
      INTEGER            ISUPPZ( * ), IWORK( * )
      DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  DSTEVR computes selected eigenvalues and, optionally, eigenvectors
*  of a real symmetric tridiagonal matrix T.  Eigenvalues and
*  eigenvectors can be selected by specifying either a range of values
*  or a range of indices for the desired eigenvalues.
*
*  Whenever possible, DSTEVR calls DSTEMR to compute the
*  eigenspectrum using Relatively Robust Representations.  DSTEMR
*  computes eigenvalues by the dqds algorithm, while orthogonal
*  eigenvectors are computed from various "good" L D L^T representations
*  (also known as Relatively Robust Representations). Gram-Schmidt
*  orthogonalization is avoided as far as possible. More specifically,
*  the various steps of the algorithm are as follows. For the i-th
*  unreduced block of T,
*     (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
*          is a relatively robust representation,
*     (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
*         relative accuracy by the dqds algorithm,
*     (c) If there is a cluster of close eigenvalues, "choose" sigma_i
*         close to the cluster, and go to step (a),
*     (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
*         compute the corresponding eigenvector by forming a
*         rank-revealing twisted factorization.
*  The desired accuracy of the output can be specified by the input
*  parameter ABSTOL.
*
*  For more details, see "A new O(n^2) algorithm for the symmetric
*  tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
*  Computer Science Division Technical Report No. UCB//CSD-97-971,
*  UC Berkeley, May 1997.
*
*
*  Note 1 : DSTEVR calls DSTEMR when the full spectrum is requested
*  on machines which conform to the ieee-754 floating point standard.
*  DSTEVR calls DSTEBZ and DSTEIN on non-ieee machines and
*  when partial spectrum requests are made.
*
*  Normal execution of DSTEMR may create NaNs and infinities and
*  hence may abort due to a floating point exception in environments
*  which do not handle NaNs and infinities in the ieee standard default
*  manner.
*
*  Arguments
*  =========
*
*  JOBZ    (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only;
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  RANGE   (input) CHARACTER*1
*          = 'A': all eigenvalues will be found.
*          = 'V': all eigenvalues in the half-open interval (VL,VU]
*                 will be found.
*          = 'I': the IL-th through IU-th eigenvalues will be found.
********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and
********** DSTEIN are called
*
*  N       (input) INTEGER
*          The order of the matrix.  N >= 0.
*
*  D       (input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the n diagonal elements of the tridiagonal matrix
*          A.
*          On exit, D may be multiplied by a constant factor chosen
*          to avoid over/underflow in computing the eigenvalues.
*
*  E       (input/output) DOUBLE PRECISION array, dimension (max(1,N-1))
*          On entry, the (n-1) subdiagonal elements of the tridiagonal
*          matrix A in elements 1 to N-1 of E.
*          On exit, E may be multiplied by a constant factor chosen
*          to avoid over/underflow in computing the eigenvalues.
*
*  VL      (input) DOUBLE PRECISION
*  VU      (input) DOUBLE PRECISION
*          If RANGE='V', the lower and upper bounds of the interval to
*          be searched for eigenvalues. VL < VU.
*          Not referenced if RANGE = 'A' or 'I'.
*
*  IL      (input) INTEGER
*  IU      (input) INTEGER
*          If RANGE='I', the indices (in ascending order) of the
*          smallest and largest eigenvalues to be returned.
*          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
*          Not referenced if RANGE = 'A' or 'V'.
*
*  ABSTOL  (input) DOUBLE PRECISION
*          The absolute error tolerance for the eigenvalues.
*          An approximate eigenvalue is accepted as converged
*          when it is determined to lie in an interval [a,b]
*          of width less than or equal to
*
*                  ABSTOL + EPS *   max( |a|,|b| ) ,
*
*          where EPS is the machine precision.  If ABSTOL is less than
*          or equal to zero, then  EPS*|T|  will be used in its place,
*          where |T| is the 1-norm of the tridiagonal matrix obtained
*          by reducing A to tridiagonal form.
*
*          See "Computing Small Singular Values of Bidiagonal Matrices
*          with Guaranteed High Relative Accuracy," by Demmel and
*          Kahan, LAPACK Working Note #3.
*
*          If high relative accuracy is important, set ABSTOL to
*          DLAMCH( 'Safe minimum' ).  Doing so will guarantee that
*          eigenvalues are computed to high relative accuracy when
*          possible in future releases.  The current code does not
*          make any guarantees about high relative accuracy, but
*          future releases will. See J. Barlow and J. Demmel,
*          "Computing Accurate Eigensystems of Scaled Diagonally
*          Dominant Matrices", LAPACK Working Note #7, for a discussion
*          of which matrices define their eigenvalues to high relative
*          accuracy.
*
*  M       (output) INTEGER
*          The total number of eigenvalues found.  0 <= M <= N.
*          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
*
*  W       (output) DOUBLE PRECISION array, dimension (N)
*          The first M elements contain the selected eigenvalues in
*          ascending order.
*
*  Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
*          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
*          contain the orthonormal eigenvectors of the matrix A
*          corresponding to the selected eigenvalues, with the i-th
*          column of Z holding the eigenvector associated with W(i).
*          Note: the user must ensure that at least max(1,M) columns are
*          supplied in the array Z; if RANGE = 'V', the exact value of M
*          is not known in advance and an upper bound must be used.
*
*  LDZ     (input) INTEGER
*          The leading dimension of the array Z.  LDZ >= 1, and if
*          JOBZ = 'V', LDZ >= max(1,N).
*
*  ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) )
*          The support of the eigenvectors in Z, i.e., the indices
*          indicating the nonzero elements in Z. The i-th eigenvector
*          is nonzero only in elements ISUPPZ( 2*i-1 ) through
*          ISUPPZ( 2*i ).
********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
*
*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*          On exit, if INFO = 0, WORK(1) returns the optimal (and
*          minimal) LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK.  LWORK >= max(1,20*N).
*
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal sizes of the WORK and IWORK
*          arrays, returns these values as the first entries of the WORK
*          and IWORK arrays, and no error message related to LWORK or
*          LIWORK is issued by XERBLA.
*
*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
*          On exit, if INFO = 0, IWORK(1) returns the optimal (and
*          minimal) LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of the array IWORK.  LIWORK >= max(1,10*N).
*
*          If LIWORK = -1, then a workspace query is assumed; the
*          routine only calculates the optimal sizes of the WORK and
*          IWORK arrays, returns these values as the first entries of
*          the WORK and IWORK arrays, and no error message related to
*          LWORK or LIWORK is issued by XERBLA.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  Internal error
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Inderjit Dhillon, IBM Almaden, USA
*     Osni Marques, LBNL/NERSC, USA
*     Ken Stanley, Computer Science Division, University of
*       California at Berkeley, USA
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE, TWO
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            ALLEIG, INDEIG, TEST, LQUERY, VALEIG, WANTZ,
     $                   TRYRAC
      CHARACTER          ORDER
      INTEGER            I, IEEEOK, IMAX, INDIBL, INDIFL, INDISP,
     $                   INDIWO, ISCALE, ITMP1, J, JJ, LIWMIN, LWMIN,
     $                   NSPLIT
      DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
     $                   TMP1, TNRM, VLL, VUU
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      DOUBLE PRECISION   DLAMCH, DLANST
      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANST
*     ..
*     .. External Subroutines ..
      EXTERNAL           DCOPY, DSCAL, DSTEBZ, DSTEMR, DSTEIN, DSTERF,
     $                   DSWAP, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..
*