--- 
:name: sstevr
:md5sum: e5ea156e311e0d701679c0e4fa1a3c85
:category: :subroutine
:arguments: 
- jobz: 
    :type: char
    :intent: input
- range: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- d: 
    :type: real
    :intent: input/output
    :dims: 
    - n
- e: 
    :type: real
    :intent: input/output
    :dims: 
    - MAX(1,n-1)
- vl: 
    :type: real
    :intent: input
- vu: 
    :type: real
    :intent: input
- il: 
    :type: integer
    :intent: input
- iu: 
    :type: integer
    :intent: input
- abstol: 
    :type: real
    :intent: input
- m: 
    :type: integer
    :intent: output
- w: 
    :type: real
    :intent: output
    :dims: 
    - n
- z: 
    :type: real
    :intent: output
    :dims: 
    - ldz
    - MAX(1,m)
- ldz: 
    :type: integer
    :intent: input
- isuppz: 
    :type: integer
    :intent: output
    :dims: 
    - 2*MAX(1,m)
- work: 
    :type: real
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: 20*n
- iwork: 
    :type: integer
    :intent: output
    :dims: 
    - MAX(1,liwork)
- liwork: 
    :type: integer
    :intent: input
    :option: true
    :default: 10*n
- info: 
    :type: integer
    :intent: output
:substitutions: 
  ldz: "lsame_(&jobz,\"V\") ? MAX(1,n) : 1"
  m: "lsame_(&range,\"I\") ? iu-il+1 : n"
:fortran_help: "      SUBROUTINE SSTEVR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  SSTEVR computes selected eigenvalues and, optionally, eigenvectors\n\
  *  of a real symmetric tridiagonal matrix T.  Eigenvalues and\n\
  *  eigenvectors can be selected by specifying either a range of values\n\
  *  or a range of indices for the desired eigenvalues.\n\
  *\n\
  *  Whenever possible, SSTEVR calls SSTEMR to compute the\n\
  *  eigenspectrum using Relatively Robust Representations.  SSTEMR\n\
  *  computes eigenvalues by the dqds algorithm, while orthogonal\n\
  *  eigenvectors are computed from various \"good\" L D L^T representations\n\
  *  (also known as Relatively Robust Representations). Gram-Schmidt\n\
  *  orthogonalization is avoided as far as possible. More specifically,\n\
  *  the various steps of the algorithm are as follows. For the i-th\n\
  *  unreduced block of T,\n\
  *     (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T\n\
  *          is a relatively robust representation,\n\
  *     (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high\n\
  *         relative accuracy by the dqds algorithm,\n\
  *     (c) If there is a cluster of close eigenvalues, \"choose\" sigma_i\n\
  *         close to the cluster, and go to step (a),\n\
  *     (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,\n\
  *         compute the corresponding eigenvector by forming a\n\
  *         rank-revealing twisted factorization.\n\
  *  The desired accuracy of the output can be specified by the input\n\
  *  parameter ABSTOL.\n\
  *\n\
  *  For more details, see \"A new O(n^2) algorithm for the symmetric\n\
  *  tridiagonal eigenvalue/eigenvector problem\", by Inderjit Dhillon,\n\
  *  Computer Science Division Technical Report No. UCB//CSD-97-971,\n\
  *  UC Berkeley, May 1997.\n\
  *\n\
  *\n\
  *  Note 1 : SSTEVR calls SSTEMR when the full spectrum is requested\n\
  *  on machines which conform to the ieee-754 floating point standard.\n\
  *  SSTEVR calls SSTEBZ and SSTEIN on non-ieee machines and\n\
  *  when partial spectrum requests are made.\n\
  *\n\
  *  Normal execution of SSTEMR may create NaNs and infinities and\n\
  *  hence may abort due to a floating point exception in environments\n\
  *  which do not handle NaNs and infinities in the ieee standard default\n\
  *  manner.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  JOBZ    (input) CHARACTER*1\n\
  *          = 'N':  Compute eigenvalues only;\n\
  *          = 'V':  Compute eigenvalues and eigenvectors.\n\
  *\n\
  *  RANGE   (input) CHARACTER*1\n\
  *          = 'A': all eigenvalues will be found.\n\
  *          = 'V': all eigenvalues in the half-open interval (VL,VU]\n\
  *                 will be found.\n\
  *          = 'I': the IL-th through IU-th eigenvalues will be found.\n\
  ********** For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and\n\
  ********** SSTEIN are called\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix.  N >= 0.\n\
  *\n\
  *  D       (input/output) REAL array, dimension (N)\n\
  *          On entry, the n diagonal elements of the tridiagonal matrix\n\
  *          A.\n\
  *          On exit, D may be multiplied by a constant factor chosen\n\
  *          to avoid over/underflow in computing the eigenvalues.\n\
  *\n\
  *  E       (input/output) REAL array, dimension (max(1,N-1))\n\
  *          On entry, the (n-1) subdiagonal elements of the tridiagonal\n\
  *          matrix A in elements 1 to N-1 of E.\n\
  *          On exit, E may be multiplied by a constant factor chosen\n\
  *          to avoid over/underflow in computing the eigenvalues.\n\
  *\n\
  *  VL      (input) REAL\n\
  *  VU      (input) REAL\n\
  *          If RANGE='V', the lower and upper bounds of the interval to\n\
  *          be searched for eigenvalues. VL < VU.\n\
  *          Not referenced if RANGE = 'A' or 'I'.\n\
  *\n\
  *  IL      (input) INTEGER\n\
  *  IU      (input) INTEGER\n\
  *          If RANGE='I', the indices (in ascending order) of the\n\
  *          smallest and largest eigenvalues to be returned.\n\
  *          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.\n\
  *          Not referenced if RANGE = 'A' or 'V'.\n\
  *\n\
  *  ABSTOL  (input) REAL\n\
  *          The absolute error tolerance for the eigenvalues.\n\
  *          An approximate eigenvalue is accepted as converged\n\
  *          when it is determined to lie in an interval [a,b]\n\
  *          of width less than or equal to\n\
  *\n\
  *                  ABSTOL + EPS *   max( |a|,|b| ) ,\n\
  *\n\
  *          where EPS is the machine precision.  If ABSTOL is less than\n\
  *          or equal to zero, then  EPS*|T|  will be used in its place,\n\
  *          where |T| is the 1-norm of the tridiagonal matrix obtained\n\
  *          by reducing A to tridiagonal form.\n\
  *\n\
  *          See \"Computing Small Singular Values of Bidiagonal Matrices\n\
  *          with Guaranteed High Relative Accuracy,\" by Demmel and\n\
  *          Kahan, LAPACK Working Note #3.\n\
  *\n\
  *          If high relative accuracy is important, set ABSTOL to\n\
  *          SLAMCH( 'Safe minimum' ).  Doing so will guarantee that\n\
  *          eigenvalues are computed to high relative accuracy when\n\
  *          possible in future releases.  The current code does not\n\
  *          make any guarantees about high relative accuracy, but\n\
  *          future releases will. See J. Barlow and J. Demmel,\n\
  *          \"Computing Accurate Eigensystems of Scaled Diagonally\n\
  *          Dominant Matrices\", LAPACK Working Note #7, for a discussion\n\
  *          of which matrices define their eigenvalues to high relative\n\
  *          accuracy.\n\
  *\n\
  *  M       (output) INTEGER\n\
  *          The total number of eigenvalues found.  0 <= M <= N.\n\
  *          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.\n\
  *\n\
  *  W       (output) REAL array, dimension (N)\n\
  *          The first M elements contain the selected eigenvalues in\n\
  *          ascending order.\n\
  *\n\
  *  Z       (output) REAL array, dimension (LDZ, max(1,M) )\n\
  *          If JOBZ = 'V', then if INFO = 0, the first M columns of Z\n\
  *          contain the orthonormal eigenvectors of the matrix A\n\
  *          corresponding to the selected eigenvalues, with the i-th\n\
  *          column of Z holding the eigenvector associated with W(i).\n\
  *          Note: the user must ensure that at least max(1,M) columns are\n\
  *          supplied in the array Z; if RANGE = 'V', the exact value of M\n\
  *          is not known in advance and an upper bound must be used.\n\
  *\n\
  *  LDZ     (input) INTEGER\n\
  *          The leading dimension of the array Z.  LDZ >= 1, and if\n\
  *          JOBZ = 'V', LDZ >= max(1,N).\n\
  *\n\
  *  ISUPPZ  (output) INTEGER array, dimension ( 2*max(1,M) )\n\
  *          The support of the eigenvectors in Z, i.e., the indices\n\
  *          indicating the nonzero elements in Z. The i-th eigenvector\n\
  *          is nonzero only in elements ISUPPZ( 2*i-1 ) through\n\
  *          ISUPPZ( 2*i ).\n\
  ********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1\n\
  *\n\
  *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal (and\n\
  *          minimal) LWORK.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The dimension of the array WORK.  LWORK >= 20*N.\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal sizes of the WORK and IWORK\n\
  *          arrays, returns these values as the first entries of the WORK\n\
  *          and IWORK arrays, and no error message related to LWORK or\n\
  *          LIWORK is issued by XERBLA.\n\
  *\n\
  *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))\n\
  *          On exit, if INFO = 0, IWORK(1) returns the optimal (and\n\
  *          minimal) LIWORK.\n\
  *\n\
  *  LIWORK  (input) INTEGER\n\
  *          The dimension of the array IWORK.  LIWORK >= 10*N.\n\
  *\n\
  *          If LIWORK = -1, then a workspace query is assumed; the\n\
  *          routine only calculates the optimal sizes of the WORK and\n\
  *          IWORK arrays, returns these values as the first entries of\n\
  *          the WORK and IWORK arrays, and no error message related to\n\
  *          LWORK or LIWORK is issued by XERBLA.\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value\n\
  *          > 0:  Internal error\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  Based on contributions by\n\
  *     Inderjit Dhillon, IBM Almaden, USA\n\
  *     Osni Marques, LBNL/NERSC, USA\n\
  *     Ken Stanley, Computer Science Division, University of\n\
  *       California at Berkeley, USA\n\
  *     Jason Riedy, Computer Science Division, University of\n\
  *       California at Berkeley, USA\n\
  *\n\
  *  =====================================================================\n\
  *\n"
