--- 
:name: zheevr
:md5sum: f47d50a9af6c562dfda0198807baa560
:category: :subroutine
:arguments: 
- jobz: 
    :type: char
    :intent: input
- range: 
    :type: char
    :intent: input
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- a: 
    :type: doublecomplex
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- vl: 
    :type: doublereal
    :intent: input
- vu: 
    :type: doublereal
    :intent: input
- il: 
    :type: integer
    :intent: input
- iu: 
    :type: integer
    :intent: input
- abstol: 
    :type: doublereal
    :intent: input
- m: 
    :type: integer
    :intent: output
- w: 
    :type: doublereal
    :intent: output
    :dims: 
    - n
- z: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - ldz
    - MAX(1,m)
- ldz: 
    :type: integer
    :intent: input
- isuppz: 
    :type: integer
    :intent: output
    :dims: 
    - 2*MAX(1,m)
- work: 
    :type: doublecomplex
    :intent: output
    :dims: 
    - MAX(1,lwork)
- lwork: 
    :type: integer
    :intent: input
    :option: true
    :default: 2*n
- rwork: 
    :type: doublereal
    :intent: output
    :dims: 
    - MAX(1,lrwork)
- lrwork: 
    :type: integer
    :intent: input
    :option: true
    :default: 24*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,\"A\") ? n : lsame_(&range,\"I\") ? iu-il+1 : 0"
:fortran_help: "      SUBROUTINE ZHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  ZHEEVR computes selected eigenvalues and, optionally, eigenvectors\n\
  *  of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can\n\
  *  be selected by specifying either a range of values or a range of\n\
  *  indices for the desired eigenvalues.\n\
  *\n\
  *  ZHEEVR first reduces the matrix A to tridiagonal form T with a call\n\
  *  to ZHETRD.  Then, whenever possible, ZHEEVR calls ZSTEMR to compute\n\
  *  eigenspectrum using Relatively Robust Representations.  ZSTEMR\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.\n\
  *\n\
  *  For each unreduced block (submatrix) of T,\n\
  *     (a) Compute T - sigma I  = L D L^T, so that L and D\n\
  *         define all the wanted eigenvalues to high relative accuracy.\n\
  *         This means that small relative changes in the entries of D and L\n\
  *         cause only small relative changes in the eigenvalues and\n\
  *         eigenvectors. The standard (unfactored) representation of the\n\
  *         tridiagonal matrix T does not have this property in general.\n\
  *     (b) Compute the eigenvalues to suitable accuracy.\n\
  *         If the eigenvectors are desired, the algorithm attains full\n\
  *         accuracy of the computed eigenvalues only right before\n\
  *         the corresponding vectors have to be computed, see steps c) and d).\n\
  *     (c) For each cluster of close eigenvalues, select a new\n\
  *         shift close to the cluster, find a new factorization, and refine\n\
  *         the shifted eigenvalues to suitable accuracy.\n\
  *     (d) For each eigenvalue with a large enough relative separation compute\n\
  *         the corresponding eigenvector by forming a rank revealing twisted\n\
  *         factorization. Go back to (c) for any clusters that remain.\n\
  *\n\
  *  The desired accuracy of the output can be specified by the input\n\
  *  parameter ABSTOL.\n\
  *\n\
  *  For more details, see DSTEMR's documentation and:\n\
  *  - Inderjit S. Dhillon and Beresford N. Parlett: \"Multiple representations\n\
  *    to compute orthogonal eigenvectors of symmetric tridiagonal matrices,\"\n\
  *    Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.\n\
  *  - Inderjit Dhillon and Beresford Parlett: \"Orthogonal Eigenvectors and\n\
  *    Relative Gaps,\" SIAM Journal on Matrix Analysis and Applications, Vol. 25,\n\
  *    2004.  Also LAPACK Working Note 154.\n\
  *  - Inderjit Dhillon: \"A new O(n^2) algorithm for the symmetric\n\
  *    tridiagonal eigenvalue/eigenvector problem\",\n\
  *    Computer Science Division Technical Report No. UCB/CSD-97-971,\n\
  *    UC Berkeley, May 1997.\n\
  *\n\
  *\n\
  *  Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested\n\
  *  on machines which conform to the ieee-754 floating point standard.\n\
  *  ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and\n\
  *  when partial spectrum requests are made.\n\
  *\n\
  *  Normal execution of ZSTEMR 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, DSTEBZ and\n\
  ********** ZSTEIN are called\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          = 'U':  Upper triangle of A is stored;\n\
  *          = 'L':  Lower triangle of A is stored.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The order of the matrix A.  N >= 0.\n\
  *\n\
  *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)\n\
  *          On entry, the Hermitian matrix A.  If UPLO = 'U', the\n\
  *          leading N-by-N upper triangular part of A contains the\n\
  *          upper triangular part of the matrix A.  If UPLO = 'L',\n\
  *          the leading N-by-N lower triangular part of A contains\n\
  *          the lower triangular part of the matrix A.\n\
  *          On exit, the lower triangle (if UPLO='L') or the upper\n\
  *          triangle (if UPLO='U') of A, including the diagonal, is\n\
  *          destroyed.\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A.  LDA >= max(1,N).\n\
  *\n\
  *  VL      (input) DOUBLE PRECISION\n\
  *  VU      (input) DOUBLE PRECISION\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) DOUBLE PRECISION\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\
  *          DLAMCH( '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\
  *          furutre 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) DOUBLE PRECISION array, dimension (N)\n\
  *          The first M elements contain the selected eigenvalues in\n\
  *          ascending order.\n\
  *\n\
  *  Z       (output) COMPLEX*16 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\
  *          If JOBZ = 'N', then Z is not referenced.\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) COMPLEX*16 array, dimension (MAX(1,LWORK))\n\
  *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
  *\n\
  *  LWORK   (input) INTEGER\n\
  *          The length of the array WORK.  LWORK >= max(1,2*N).\n\
  *          For optimal efficiency, LWORK >= (NB+1)*N,\n\
  *          where NB is the max of the blocksize for ZHETRD and for\n\
  *          ZUNMTR as returned by ILAENV.\n\
  *\n\
  *          If LWORK = -1, then a workspace query is assumed; the routine\n\
  *          only calculates the optimal sizes of the WORK, RWORK and\n\
  *          IWORK arrays, returns these values as the first entries of\n\
  *          the WORK, RWORK and IWORK arrays, and no error message\n\
  *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.\n\
  *\n\
  *  RWORK   (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))\n\
  *          On exit, if INFO = 0, RWORK(1) returns the optimal\n\
  *          (and minimal) LRWORK.\n\
  *\n\
  * LRWORK   (input) INTEGER\n\
  *          The length of the array RWORK.  LRWORK >= max(1,24*N).\n\
  *\n\
  *          If LRWORK = -1, then a workspace query is assumed; the\n\
  *          routine only calculates the optimal sizes of the WORK, RWORK\n\
  *          and IWORK arrays, returns these values as the first entries\n\
  *          of the WORK, RWORK and IWORK arrays, and no error message\n\
  *          related to LWORK or LRWORK or 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\n\
  *          (and minimal) LIWORK.\n\
  *\n\
  * LIWORK   (input) INTEGER\n\
  *          The dimension of the array IWORK.  LIWORK >= max(1,10*N).\n\
  *\n\
  *          If LIWORK = -1, then a workspace query is assumed; the\n\
  *          routine only calculates the optimal sizes of the WORK, RWORK\n\
  *          and IWORK arrays, returns these values as the first entries\n\
  *          of the WORK, RWORK and IWORK arrays, and no error message\n\
  *          related to LWORK or LRWORK 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"