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## org.netlib.lapack
Class SSTEMR

    java.lang.Object
      org.netlib.lapack.SSTEMR

    public class SSTEMR

extends java.lang.Object

    SSTEMR is a simplified interface to the JLAPACK routine sstemr.
    This interface converts Java-style 2D row-major arrays into
    the 1D column-major linearized arrays expected by the lower
    level JLAPACK routines.  Using this interface also allows you
    to omit offset and leading dimension arguments.  However, because
    of these conversions, these routines will be slower than the low
    level ones.  Following is the description from the original Fortran
    source.  Contact seymour@cs.utk.edu with any questions.

     *     ..
     *
     *  Purpose
     *  =======
     *
     *  SSTEMR computes selected eigenvalues and, optionally, eigenvectors
     *  of a real symmetric tridiagonal matrix T. Any such unreduced matrix h
     *  a well defined set of pairwise different real eigenvalues, the corres
     *  real eigenvectors are pairwise orthogonal.
     *
     *  The spectrum may be computed either completely or partially by specif
     *  either an interval (VL,VU] or a range of indices IL:IU for the desire
     *  eigenvalues.
     *
     *  Depending on the number of desired eigenvalues, these are computed ei
     *  by bisection or the dqds algorithm. Numerically orthogonal eigenvecto
     *  computed by the use of various suitable L D L^T factorizations near c
     *  of close eigenvalues (referred to as RRRs, Relatively Robust
     *  Representations). An informal sketch of the algorithm follows.
     *
     *  For each unreduced block (submatrix) of T,
     *     (a) Compute T - sigma I  = L D L^T, so that L and D
     *         define all the wanted eigenvalues to high relative accuracy.
     *         This means that small relative changes in the entries of D and
     *         cause only small relative changes in the eigenvalues and
     *         eigenvectors. The standard (unfactored) representation of the

     *         tridiagonal matrix T does not have this property in general.
     *     (b) Compute the eigenvalues to suitable accuracy.
     *         If the eigenvectors are desired, the algorithm attains full
     *         accuracy of the computed eigenvalues only right before
     *         the corresponding vectors have to be computed, see steps c) an
     *     (c) For each cluster of close eigenvalues, select a new
     *         shift close to the cluster, find a new factorization, and refi
     *         the shifted eigenvalues to suitable accuracy.
     *     (d) For each eigenvalue with a large enough relative separation co
     *         the corresponding eigenvector by forming a rank revealing twis
     *         factorization. Go back to (c) for any clusters that remain.
     *
     *  For more details, see:
     *  - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representat
     *    to compute orthogonal eigenvectors of symmetric tridiagonal matrice
     *    Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
     *  - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors an
     *    Relative Gaps," SIAM Journal on Matrix Analysis and Applications, V
     *    2004.  Also LAPACK Working Note 154.
     *  - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
     *    tridiagonal eigenvalue/eigenvector problem",
     *    Computer Science Division Technical Report No. UCB/CSD-97-971,
     *    UC Berkeley, May 1997.
     *
     *  Notes:
     *  1.SSTEMR works only on machines which follow IEEE-754
     *  floating-point standard in their handling of infinities and NaNs.
     *  This permits the use of efficient inner loops avoiding a check for
     *  zero divisors.
     *
     *  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.
     *
     *  N       (input) INTEGER
     *          The order of the matrix.  N >= 0.
     *
     *  D       (input/output) REAL array, dimension (N)
     *          On entry, the N diagonal elements of the tridiagonal matrix
     *          T. On exit, D is overwritten.
     *
     *  E       (input/output) REAL array, dimension (N)
     *          On entry, the (N-1) subdiagonal elements of the tridiagonal
     *          matrix T in elements 1 to N-1 of E. E(N) need not be set on
     *          input, but is used internally as workspace.
     *          On exit, E is overwritten.
     *
     *  VL      (input) REAL
     *  VU      (input) REAL
     *          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.
     *          Not referenced if RANGE = 'A' or 'V'.
     *
     *  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) REAL array, dimension (N)
     *          The first M elements contain the selected eigenvalues in
     *          ascending order.
     *
     *  Z       (output) REAL array, dimension (LDZ, max(1,M) )
     *          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
     *          contain the orthonormal eigenvectors of the matrix T
     *          corresponding to the selected eigenvalues, with the i-th
     *          column of Z holding the eigenvector associated with W(i).
     *          If JOBZ = 'N', then Z is not referenced.
     *          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 can be computed with a workspace

     *          query by setting NZC = -1, see below.
     *
     *  LDZ     (input) INTEGER
     *          The leading dimension of the array Z.  LDZ >= 1, and if
     *          JOBZ = 'V', then LDZ >= max(1,N).
     *
     *  NZC     (input) INTEGER
     *          The number of eigenvectors to be held in the array Z.
     *          If RANGE = 'A', then NZC >= max(1,N).
     *          If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,
     *          If RANGE = 'I', then NZC >= IU-IL+1.
     *          If NZC = -1, then a workspace query is assumed; the
     *          routine calculates the number of columns of the array Z that

     *          are needed to hold the eigenvectors.
     *          This value is returned as the first entry of the Z array, and
     *          no error message related to NZC is issued by XERBLA.
     *
     *  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 computed eigen
     *          is nonzero only in elements ISUPPZ( 2*i-1 ) through
     *          ISUPPZ( 2*i ). This is relevant in the case when the matrix
     *          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
     *
     *  TRYRAC  (input/output) LOGICAL
     *          If TRYRAC.EQ..TRUE., indicates that the code should check whe
     *          the tridiagonal matrix defines its eigenvalues to high relati
     *          accuracy.  If so, the code uses relative-accuracy preserving

     *          algorithms that might be (a bit) slower depending on the matr
     *          If the matrix does not define its eigenvalues to high relativ
     *          accuracy, the code can uses possibly faster algorithms.
     *          If TRYRAC.EQ..FALSE., the code is not required to guarantee
     *          relatively accurate eigenvalues and can use the fastest possi
     *          techniques.
     *          On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix
     *          does not define its eigenvalues to high relative accuracy.
     *
     *  WORK    (workspace/output) REAL array, dimension (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(1,18*N)
     *          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
     *          If LWORK = -1, then a workspace query is assumed; the routine
     *          only calculates the optimal size of the WORK array, returns
     *          this value as the first entry of the WORK array, and no error
     *          message related to LWORK is issued by XERBLA.
     *
     *  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
     *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
     *
     *  LIWORK  (input) INTEGER
     *          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
     *          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
     *          if only the eigenvalues are to be computed.
     *          If LIWORK = -1, then a workspace query is assumed; the
     *          routine only calculates the optimal size of the IWORK array,

     *          returns this value as the first entry of the IWORK array, and
     *          no error message related to LIWORK is issued by XERBLA.
     *
     *  INFO    (output) INTEGER
     *          On exit, INFO
     *          = 0:  successful exit
     *          < 0:  if INFO = -i, the i-th argument had an illegal value
     *          > 0:  if INFO = 1X, internal error in SLARRE,
     *                if INFO = 2X, internal error in SLARRV.
     *                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
     *                the nonzero error code returned by SLARRE or
     *                SLARRV, respectively.
     *
     *
     *  Further Details
     *  ===============
     *
     *  Based on contributions by
     *     Beresford Parlett, University of California, Berkeley, USA
     *     Jim Demmel, University of California, Berkeley, USA
     *     Inderjit Dhillon, University of Texas, Austin, USA
     *     Osni Marques, LBNL/NERSC, USA
     *     Christof Voemel, University of California, Berkeley, USA
     *
     *  =====================================================================
     *
     *     .. Parameters ..

Constructor Summary
`SSTEMR()`

Method Summary
`static void` | `SSTEMR(java.lang.String jobz, java.lang.String range, int n, float[] d, float[] e, float vl, float vu, int il, int iu, intW m, float[] w, float[][] z, int nzc, int[] isuppz, booleanW tryrac, float[] work, int lwork, int[] iwork, int liwork, intW info)`

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### SSTEMR

    public SSTEMR()

Method Detail

### SSTEMR

    public static void SSTEMR(java.lang.String jobz,
                              java.lang.String range,
                              int n,
                              float[] d,
                              float[] e,
                              float vl,
                              float vu,
                              int il,
                              int iu,
                              intW m,
                              float[] w,
                              float[][] z,
                              int nzc,
                              int[] isuppz,
                              booleanW tryrac,
                              float[] work,
                              int lwork,
                              int[] iwork,
                              int liwork,
                              intW info)

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