LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
 All Files Functions Groups
zstegr.f File Reference

Go to the source code of this file.



Function/Subroutine Documentation

subroutine zstegr ( character  JOBZ,
character  RANGE,
integer  N,
double precision, dimension( * )  D,
double precision, dimension( * )  E,
double precision  VL,
double precision  VU,
integer  IL,
integer  IU,
double precision  ABSTOL,
integer  M,
double precision, dimension( * )  W,
complex*16, dimension( ldz, * )  Z,
integer  LDZ,
integer, dimension( * )  ISUPPZ,
double precision, dimension( * )  WORK,
integer  LWORK,
integer, dimension( * )  IWORK,
integer  LIWORK,
integer  INFO 


Download ZSTEGR + dependencies [TGZ] [ZIP] [TXT]
 ZSTEGR computes selected eigenvalues and, optionally, eigenvectors
 of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
 a well defined set of pairwise different real eigenvalues, the corresponding
 real eigenvectors are pairwise orthogonal.

 The spectrum may be computed either completely or partially by specifying
 either an interval (VL,VU] or a range of indices IL:IU for the desired

 ZSTEGR is a compatability wrapper around the improved ZSTEMR routine.
 See DSTEMR for further details.

 One important change is that the ABSTOL parameter no longer provides any
 benefit and hence is no longer used.

 Note : ZSTEGR and ZSTEMR work only on machines which follow
 IEEE-754 floating-point standard in their handling of infinities and
 NaNs.  Normal execution may create these exceptiona values and hence
 may abort due to a floating point exception in environments which
 do not conform to the IEEE-754 standard.
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.
          RANGE is 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 is INTEGER
          The order of the matrix.  N >= 0.
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the N diagonal elements of the tridiagonal matrix
          T. On exit, D is overwritten.
          E is DOUBLE PRECISION 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.

          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 is INTEGER
          IU is 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'.
          Unused.  Was the absolute error tolerance for the
          eigenvalues/eigenvectors in previous versions.
          M is INTEGER
          The total number of eigenvalues found.  0 <= M <= N.
          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
          W is DOUBLE PRECISION array, dimension (N)
          The first M elements contain the selected eigenvalues in
          ascending order.
          Z is COMPLEX*16 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 an upper bound must be used.
          Supplying N columns is always safe.
          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', then LDZ >= max(1,N).
          ISUPPZ is 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 eigenvector
          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.
          WORK is DOUBLE PRECISION array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal
          (and minimal) LWORK.
          LWORK is 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 is INTEGER array, dimension (LIWORK)
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
          LIWORK is 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 is 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 DLARRE,
                if INFO = 2X, internal error in ZLARRV.
                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
                the nonzero error code returned by DLARRE or
                ZLARRV, respectively.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, LBNL/NERSC, USA

Definition at line 255 of file zstegr.f.

Here is the call graph for this function: