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zstegr.f(3) LAPACK zstegr.f(3)

zstegr.f -


subroutine zstegr (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO)
 
ZSTEGR

ZSTEGR
Purpose:
 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 eigenvalues.
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.
Parameters:
JOBZ
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors.
RANGE
          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
          N is INTEGER
          The order of the matrix.  N >= 0.
D
          D is DOUBLE PRECISION array, dimension (N)
          On entry, the N diagonal elements of the tridiagonal matrix
          T. On exit, D is overwritten.
E
          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.
VL
          VL is DOUBLE PRECISION
VU
          VU is 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
          IL is INTEGER
IU
          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'.
ABSTOL
          ABSTOL is DOUBLE PRECISION
          Unused.  Was the absolute error tolerance for the
          eigenvalues/eigenvectors in previous versions.
M
          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
          W is DOUBLE PRECISION array, dimension (N)
          The first M elements contain the selected eigenvalues in
          ascending order.
Z
          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
          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          JOBZ = 'V', then LDZ >= max(1,N).
ISUPPZ
          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
          WORK is DOUBLE PRECISION array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal
          (and minimal) LWORK.
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
          IWORK is INTEGER array, dimension (LIWORK)
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
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
          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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Inderjit Dhillon, IBM Almaden, USA
 

Osni Marques, LBNL/NERSC, USA
 

Christof Voemel, LBNL/NERSC, USA
 
Definition at line 255 of file zstegr.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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