.TH "stegr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
stegr \- stegr: eig, bisection, see stemr
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcstegr\fP (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz, work, lwork, iwork, liwork, info)"
.br
.RI "\fBCSTEGR\fP "
.ti -1c
.RI "subroutine \fBdstegr\fP (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz, work, lwork, iwork, liwork, info)"
.br
.RI "\fBDSTEGR\fP "
.ti -1c
.RI "subroutine \fBsstegr\fP (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz, work, lwork, iwork, liwork, info)"
.br
.RI "\fBSSTEGR\fP "
.ti -1c
.RI "subroutine \fBzstegr\fP (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz, work, lwork, iwork, liwork, info)"
.br
.RI "\fBZSTEGR\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cstegr (character jobz, character range, integer n, real, dimension( * ) d, real, dimension( * ) e, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, integer, dimension( * ) isuppz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBCSTEGR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CSTEGR 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\&.
!>
!> CSTEGR is a compatibility wrapper around the improved CSTEMR routine\&.
!> See SSTEMR for further details\&.
!>
!> One important change is that the ABSTOL parameter no longer provides any
!> benefit and hence is no longer used\&.
!>
!> Note : CSTEGR and CSTEMR work only on machines which follow
!> IEEE-754 floating-point standard in their handling of infinities and
!> NaNs\&.  Normal execution may create these exceptional values and hence
!> may abort due to a floating point exception in environments which
!> do not conform to the IEEE-754 standard\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors\&.
!> 
.fi
.PP
.br
\fIRANGE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>          On entry, the N diagonal elements of the tridiagonal matrix
!>          T\&. On exit, D is overwritten\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is 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\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is REAL
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIVU\fP 
.PP
.nf
!>          VU is REAL
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIIL\fP 
.PP
.nf
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIIU\fP 
.PP
.nf
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIABSTOL\fP 
.PP
.nf
!>          ABSTOL is REAL
!>          Unused\&.  Was the absolute error tolerance for the
!>          eigenvalues/eigenvectors in previous versions\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is REAL array, dimension (N)
!>          The first M elements contain the selected eigenvalues in
!>          ascending order\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is COMPLEX 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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= 1, and if
!>          JOBZ = 'V', then LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal
!>          (and minimal) LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (LIWORK)
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&.
!> 
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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 SLARRE,
!>                if INFO = 2X, internal error in CLARRV\&.
!>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
!>                the nonzero error code returned by SLARRE or
!>                CLARRV, respectively\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Inderjit Dhillon, IBM Almaden, USA 
.br
Osni Marques, LBNL/NERSC, USA 
.br
Christof Voemel, LBNL/NERSC, USA 
.br
.RE
.PP

.PP
Definition at line \fB262\fP of file \fBcstegr\&.f\fP\&.
.SS "subroutine dstegr (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, double precision, dimension( ldz, * ) z, integer ldz, integer, dimension( * ) isuppz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBDSTEGR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DSTEGR 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\&.
!>
!> DSTEGR is a compatibility wrapper around the improved DSTEMR 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 : DSTEGR and DSTEMR work only on machines which follow
!> IEEE-754 floating-point standard in their handling of infinities and
!> NaNs\&.  Normal execution may create these exceptional values and hence
!> may abort due to a floating point exception in environments which
!> do not conform to the IEEE-754 standard\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors\&.
!> 
.fi
.PP
.br
\fIRANGE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the N diagonal elements of the tridiagonal matrix
!>          T\&. On exit, D is overwritten\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is DOUBLE PRECISION
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIVU\fP 
.PP
.nf
!>          VU is DOUBLE PRECISION
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIIL\fP 
.PP
.nf
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIIU\fP 
.PP
.nf
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIABSTOL\fP 
.PP
.nf
!>          ABSTOL is DOUBLE PRECISION
!>          Unused\&.  Was the absolute error tolerance for the
!>          eigenvalues/eigenvectors in previous versions\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is DOUBLE PRECISION array, dimension (N)
!>          The first M elements contain the selected eigenvalues in
!>          ascending order\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is DOUBLE PRECISION 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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= 1, and if
!>          JOBZ = 'V', then LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal
!>          (and minimal) LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (LIWORK)
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&.
!> 
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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 DLARRV\&.
!>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
!>                the nonzero error code returned by DLARRE or
!>                DLARRV, respectively\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Inderjit Dhillon, IBM Almaden, USA 
.br
Osni Marques, LBNL/NERSC, USA 
.br
Christof Voemel, LBNL/NERSC, USA 
.br
.RE
.PP

.PP
Definition at line \fB262\fP of file \fBdstegr\&.f\fP\&.
.SS "subroutine sstegr (character jobz, character range, integer n, real, dimension( * ) d, real, dimension( * ) e, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, integer, dimension( * ) isuppz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fBSSTEGR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SSTEGR 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\&.
!>
!> SSTEGR is a compatibility wrapper around the improved SSTEMR routine\&.
!> See SSTEMR for further details\&.
!>
!> One important change is that the ABSTOL parameter no longer provides any
!> benefit and hence is no longer used\&.
!>
!> Note : SSTEGR and SSTEMR work only on machines which follow
!> IEEE-754 floating-point standard in their handling of infinities and
!> NaNs\&.  Normal execution may create these exceptional values and hence
!> may abort due to a floating point exception in environments which
!> do not conform to the IEEE-754 standard\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors\&.
!> 
.fi
.PP
.br
\fIRANGE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is REAL array, dimension (N)
!>          On entry, the N diagonal elements of the tridiagonal matrix
!>          T\&. On exit, D is overwritten\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          E is 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\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is REAL
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIVU\fP 
.PP
.nf
!>          VU is REAL
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIIL\fP 
.PP
.nf
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIIU\fP 
.PP
.nf
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIABSTOL\fP 
.PP
.nf
!>          ABSTOL is REAL
!>          Unused\&.  Was the absolute error tolerance for the
!>          eigenvalues/eigenvectors in previous versions\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is REAL array, dimension (N)
!>          The first M elements contain the selected eigenvalues in
!>          ascending order\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is 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 an upper bound must be used\&.
!>          Supplying N columns is always safe\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= 1, and if
!>          JOBZ = 'V', then LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal
!>          (and minimal) LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (LIWORK)
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&.
!> 
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Inderjit Dhillon, IBM Almaden, USA 
.br
Osni Marques, LBNL/NERSC, USA 
.br
Christof Voemel, LBNL/NERSC, USA 
.br
.RE
.PP

.PP
Definition at line \fB262\fP of file \fBsstegr\&.f\fP\&.
.SS "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)"

.PP
\fBZSTEGR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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 compatibility wrapper around the improved ZSTEMR routine\&.
!> See ZSTEMR 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 exceptional values and hence
!> may abort due to a floating point exception in environments which
!> do not conform to the IEEE-754 standard\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors\&.
!> 
.fi
.PP
.br
\fIRANGE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fID\fP 
.PP
.nf
!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the N diagonal elements of the tridiagonal matrix
!>          T\&. On exit, D is overwritten\&.
!> 
.fi
.PP
.br
\fIE\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is DOUBLE PRECISION
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIVU\fP 
.PP
.nf
!>          VU is DOUBLE PRECISION
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIIL\fP 
.PP
.nf
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIIU\fP 
.PP
.nf
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIABSTOL\fP 
.PP
.nf
!>          ABSTOL is DOUBLE PRECISION
!>          Unused\&.  Was the absolute error tolerance for the
!>          eigenvalues/eigenvectors in previous versions\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is DOUBLE PRECISION array, dimension (N)
!>          The first M elements contain the selected eigenvalues in
!>          ascending order\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDZ >= 1, and if
!>          JOBZ = 'V', then LDZ >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal
!>          (and minimal) LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (LIWORK)
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&.
!> 
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Inderjit Dhillon, IBM Almaden, USA 
.br
Osni Marques, LBNL/NERSC, USA 
.br
Christof Voemel, LBNL/NERSC, USA 
.br
.RE
.PP

.PP
Definition at line \fB262\fP of file \fBzstegr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.