Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       stegr - stegr: eig, bisection, see stemr

SYNOPSIS

   Functions
       subroutine cstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz,
           work, lwork, iwork, liwork, info)
           CSTEGR
       subroutine dstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz,
           work, lwork, iwork, liwork, info)
           DSTEGR
       subroutine sstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz,
           work, lwork, iwork, liwork, info)
           SSTEGR
       subroutine zstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz,
           work, lwork, iwork, liwork, info)
           ZSTEGR

Detailed Description

Function Documentation

   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)
       CSTEGR

       Purpose:

            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.

       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 REAL array, dimension (N)
                     On entry, the N diagonal elements of the tridiagonal matrix
                     T. On exit, D is overwritten.

           E

                     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.

           VL

                     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'.

           VU

                     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'.

           IL

                     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'.

           IU

                     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'.

           ABSTOL

                     ABSTOL is REAL
                     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 REAL array, dimension (N)
                     The first M elements contain the selected eigenvalues in
                     ascending order.

           Z

                     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.

           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 REAL 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 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Inderjit Dhillon, IBM Almaden, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, LBNL/NERSC, USA

   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)
       DSTEGR

       Purpose:

            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.

       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

                     If RANGE='V', the lower bound of the interval to
                     be searched for eigenvalues. VL < VU.
                     Not referenced if RANGE = 'A' or 'I'.

           VU

                     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'.

           IL

                     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'.

           IU

                     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'.

           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 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.

           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 DLARRV.
                           Here, the digit X = ABS( IINFO ) < 10, where IINFO is
                           the nonzero error code returned by DLARRE or
                           DLARRV, respectively.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Inderjit Dhillon, IBM Almaden, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, LBNL/NERSC, USA

   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)
       SSTEGR

       Purpose:

            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.

       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 REAL array, dimension (N)
                     On entry, the N diagonal elements of the tridiagonal matrix
                     T. On exit, D is overwritten.

           E

                     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.

           VL

                     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'.

           VU

                     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'.

           IL

                     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'.

           IU

                     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'.

           ABSTOL

                     ABSTOL is REAL
                     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 REAL array, dimension (N)
                     The first M elements contain the selected eigenvalues in
                     ascending order.

           Z

                     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.

           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 REAL 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 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Inderjit Dhillon, IBM Almaden, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, LBNL/NERSC, USA

   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)
       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 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.

       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

                     If RANGE='V', the lower bound of the interval to
                     be searched for eigenvalues. VL < VU.
                     Not referenced if RANGE = 'A' or 'I'.

           VU

                     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'.

           IL

                     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'.

           IU

                     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'.

           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.

       Contributors:
           Inderjit Dhillon, IBM Almaden, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, LBNL/NERSC, USA

Author

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