stegr(3)

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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