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Manual

stegr

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 is INTEGER
The order of the matrix. N >= 0.

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

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 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 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 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 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 is INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = ’A’, M = N, and if RANGE = ’I’, M = IU-IL+1.

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

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, doubleprecision, dimension( * ) d, double precision, dimension( * ) e, doubleprecision vl, double precision vu, integer il, integer iu, doubleprecision abstol, integer m, double precision, dimension( * ) w, doubleprecision, 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

N is INTEGER
The order of the matrix. N >= 0.

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

E is DOUBLE PRECISION array, dimension (N)
On entry, the (N-1) subdiagonal elements of the tridiagonal
matrix T in elements 1 to N-1 of E. E(N) need not be set on
input, but is used internally as workspace.
On exit, E is overwritten.

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 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 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 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 is INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = ’A’, M = N, and if RANGE = ’I’, M = IU-IL+1.

W is DOUBLE PRECISION array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order.

Z is 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

WORK

WORK is DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
(and minimal) LWORK.

LWORK

IWORK

IWORK is INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

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

N is INTEGER
The order of the matrix. N >= 0.

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

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 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 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 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 is INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = ’A’, M = N, and if RANGE = ’I’, M = IU-IL+1.

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

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

WORK

WORK is REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
(and minimal) LWORK.

LWORK

IWORK

IWORK is INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

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, doubleprecision, dimension( * ) d, double precision, dimension( * ) e, doubleprecision vl, double precision vu, integer il, integer iu, doubleprecision abstol, integer m, double precision, dimension( * ) w,complex16, 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

N is INTEGER
The order of the matrix. N >= 0.

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

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 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 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 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 is INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = ’A’, M = N, and if RANGE = ’I’, M = IU-IL+1.

W is DOUBLE PRECISION array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order.

Z is COMPLEX*16 array, dimension (LDZ, max(1,M) )
If JOBZ = ’V’, and if INFO = 0, then the first M columns of Z
contain the orthonormal eigenvectors of the matrix T
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If JOBZ = ’N’, then Z is not referenced.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = ’V’, the exact value of M
is not known in advance and an upper bound must be used.
Supplying N columns is always safe.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ’V’, then LDZ >= max(1,N).

ISUPPZ

WORK

WORK is DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
(and minimal) LWORK.

LWORK

IWORK

IWORK is INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

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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