Man page - heevx(3)

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Manual

heevx

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cheevx (character jobz, character range, character uplo, integern, complex, dimension( lda, * ) a, integer lda, real vl, real vu,integer il, integer iu, real abstol, integer m, real, dimension( * ) w,complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * )work, integer lwork, real, dimension( * ) rwork, integer, dimension( *) iwork, integer, dimension( * ) ifail, integer info)
subroutine dsyevx (character jobz, character range, character uplo, integern, double precision, dimension( lda, * ) a, integer lda, doubleprecision vl, double precision vu, integer il, integer iu, doubleprecision abstol, integer m, double precision, dimension( * ) w, doubleprecision, dimension( ldz, * ) z, integer ldz, double precision,dimension( * ) work, integer lwork, integer, dimension( * ) iwork,integer, dimension( * ) ifail, integer info)
subroutine ssyevx (character jobz, character range, character uplo, integern, real, dimension( lda, * ) a, integer lda, real vl, real vu, integeril, integer iu, real abstol, integer m, real, dimension( * ) w, real,dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integerlwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail,integer info)
subroutine zheevx (character jobz, character range, character uplo, integern, complex*16, dimension( lda, * ) a, integer lda, 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, complex*16, dimension( * ) work, integerlwork, double precision, dimension( * ) rwork, integer, dimension( * )iwork, integer, dimension( * ) ifail, integer info)
Author

NAME

heevx - {he,sy}evx: eig, bisection

SYNOPSIS

Functions

subroutine cheevx (jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, rwork, iwork, ifail, info)
CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
subroutine dsyevx (jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, iwork, ifail, info)
DSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine ssyevx (jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, iwork, ifail, info)
SSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine zheevx (jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, rwork, iwork, ifail, info)
ZHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Detailed Description

Function Documentation

subroutine cheevx (character jobz, character range, character uplo, integern, complex, dimension( lda, * ) a, integer lda, real vl, real vu,integer il, integer iu, real abstol, integer m, real, dimension( * ) w,complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * )work, integer lwork, real, dimension( * ) rwork, integer, dimension( *) iwork, integer, dimension( * ) ifail, integer info)

CHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Purpose:

CHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.

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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N

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

A

A is COMPLEX array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = ’U’, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ’L’,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO=’L’) or the upper
triangle (if UPLO=’U’) of A, including the diagonal, is
destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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; IL = 1 and IU = 0 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; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = ’A’ or ’V’.

ABSTOL

ABSTOL is REAL
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to

ABSTOL + EPS * max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH(’S’), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH(’S’).

See ’Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy,’ by Demmel and
Kahan, LAPACK Working Note #3.

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)
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.

Z

Z is COMPLEX array, dimension (LDZ, max(1,M))
If JOBZ = ’V’, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
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.

LDZ

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

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise 2*N.
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the max of the blocksize for CHETRD and for
CUNMTR as returned by ILAENV.

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.

RWORK

RWORK is REAL array, dimension (7*N)

IWORK

IWORK is INTEGER array, dimension (5*N)

IFAIL

IFAIL is INTEGER array, dimension (N)
If JOBZ = ’V’, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = ’N’, then IFAIL is not referenced.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsyevx (character jobz, character range, character uplo, integern, double precision, dimension( lda, * ) a, integer lda, doubleprecision vl, double precision vu, integer il, integer iu, doubleprecision abstol, integer m, double precision, dimension( * ) w, doubleprecision, dimension( ldz, * ) z, integer ldz, double precision,dimension( * ) work, integer lwork, integer, dimension( * ) iwork,integer, dimension( * ) ifail, integer info)

DSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

Purpose:

DSYEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.

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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N

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

A

A is DOUBLE PRECISION array, dimension (LDA, N)
On entry, the symmetric matrix A. If UPLO = ’U’, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ’L’,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO=’L’) or the upper
triangle (if UPLO=’U’) of A, including the diagonal, is
destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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; IL = 1 and IU = 0 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; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = ’A’ or ’V’.

ABSTOL

ABSTOL is DOUBLE PRECISION
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to

ABSTOL + EPS * max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH(’S’), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH(’S’).

See ’Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy,’ by Demmel and
Kahan, LAPACK Working Note #3.

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)
On normal exit, 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’, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
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.

LDZ

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

WORK

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

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise 8*N.
For optimal efficiency, LWORK >= (NB+3)*N,
where NB is the max of the blocksize for DSYTRD and DORMTR
returned by ILAENV.

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 (5*N)

IFAIL

IFAIL is INTEGER array, dimension (N)
If JOBZ = ’V’, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = ’N’, then IFAIL is not referenced.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssyevx (character jobz, character range, character uplo, integern, real, dimension( lda, * ) a, integer lda, real vl, real vu, integeril, integer iu, real abstol, integer m, real, dimension( * ) w, real,dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integerlwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail,integer info)

SSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

Purpose:

SSYEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.

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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N

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

A

A is REAL array, dimension (LDA, N)
On entry, the symmetric matrix A. If UPLO = ’U’, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ’L’,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO=’L’) or the upper
triangle (if UPLO=’U’) of A, including the diagonal, is
destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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; IL = 1 and IU = 0 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; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = ’A’ or ’V’.

ABSTOL

ABSTOL is REAL
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to

ABSTOL + EPS * max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH(’S’), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH(’S’).

See ’Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy,’ by Demmel and
Kahan, LAPACK Working Note #3.

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)
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.

Z

Z is REAL array, dimension (LDZ, max(1,M))
If JOBZ = ’V’, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
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.

LDZ

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

WORK

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

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise 8*N.
For optimal efficiency, LWORK >= (NB+3)*N,
where NB is the max of the blocksize for SSYTRD and SORMTR
returned by ILAENV.

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 (5*N)

IFAIL

IFAIL is INTEGER array, dimension (N)
If JOBZ = ’V’, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = ’N’, then IFAIL is not referenced.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zheevx (character jobz, character range, character uplo, integern, complex*16, dimension( lda, * ) a, integer lda, 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, complex*16, dimension( * ) work, integerlwork, double precision, dimension( * ) rwork, integer, dimension( * )iwork, integer, dimension( * ) ifail, integer info)

ZHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Purpose:

ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.

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.

UPLO

UPLO is CHARACTER*1
= ’U’: Upper triangle of A is stored;
= ’L’: Lower triangle of A is stored.

N

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

A

A is COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = ’U’, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ’L’,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, the lower triangle (if UPLO=’L’) or the upper
triangle (if UPLO=’U’) of A, including the diagonal, is
destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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; IL = 1 and IU = 0 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; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = ’A’ or ’V’.

ABSTOL

ABSTOL is DOUBLE PRECISION
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to

ABSTOL + EPS * max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH(’S’), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH(’S’).

See ’Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy,’ by Demmel and
Kahan, LAPACK Working Note #3.

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)
On normal exit, 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’, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
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.

LDZ

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

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise 2*N.
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the max of the blocksize for ZHETRD and for
ZUNMTR as returned by ILAENV.

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.

RWORK

RWORK is DOUBLE PRECISION array, dimension (7*N)

IWORK

IWORK is INTEGER array, dimension (5*N)

IFAIL

IFAIL is INTEGER array, dimension (N)
If JOBZ = ’V’, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = ’N’, then IFAIL is not referenced.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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