Man page - hegvd(3)

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Manual

hegvd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chegvd (integer itype, character jobz, character uplo, integern, complex, dimension( lda, * ) a, integer lda, complex, dimension(ldb, * ) b, integer ldb, real, dimension( * ) w, complex, dimension( *) work, integer lwork, real, dimension( * ) rwork, integer lrwork,integer, dimension( * ) iwork, integer liwork, integer info)
subroutine dsygvd (integer itype, character jobz, character uplo, integern, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( ldb, * ) b, integer ldb, double precision,dimension( * ) w, double precision, dimension( * ) work, integer lwork,integer, dimension( * ) iwork, integer liwork, integer info)
subroutine ssygvd (integer itype, character jobz, character uplo, integern, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * )b, integer ldb, real, dimension( * ) w, real, dimension( * ) work,integer lwork, integer, dimension( * ) iwork, integer liwork, integerinfo)
subroutine zhegvd (integer itype, character jobz, character uplo, integern, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,integer liwork, integer info)
Author

NAME

hegvd - {he,sy}gvd: eig, divide and conquer

SYNOPSIS

Functions

subroutine chegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, lrwork, iwork, liwork, info)
CHEGVD
subroutine dsygvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, iwork, liwork, info)
DSYGVD
subroutine ssygvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, iwork, liwork, info)
SSYGVD
subroutine zhegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHEGVD

Detailed Description

Function Documentation

subroutine chegvd (integer itype, character jobz, character uplo, integern, complex, dimension( lda, * ) a, integer lda, complex, dimension(ldb, * ) b, integer ldb, real, dimension( * ) w, complex, dimension( *) work, integer lwork, real, dimension( * ) rwork, integer lrwork,integer, dimension( * ) iwork, integer liwork, integer info)

CHEGVD

Purpose:

CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

A

A is COMPLEX array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.

On exit, if JOBZ = ā€™Vā€™, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then on exit the upper triangle (if UPLO=ā€™Uā€™)
or the lower triangle (if UPLO=ā€™Lā€™) of A, including the
diagonal, is destroyed.

LDA

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

B

B is COMPLEX array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.

LDB

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

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

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.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= N + 1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 2*N + N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

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

LRWORK

LRWORK is INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK >= N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

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

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPOTRF or CHEEVD returned an error code:
<= N: if INFO = i and JOBZ = ā€™Nā€™, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = ā€™Vā€™, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified so that no backsubstitution is performed if CHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

subroutine dsygvd (integer itype, character jobz, character uplo, integern, double precision, dimension( lda, * ) a, integer lda, doubleprecision, dimension( ldb, * ) b, integer ldb, double precision,dimension( * ) w, double precision, dimension( * ) work, integer lwork,integer, dimension( * ) iwork, integer liwork, integer info)

DSYGVD

Purpose:

DSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA, N)
On entry, the symmetric matrix A. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.

On exit, if JOBZ = ā€™Vā€™, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then on exit the upper triangle (if UPLO=ā€™Uā€™)
or the lower triangle (if UPLO=ā€™Lā€™) of A, including the
diagonal, is destroyed.

LDA

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

B

B is DOUBLE PRECISION array, dimension (LDB, N)
On entry, the symmetric matrix B. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T.

LDB

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

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

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 dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= 2*N+1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

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

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPOTRF or DSYEVD returned an error code:
<= N: if INFO = i and JOBZ = ā€™Nā€™, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = ā€™Vā€™, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified so that no backsubstitution is performed if DSYEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

subroutine ssygvd (integer itype, character jobz, character uplo, integern, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * )b, integer ldb, real, dimension( * ) w, real, dimension( * ) work,integer lwork, integer, dimension( * ) iwork, integer liwork, integerinfo)

SSYGVD

Purpose:

SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

A

A is REAL array, dimension (LDA, N)
On entry, the symmetric matrix A. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.

On exit, if JOBZ = ā€™Vā€™, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then on exit the upper triangle (if UPLO=ā€™Uā€™)
or the lower triangle (if UPLO=ā€™Lā€™) of A, including the
diagonal, is destroyed.

LDA

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

B

B is REAL array, dimension (LDB, N)
On entry, the symmetric matrix B. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T.

LDB

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

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

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 dimension of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= 2*N+1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 1 + 6*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

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

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPOTRF or SSYEVD returned an error code:
<= N: if INFO = i and JOBZ = ā€™Nā€™, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = ā€™Vā€™, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified so that no backsubstitution is performed if SSYEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

subroutine zhegvd (integer itype, character jobz, character uplo, integern, complex*16, dimension( lda, * ) a, integer lda, complex*16,dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,integer liwork, integer info)

ZHEGVD

Purpose:

ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

ITYPE

ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangles of A and B are stored;
= ā€™Lā€™: Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.

On exit, if JOBZ = ā€™Vā€™, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = ā€™Nā€™, then on exit the upper triangle (if UPLO=ā€™Uā€™)
or the lower triangle (if UPLO=ā€™Lā€™) of A, including the
diagonal, is destroyed.

LDA

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

B

B is COMPLEX*16 array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = ā€™Uā€™, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = ā€™Lā€™,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.

LDB

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

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

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.
If N <= 1, LWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK >= N + 1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK >= 2*N + N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

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

LRWORK

LRWORK is INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK >= N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK >= 1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

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

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK >= 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEVD returned an error code:
<= N: if INFO = i and JOBZ = ā€™Nā€™, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = ā€™Vā€™, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
principal minor of order i of B is not positive.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified so that no backsubstitution is performed if ZHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Author

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