Man page - hegv(3)

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Manual

hegv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chegv (integer itype, character jobz, character uplo, integer n,complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *) b, integer ldb, real, dimension( * ) w, complex, dimension( * ) work,integer lwork, real, dimension( * ) rwork, integer info)
subroutine dsygv (integer itype, character jobz, character uplo, integer n,double precision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,double precision, dimension( * ) work, integer lwork, integer info)
subroutine ssygv (integer itype, character jobz, character uplo, integer n,real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, real, dimension( * ) w, real, dimension( * ) work, integerlwork, integer info)
subroutine zhegv (integer itype, character jobz, character uplo, integer n,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 info)
Author

NAME

hegv - {he,sy}gv: eig, QR iteration

SYNOPSIS

Functions

subroutine chegv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info)
CHEGV
subroutine dsygv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, info)
DSYGV
subroutine ssygv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, info)
SSYGV
subroutine zhegv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info)
ZHEGV

Detailed Description

Function Documentation

subroutine chegv (integer itype, character jobz, character uplo, integer n,complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *) b, integer ldb, real, dimension( * ) w, complex, dimension( * ) work,integer lwork, real, dimension( * ) rwork, integer info)

CHEGV

Purpose:

CHEGV 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.

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 positive definite 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. LWORK >= max(1,2*N-1).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for CHETRD 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 (max(1, 3*N-2))

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPOTRF or CHEEV returned an error code:
<= N: if INFO = i, CHEEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> 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.

subroutine dsygv (integer itype, character jobz, character uplo, integer n,double precision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,double precision, dimension( * ) work, integer lwork, integer info)

DSYGV

Purpose:

DSYGV 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.

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 positive definite 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 length of the array WORK. LWORK >= max(1,3*N-1).
For optimal efficiency, LWORK >= (NB+2)*N,
where NB is the blocksize for DSYTRD 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPOTRF or DSYEV returned an error code:
<= N: if INFO = i, DSYEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> 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.

subroutine ssygv (integer itype, character jobz, character uplo, integer n,real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, real, dimension( * ) w, real, dimension( * ) work, integerlwork, integer info)

SSYGV

Purpose:

SSYGV 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.

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 positive definite 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 length of the array WORK. LWORK >= max(1,3*N-1).
For optimal efficiency, LWORK >= (NB+2)*N,
where NB is the blocksize for SSYTRD 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPOTRF or SSYEV returned an error code:
<= N: if INFO = i, SSYEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> 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.

subroutine zhegv (integer itype, character jobz, character uplo, integer n,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 info)

ZHEGV

Purpose:

ZHEGV 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.

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 positive definite 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. LWORK >= max(1,2*N-1).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for ZHETRD 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 (max(1, 3*N-2))

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEV returned an error code:
<= N: if INFO = i, ZHEEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> 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.

Author

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