Man page - heev(3)

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Manual

heev

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cheev (character jobz, character uplo, integer n, complex,dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex,dimension( * ) work, integer lwork, real, dimension( * ) rwork, integerinfo)
subroutine dsyev (character jobz, character uplo, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) w, double precision, dimension( * ) work, integer lwork,integer info)
subroutine ssyev (character jobz, character uplo, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,dimension( * ) work, integer lwork, integer info)
subroutine zheev (character jobz, character uplo, integer n, complex*16,dimension( lda, * ) a, integer lda, double precision, dimension( * ) w,complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer info)
Author

NAME

heev - {he,sy}ev: eig, QR iteration

SYNOPSIS

Functions

subroutine cheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
subroutine dsyev (jobz, uplo, n, a, lda, w, work, lwork, info)
DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine ssyev (jobz, uplo, n, a, lda, w, work, lwork, info)
SSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine zheev (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Detailed Description

Function Documentation

subroutine cheev (character jobz, character uplo, integer n, complex,dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex,dimension( * ) work, integer lwork, real, dimension( * ) rwork, integerinfo)

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

Purpose:

CHEEV computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A.

Parameters

JOBZ

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

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = 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
orthonormal eigenvectors of the matrix A.
If JOBZ = ā€™Nā€™, then on exit the lower triangle (if UPLO=ā€™Lā€™)
or the upper triangle (if UPLO=ā€™Uā€™) of A, including the
diagonal, is destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsyev (character jobz, character uplo, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) w, double precision, dimension( * ) work, integer lwork,integer info)

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

Purpose:

DSYEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A.

Parameters

JOBZ

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

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = 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
orthonormal eigenvectors of the matrix A.
If JOBZ = ā€™Nā€™, then on exit the lower triangle (if UPLO=ā€™Lā€™)
or the upper triangle (if UPLO=ā€™Uā€™) of A, including the
diagonal, is destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssyev (character jobz, character uplo, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,dimension( * ) work, integer lwork, integer info)

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

Purpose:

SSYEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A.

Parameters

JOBZ

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

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = 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
orthonormal eigenvectors of the matrix A.
If JOBZ = ā€™Nā€™, then on exit the lower triangle (if UPLO=ā€™Lā€™)
or the upper triangle (if UPLO=ā€™Uā€™) of A, including the
diagonal, is destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zheev (character jobz, character uplo, integer n, complex*16,dimension( lda, * ) a, integer lda, double precision, dimension( * ) w,complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer info)

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

Purpose:

ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A.

Parameters

JOBZ

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

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: 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 = 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
orthonormal eigenvectors of the matrix A.
If JOBZ = ā€™Nā€™, then on exit the lower triangle (if UPLO=ā€™Lā€™)
or the upper triangle (if UPLO=ā€™Uā€™) of A, including the
diagonal, is destroyed.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= 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: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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