Man page - heevd(3)

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Manual

heevd

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cheevd (character jobz, character uplo, integer n, complex,dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex,dimension( * ) work, integer lwork, real, dimension( * ) rwork, integerlrwork, integer, dimension( * ) iwork, integer liwork, integer info)
subroutine dsyevd (character jobz, character uplo, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) w, double precision, dimension( * ) work, integer lwork,integer, dimension( * ) iwork, integer liwork, integer info)
subroutine ssyevd (character jobz, character uplo, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,dimension( * ) work, integer lwork, integer, dimension( * ) iwork,integer liwork, integer info)
subroutine zheevd (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 lrwork, integer, dimension( * ) iwork,integer liwork, integer info)
Author

NAME

heevd - {he,sy}evd: eig, divide and conquer

SYNOPSIS

Functions

subroutine cheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)
CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
subroutine dsyevd (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine ssyevd (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
subroutine zheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Detailed Description

Function Documentation

subroutine cheevd (character jobz, character uplo, integer n, complex,dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex,dimension( * ) work, integer lwork, real, dimension( * ) rwork, integerlrwork, integer, dimension( * ) iwork, integer liwork, integer info)

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

Purpose:

CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.

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.
If N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be at least N + 1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least 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 must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK must be at least N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK must be at least
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 must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK must be at least 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: 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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified description of INFO. Sven, 16 Feb 05.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

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

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

Purpose:

DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.

Because of large use of BLAS of level 3, DSYEVD needs N**2 more
workspace than DSYEVX.

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 dimension of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be at least 2*N+1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least
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 must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK must be at least 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: 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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee
Modified description of INFO. Sven, 16 Feb 05.

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

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

Purpose:

SSYEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.

Because of large use of BLAS of level 3, SSYEVD needs N**2 more
workspace than SSYEVX.

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 dimension of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be at least 2*N+1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least
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 must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK must be at least 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: 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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee
Modified description of INFO. Sven, 16 Feb 05.

subroutine zheevd (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 lrwork, integer, dimension( * ) iwork,integer liwork, integer info)

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

Purpose:

ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.

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.
If N <= 1, LWORK must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be at least N + 1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be at least 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 must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LRWORK must be at least N.
If JOBZ = ā€™Vā€™ and N > 1, LRWORK must be at least
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 must be at least 1.
If JOBZ = ā€™Nā€™ and N > 1, LIWORK must be at least 1.
If JOBZ = ā€™Vā€™ and N > 1, LIWORK must be at least 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: 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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Modified description of INFO. Sven, 16 Feb 05.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Author

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