table of contents
| heevd(3) | LAPACK | heevd(3) |
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, integer lrwork, 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
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then 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).
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 = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ = 'V' 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 (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 = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' 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 = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' 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 = 'N', 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 = 'V', 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, double precision, 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
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then 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).
W
W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK
WORK is DOUBLE PRECISION array,
dimension (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 = 'N' and N > 1, LWORK must be at least 2*N+1.
If JOBZ = 'V' 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 = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' 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 = 'N', 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 = 'V', 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.
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
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then 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).
W
W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK
WORK is REAL array,
dimension (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 = 'N' and N > 1, LWORK must be at least 2*N+1.
If JOBZ = 'V' 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 = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' 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 = 'N', 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 = 'V', 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.
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
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then 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).
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 = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ = 'V' 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 (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 = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' 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 = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' 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 = 'N', 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 = 'V', 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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