ZHEEVD(3F) ZHEEVD(3F)
ZHEEVD - compute all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A
SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 A( LDA, * ), WORK( * )
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading Nby-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
Page 1
ZHEEVD(3F) ZHEEVD(3F)
destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) 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.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
optimal LRWORK.
LRWORK (input) 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 + 4*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k
such that 2**k >= N .
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) 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
2 + 5*N.
INFO (output) 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 offdiagonal
elements of an intermediate tridiagonal form did not
converge to zero.
ZHEEVD(3F) ZHEEVD(3F)
ZHEEVD - compute all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A
SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 A( LDA, * ), WORK( * )
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits which
subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading Nby-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
Page 1
ZHEEVD(3F) ZHEEVD(3F)
destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) 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.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
optimal LRWORK.
LRWORK (input) 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 + 4*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k
such that 2**k >= N .
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) 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
2 + 5*N.
INFO (output) 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 offdiagonal
elements of an intermediate tridiagonal form did not
converge to zero.
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