ZSTEDC(3F) ZSTEDC(3F)
ZSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), RWORK( * )
COMPLEX*16 WORK( * ), Z( LDZ, * )
ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method. The
eigenvectors of a full or band complex Hermitian matrix can also be found
if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to
tridiagonal form.
This code 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. See DLAED3 for details.
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'I': Compute eigenvectors of tridiagonal matrix also.
= 'V': Compute eigenvectors of original Hermitian matrix also.
On entry, Z contains the unitary matrix used to reduce the
original matrix to tridiagonal form.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On
exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix. On
exit, E has been destroyed.
Page 1
ZSTEDC(3F) ZSTEDC(3F)
Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the unitary matrix used
in the reduction to tridiagonal form. On exit, if INFO = 0, then
if COMPZ = 'V', Z contains the orthonormal eigenvectors of the
original Hermitian matrix, and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix. If
COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1. If eigenvectors
are desired, then LDZ >= max(1,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If COMPZ = 'N' or 'I', or N <=
1, LWORK must be at least 1. If COMPZ = 'V' and N > 1, LWORK
must be at least N*N.
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 COMPZ = 'N' or N <= 1,
LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK must
be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
smallest integer k such that 2**k >= N. If COMPZ = 'I' and N >
1, LRWORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 .
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 COMPZ = 'N' or N <= 1,
LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK must
be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or 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: 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).
ZSTEDC(3F) ZSTEDC(3F)
ZSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
IWORK, LIWORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), RWORK( * )
COMPLEX*16 WORK( * ), Z( LDZ, * )
ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method. The
eigenvectors of a full or band complex Hermitian matrix can also be found
if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to
tridiagonal form.
This code 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. See DLAED3 for details.
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'I': Compute eigenvectors of tridiagonal matrix also.
= 'V': Compute eigenvectors of original Hermitian matrix also.
On entry, Z contains the unitary matrix used to reduce the
original matrix to tridiagonal form.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On
exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix. On
exit, E has been destroyed.
Page 1
ZSTEDC(3F) ZSTEDC(3F)
Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the unitary matrix used
in the reduction to tridiagonal form. On exit, if INFO = 0, then
if COMPZ = 'V', Z contains the orthonormal eigenvectors of the
original Hermitian matrix, and if COMPZ = 'I', Z contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix. If
COMPZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1. If eigenvectors
are desired, then LDZ >= max(1,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If COMPZ = 'N' or 'I', or N <=
1, LWORK must be at least 1. If COMPZ = 'V' and N > 1, LWORK
must be at least N*N.
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 COMPZ = 'N' or N <= 1,
LRWORK must be at least 1. If COMPZ = 'V' and N > 1, LRWORK must
be at least 1 + 3*N + 2*N*lg N + 3*N**2 , where lg( N ) =
smallest integer k such that 2**k >= N. If COMPZ = 'I' and N >
1, LRWORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 .
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 COMPZ = 'N' or N <= 1,
LIWORK must be at least 1. If COMPZ = 'V' or N > 1, LIWORK must
be at least 6 + 6*N + 5*N*lg N. If COMPZ = 'I' or 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: 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).
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