SSTEDC(3F) SSTEDC(3F)
SSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method. The
eigenvectors of a full or band real symmetric matrix can also be found if
SSYTRD or SSPTRD or SSBTRD 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 SLAED3 for details.
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'I': Compute eigenvectors of tridiagonal matrix also.
= 'V': Compute eigenvectors of original dense symmetric matrix
also. On entry, Z contains the orthogonal 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) REAL 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) REAL array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix. On
exit, E has been destroyed.
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SSTEDC(3F) SSTEDC(3F)
Z (input/output) REAL array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the orthogonal 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 symmetric 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) REAL 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 N <= 1 then
LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK
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
then LWORK must be at least ( 1 + 3*N + 2*N*lg N + 2*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 then
LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then LIWORK
must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I' and N >
1 then 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).
SSTEDC(3F) SSTEDC(3F)
SSTEDC - compute all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method. The
eigenvectors of a full or band real symmetric matrix can also be found if
SSYTRD or SSPTRD or SSBTRD 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 SLAED3 for details.
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= 'I': Compute eigenvectors of tridiagonal matrix also.
= 'V': Compute eigenvectors of original dense symmetric matrix
also. On entry, Z contains the orthogonal 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) REAL 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) REAL array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix. On
exit, E has been destroyed.
Page 1
SSTEDC(3F) SSTEDC(3F)
Z (input/output) REAL array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the orthogonal 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 symmetric 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) REAL 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 N <= 1 then
LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK
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
then LWORK must be at least ( 1 + 3*N + 2*N*lg N + 2*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 then
LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then LIWORK
must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I' and N >
1 then 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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