SLAED0(3F) SLAED0(3F)
SLAED0 - compute all eigenvalues and corresponding eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
IWORK, INFO )
INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
INTEGER IWORK( * )
REAL D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), WORK(
* )
SLAED0 computes all eigenvalues and corresponding eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
ICOMPQ (input) INTEGER
= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense symmetric matrix
also. On entry, Q contains the orthogonal matrix used to reduce
the original matrix to tridiagonal form. = 2: Compute
eigenvalues and eigenvectors of tridiagonal matrix.
QSIZ (input) INTEGER
The dimension of the orthogonal matrix used to reduce the full
matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the main diagonal of the tridiagonal matrix. On exit,
its eigenvalues.
E (input) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix. On exit, E
has been destroyed.
Q (input/output) REAL array, dimension (LDQ, N)
On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ =
0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a
subset of the columns of the orthogonal matrix used to reduce the
full matrix to tridiagonal form corresponding to the subset of the
full matrix which is being decomposed at this time. If ICOMPQ = 2
On entry, Q will be the identity matrix. On exit, Q contains the
eigenvectors of the tridiagonal matrix.
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SLAED0(3F) SLAED0(3F)
LDQ (input) INTEGER
The leading dimension of the array Q. If eigenvectors are
desired, then LDQ >= max(1,N). In any case, LDQ >= 1.
QSTORE (workspace) REAL array, dimension (LDQS, N) Referenced only
when ICOMPQ = 1. Used to store parts of the eigenvector matrix
when the updating matrix multiplies take place.
LDQS (input) INTEGER
The leading dimension of the array QSTORE. If ICOMPQ = 1, then
LDQS >= max(1,N). In any case, LDQS >= 1.
WORK (workspace) REAL array,
dimension (1 + 3*N + 2*N*lg N + 2*N**2) ( lg( N ) = smallest
integer k such that 2^k >= N )
IWORK (workspace) INTEGER array,
If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 +
6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N
) If ICOMPQ = 2, the dimension of IWORK 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).
SLAED0(3F) SLAED0(3F)
SLAED0 - compute all eigenvalues and corresponding eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE SLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
IWORK, INFO )
INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
INTEGER IWORK( * )
REAL D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), WORK(
* )
SLAED0 computes all eigenvalues and corresponding eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
ICOMPQ (input) INTEGER
= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense symmetric matrix
also. On entry, Q contains the orthogonal matrix used to reduce
the original matrix to tridiagonal form. = 2: Compute
eigenvalues and eigenvectors of tridiagonal matrix.
QSIZ (input) INTEGER
The dimension of the orthogonal matrix used to reduce the full
matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the main diagonal of the tridiagonal matrix. On exit,
its eigenvalues.
E (input) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix. On exit, E
has been destroyed.
Q (input/output) REAL array, dimension (LDQ, N)
On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ =
0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a
subset of the columns of the orthogonal matrix used to reduce the
full matrix to tridiagonal form corresponding to the subset of the
full matrix which is being decomposed at this time. If ICOMPQ = 2
On entry, Q will be the identity matrix. On exit, Q contains the
eigenvectors of the tridiagonal matrix.
Page 1
SLAED0(3F) SLAED0(3F)
LDQ (input) INTEGER
The leading dimension of the array Q. If eigenvectors are
desired, then LDQ >= max(1,N). In any case, LDQ >= 1.
QSTORE (workspace) REAL array, dimension (LDQS, N) Referenced only
when ICOMPQ = 1. Used to store parts of the eigenvector matrix
when the updating matrix multiplies take place.
LDQS (input) INTEGER
The leading dimension of the array QSTORE. If ICOMPQ = 1, then
LDQS >= max(1,N). In any case, LDQS >= 1.
WORK (workspace) REAL array,
dimension (1 + 3*N + 2*N*lg N + 2*N**2) ( lg( N ) = smallest
integer k such that 2^k >= N )
IWORK (workspace) INTEGER array,
If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 +
6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N
) If ICOMPQ = 2, the dimension of IWORK 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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