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.TH SLAED0 l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
SLAED0 - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
.SH SYNOPSIS
.TP 19
SUBROUTINE SLAED0(
ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
WORK, IWORK, INFO )
.TP 19
.ti +4
INTEGER
ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
.TP 19
.ti +4
INTEGER
IWORK( * )
.TP 19
.ti +4
REAL
D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
WORK( * )
.SH PURPOSE
SLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.
.SH ARGUMENTS
.TP 8
ICOMPQ (input) INTEGER
= 0: Compute eigenvalues only.
.br
= 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.
.TP 7
QSIZ (input) INTEGER
The dimension of the orthogonal matrix used to reduce
the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
.TP 7
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
.TP 7
D (input/output) REAL array, dimension (N)
On entry, the main diagonal of the tridiagonal matrix.
On exit, its eigenvalues.
.TP 7
E (input) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
.TP 7
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.
.TP 7
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.
.TP 7
LDQS (input) INTEGER
The leading dimension of the array QSTORE. If ICOMPQ = 1,
then LDQS >= max(1,N). In any case, LDQS >= 1.
.TP 7
WORK (workspace) REAL array,
If ICOMPQ = 0 or 1, the dimension of WORK must be at least
1 + 3*N + 2*N*lg N + 2*N**2
( lg( N ) = smallest integer k
such that 2^k >= N )
If ICOMPQ = 2, the dimension of WORK must be at least
4*N + N**2.
.TP 7
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
3 + 5*N.
.TP 7
INFO (output) INTEGER
= 0: successful exit.
.br
< 0: if INFO = -i, the i-th argument had an illegal value.
.br
> 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).
.SH FURTHER DETAILS
Based on contributions by
.br
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
.br
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