SLAED0(3) computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

## SYNOPSIS

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( * )

## PURPOSE

SLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

## ARGUMENTS

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.
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,
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.
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.
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).

## FURTHER DETAILS

Based on contributions by

Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA