
DSBEVD(l) ) DSBEVD(l)
NAME
DSBEVD  compute all the eigenvalues and, optionally, eigenvectors of a real symmetric
band matrix A
SYNOPSIS
SUBROUTINE DSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
PURPOSE
DSBEVD computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band
matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arith
metic. 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 XMP, Cray YMP, Cray C90, or
Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
ARGUMENTS
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub
diagonals if UPLO = 'L'. KD >= 0.
AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band matrix A, stored in
the first KD+1 rows of the array. The jth column of A is stored in the jth col
umn of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for
max(1,jkd)<=i<=j; if UPLO = 'L', AB(1+ij,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, AB is overwritten by values generated during the reduction to tridiagonal
form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal
matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal
and first subdiagonal of T are returned in the first two rows of AB.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the
matrix A, with the ith column of Z holding the eigenvector associated with W(i).
If JOBZ = 'N', then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >=
max(1,N).
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. IF N <= 1, LWORK must be at least
1. If JOBZ = 'N' and N > 2, LWORK must be at least 2*N. If JOBZ = 'V' and N >
2, LWORK must be at least ( 1 + 5*N + 2*N**2 ).
If LWORK = 1, then a workspace query is assumed; the routine only calculates the
optimal size of the WORK array, returns this value as the first entry of the WORK
array, and no error message related to LWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array LIWORK. If JOBZ = 'N' or N <= 1, LIWORK must be at
least 1. If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
If LIWORK = 1, then a workspace query is assumed; the routine only calculates the
optimal size of the IWORK array, returns this value as the first entry of the
IWORK array, and no error message related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i offdiagonal elements of an
intermediate tridiagonal form did not converge to zero.
LAPACK version 3.0 15 June 2000 DSBEVD(l) 
