SSBEVD(1) LAPACK driver routine (version 3.2) SSBEVD(1)NAME
SSBEVD - computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A
SYNOPSIS
SUBROUTINE SSBEVD( 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( * )
REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
PURPOSE
SSBEVD 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 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 dig‐
its, 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 subdiagonals if UPLO = 'L'. KD >= 0.
AB (input/output) REAL 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 j-th
column of A is stored in the j-th column of the array AB as
follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+kd). On exit, AB is overwritten by values gener‐
ated 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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) REAL array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th 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) REAL 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 sizes
of the WORK and IWORK arrays, returns these values as the first
entries of the WORK and IWORK arrays, and no error message
related to LWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,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 sizes
of the WORK and IWORK arrays, returns these values as the first
entries of the WORK and IWORK arrays, and no error message
related to LWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i off-
diagonal elements of an intermediate tridiagonal form did not
converge to zero.
LAPACK driver routine (version 3November 2008 SSBEVD(1)
