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 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) 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 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 generated during the
reduction to tridiagonal form. If UPLO = 'U', the first super‐
diagonal 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 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) 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 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 version 3.0 15 June 2000 DSBEVD(l)
