DSBEVD(3F)DSBEVD(3F)NAMEDSBEVD - 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, *
)
PURPOSEDSBEVD 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 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 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
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DSBEVD(3F)DSBEVD(3F)
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 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 LWORK > 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
+ 4*N + 2*N*lg N + 3*N**2 ), where lg( N ) = smallest integer k
such that 2**k >= N.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 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 2 + 5*N.
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.
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