ssbevd(3)

NAME

SSBEVD - compute 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 assump

tions 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 hexadeci

mal 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) REAL array, dimension (LDAB, N)

On entry, the upper or lower triangle of the sym

metric 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 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 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 (LI

WORK)

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 ille

gal value
> 0: if INFO = i, the algorithm failed to con

verge; i off-diagonal elements of an intermediate tridiagonal

form did not converge to zero.

LAPACK version 3.0 15 June 2000

SSBEVD(3)