dspevd(3)

NAME

DSPEVD - compute all the eigenvalues and, optionally,

eigenvectors of a real symmetric matrix A in packed storage

SYNOPSIS

SUBROUTINE  DSPEVD(  JOBZ,  UPLO,  N, AP, W, Z, LDZ, WORK,
LWORK, IWORK, LIWORK, INFO )
    CHARACTER      JOBZ, UPLO
    INTEGER        INFO, LDZ, LIWORK, LWORK, N
    INTEGER        IWORK( * )
    DOUBLE         PRECISION AP( * ), W( * ), WORK(  *  ),
Z( LDZ, * )

PURPOSE

DSPEVD computes all the eigenvalues and, optionally,

eigenvectors of a real symmetric matrix A in packed storage. 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.

AP (input/output) DOUBLE PRECISION array, dimension

(N*(N+1)/2)

On entry, the upper or lower triangle of the sym

metric matrix A, packed columnwise in a linear array. The j-th

column of A is stored in the array AP as follows: if UPLO = 'U',

AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +

(j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated

during the reduction to tridiagonal form. If UPLO = 'U', the di

agonal and first superdiagonal of the tridiagonal matrix T over

write the corresponding elements of A, and if UPLO = 'L', the di

agonal and first subdiagonal of T overwrite the corresponding el

ements of A.

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 > 1, LWORK must be

at least 2*N. If JOBZ = 'V' and N > 1, LWORK must be at least 1

+ 6*N + 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 IWORK. If JOBZ = 'N'

or N <= 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1,

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

DSPEVD(3)