SSPEVD(1) LAPACK driver routine (version 3.2) SSPEVD(1)NAME
SSPEVD - computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric matrix A in packed storage
SYNOPSIS
SUBROUTINE SSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * )
PURPOSE
SSPEVD 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 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.
AP (input/output) REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric 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 over‐
written by values generated during the reduction to tridiagonal
form. If UPLO = 'U', the diagonal and first superdiagonal of
the tridiagonal matrix T overwrite the corresponding elements
of A, and if UPLO = 'L', the diagonal and first subdiagonal of
T overwrite the corresponding elements of A.
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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required 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 required 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 required 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 required
sizes of the WORK and IWORK arrays, returns these values as the
first entries of the WORK and IWORK arrays, and no error mes‐
sage 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 SSPEVD(1)
