SSPEVD - compute all the eigenvalues and, optionally,
eigenvectors of a real symmetric matrix A in packed stor
age
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 stor
age. 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 hexadecimal or decimal machines with
out 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) REAL 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
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 associ
ated with W(i). If JOBZ = 'N', then Z is not ref
erenced.
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 >
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
(LIWORK)
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
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.
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