dspgvx.f (3) Linux Manual Page
dspgvx.f –
Synopsis
Functions/Subroutines
subroutine dspgvx (ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO)DSPGST
Function/Subroutine Documentation
subroutine dspgvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )BP, double precisionVL, double precisionVU, integerIL, integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)
DSPGST Purpose:
DSPGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
and B are assumed to be symmetric, stored in packed storage, and B
is also positive definite. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
Parameters:
- ITYPE
ITYPE is INTEGER
JOBZ
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*xJOBZ is CHARACTER*1
RANGE
= ‘N’: Compute eigenvalues only;
= ‘V’: Compute eigenvalues and eigenvectors.RANGE is CHARACTER*1
UPLO
= ‘A’: all eigenvalues will be found.
= ‘V’: all eigenvalues in the half-open interval (VL,VU]
will be found.
= ‘I’: the IL-th through IU-th eigenvalues will be found.UPLO is CHARACTER*1
N
= ‘U’: Upper triangle of A and B are stored;
= ‘L’: Lower triangle of A and B are stored.N is INTEGER
AP
The order of the matrix pencil (A,B). N >= 0.AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
BP
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, the contents of AP are destroyed.BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
VL
On entry, the upper or lower triangle of the symmetric matrix
B, packed columnwise in a linear array. The j-th column of B
is stored in the array BP as follows:
if UPLO = ‘U’, BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = ‘L’, BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
On exit, the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T, in the same storage
format as B.VL is DOUBLE PRECISION
VUVU is DOUBLE PRECISION
IL
If RANGE=’V’, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = ‘A’ or ‘I’.IL is INTEGER
IUIU is INTEGER
ABSTOL
If RANGE=’I’, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = ‘A’ or ‘V’.ABSTOL is DOUBLE PRECISION
M
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH(‘S’), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH(‘S’).M is INTEGER
W
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = ‘A’, M = N, and if RANGE = ‘I’, M = IU-IL+1.W is DOUBLE PRECISION array, dimension (N)
Z
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
LDZ
If JOBZ = ‘N’, then Z is not referenced.
If JOBZ = ‘V’, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = ‘V’, the exact value of M
is not known in advance and an upper bound must be used.LDZ is INTEGER
WORK
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ‘V’, LDZ >= max(1,N).WORK is DOUBLE PRECISION array, dimension (8*N)
IWORKIWORK is INTEGER array, dimension (5*N)
IFAILIFAIL is INTEGER array, dimension (N)
INFO
If JOBZ = ‘V’, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = ‘N’, then IFAIL is not referenced.INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEVX returned an error code:
<= N: if INFO = i, DSPEVX failed to converge;
i eigenvectors failed to converge. Their indices
are stored in array IFAIL.
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Author:
- Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- November 2011
Contributors:
- Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Definition at line 262 of file dspgvx.f.