SSYGVX (3) Linux Manual Page

ssygvx.f –

Synopsis

Functions/Subroutines

subroutine ssygvx (ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO)
SSYGST

Function/Subroutine Documentation

subroutine ssygvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

SSYGST

Purpose:

 SSYGVX 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 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

 Specifies the problem type to be solved:

 = 1: A*x = (lambda)*B*x

 = 2: A*B*x = (lambda)*x

 = 3: B*A*x = (lambda)*x

JOBZ

 JOBZ is CHARACTER*1

 = ‘N’: Compute eigenvalues only;

 = ‘V’: Compute eigenvalues and eigenvectors.

RANGE

 RANGE is CHARACTER*1

 = ‘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

 UPLO is CHARACTER*1

 = ‘U’: Upper triangle of A and B are stored;

 = ‘L’: Lower triangle of A and B are stored.

N

 N is INTEGER

 The order of the matrix pencil (A,B). N >= 0.

A

 A is REAL array, dimension (LDA, N)

 On entry, the symmetric matrix A. If UPLO = ‘U’, the

 leading N-by-N upper triangular part of A contains the

 upper triangular part of the matrix A. If UPLO = ‘L’,

 the leading N-by-N lower triangular part of A contains

 the lower triangular part of the matrix A.

 On exit, the lower triangle (if UPLO=’L’) or the upper

 triangle (if UPLO=’U’) of A, including the diagonal, is

 destroyed.

LDA

 LDA is INTEGER

 The leading dimension of the array A. LDA >= max(1,N).

B

 B is REAL array, dimension (LDA, N)

 On entry, the symmetric matrix B. If UPLO = ‘U’, the

 leading N-by-N upper triangular part of B contains the

 upper triangular part of the matrix B. If UPLO = ‘L’,

 the leading N-by-N lower triangular part of B contains

 the lower triangular part of the matrix B.

 On exit, if INFO <= N, the part of B containing the matrix is

 overwritten by the triangular factor U or L from the Cholesky

 factorization B = U**T*U or B = L*L**T.

LDB

 LDB is INTEGER

 The leading dimension of the array B. LDB >= max(1,N).

VL

 VL is REAL

VU

 VU is REAL

 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

 IL is INTEGER

IU

 IU is INTEGER

 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

 ABSTOL is REAL

 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 C to tridiagonal form, where C is the symmetric

 matrix of the standard symmetric problem to which the

 generalized problem is transformed.

 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*SLAMCH(‘S’).

M

 M is INTEGER

 The total number of eigenvalues found. 0 <= M <= N.

 If RANGE = ‘A’, M = N, and if RANGE = ‘I’, M = IU-IL+1.

W

 W is REAL array, dimension (N)

 On normal exit, the first M elements contain the selected

 eigenvalues in ascending order.

Z

 Z is REAL array, dimension (LDZ, max(1,M))

 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

 LDZ is INTEGER

 The leading dimension of the array Z. LDZ >= 1, and if

 JOBZ = ‘V’, LDZ >= max(1,N).

WORK

 WORK is REAL array, dimension (MAX(1,LWORK))

 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER

 The length of the array WORK. LWORK >= max(1,8*N).

 For optimal efficiency, LWORK >= (NB+3)*N,

 where NB is the blocksize for SSYTRD returned by ILAENV.

 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

 IWORK is INTEGER array, dimension (5*N)

IFAIL

 IFAIL is INTEGER array, dimension (N)

 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

 INFO is INTEGER

 = 0: successful exit

 < 0: if INFO = -i, the i-th argument had an illegal value

 > 0: SPOTRF or SSYEVX returned an error code:

 <= N: if INFO = i, SSYEVX 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 289 of file ssygvx.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.