chpgvx-f(3)

chpgvx.f –

Synopsis

Functions/Subroutines

subroutine chpgvx (ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
CHPGST

Function/Subroutine Documentation

subroutine chpgvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, complex, dimension( * )AP, complex, dimension( * )BP, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, real, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

CHPGST

Purpose:

 CHPGVX computes selected eigenvalues and, optionally, eigenvectors
 of a complex generalized Hermitian-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 Hermitian, stored in packed format, 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 triangles of A and B are stored;
 = 'L': Lower triangles of A and B are stored.

 N is INTEGER
 The order of the matrices A and B. N >= 0.

 AP is COMPLEX array, dimension (N*(N+1)/2)
 On entry, the upper or lower triangle of the Hermitian 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 COMPLEX array, dimension (N*(N+1)/2)
 On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, in the same storage
 format as B.

 VL is REAL

 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 is INTEGER

 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 AP to tridiagonal form.
 Eigenvalues will be computed most accurately when ABSTOL is
 set to twice the underflow threshold 2*SLAMCH('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 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 is REAL array, dimension (N)
 On normal exit, the first M elements contain the selected
 eigenvalues in ascending order.

 Z is COMPLEX array, dimension (LDZ, N)
 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**H*B*Z = I;
 if ITYPE = 3, Z**H*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 COMPLEX array, dimension (2*N)

RWORK

 RWORK is REAL array, dimension (7*N)

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: CPPTRF or CHPEVX returned an error code:
 <= N: if INFO = i, CHPEVX 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 267 of file chpgvx.f.

Author

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