chpevx.f (3) Linux Manual Page

chpevx.f –

Synopsis

Functions/Subroutines

subroutine chpevx (JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
CHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

subroutine chpevx (characterJOBZ, characterRANGE, characterUPLO, integerN, complex, dimension( * )AP, 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)

CHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

 CHPEVX computes selected eigenvalues and, optionally, eigenvectors

 of a complex Hermitian matrix A in packed storage.

 Eigenvalues/vectors can be selected by specifying either a range of

 values or a range of indices for the desired eigenvalues.

 

Parameters:

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 is stored;

 = ‘L’: Lower triangle of A is stored.

N

 N is INTEGER

 The order of the matrix A. N >= 0.

AP

 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, AP is overwritten 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.

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 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’).

 See "Computing Small Singular Values of Bidiagonal Matrices

 with Guaranteed High Relative Accuracy," by Demmel and

 Kahan, LAPACK Working Note #3.

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)

 If INFO = 0, the selected eigenvalues in ascending order.

Z

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

 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).

 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.

 If JOBZ = ‘N’, then Z is not referenced.

 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: if INFO = i, then i eigenvectors failed to converge.

 Their indices are stored in array IFAIL.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 232 of file chpevx.f.

Author

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