chpevx
chpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
SUBROUTINE CHPEVX( JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL,
* NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
COMPLEX A(*), Z(LDZ,*), WORK(*)
INTEGER N, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK3(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL W(*), WORK2(*)
SUBROUTINE CHPEVX_64( JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU,
* ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
COMPLEX A(*), Z(LDZ,*), WORK(*)
INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK3(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL W(*), WORK2(*)
SUBROUTINE HPEVX( JOBZ, RANGE, UPLO, [N], A, VL, VU, IL, IU, ABTOL,
* [NFOUND], W, Z, [LDZ], [WORK], [WORK2], [IWORK3], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX, DIMENSION(:) :: A, WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK3, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: W, WORK2
SUBROUTINE HPEVX_64( JOBZ, RANGE, UPLO, [N], A, VL, VU, IL, IU,
* ABTOL, [NFOUND], W, Z, [LDZ], [WORK], [WORK2], [IWORK3], IFAIL,
* [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX, DIMENSION(:) :: A, WORK
COMPLEX, DIMENSION(:,:) :: Z
INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: W, WORK2
#include <sunperf.h>
void chpevx(char jobz, char range, char uplo, int n, complex *a, float vl, float vu, int il, int iu, float abtol, int *nfound, float *w, complex *z, int ldz, int *ifail, int *info);
void chpevx_64(char jobz, char range, char uplo, long n, complex *a, float vl, float vu, long il, long iu, float abtol, long *nfound, float *w, complex *z, long ldz, long *ifail, long *info);
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.
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* JOBZ (input)
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* RANGE (input)
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* UPLO (input)
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* N (input)
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The order of the matrix A. N >= 0.
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* A (input/output)
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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 A as follows:
if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, A 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.
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* VL (input)
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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'.
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* VU (input)
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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'.
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* IL (input)
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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'.
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* IU (input)
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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'.
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* ABTOL (input)
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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
ABTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABTOL 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 ABTOL 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 ABTOL 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.
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* NFOUND (input)
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The total number of eigenvalues found. 0 <= NFOUND <= N.
If RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU-IL+1.
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* W (output)
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If INFO = 0, the selected eigenvalues in ascending order.
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* Z (input)
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If JOBZ = 'V', then if INFO = 0, the first NFOUND 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,NFOUND) columns are
supplied in the array Z; if RANGE = 'V', the exact value of NFOUND
is not known in advance and an upper bound must be used.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
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* WORK (workspace)
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dimension(2*N)
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* WORK2 (workspace)
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* IWORK3 (workspace)
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* IFAIL (output)
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If JOBZ = 'V', then if INFO = 0, the first NFOUND 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.
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* INFO (output)
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