chbgvx
chbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
SUBROUTINE CHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
* Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK,
* IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)
INTEGER N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL W(*), RWORK(*)
SUBROUTINE CHBGVX_64( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
* LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
* IWORK, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER*8 IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL W(*), RWORK(*)
SUBROUTINE HBGVX( JOBZ, RANGE, UPLO, [N], KA, KB, AB, [LDAB], BB,
* [LDBB], Q, [LDQ], VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK],
* [RWORK], [IWORK], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, Q, Z
INTEGER :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, RWORK
SUBROUTINE HBGVX_64( JOBZ, RANGE, UPLO, [N], KA, KB, AB, [LDAB], BB,
* [LDBB], Q, [LDQ], VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK],
* [RWORK], [IWORK], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, Q, Z
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, RWORK
#include <sunperf.h>
void chbgvx(char jobz, char range, char uplo, int n, int ka, int kb, complex *ab, int ldab, complex *bb, int ldbb, complex *q, int ldq, float vl, float vu, int il, int iu, float abstol, int *m, float *w, complex *z, int ldz, int *ifail, int *info);
void chbgvx_64(char jobz, char range, char uplo, long n, long ka, long kb, complex *ab, long ldab, complex *bb, long ldbb, complex *q, long ldq, float vl, float vu, long il, long iu, float abstol, long *m, float *w, complex *z, long ldz, long *ifail, long *info);
chbgvx computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite. Eigenvalues and
eigenvectors can be selected by specifying either all eigenvalues,
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 matrices A and B. N >= 0.
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* KA (input)
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The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
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* KB (input)
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The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
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* AB (input/output)
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On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first ka+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
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* LDAB (input)
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The leading dimension of the array AB. LDAB >= KA+1.
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* BB (input/output)
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On entry, the upper or lower triangle of the Hermitian band
matrix B, stored in the first kb+1 rows of the array. The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization
B = S**H*S, as returned by CPBSTF.
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* LDBB (input)
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The leading dimension of the array BB. LDBB >= KB+1.
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* Q (output)
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If JOBZ = 'V', the n-by-n matrix used in the reduction of
A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
and consequently C to tridiagonal form.
If JOBZ = 'N', the array Q is not referenced.
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* LDQ (input)
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The leading dimension of the array Q. If JOBZ = 'N',
LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
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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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* ABSTOL (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
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').
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* M (output)
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The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
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* W (output)
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If INFO = 0, the eigenvalues in ascending order.
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* Z (input)
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If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the
eigenvector associated with W(i). The eigenvectors are
normalized so that Z**H*B*Z = I.
If JOBZ = 'N', then Z is not referenced.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= N.
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* WORK (workspace)
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dimension(N)
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* RWORK (workspace)
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dimension(7*N)
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* IWORK (workspace)
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dimension(5*N)
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* IFAIL (output)
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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.
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* INFO (output)
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