zhbgvx

NAME

zhbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

SYNOPSIS 

  SUBROUTINE ZHBGVX( 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
  DOUBLE 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(*)
  DOUBLE PRECISION VL, VU, ABSTOL
  DOUBLE PRECISION W(*), RWORK(*)
 
  SUBROUTINE ZHBGVX_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
  DOUBLE 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(*)
  DOUBLE PRECISION VL, VU, ABSTOL
  DOUBLE PRECISION W(*), RWORK(*)

F95 INTERFACE 

  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(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: AB, BB, Q, Z
  INTEGER :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
  INTEGER, DIMENSION(:) :: IWORK, IFAIL
  REAL(8) :: VL, VU, ABSTOL
  REAL(8), 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(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: AB, BB, Q, Z
  INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
  INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
  REAL(8) :: VL, VU, ABSTOL
  REAL(8), DIMENSION(:) :: W, RWORK

C INTERFACE

#include <sunperf.h>

void zhbgvx(char jobz, char range, char uplo, int n, int ka, int kb, doublecomplex *ab, int ldab, doublecomplex *bb, int ldbb, doublecomplex *q, int ldq, double vl, double vu, int il, int iu, double abstol, int *m, double *w, doublecomplex *z, int ldz, int *ifail, int *info);

void zhbgvx_64(char jobz, char range, char uplo, long n, long ka, long kb, doublecomplex *ab, long ldab, doublecomplex *bb, long ldbb, doublecomplex *q, long ldq, double vl, double vu, long il, long iu, double abstol, long *m, double *w, doublecomplex *z, long ldz, long *ifail, long *info);

PURPOSE

zhbgvx 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.

ARGUMENTS

* JOBZ (input)
* RANGE (input)

* UPLO (input)

* N (input)
The order of the matrices A and B. N >= 0.

* KA (input)
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.

* KB (input)
The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0.

* AB (input/output)
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.

* LDAB (input)
The leading dimension of the array AB. LDAB >= KA+1.

* BB (input/output)
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.

* LDBB (input)
The leading dimension of the array BB. LDBB >= KB+1.

* Q (output)
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.

* LDQ (input)
The leading dimension of the array Q. If JOBZ = 'N', LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).

* VL (input)
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'.

* VU (input)
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 (input)
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'.

* IU (input)
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 (input)
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 (output)
The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

* W (output)
If INFO = 0, the eigenvalues in ascending order.

* Z (input)
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.

* LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N.

* WORK (workspace)
dimension(N)

* RWORK (workspace)
dimension(7*N)

* IWORK (workspace)
dimension(5*N)

* IFAIL (output)
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 (output)