chbgv

NAME

chbgv - 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 CHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, 
 *      LDZ, WORK, RWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
  INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
  REAL W(*), RWORK(*)
 
  SUBROUTINE CHBGV_64( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, 
 *      Z, LDZ, WORK, RWORK, INFO)
  CHARACTER * 1 JOBZ, UPLO
  COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
  INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
  REAL W(*), RWORK(*)

F95 INTERFACE

  SUBROUTINE HBGV( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W, 
 *       Z, [LDZ], [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: AB, BB, Z
  INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
  REAL, DIMENSION(:) :: W, RWORK
 
  SUBROUTINE HBGV_64( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], 
 *       W, Z, [LDZ], [WORK], [RWORK], [INFO])
  CHARACTER(LEN=1) :: JOBZ, UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: AB, BB, Z
  INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
  REAL, DIMENSION(:) :: W, RWORK

C INTERFACE

#include <sunperf.h>

void chbgv(char jobz, char uplo, int n, int ka, int kb, complex *ab, int ldab, complex *bb, int ldbb, float *w, complex *z, int ldz, int *info);

void chbgv_64(char jobz, char uplo, long n, long ka, long kb, complex *ab, long ldab, complex *bb, long ldbb, float *w, complex *z, long ldz, long *info);

PURPOSE

chbgv 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.

ARGUMENTS

* JOBZ (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.

* 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(3*N)

* INFO (output)