---
name: "chbgv"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/chbgv/3lapack"
---

# chbgv(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE CHBGV(

  JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, RWORK, INFO )

- CHARACTER

  JOBZ, UPLO

- INTEGER

  INFO, KA, KB, LDAB, LDBB, LDZ, N

- REAL

  RWORK( \* ), W( \* )

- COMPLEX

  AB( LDAB, \* ), BB( LDBB, \* ), WORK( \* ), Z( LDZ, \* )

## 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) CHARACTER\*1

  \= 'N':  Compute eigenvalues only;\
   \= 'V':  Compute eigenvalues and eigenvectors.

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangles of A and B are stored;\
   \= 'L':  Lower triangles of A and B are stored.

- N (input) INTEGER

  The order of the matrices A and B.  N \>= 0.

- KA (input) INTEGER

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

- KB (input) INTEGER

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

- AB (input/output) COMPLEX array, dimension (LDAB, N)

  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) INTEGER

  The leading dimension of the array AB.  LDAB \>= KA+1.

- BB (input/output) COMPLEX array, dimension (LDBB, N)

  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) INTEGER

  The leading dimension of the array BB.  LDBB \>= KB+1.

- W (output) REAL array, dimension (N)

  If INFO = 0, the eigenvalues in ascending order.

- Z (output) COMPLEX array, dimension (LDZ, N)

  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) INTEGER

  The leading dimension of the array Z.  LDZ \>= 1, and if JOBZ = 'V', LDZ \>= N.

- WORK (workspace) COMPLEX array, dimension (N)

  - RWORK (workspace) REAL array, dimension (3\*N)

  - INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value\
   \> 0:  if INFO = i, and i is:\
   \<= N:  the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; \> N:   if INFO = N + i, for 1 \<= i \<= N, then CPBSTF\
   returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.