---
name: "chbgvd.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/chbgvd.f"
---

# chbgvd.f(3)

## NAME

SRC/chbgvd.f

## SYNOPSIS

### Functions/Subroutines

subroutine **chbgvd** (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)\
 **CHBGVD**

## Function/Subroutine Documentation

### subroutine chbgvd (character jobz, character uplo, integer n, integer ka, integer kb, complex, dimension( ldab, \* ) ab, integer ldab, complex, dimension( ldbb, \* ) bb, integer ldbb, real, dimension( \* ) w, complex, dimension( ldz, \* ) z, integer ldz, complex, dimension( \* ) work, integer lwork, real, dimension( \* ) rwork, integer lrwork, integer, dimension( \* ) iwork, integer liwork, integer info)

**CHBGVD**

**Purpose:**

```
!>
!> CHBGVD 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.  If eigenvectors are
!> desired, it uses a divide and conquer algorithm.
!>
!>
```

**Parameters**

*JOBZ*

```
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors.
!>
```

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangles of A and B are stored;
!>          = 'L':  Lower triangles of A and B are stored.
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>
```

*KA*

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

*KB*

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

*AB*

```
!>          AB is 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*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KA+1.
!>
```

*BB*

```
!>          BB is 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*

```
!>          LDBB is INTEGER
!>          The leading dimension of the array BB.  LDBB >= KB+1.
!>
```

*W*

```
!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!>
```

*Z*

```
!>          Z is 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*

```
!>          LDZ is INTEGER
!>          The leading dimension of the array Z.  LDZ >= 1, and if
!>          JOBZ = 'V', LDZ >= N.
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO=0, WORK(1) returns the optimal LWORK.
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If N <= 1,               LWORK >= 1.
!>          If JOBZ = 'N' and N > 1, LWORK >= N.
!>          If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal sizes of the WORK, RWORK and
!>          IWORK arrays, returns these values as the first entries of
!>          the WORK, RWORK and IWORK arrays, and no error message
!>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (MAX(1,LRWORK))
!>          On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
!>
```

*LRWORK*

```
!>          LRWORK is INTEGER
!>          The dimension of array RWORK.
!>          If N <= 1,               LRWORK >= 1.
!>          If JOBZ = 'N' and N > 1, LRWORK >= N.
!>          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
!>
!>          If LRWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal sizes of the WORK, RWORK
!>          and IWORK arrays, returns these values as the first entries
!>          of the WORK, RWORK and IWORK arrays, and no error message
!>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
!>
```

*LIWORK*

```
!>          LIWORK is INTEGER
!>          The dimension of array IWORK.
!>          If JOBZ = 'N' or N <= 1, LIWORK >= 1.
!>          If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
!>
!>          If LIWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal sizes of the WORK, RWORK
!>          and IWORK arrays, returns these values as the first entries
!>          of the WORK, RWORK and IWORK arrays, and no error message
!>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
!>
```

*INFO*

```
!>          INFO is 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.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line **243** of file **chbgvd.f**.

## Author

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