---
name: "chbgvx.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/chbgvx.f"
---

# chbgvx.f(3)

## NAME

SRC/chbgvx.f

## SYNOPSIS

### Functions/Subroutines

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)\
 **CHBGVX**

## Function/Subroutine Documentation

### subroutine chbgvx (character jobz, character range, character uplo, integer n, integer ka, integer kb, complex, dimension( ldab, \* ) ab, integer ldab, complex, dimension( ldbb, \* ) bb, integer ldbb, complex, dimension( ldq, \* ) q, integer ldq, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( \* ) w, complex, dimension( ldz, \* ) z, integer ldz, complex, dimension( \* ) work, real, dimension( \* ) rwork, integer, dimension( \* ) iwork, integer, dimension( \* ) ifail, integer info)

**CHBGVX**

**Purpose:**

```
!>
!> 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.
!>
```

**Parameters**

*JOBZ*

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

*RANGE*

```
!>          RANGE is CHARACTER*1
!>          = 'A': all eigenvalues will be found;
!>          = 'V': all eigenvalues in the half-open interval (VL,VU]
!>                 will be found;
!>          = 'I': the IL-th through IU-th eigenvalues will be found.
!>
```

*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.
!>
```

*Q*

```
!>          Q is COMPLEX array, dimension (LDQ, N)
!>          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*

```
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.  If JOBZ = 'N',
!>          LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
!>
```

*VL*

```
!>          VL is REAL
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues. VL < VU.
!>          Not referenced if RANGE = 'A' or 'I'.
!>
```

*VU*

```
!>          VU is REAL
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues. VL < VU.
!>          Not referenced if RANGE = 'A' or 'I'.
!>
```

*IL*

```
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue 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*

```
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue 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*

```
!>          ABSTOL is REAL
!>          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*

```
!>          M is INTEGER
!>          The total number of eigenvalues found.  0 <= M <= N.
!>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+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 (N)
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (7*N)
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (5*N)
!>
```

*IFAIL*

```
!>          IFAIL is INTEGER array, dimension (N)
!>          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*

```
!>          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:  then i eigenvectors failed to converge.  Their
!>                    indices are stored in array IFAIL.
!>             > 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 **297** of file **chbgvx.f**.

## Author

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