# zhbgv.f man page

zhbgv.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zhbgv (characterJOBZ, characterUPLO, integerN, integerKA, integerKB, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldbb, * )BB, integerLDBB, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

**ZHBGST**

**Purpose:**

```
ZHBGV 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.
```

**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*16 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*16 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 ZPBSTF.
```

*LDBB*

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

*W*

```
W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
```

*Z*

```
Z is COMPLEX*16 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*16 array, dimension (N)`

*RWORK*

`RWORK is DOUBLE PRECISION array, dimension (3*N)`

*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 ZPBSTF
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.

**Date:**

November 2011

Definition at line 183 of file zhbgv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zhbgv(3) is an alias of zhbgv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK