# zhbevx.f man page

zhbevx.f —

## Synopsis

### Functions/Subroutines

subroutinezhbevx(JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

## Function/Subroutine Documentation

### subroutine zhbevx (characterJOBZ, characterRANGE, characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldq, * )Q, integerLDQ, double precisionVL, double precisionVU, integerIL, integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

**ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices**

**Purpose:**

```
ZHBEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
can be selected by specifying either 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 triangle of A is stored;
= 'L': Lower triangle of A is stored.
```

*N*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*KD*

```
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, AB is overwritten by values generated during the
reduction to tridiagonal form.
```

*LDAB*

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

*Q*

```
Q is COMPLEX*16 array, dimension (LDQ, N)
If JOBZ = 'V', the N-by-N unitary matrix used in the
reduction 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 = 'V', then
LDQ >= max(1,N).
```

*VL*

`VL is DOUBLE PRECISION`

*VU*

```
VU is DOUBLE PRECISION
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
```

*IL*

`IL is INTEGER`

*IU*

```
IU is INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues 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 DOUBLE PRECISION
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 AB to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
```

*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 DOUBLE PRECISION array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order.
```

*Z*

```
Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
If JOBZ = 'N', then Z is not referenced.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
```

*LDZ*

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

*WORK*

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

*RWORK*

`RWORK is DOUBLE PRECISION 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, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 259 of file zhbevx.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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