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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

```NAME
LAPACK-3  -  computes all the eigenvalues and, optionally, eigenvectors
of a complex Hermitian band matrix A

SYNOPSIS
SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,  RWORK,
INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, KD, LDAB, LDZ, N

DOUBLE        PRECISION RWORK( * ), W( * )

COMPLEX*16    AB( LDAB, * ), WORK( * ), Z( LDZ, * )

PURPOSE
ZHBEV  computes  all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian band matrix A.

ARGUMENTS
JOBZ    (input) CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

KD      (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB      (input/output) 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.  If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD + 1.

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

Z       (output) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(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 >= max(1,N).

WORK    (workspace) COMPLEX*16 array, dimension (N)

RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

LAPACK driver routine (version 3.March 2011                       LAPACK-3(3)
```