# ?hbev

Computes all eigenvalues and, optionally, eigenvectors of a Hermitian band matrix.

## Syntax

FORTRAN 77:

call chbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)

call zhbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)

Fortran 95:

call hbev(a, w [,uplo] [,z] [,info])

## Description

This routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.

## Input Parameters

jobz

  CHARACTER*1. Must be 'N' or 'V'.

  If `jobz = 'N'`, then only eigenvalues are computed.

  If `jobz = 'V'`, then eigenvalues and eigenvectors are computed.

uplo

  CHARACTER*1. Must be 'U' or 'L'.

  If `uplo = 'U'`, ab stores the upper triangular part of A.

  If `uplo = 'L'`, ab stores the lower triangular part of A.

n

  INTEGER. The order of the matrix A (`n ≥ 0`).

kd

  INTEGER. The number of super- or sub-diagonals in A

  (`kd ≥ 0`).

ab, work

  COMPLEX for chbev

  DOUBLE COMPLEX for zhbev.

  Arrays:

  ab (ldab,*) is an array containing either upper or lower triangular part of the Hermitian matrix A (as specified by uplo) in band storage format.

  The second dimension of ab must be at least max(1, n).

  work (*) is a workspace array.

  The dimension of work must be at least max(1, n).

ldab

  INTEGER. The leading dimension of ab; must be at least kd +1.

ldz

  INTEGER. The leading dimension of the output array z.

  Constraints:

  if `jobz = 'N'`, then `ldz ≥ 1`;

  if `jobz = 'V'`, then ldz ≥ max(1, n) .

rwork

  REAL for chbev

  DOUBLE PRECISION for zhbev

  Workspace array, DIMENSION at least max(1, 3n-2).

## Output Parameters

w

  REAL for chbev

  DOUBLE PRECISION for zhbev

  Array, DIMENSION at least max(1, n).

  If `info = 0`, contains the eigenvalues in ascending order.

z

  COMPLEX for chbev

  DOUBLE COMPLEX for zhbev.

  Array z(ldz,*).

  The second dimension of z must be at least max(1, 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.

ab

  On exit, this array is overwritten by the 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.

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info = -i`, the ith parameter had an illegal value.

  If `info = i`, then the algorithm failed to converge;

  i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see Fortran 95 Interface Conventions.

Specific details for the routine hbev interface are the following:

a

  Stands for argument ab in Fortan 77 interface. Holds the array A of size (kd+1,n).

w

  Holds the vector of length (n).

z

  Holds the matrix Z of size (n, n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

jobz

  Restored based on the presence of the argument z as follows:

  `jobz = 'V'`, if z is present,

  `jobz = 'N'`, if z is omitted.

Parent topic: Symmetric Eigenproblems