# zhbev.f man page

zhbev.f

## Synopsis

### Functions/Subroutines

subroutine **zhbev** (JOBZ, UPLO, **N**, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO)

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

## Function/Subroutine Documentation

### subroutine zhbev (character JOBZ, character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) W, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)

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

**Purpose:**

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

**Parameters:**-
*JOBZ*JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.

*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. 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*LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 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 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*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 (max(1,3*N-2))

*INFO*INFO is 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.

**Author:**-
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 154 of file zhbev.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhbev(3) is an alias of zhbev.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK