# chbevd.f man page

chbevd.f

## Synopsis

### Functions/Subroutines

subroutine chbevd (JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

## Function/Subroutine Documentation

### subroutine chbevd (character JOBZ, character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) W, complex, dimension( ldz, * ) Z, integer LDZ, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, integer LRWORK, integer, dimension( * ) IWORK, integer LIWORK, integer INFO)

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

Purpose:

``` CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A.  If eigenvectors are desired, it
uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.```
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 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 REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.```

Z

```          Z is COMPLEX 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 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.
If N <= 1,               LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N.
If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.```

RWORK

```          RWORK is REAL array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.```

LRWORK

```          LRWORK is INTEGER
The dimension of array RWORK.
If N <= 1,               LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.```

IWORK

```          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.```

LIWORK

```          LIWORK is INTEGER
The dimension of array IWORK.
If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N .

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.```

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

NAG Ltd.

Date:

December 2016

Definition at line 217 of file chbevd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK