# zheev.f man page

zheev.f —

## Synopsis

### Functions/Subroutines

subroutinezheev(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO)ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

## Function/Subroutine Documentation

### subroutine zheev (characterJOBZ, characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )W, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)

**ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices**

**Purpose:**

```
ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian 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.
```

*A*

```
A is COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
```

*LDA*

```
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
```

*W*

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

*WORK*

```
WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
```

*LWORK*

```
LWORK is INTEGER
The length of the array WORK. LWORK >= max(1,2*N-1).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for ZHETRD returned by ILAENV.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
```

*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:**

November 2011

Definition at line 140 of file zheev.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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