---
name: "zheevd.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zheevd.f"
---

# zheevd.f(3)

## NAME

SRC/zheevd.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zheevd** (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)\
  **ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices**

## Function/Subroutine Documentation

### subroutine zheevd (character jobz, character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) w, complex\*16, dimension( \* ) work, integer lwork, double precision, dimension( \* ) rwork, integer lrwork, integer, dimension( \* ) iwork, integer liwork, integer info)

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

**Purpose:**

```
!>
!> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
!> complex Hermitian matrix A.  If eigenvectors are desired, it uses a
!> divide and conquer algorithm.
!>
!>
```

**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.
!>          If N <= 1,                LWORK must be at least 1.
!>          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
!>          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + 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 DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
!>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
!>
```

*LRWORK*

```
!>          LRWORK is INTEGER
!>          The dimension of the 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 the array IWORK.
!>          If N <= 1,                LIWORK must be at least 1.
!>          If JOBZ  = 'N' and 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 and JOBZ = 'N', then the algorithm failed
!>                to converge; i off-diagonal elements of an intermediate
!>                tridiagonal form did not converge to zero;
!>                if INFO = i and JOBZ = 'V', then the algorithm failed
!>                to compute an eigenvalue while working on the submatrix
!>                lying in rows and columns INFO/(N+1) through
!>                mod(INFO,N+1).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Modified description of INFO. Sven, 16 Feb 05.

**Contributors:**

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line **196** of file **zheevd.f**.

## Author

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