zhpevd.f man page

zhpevd.f

Synopsis

Functions/Subroutines

subroutine zhpevd (JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

subroutine zhpevd (character JOBZ, character UPLO, integer N, complex*16, dimension( * ) AP, double precision, dimension( * ) W, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, integer LRWORK, integer, dimension( * ) IWORK, integer LIWORK, integer INFO)

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

Purpose:

``` ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage.  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.```

AP

```          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array.  The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the
reduction to tridiagonal form.  If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.```

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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of 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.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required 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 required 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 required 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 required 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 required 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:

June 2017

Definition at line 202 of file zhpevd.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK