# elpa_generalized_eigenvalues - Man Page

computes the eigenvalues of a generalized eigenvalue problem for real symmetric or complex hermitian matrices

## Synopsis

### Fortran Interface

use elpa
class(elpa_t), pointer :: elpa

call elpa%generalized_eigenvalues (a, b, ev, is_already_decomopsed, error)

With the definitions of the input and output variables:

class(elpa_t) :: elpa  ! returns an instance of the ELPA object

datatype :: a

The matrix a for which the eigenvalues should be computed. The dimensions of matrix a must be set BEFORE with the methods elpa_set(3) and elpa_setup(3). The datatype of the matrix can be one of "real(kind=c_double)", "real(kind=c_float)", "complex(kind=c_double)", or "complex(kind=c_float)"

datatype :: b

The matrix b defining the generalized eigenvalue problem. The dimensions and datatype of the matrix b has to be the same as for matrix a.

datatype :: ev

The vector ev where the eigenvalues will be stored in ascending order. The datatype of the vector ev can be either "real(kind=c_double)", or "real(kind=c_float)", depending of the datatype of the matrix. Note that complex hermitian matrices also have real valued eigenvalues.

Has to be set to .false. for the first call with a given b and .true. for each subsequent call with the same b, since b then already contains decomposition and thus the decomposing step is skipped.

integer, optional :: error

The return error code of the function. Should be "ELPA_OK". The error code can be querried with the function elpa_strerr(3)

### C Interface

#include <elpa/elpa.h>
elpa_t handle;

void elpa_generalized_eigenvalues(elpa_t handle, datatype *a, datatype *b, datatype *ev, int is_already_decomposed, int *error);

With the definitions of the input and output variables:

elpa_t handle;

The handle to the ELPA object

datatype *a;

The matrix a for which the eigenvalues should be computed. The dimensions of the matrix must be set BEFORE with the methods elpa_set(3) and elpa_setup(3). The datatype can be one of "double", "float", "double complex", or "float complex".

datatype *b;

The matrix b defining the generalized eigenvalue problem. The dimensions and the datatype of the matrix b must be the same as matrix a.

datatype *ev;

The storage for the computed eigenvalues. Eigenvalues will be stored in ascendig order. The datatype can be either "double" or "float". Note that the eigenvalues of complex hermitian matrices are also real.

Has to be set to 0 for the first call with a given b and 1 for each subsequent call with the same b, since b then already contains decomposition and thus the decomposing step is skipped.

int *error;

The error code of the function. Should be "ELPA_OK". The error codes can be querried with elpa_strerr(3)

## Description

Compute the generalized eigenvalues and (parts of) the eigenvector spectrum of a real symmtric or complex hermitian matrix.The functions elpa_init(3), elpa_allocate(3), elpa_set(3), and elpa_setup(3) must be called BEFORE elpa_generalized_eigenvalues can be called. Especially the number of eigenvectors to be computed can be set with elpa_set(3). Unlike in the case of ordinary eigenvalue problem, the generalized problem calls some external scalapack routines. The user is responsible for initialization of the blacs context, which then has to be passed to elpa by elpa_set(3) BEFORE elpa_generalized_eigenvalues can be called.