e) e%hermitian_multiply ! multiply a**T *b or a**H *b (replaces f) and g) from legacy API)

7. when not needed anymore, destroy the instance

call e%destroy()

8. when *ELPA* is not needed anymore, unitialize the *ELPA* library

call elpa_uninit()

### Online and local documentation ###

Local documentation (via man pages) should be available (if *ELPA* has been installed with the documentation):

For example "man elpa2_print_kernels" should provide the documentation for the *ELPA* program which prints all

the available kernels.

Also a [online doxygen documentation] (http://elpa.mpcdf.mpg.de/html/Documentation/ELPA-2017.05.001/html/index.html)

for each *ELPA* release is available.

## API of the *ELPA* library ##

With release 2017.05.001 of the *ELPA* library the interface has been rewritten substantially, in order to have a more

generic interface and avoid future interface changes.

For compatibility reasons the interface defined in the previous release 2016.11.001 is also still available

IF AND ONLY IF *ELPA* has been build with support of this legacy interface. If you want to use the legacy

interface, please look to section "B) Using the legacy API of the *ELPA* library.

The legacy API defines all the functionallity as has been defined in *ELPA* release 2016.11.011. Note, however,

that all future features of *ELPA* will only be accessible via the new API defined in release 2017.05.001.

## A) Using the final API definition of the *ELPA* library ##

Using *ELPA* with the latest API is done in the following steps

- include elpa headers (C-Case) or use the Fortran module

- define a instance of the elpa type

- call elpa_init

- call elpa_allocate to allocate an instance of *ELPA*

- use ELPA-type function "set" to set matrix parameters

- call ELPA-type function "setup"

- set or get all possible ELPA options with ELPA-type functions get/set

- call ELPA-type function solve or others

- call ELPA-type function destroy

- call elpa_uninit

## B) Using the legacy API of the *ELPA* library ##

The following description describes the usage of the *ELPA* library with the legacy interface.

### General concept of the *ELPA* library ###

The *ELPA* library consists of two main parts:

-*ELPA 1stage* solver

-*ELPA 2stage* solver

Both variants of the *ELPA* solvers are available for real or complex singe and double precision valued matrices.

Thus *ELPA* provides the following user functions (see man pages or [online] (http://elpa.mpcdf.mpg.de/html/Documentation/ELPA-2016.11.001/html/index.html) for details):

- elpa_get_communicators : set the row / column communicators for *ELPA*

- elpa_solve_evp_complex_1stage_{single|double} : solve a {single|double} precision complex eigenvalue proplem with the *ELPA 1stage* solver

- elpa_solve_evp_real_1stage_{single|double} : solve a {single|double} precision real eigenvalue proplem with the *ELPA 1stage* solver

- elpa_solve_evp_complex_2stage_{single|double} : solve a {single|double} precision complex eigenvalue proplem with the *ELPA 2stage* solver

- elpa_solve_evp_real_2stage_{single|double} : solve a {single|double} precision real eigenvalue proplem with the *ELPA 2stage* solver

- elpa_solve_evp_real_{single|double} : driver for the {single|double} precision real *ELPA 1stage* or *ELPA 2stage* solver

- elpa_solve_evp_complex_{single|double} : driver for the {single|double} precision complex *ELPA 1stage* or *ELPA 2stage* solver

Furthermore *ELPA* provides the utility binary "elpa2_print_available_kernels": it tells the user

which *ELPA 2stage* compute kernels have been installed and which default kernels are set

If you want to solve an eigenvalue problem with *ELPA*, you have to decide whether you

want to use *ELPA 1stage* or *ELPA 2stage* solver. Normally, *ELPA 2stage* is the better

choice since it is faster, but there a matrix dimensions where *ELPA 1stage* is supperior.

Independent of the choice of the solver, the concept of calling *ELPA* is always the same:

#### MPI version of *ELPA* ####

In this case, *ELPA* relies on a BLACS distributed matrix.

To solve a Eigenvalue problem of this matrix with *ELPA*, one has

1. to include the *ELPA* header (C case) or module (Fortran)

2. to create row and column MPI communicators for ELPA (with "elpa_get_communicators")

3. to call to the *ELPA driver* or directly call *ELPA 1stage* or *ELPA 2stage* for the matrix.

Here is a very simple MPI code snippet for using *ELPA 1stage*: For the definition of all variables

please have a look at the man pages and/or the online documentation (see above). A full version

of a simple example program can be found in ./test_project/src.

! All ELPA routines need MPI communicators for communicating within

! rows or columns of processes, these are set in get_elpa_communicators

With the definintions of the input and output variables:

integer, intent(in) na: global dimension of quadratic matrix a to solve

integer, intent(in) nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

real*{4|8}, intent(inout) a: locally distributed part of the matrix a. The local dimensions are lda x matrixCols

integer, intent(in) lda: leading dimension of locally distributed matrix a

real*{4|8}, intent(inout) ev: on output the first nev computed eigenvalues

real*{4|8}, intent(inout) q: on output the first nev computed eigenvectors

integer, intent(in) ldq: leading dimension of matrix q which stores the eigenvectors

integer, intent(in) nblk: blocksize of block cyclic distributin, must be the same in both directions

integer, intent(in) matrixCols: number of columns of locally distributed matrices a and q

integer, intent(in) mpi_comm_rows: communicator for communication in rows. Constructed with get_elpa_communicators(3)

integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with get_elpa_communicators(3)

logical success: return value indicating success or failure

C INTERFACE

#include "elpa.h"

success = elpa_solve_evp_real_1stage_{single|double} (int na, int nev, double *a, int lda, double *ev, double *q, int ldq, int nblk, int matrixCols, int

mpi_comm_rows, int mpi_comm_cols);

With the definintions of the input and output variables:

int na: global dimension of quadratic matrix a to solve

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

{float|double} *a: pointer to locally distributed part of the matrix a. The local dimensions are lda x matrixCols

int lda: leading dimension of locally distributed matrix a

{float|double} *ev: pointer to memory containing on output the first nev computed eigenvalues

{float|double} *q: pointer to memory containing on output the first nev computed eigenvectors

int ldq: leading dimension of matrix q which stores the eigenvectors

int nblk: blocksize of block cyclic distributin, must be the same in both directions

int matrixCols: number of columns of locally distributed matrices a and q

int mpi_comm_rows: communicator for communication in rows. Constructed with get_elpa_communicators(3)

int mpi_comm_cols: communicator for communication in colums. Constructed with get_elpa_communicators(3)

int success: return value indicating success (1) or failure (0)

DESCRIPTION

Solve the real eigenvalue problem with the 1-stage solver. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the

get_elpa_communicators(3) function. The distributed quadratic marix a has global dimensions na x na, and a local size lda x matrixCols.

The solver will compute the first nev eigenvalues, which will be stored on exit in ev. The eigenvectors corresponding to the eigenvalues

will be stored in q. All memory of the arguments must be allocated outside the call to the solver.

With the definintions of the input and output variables:

integer, intent(in) na: global dimension of quadratic matrix a to solve

integer, intent(in) nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

complex*{8|16}, intent(inout) a: locally distributed part of the matrix a. The local dimensions are lda x matrixCols

integer, intent(in) lda: leading dimension of locally distributed matrix a

real*{4|8}, intent(inout) ev: on output the first nev computed eigenvalues

complex*{8|16}, intent(inout) q: on output the first nev computed eigenvectors

integer, intent(in) ldq: leading dimension of matrix q which stores the eigenvectors

integer, intent(in) nblk: blocksize of block cyclic distributin, must be the same in both directions

integer, intent(in) matrixCols: number of columns of locally distributed matrices a and q

integer, intent(in) mpi_comm_rows: communicator for communication in rows. Constructed with get_elpa_communicators(3)

integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with get_elpa_communicators(3)

logical success: return value indicating success or failure

C INTERFACE

#include "elpa.h"

#include <complex.h>

success = elpa_solve_evp_complex_1stage_{single|double} (int na, int nev, double complex *a, int lda, double *ev, double complex*q, int ldq, int nblk, int

matrixCols, int mpi_comm_rows, int mpi_comm_cols);

With the definintions of the input and output variables:

int na: global dimension of quadratic matrix a to solve

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

{float|double} complex *a: pointer to locally distributed part of the matrix a. The local dimensions are lda x matrixCols

int lda: leading dimension of locally distributed matrix a

{float|double} *ev: pointer to memory containing on output the first nev computed eigenvalues

{float|double} complex *q: pointer to memory containing on output the first nev computed eigenvectors

int ldq: leading dimension of matrix q which stores the eigenvectors

int nblk: blocksize of block cyclic distributin, must be the same in both directions

int matrixCols: number of columns of locally distributed matrices a and q

int mpi_comm_rows: communicator for communication in rows. Constructed with get_elpa_communicators(3)

int mpi_comm_cols: communicator for communication in colums. Constructed with get_elpa_communicators(3)

int success: return value indicating success (1) or failure (0)

DESCRIPTION

Solve the complex eigenvalue problem with the 1-stage solver. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the

get_elpa_communicators(3) function. The distributed quadratic marix a has global dimensions na x na, and a local size lda x matrixCols.

The solver will compute the first nev eigenvalues, which will be stored on exit in ev. The eigenvectors corresponding to the eigenvalues

will be stored in q. All memory of the arguments must be allocated outside the call to the solver.

The *ELPA 1stage* solver, does not need or accept any other parameters than in the above

specification.

#### Using *ELPA 2stage* ####

The *ELPA 2stage* solver can be used in the same manner, as the *ELPA 1stage* solver.

However, the 2 stage solver, can be used with different compute kernels, which offers

more possibilities for configuration.

It is recommended to first call the utillity program

elpa2_print_kernels

which will tell all the compute kernels that can be used with *ELPA 2stage*". It will

also give information, whether a kernel can be set via environment variables.

##### Using the default kernels #####

If no kernel is set either via an environment variable or the *ELPA 2stage API* then

the default kernels will be set.

##### Setting the *ELPA 2stage* compute kernels #####

##### Setting the *ELPA 2stage* compute kernels with environment variables#####

If the *ELPA* installation allows setting ther compute kernels with enviroment variables,

setting the variables "REAL_ELPA_KERNEL" and "COMPLEX_ELPA_KERNEL" will set the compute

kernels. The environment variable setting will take precedence over all other settings!

The utility program "elpa2_print_kernels" can list which kernels are available and which

would be choosen. This reflects, as well the setting of the default kernel or the settings

with the environment variables

##### Setting the *ELPA 2stage* compute kernels with API calls#####

It is also possible to set the *ELPA 2stage* compute kernels via the API.

As an example the API for ELPA real double-precision 2stage is shown:

Generalized interface to the ELPA 1stage and 2stage solver for real-valued problems

With the definintions of the input and output variables:

integer, intent(in) na: global dimension of quadratic matrix a to solve

integer, intent(in) nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

real*8, intent(inout) a: locally distributed part of the matrix a. The local dimensions are lda x matrixCols

integer, intent(in) lda: leading dimension of locally distributed matrix a

real*8, intent(inout) ev: on output the first nev computed eigenvalues"

real*8, intent(inout) q: on output the first nev computed eigenvectors"

integer, intent(in) ldq: leading dimension of matrix q which stores the eigenvectors

integer, intent(in) nblk: blocksize of block cyclic distributin, must be the same in both directions

integer, intent(in) matrixCols: number of columns of locally distributed matrices a and q

integer, intent(in) mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators

integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators

integer, intent(in) mpi_comm_all: communicator for all processes in the processor set involved in ELPA

integer, intent(in), optional: THIS_REAL_ELPA_KERNEL: optional argument, choose the compute kernel for 2-stage solver

logical, intent(in), optional: useQR: optional argument; switches to QR-decomposition if set to .true.

logical, intent(in), optional: useQPU: decide whether the GPU version should be used or not

character(*), optional method: use 1stage solver if "1stage", use 2stage solver if "2stage", (at the moment) use 2stage solver if "auto"

logical success: return value indicating success or failure

C INTERFACE

#include "elpa.h"

success = elpa_solve_evp_real_double (int na, int nev, double *a, int lda, double *ev, double *q, int ldq, int nblk, int matrixCols, int mpi_comm_rows, int mpi_comm_cols, int mpi_comm_all, int THIS_ELPA_REAL_KERNEL, int useQR, int useGPU, char *method);"

With the definintions of the input and output variables:"

int na: global dimension of quadratic matrix a to solve

int nev: number of eigenvalues to be computed; the first nev eigenvalules are calculated

double *a: pointer to locally distributed part of the matrix a. The local dimensions are lda x matrixCols

int lda: leading dimension of locally distributed matrix a

double *ev: pointer to memory containing on output the first nev computed eigenvalues

double *q: pointer to memory containing on output the first nev computed eigenvectors

int ldq: leading dimension of matrix q which stores the eigenvectors

int nblk: blocksize of block cyclic distributin, must be the same in both directions

int matrixCols: number of columns of locally distributed matrices a and q

int mpi_comm_rows: communicator for communication in rows. Constructed with elpa_get_communicators

int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators

int mpi_comm_all: communicator for all processes in the processor set involved in ELPA

int THIS_ELPA_REAL_KERNEL: choose the compute kernel for 2-stage solver

int useQR: if set to 1 switch to QR-decomposition

int useGPU: decide whether the GPU version should be used or not

char *method: use 1stage solver if "1stage", use 2stage solver if "2stage", (at the moment) use 2stage solver if "auto"

int success: return value indicating success (1) or failure (0)

DESCRIPTION

Solve the real eigenvalue problem. The value of method desides whether the 1stage or 2stage solver is used. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the elpa_get_communicators function. The distributed quadratic marix a has global dimensions na x na, and a local size lda x matrixCols. The solver will compute the first nev eigenvalues, which will be stored on exit in ev. The eigenvectors corresponding to the eigenvalues will be stored in q. All memory of the arguments must be allocated outside the call to the solver.

##### Setting up the GPU version of *ELPA* 1 and 2 stage #####

Since release ELPA 2016.011.001.pre *ELPA* offers GPU support, IF *ELPA* has been build with the configure option "--enabble-gpu-support".

At run-time the GPU version can be used by setting the environment variable "ELPA_USE_GPU" to "yes", or by calling the *ELPA* functions

(elpa_solve_evp_real_{double|single}, elpa_solve_evp_real_1stage_{double|single}, elpa_solve_evp_real_2stage_{double|single}) with the

argument "useGPU = .true." or "useGPU = 1" for the Fortran and C case, respectively. Please, not that similiar to the choice of the

*ELPA* 2stage compute kernels, the enviroment variable takes precendence over the setting in the API call.

Further note that it is NOT allowed to define the usage of GPUs AND to EXPLICITLY set an ELPA 2stage compute kernel other than

"REAL_ELPA_KERNEL_GPU" or "COMPLEX_ELPA_KERNEL_GPU".