## Users guide for the *ELPA* library ##
This document provides the guide for using the *ELPA* library in user applications.
### 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-2018.05.001.rc1/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 to 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 functionality as it 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 or later.
## 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 "elpa/elpa.h" (C-Case) or use the Fortran module "use elpa"
- define a instance of the elpa type
- call elpa_init
- call elpa_allocate to allocate an instance of *ELPA*
note that you can define (and configure individually) as many different instances
for ELPA as you want, e.g. one for CPU only computations and for larger matrices on GPUs
- use ELPA-type function "set" to set matrix and MPI parameters
- call the ELPA-type function "setup"
- set or get all possible ELPA tunable options with ELPA-type functions get/set
At the moment the following tunable options are available:
- "solver" can either be ELPA_SOLVER_1STAGE or ELPA_SOLVER_2STAGE
- "real_kernel" can be one of the available real kernels (a list of available kernels can be
queried with the ELPA helper binary elpa2_print_kernels)
- "complex_kernel" can be one of the available complex kernels (a list of available kernels can be
- "qr" can be either 0 or 1, switches QR decomposition off/on for ELPA_SOLVER_2STAGE
only available in real-case for blocksize at least 64
- "gpu" can be either 0 or 1, switches GPU computations off or on, assuming that the installation
of the ELPA library has been build with GPU support enables
- "timings" can be either 0 or 1, switches time measurements off or on
- "debug" can be either 0 or 1, switches detailed debug messages off/on
- call ELPA-type function solve or others
At the moment the following ELPA compute functions are available:
- "eigenvectors" solves the eigenvalue problem for single/double real/complex valued matrices and
returns the eigenvalues AND eigenvectors
- "eigenvalues" solves the eigenvalue problem for single/double real/complex valued matrices and
returns the eigenvalues
- "hermetian_multipy" computes C = A^T * B (real) or C = A^H * B (complex) for single/double
real/complex matrices
- "cholesky" does a cholesky factorization for a single/double real/complex matrix
- "invert_triangular" inverts a single/double real/complex triangular matrix
- "solve_tridiagonal" solves the single/double eigenvalue problem for a real tridiagonal matrix
- if the ELPA object is not needed any more call ELPA-type function destroy
- call elpa_uninit at the end of the program
## 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-2018.05.001.rc1/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 are matrix dimensions where *ELPA 1stage* is superior.
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_1stage_legacy_api/src.
! All ELPA routines need MPI communicators for communicating within
! rows or columns of processes, these are set in elpa_get_communicators
success = elpa_get_communicators(mpi_comm_world, my_prow, my_pcol, &
mpi_comm_rows, mpi_comm_cols)
if (myid==0) then
print '(a)','| Past split communicator setup for rows and columns.'
end if
! Determine the necessary size of the distributed matrices,
! we use the Scalapack tools routine NUMROC for that.
na_rows = numroc(na, nblk, my_prow, 0, np_rows)
na_cols = numroc(na, nblk, my_pcol, 0, np_cols)
!-------------------------------------------------------------------------------
! Calculate eigenvalues/eigenvectors
if (myid==0) then
print '(a)','| Entering one-step ELPA solver ... '
print *
end if
success = elpa_solve_evp_real_1stage_{single|double} (na, nev, a, na_rows, ev, z, na_rows, nblk, &
matrixCols, mpi_comm_rows, mpi_comm_cols)
if (myid==0) then
print '(a)','| One-step ELPA solver complete.'
print *
end if
#### Shared-memory version of *ELPA* ####
If the *ELPA* library has been compiled with the configure option "--with-mpi=0",
no MPI will be used.
Still the **same** call sequence as in the MPI case can be used (see above).
#### Setting the row and column communicators ####
SYNOPSIS
FORTRAN INTERFACE
use elpa1
success = elpa_get_communicators (mpi_comm_global, my_prow, my_pcol, mpi_comm_rows, mpi_comm_cols)
integer, intent(in) mpi_comm_global: global communicator for the calculation
integer, intent(in) my_prow: row coordinate of the calling process in the process grid
integer, intent(in) my_pcol: column coordinate of the calling process in the process grid
integer, intent(out) mpi_comm_row: communicator for communication within rows of processes
integer, intent(out) mpi_comm_row: communicator for communication within columns of processes
integer success: return value indicating success or failure of the underlying MPI_COMM_SPLIT function
C INTERFACE
#include "elpa_generated.h"
success = elpa_get_communicators (int mpi_comm_world, int my_prow, my_pcol, int *mpi_comm_rows, int *Pmpi_comm_cols);
int mpi_comm_global: global communicator for the calculation
int my_prow: row coordinate of the calling process in the process grid
int my_pcol: column coordinate of the calling process in the process grid
int *mpi_comm_row: pointer to the communicator for communication within rows of processes
int *mpi_comm_row: pointer to the communicator for communication within columns of processes
int success: return value indicating success or failure of the underlying MPI_COMM_SPLIT function
#### Using *ELPA 1stage* ####
After setting up the *ELPA* row and column communicators (by calling elpa_get_communicators),
only the real or complex valued solver has to be called:
SYNOPSIS
FORTRAN INTERFACE
use elpa1
success = elpa_solve_evp_real_1stage_{single|double} (na, nev, a(lda,matrixCols), ev(nev), q(ldq, matrixCols), ldq, nblk, matrixCols, mpi_comm_rows,
mpi_comm_cols)
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 elpa_get_communicators(3)
integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_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 elpa_get_communicators(3)
int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_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
elpa_get_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.
FORTRAN INTERFACE
use elpa1
success = elpa_solve_evp_complex_1stage_{single|double} (na, nev, a(lda,matrixCols), ev(nev), q(ldq, matrixCols), ldq, nblk, matrixCols, mpi_comm_rows,
mpi_comm_cols)
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 elpa_get_communicators(3)
integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)
logical success: return value indicating success or failure
C INTERFACE
#include "elpa.h"
#include
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 elpa_get_communicators(3)
int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_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
elpa_get_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 utility 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 their compute kernels with environment 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 chosen. This reflects the setting of the default kernel as well as the setting
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:
SYNOPSIS
FORTRAN INTERFACE
use elpa1
use elpa2
success = elpa_solve_evp_real_2stage_double (na, nev, a(lda,matrixCols), ev(nev), q(ldq, matrixCols), ldq, nblk, matrixCols, mpi_comm_rows,
mpi_comm_cols, mpi_comm_all, THIS_REAL_ELPA_KERNEL, useQR, useGPU)
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 elpa_get_communicators(3)
integer, intent(in) mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)
integer, intent(in) mpi_comm_all: communicator for all processes in the processor set involved in ELPA
logical, intent(in), optional: useQR: optional argument; switches to QR-decomposition if set to .true.
logical, intent(in), optional: useGPU: decide whether GPUs should be used ore not
logical success: return value indicating success or failure
C INTERFACE
#include "elpa.h"
success = elpa_solve_evp_real_2stage_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);
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(3)
int mpi_comm_cols: communicator for communication in colums. Constructed with elpa_get_communicators(3)
int mpi_comm_all: communicator for all processes in the processor set involved in ELPA
int useQR: if set to 1 switch to QR-decomposition
int useGPU: decide whether the GPU version should be used or not
int success: return value indicating success (1) or failure (0)
DESCRIPTION
Solve the real eigenvalue problem with the 2-stage solver. The ELPA communicators mpi_comm_rows and mpi_comm_cols are obtained with the
elpa_get_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.
##### Setting up *ELPA 1stage* or *ELPA 2stage* with the *ELPA driver interface* #####
Since release ELPA 2016.005.004 a driver routine allows to choose more easily which solver (1stage or 2stage) will be used.
As an exmple the real double-precision case is explained:
SYNOPSIS
FORTRAN INTERFACE
use elpa_driver
success = elpa_solve_evp_real_double (na, nev, a(lda,matrixCols), ev(nev), q(ldq, matrixCols), ldq, nblk, matrixCols, mpi_comm_rows, mpi_comm_cols, mpi_comm_all, THIS_REAL_ELPA_KERNEL=THIS_REAL_ELPA_KERNEL, useQR, useGPU, method=method)
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".