using.org

# This file is part of the Chameleon User's Guide.
# Copyright (C) 2017 Inria
# See the file ../users_guide.org for copying conditions.

** Linking an external application with Chameleon libraries
   Compilation and link with Chameleon libraries have been tested with
   the GNU compiler suite ~gcc/gfortran~ and the Intel compiler suite
   ~icc/ifort~.

*** Flags required
    The compiler, linker flags that are necessary to build an
    application using Chameleon are given through the [[https://www.freedesktop.org/wiki/Software/pkg-config/][pkg-config]]
    mechanism.
    #+begin_src
    export PKG_CONFIG_PATH=/home/jdoe/install/chameleon/lib/pkgconfig:$PKG_CONFIG_PATH
    pkg-config --cflags chameleon
    pkg-config --libs chameleon
    pkg-config --libs --static chameleon
    #+end_src
    The .pc files required are located in the sub-directory
    ~lib/pkgconfig~ of your Chameleon install directory.
*** Static linking in C
    Lets imagine you have a file ~main.c~ that you want to link with
    Chameleon static libraries.  Lets consider
    ~/home/yourname/install/chameleon~ is the install directory
    of Chameleon containing sub-directories ~include/~ and
    ~lib/~.  Here could be your compilation command with gcc
    compiler:
    #+begin_src
    gcc -I/home/yourname/install/chameleon/include -o main.o -c main.c
    #+end_src
    Now if you want to link your application with Chameleon static libraries, you
    could do:
    #+begin_src
    gcc main.o -o main                                         \
    /home/yourname/install/chameleon/lib/libchameleon.a        \
    /home/yourname/install/chameleon/lib/libchameleon_starpu.a \
    /home/yourname/install/chameleon/lib/libcoreblas.a         \
    -lstarpu-1.2 -Wl,--no-as-needed -lmkl_intel_lp64           \
    -lmkl_sequential -lmkl_core -lpthread -lm -lrt
    #+end_src
    As you can see in this example, we also link with some dynamic
    libraries *starpu-1.2*, *Intel MKL* libraries (for
    BLAS/LAPACK/CBLAS/LAPACKE), *pthread*, *m* (math) and *rt*. These
    libraries will depend on the configuration of your Chameleon
    build.  You can find these dependencies in .pc files we generate
    during compilation and that are installed in the sub-directory
    ~lib/pkgconfig~ of your Chameleon install directory.  Note also that
    you could need to specify where to find these libraries with *-L*
    option of your compiler/linker.

    Before to run your program, make sure that all shared libraries
    paths your executable depends on are known.  Enter ~ldd main~
    to check.  If some shared libraries paths are missing append them
    in the LD_LIBRARY_PATH (for Linux systems) environment
    variable (DYLD_LIBRARY_PATH on Mac).

*** Dynamic linking in C
    For dynamic linking (need to build Chameleon with CMake option
    BUILD_SHARED_LIBS=ON) it is similar to static compilation/link but
    instead of specifying path to your static libraries you indicate
    the path to dynamic libraries with *-L* option and you give
    the name of libraries with *-l* option like this:
    #+begin_src
    gcc main.o -o main \
    -L/home/yourname/install/chameleon/lib \
    -lchameleon -lchameleon_starpu -lcoreblas \
    -lstarpu-1.2 -Wl,--no-as-needed -lmkl_intel_lp64 \
    -lmkl_sequential -lmkl_core -lpthread -lm -lrt
    #+end_src
    Note that an update of your environment variable LD_LIBRARY_PATH
    (DYLD_LIBRARY_PATH on Mac) with the path of the libraries could be
    required before executing
    #+begin_src
    export LD_LIBRARY_PATH=path/to/libs:path/to/chameleon/lib
    #+end_src

# # *** Build a Fortran program with Chameleon                         :noexport:
# #
# #     Chameleon provides a Fortran interface to user functions. Example:
# #     #+begin_src
# #     call morse_version(major, minor, patch) !or
# #     call MORSE_VERSION(major, minor, patch)
# #     #+end_src
# #
# #     Build and link are very similar to the C case.
# #
# #     Compilation example:
# #     #+begin_src
# #     gfortran -o main.o -c main.f90
# #     #+end_src
# #
# #     Static linking example:
# #     #+begin_src
# #     gfortran main.o -o main                                    \
# #     /home/yourname/install/chameleon/lib/libchameleon.a        \
# #     /home/yourname/install/chameleon/lib/libchameleon_starpu.a \
# #     /home/yourname/install/chameleon/lib/libcoreblas.a         \
# #     -lstarpu-1.2 -Wl,--no-as-needed -lmkl_intel_lp64           \
# #     -lmkl_sequential -lmkl_core -lpthread -lm -lrt
# #     #+end_src
# #
# #     Dynamic linking example:
# #     #+begin_src
# #     gfortran main.o -o main                          \
# #     -L/home/yourname/install/chameleon/lib           \
# #     -lchameleon -lchameleon_starpu -lcoreblas        \
# #     -lstarpu-1.2 -Wl,--no-as-needed -lmkl_intel_lp64 \
# #     -lmkl_sequential -lmkl_core -lpthread -lm -lrt
# #     #+end_src

** Using Chameleon executables

   Chameleon provides several test executables that are compiled and
   linked with Chameleon's dependencies.  Instructions about the
   arguments to give to executables are accessible thanks to the
   option ~-[-]help~ or ~-[-]h~.  This set of binaries are separated into
   three categories and can be found in three different directories:
   * *example*: contains examples of API usage and more specifically the
     sub-directory ~lapack_to_morse/~ provides a tutorial that explains
     how to use Chameleon functionalities starting from a full LAPACK
     code, see [[sec:tuto][Tutorial LAPACK to Chameleon]]
   * *testing*: contains testing drivers to check numerical correctness of
     Chameleon linear algebra routines with a wide range of parameters
     #+begin_src
     ./testing/stesting 4 1 LANGE 600 100 700
     #+end_src
     Two first arguments are the number of cores and gpus to use.
     The third one is the name of the algorithm to test.
     The other arguments depend on the algorithm, here it lies for the number of
     rows, columns and leading dimension of the problem.

     Name of algorithms available for testing are:
     * LANGE: norms of matrices Infinite, One, Max, Frobenius
     * GEMM: general matrix-matrix multiply
     * HEMM: hermitian matrix-matrix multiply
     * HERK: hermitian matrix-matrix rank k update
     * HER2K: hermitian matrix-matrix rank 2k update
     * SYMM: symmetric matrix-matrix multiply
     * SYRK: symmetric matrix-matrix rank k update
     * SYR2K: symmetric matrix-matrix rank 2k update
     * PEMV: matrix-vector multiply with pentadiagonal matrix
     * TRMM: triangular matrix-matrix multiply
     * TRSM: triangular solve, multiple rhs
     * POSV: solve linear systems with symmetric positive-definite matrix
     * GESV_INCPIV: solve linear systems with general matrix
     * GELS: linear least squares with general matrix
     * GELS_HQR: gels with hierarchical tree
     * GELS_SYSTOLIC: gels with systolic tree
   * *timing*: contains timing drivers to assess performances of
     Chameleon routines. There are two sets of executables, those who
     do not use the tile interface and those who do (with _tile in the
     name of the executable). Executables without tile interface
     allocates data following LAPACK conventions and these data can be
     given as arguments to Chameleon routines as you would do with
     LAPACK. Executables with tile interface generate directly the
     data in the format Chameleon tile algorithms used to submit tasks
     to the runtime system. Executables with tile interface should be
     more performant because no data copy from LAPACK matrix layout to
     tile matrix layout are necessary. Calling example:
     #+begin_src
     ./timing/time_dpotrf --n_range=1000:10000:1000 --nb=320
                          --threads=9 --gpus=3
                          --nowarmup
     #+end_src

     List of main options that can be used in timing:
     * ~--help~: show usage
     * ~--threads~: Number of CPU workers (default:
       ~_SC_NPROCESSORS_ONLN~)
     * ~--gpus~: number of GPU workers (default: ~0~)
     * ~--n_range=R~: range of N values, with ~R=Start:Stop:Step~
       (default: ~500:5000:500~)
     * ~--m=X~: dimension (M) of the matrices (default: ~N~)
     * ~--k=X~: dimension (K) of the matrices (default: ~1~), useful for
       GEMM algorithm (k is the shared dimension and must be defined
       >1 to consider matrices and not vectors)
     * ~--nrhs=X~: number of right-hand size (default: ~1~)
     * ~--nb=X~: block/tile size. (default: ~128~)
     * ~--ib=X~: inner-blocking/IB size. (default: ~32~)
     * ~--niter=X~: number of iterations performed for each test
       (default: ~1~)
     * ~--rhblk=X~: if X > 0, enable Householder mode for QR and LQ
       factorization. X is the size of each subdomain (default: ~0~)
     * ~--[no]check~: check result (default: ~nocheck~)
     * ~--[no]profile~: print profiling informations (default:
       ~noprofile~)
     * ~--[no]trace~: enable/disable trace generation (default: ~notrace~)
     * ~--[no]dag~: enable/disable DAG generation (default: ~nodag~)
     * ~--[no]inv~: check on inverse (default: ~noinv~)
     * ~--nocpu~: all GPU kernels are exclusively executed on GPUs
     * ~--ooc~: Enable out-of-core (available only with StarPU)
     * ~--bound~: Compare result to area bound (available only with
       StarPU) (default: ~0~)

     List of timing algorithms available:
     * LANGE: norms of matrices
     * GEMM: general matrix-matrix multiply
     * TRSM: triangular solve
     * POTRF: Cholesky factorization with a symmetric
       positive-definite matrix
     * POTRI: Cholesky inversion
     * POSV: solve linear systems with symmetric positive-definite matrix
     * GETRF_NOPIV: LU factorization of a general matrix using the tile LU algorithm without row pivoting
     * GESV_NOPIV: solve linear system for a general matrix using the tile LU algorithm without row pivoting
     * GETRF_INCPIV: LU factorization of a general matrix using the tile LU algorithm with partial tile pivoting with row interchanges
     * GESV_INCPIV: solve linear system for a general matrix using the tile LU algorithm with partial tile pivoting with row interchanges matrix
     * GEQRF: QR factorization of a general matrix
     * GELQF: LQ factorization of a general matrix
     * QEQRF_HQR: GEQRF with hierarchical tree
     * QEQRS: solve linear systems using a QR factorization
     * GELS: solves overdetermined or underdetermined linear systems involving a general matrix using the QR or the LQ factorization
     * GESVD: general matrix singular value decomposition

*** Execution trace using StarPU
    <<sec:trace>>

    StarPU can generate its own trace log files by compiling it with
    the ~--with-fxt~ option at the configure step (you can have to
    specify the directory where you installed FxT by giving
    ~--with-fxt=...~ instead of ~--with-fxt~ alone).  By doing so, traces
    are generated after each execution of a program which uses StarPU
    in the directory pointed by the STARPU_FXT_PREFIX environment
    variable.
    #+begin_example
    export STARPU_FXT_PREFIX=/home/jdoe/fxt_files/
    #+end_example
    When executing a ~./timing/...~ Chameleon program, if it has been
    enabled (StarPU compiled with FxT and
    *-DCHAMELEON_ENABLE_TRACING=ON*), you can give the option ~--trace~ to
    tell the program to generate trace log files.

    Finally, to generate the trace file which can be opened with [[http://vite.gforge.inria.fr/][Vite]]
    program, you can use the *starpu_fxt_tool* executable of StarPU.
    This tool should be in ~$STARPU_INSTALL_REPOSITORY/bin~.  You can
    use it to generate the trace file like this:
    #+begin_src
    path/to/your/install/starpu/bin/starpu_fxt_tool -i prof_filename
    #+end_src
    There is one file per mpi processus (prof_filename_0,
    prof_filename_1 ...).  To generate a trace of mpi programs you can
    call it like this:
    #+begin_src
    path/to/your/install/starpu/bin/starpu_fxt_tool -i prof_filename*
    #+end_src
    The trace file will be named paje.trace (use -o option to specify
    an output name).  Alternatively, for non mpi execution (only one
    processus and profiling file), you can set the environment
    variable *STARPU_GENERATE_TRACE=1* to automatically generate the
    paje trace file.

*** Use simulation mode with StarPU-SimGrid
    <<sec:simu>>

    Simulation mode can be activated by setting the cmake option
    CHAMELEON_SIMULATION to ON.  This mode allows you to simulate
    execution of algorithms with StarPU compiled with [[http://simgrid.gforge.inria.fr/][SimGrid]].  To do
    so, we provide some perfmodels in the simucore/perfmodels/
    directory of Chameleon sources.  To use these perfmodels, please
    set your *STARPU_HOME* environment variable to
    ~path/to/your/chameleon_sources/simucore/perfmodels~.  Finally, you
    need to set your *STARPU_HOSTNAME* environment variable to the name
    of the machine to simulate.  For example: *STARPU_HOSTNAME=mirage*.
    Note that only POTRF kernels with block sizes of 320 or 960
    (simple and double precision) on /mirage/ and /sirocco/ machines are
    available for now.  Database of models is subject to change.

** Chameleon API

   Chameleon provides routines to solve dense general systems of
   linear equations, symmetric positive definite systems of linear
   equations and linear least squares problems, using LU, Cholesky, QR
   and LQ factorizations.  Real arithmetic and complex arithmetic are
   supported in both single precision and double precision.  Routines
   that compute linear algebra are of the following form:
   #+begin_src
   MORSE_name[_Tile[_Async]]
   #+end_src
   * all user routines are prefixed with *MORSE*
   * in the pattern *MORSE_name[_Tile[_Async]]*, /name/ follows the
     BLAS/LAPACK naming scheme for algorithms (/e.g./ sgemm for general
     matrix-matrix multiply simple precision)
   * Chameleon provides three interface levels
     * *MORSE_name*: simplest interface, very close to CBLAS and
       LAPACKE, matrices are given following the LAPACK data layout
       (1-D array column-major).  It involves copy of data from LAPACK
       layout to tile layout and conversely (to update LAPACK data),
       see [[sec:tuto_step1][Step1]].
     * *MORSE_name_Tile*: the tile interface avoid copies between LAPACK
       and tile layouts. It is the standard interface of Chameleon and
       it should achieved better performance than the previous
       simplest interface. The data are given through a specific
       structure called a descriptor, see [[sec:tuteo_step2][Step2]].
     * *MORSE_name_Tile_Async*: similar to the tile interface, it avoids
       synchonization barrier normally called between *Tile* routines.
       At the end of an *Async* function, completion of tasks is not
       guaranteed and data are not necessarily up-to-date.  To ensure
       that tasks have been all executed, a synchronization function
       has to be called after the sequence of *Async* functions, see
       [[tuto_step4][Step4]].

   MORSE routine calls have to be preceded from
   #+begin_src
   MORSE_Init( NCPU, NGPU );
   #+end_src
   to initialize MORSE and the runtime system and followed by
   #+begin_src
   MORSE_Finalize();
   #+end_src
   to free some data and finalize the runtime and/or MPI.

*** Tutorial LAPACK to Chameleon
    <<sec:tuto>>

    This tutorial is dedicated to the API usage of Chameleon.  The
    idea is to start from a simple code and step by step explain how
    to use Chameleon routines.  The first step is a full BLAS/LAPACK
    code without dependencies to Chameleon, a code that most users
    should easily understand.  Then, the different interfaces
    Chameleon provides are exposed, from the simplest API (step1) to
    more complicated ones (until step4).  The way some important
    parameters are set is discussed in step5.  step6 is an example
    about distributed computation with MPI.  Finally step7 shows how
    to let Chameleon initialize user's data (matrices/vectors) in
    parallel.

    Source files can be found in the ~example/lapack_to_morse/~
    directory.  If CMake option *CHAMELEON_ENABLE_EXAMPLE* is ON then
    source files are compiled with the project libraries.  The
    arithmetic precision is /double/.  To execute a step
    *X*, enter the following command:
    #+begin_src
    ./stepX --option1 --option2 ...
    #+end_src
    Instructions about the arguments to give to executables are
    accessible thanks to the option ~-[-]help~ or ~-[-]h~.  Note there
    exist default values for options.

    For all steps, the program solves a linear system $Ax=B$ The
    matrix values are randomly generated but ensure that matrix \$A\$ is
    symmetric positive definite so that $A$ can be factorized in a
    $LL^T$ form using the Cholesky factorization.


    The different steps of the tutorial are:
    * Step0: a simple Cholesky example using the C interface of BLAS/LAPACK
    * Step1: introduces the LAPACK equivalent interface of Chameleon
    * Step2: introduces the tile interface
    * Step3: indicates how to give your own tile matrix to Chameleon
    * Step4: introduces the tile async interface
    * Step5: shows how to set some important parameters
    * Step6: introduces how to benefit from MPI in Chameleon
    * Step7: introduces how to let Chameleon initialize the user's matrix data

**** Step0
     The C interface of BLAS and LAPACK, that is, CBLAS and LAPACKE,
     are used to solve the system. The size of the system (matrix) and
     the number of right hand-sides can be given as arguments to the
     executable (be careful not to give huge numbers if you do not
     have an infinite amount of RAM!).  As for every step, the
     correctness of the solution is checked by calculating the norm
     $||Ax-B||/(||A||||x||+||B||)$.  The time spent in
     factorization+solve is recorded and, because we know exactly the
     number of operations of these algorithms, we deduce the number of
     operations that have been processed per second (in GFlops/s).
     The important part of the code that solves the problem is:
     #+begin_example
     /* Cholesky factorization:
      * A is replaced by its factorization L or L^T depending on uplo */
     LAPACKE_dpotrf( LAPACK_COL_MAJOR, 'U', N, A, N );
     /* Solve:
      * B is stored in X on entry, X contains the result on exit.
      * Forward ...
      */
     cblas_dtrsm(
         CblasColMajor,
         CblasLeft,
         CblasUpper,
         CblasConjTrans,
         CblasNonUnit,
         N, NRHS, 1.0, A, N, X, N);
     /* ... and back substitution */
     cblas_dtrsm(
         CblasColMajor,
         CblasLeft,
         CblasUpper,
         CblasNoTrans,
         CblasNonUnit,
         N, NRHS, 1.0, A, N, X, N);
     #+end_example

**** Step1
     <<sec:tuto_step1>>

     It introduces the simplest Chameleon interface which is
     equivalent to CBLAS/LAPACKE.  The code is very similar to step0
     but instead of calling CBLAS/LAPACKE functions, we call Chameleon
     equivalent functions.  The solving code becomes:
     #+begin_example
     /* Factorization: */
     MORSE_dpotrf( UPLO, N, A, N );
     /* Solve: */
     MORSE_dpotrs(UPLO, N, NRHS, A, N, X, N);
     #+end_example
     The API is almost the same so that it is easy to use for beginners.
     It is important to keep in mind that before any call to MORSE routines,
     *MORSE_Init* has to be invoked to initialize MORSE and the runtime system.
     Example:
     #+begin_example
     MORSE_Init( NCPU, NGPU );
     #+end_example
     After all MORSE calls have been done, a call to *MORSE_Finalize* is
     required to free some data and finalize the runtime and/or MPI.
     #+begin_example
     MORSE_Finalize();
     #+end_example
     We use MORSE routines with the LAPACK interface which means the
     routines accepts the same matrix format as LAPACK (1-D array
     column-major).  Note that we copy the matrix to get it in our own
     tile structures, see details about this format here [[sec:tile][Tile Data
     Layout]].  This means you can get an overhead coming from copies.

**** Step2
     <<sec:tuto_step2>>

     This program is a copy of step1 but instead of using the LAPACK interface which
     reads to copy LAPACK matrices inside MORSE routines we use the tile interface.
     We will still use standard format of matrix but we will see how to give this
     matrix to create a MORSE descriptor, a structure wrapping data on which we want
     to apply sequential task-based algorithms.
     The solving code becomes:
     #+begin_example
     /* Factorization: */
     MORSE_dpotrf_Tile( UPLO, descA );
     /* Solve: */
     MORSE_dpotrs_Tile( UPLO, descA, descX );
     #+end_example
     To use the tile interface, a specific structure *MORSE_desc_t* must be
     created.
     This can be achieved from different ways.
     1. Use the existing function *MORSE_Desc_Create*: means the matrix
        data are considered contiguous in memory as it is considered
        in PLASMA ([[sec:tile][Tile Data Layout]]).
     2. Use the existing function *MORSE_Desc_Create_OOC*: means the
        matrix data is allocated on-demand in memory tile by tile, and
        possibly pushed to disk if that does not fit memory.
     3. Use the existing function *MORSE_Desc_Create_User*: it is more
        flexible than *Desc_Create* because you can give your own way to
        access to tile data so that your tiles can be allocated
        wherever you want in memory, see next paragraph [[sec:tuto_step3][Step3]].
     4. Create you own function to fill the descriptor.  If you
        understand well the meaning of each item of *MORSE_desc_t*, you
        should be able to fill correctly the structure.

     In Step2, we use the first way to create the descriptor:
     #+begin_example
     MORSE_Desc_Create(&descA, NULL, MorseRealDouble,
                       NB, NB, NB*NB, N, N,
                       0, 0, N, N,
                       1, 1);
     #+end_example
     * *descA* is the descriptor to create.
     * The second argument is a pointer to existing data. The existing
       data must follow LAPACK/PLASMA matrix layout [[sec:tile][Tile Data Layout]]
       (1-D array column-major) if *MORSE_Desc_Create* is used to create
       the descriptor. The *MORSE_Desc_Create_User* function can be used
       if you have data organized differently. This is discussed in
       the next paragraph [[sec_tuto_step3][Step3]].  Giving a *NULL* pointer means you let
       the function allocate memory space.  This requires to copy your
       data in the memory allocated by the *Desc_Create.  This can be
       done with
       #+begin_example
       MORSE_Lapack_to_Tile(A, N, descA);
       #+end_example
     * Third argument of @code{Desc_Create} is the datatype (used for
       memory allocation).
     * Fourth argument until sixth argument stand for respectively,
       the number of rows (*NB*), columns (*NB*) in each tile, the total
       number of values in a tile (*NB*NB*), the number of rows (*N*),
       colmumns (*N*) in the entire matrix.
     * Seventh argument until ninth argument stand for respectively,
       the beginning row (0), column (0) indexes of the submatrix and
       the number of rows (N), columns (N) in the submatrix.  These
       arguments are specific and used in precise cases.  If you do
       not consider submatrices, just use 0, 0, NROWS, NCOLS.
     * Two last arguments are the parameter of the 2-D block-cyclic
       distribution grid, see [[http://www.netlib.org/scalapack/slug/node75.html][ScaLAPACK]].  To be able to use other data
       distribution over the nodes, *MORSE_Desc_Create_User* function
       should be used.

**** Step3
     <<sec:tuto_step3>>

     This program makes use of the same interface than Step2 (tile
     interface) but does not allocate LAPACK matrices anymore so that
     no copy between LAPACK matrix layout and tile matrix layout are
     necessary to call MORSE routines.  To generate random right
     hand-sides you can use:
     #+begin_example
     /* Allocate memory and initialize descriptor B */
     MORSE_Desc_Create(&descB,  NULL, MorseRealDouble,
                       NB, NB,  NB*NB, N, NRHS,
                       0, 0, N, NRHS, 1, 1);
     /* generate RHS with random values */
     MORSE_dplrnt_Tile( descB, 5673 );
     #+end_example
     The other important point is that is it possible to create a
     descriptor, the necessary structure to call MORSE efficiently, by
     giving your own pointer to tiles if your matrix is not organized
     as a 1-D array column-major.  This can be achieved with the
     *MORSE_Desc_Create_User* routine.  Here is an example:
     #+begin_example
     MORSE_Desc_Create_User(&descA, matA, MorseRealDouble,
                            NB, NB, NB*NB, N, N,
                            0, 0, N, N, 1, 1,
                            user_getaddr_arrayofpointers,
                            user_getblkldd_arrayofpointers,
                            user_getrankof_zero);
     #+end_example
     Firsts arguments are the same than *MORSE_Desc_Create* routine.
     Following arguments allows you to give pointer to functions that
     manage the access to tiles from the structure given as second
     argument.  Here for example, *matA* is an array containing
     addresses to tiles, see the function *allocate_tile_matrix*
     defined in step3.h.  The three functions you have to
     define for *Desc_Create_User* are:
     * a function that returns address of tile $A(m,n)$, m and n
       standing for the indexes of the tile in the global matrix. Lets
       consider a matrix @math{4x4} with tile size 2x2, the matrix
       contains four tiles of indexes: $A(m=0,n=0)$, $A(m=0,n=1)$,
       $A(m=1,n=0)$, $A(m=1,n=1)$
     * a function that returns the leading dimension of tile $A(m,*)$
     * a function that returns MPI rank of tile $A(m,n)$

     Examples for these functions are vizible in step3.h.  Note that
     the way we define these functions is related to the tile matrix
     format and to the data distribution considered.  This example
     should not be used with MPI since all tiles are affected to
     processus 0, which means a large amount of data will be
     potentially transfered between nodes.

**** Step4
     <<sec:tuto_step4>>

     This program is a copy of step2 but instead of using the tile
     interface, it uses the tile async interface.  The goal is to
     exhibit the runtime synchronization barriers.  Keep in mind that
     when the tile interface is called, like *MORSE_dpotrf_Tile*,
     a synchronization function, waiting for the actual execution and
     termination of all tasks, is called to ensure the proper
     completion of the algorithm (i.e. data are up-to-date).  The code
     shows how to exploit the async interface to pipeline subsequent
     algorithms so that less synchronisations are done.  The code
     becomes:
     #+begin_example
     /* Morse structure containing parameters and a structure to interact with
      * the Runtime system */
     MORSE_context_t *morse;
     /* MORSE sequence uniquely identifies a set of asynchronous function calls
      * sharing common exception handling */
     MORSE_sequence_t *sequence = NULL;
     /* MORSE request uniquely identifies each asynchronous function call */
     MORSE_request_t request = MORSE_REQUEST_INITIALIZER;
     int status;

     ...

     morse_sequence_create(morse, &sequence);

     /* Factorization: */
     MORSE_dpotrf_Tile_Async( UPLO, descA, sequence, &request );

     /* Solve: */
     MORSE_dpotrs_Tile_Async( UPLO, descA, descX, sequence, &request);

     /* Synchronization barrier (the runtime ensures that all submitted tasks
      * have been terminated */
     RUNTIME_barrier(morse);
     /* Ensure that all data processed on the gpus we are depending on are back
      * in main memory */
     RUNTIME_desc_getoncpu(descA);
     RUNTIME_desc_getoncpu(descX);

     status = sequence->status;
     #+end_example

     Here the sequence of *dpotrf* and *dpotrs* algorithms is processed
     without synchronization so that some tasks of *dpotrf* and *dpotrs*
     can be concurently executed which could increase performances.
     The async interface is very similar to the tile one.  It is only
     necessary to give two new objects *MORSE_sequence_t* and
     *MORSE_request_t* used to handle asynchronous function calls.

     #+CAPTION: POTRI (POTRF, TRTRI, LAUUM) algorithm with and without synchronization barriers, courtesey of the [[http://icl.cs.utk.edu/plasma/][PLASMA]] team.
     #+NAME: fig:potri_async
     #+ATTR_HTML: :width 640px :align center
     [[file:potri_async.png]]

**** Step5
     <<sec:tuto_step5>>

     Step5 shows how to set some important parameters.  This program
     is a copy of Step4 but some additional parameters are given by
     the user.  The parameters that can be set are:
     * number of Threads
     * number of GPUs

       The number of workers can be given as argument
       to the executable with ~--threads=~ and ~--gpus=~ options.  It is
       important to notice that we assign one thread per gpu to
       optimize data transfer between main memory and devices memory.
       The number of workers of each type CPU and CUDA
       must be given at *MORSE_Init*.
       #+begin_example
       if ( iparam[IPARAM_THRDNBR] == -1 ) {
           get_thread_count( &(iparam[IPARAM_THRDNBR]) );
           /* reserve one thread par cuda device to optimize memory transfers */
           iparam[IPARAM_THRDNBR] -=iparam[IPARAM_NCUDAS];
       }
       NCPU = iparam[IPARAM_THRDNBR];
       NGPU = iparam[IPARAM_NCUDAS];
       /* initialize MORSE with main parameters */
       MORSE_Init( NCPU, NGPU );
       #+end_example

     * matrix size
     * number of right-hand sides
     * block (tile) size

       The problem size is given with ~--n=~ and ~--nrhs=~ options.  The
       tile size is given with option ~--nb=~.  These parameters are
       required to create descriptors.  The size tile NB is a key
       parameter to get performances since it defines the granularity
       of tasks.  If NB is too large compared to N, there are few
       tasks to schedule.  If the number of workers is large this
       leads to limit parallelism.  On the contrary, if NB is too
       small (/i.e./ many small tasks), workers could not be correctly
       fed and the runtime systems operations could represent a
       substantial overhead.  A trade-off has to be found depending on
       many parameters: problem size, algorithm (drive data
       dependencies), architecture (number of workers, workers speed,
       workers uniformity, memory bus speed).  By default it is set
       to 128.  Do not hesitate to play with this parameter and
       compare performances on your machine.

     * inner-blocking size

        The inner-blocking size is given with option ~--ib=~.
        This parameter is used by kernels (optimized algorithms applied on tiles) to
        perform subsequent operations with data block-size that fits the cache of
        workers.
        Parameters NB and IB can be given with *MORSE_Set* function:
        #+begin_example
        MORSE_Set(MORSE_TILE_SIZE,        iparam[IPARAM_NB] );
        MORSE_Set(MORSE_INNER_BLOCK_SIZE, iparam[IPARAM_IB] );
        #+end_example

**** Step6
     <<sec:tuto_step6>>

     This program is a copy of Step5 with some additional parameters
     to be set for the data distribution.  To use this program
     properly MORSE must use StarPU Runtime system and MPI option must
     be activated at configure.  The data distribution used here is
     2-D block-cyclic, see for example [[http://www.netlib.org/scalapack/slug/node75.html][ScaLAPACK]] for explanation.  The
     user can enter the parameters of the distribution grid at
     execution with ~--p=~ option.  Example using OpenMPI on four nodes
     with one process per node:
     #+begin_example
     mpirun -np 4 ./step6 --n=10000 --nb=320 --ib=64 --threads=8 --gpus=2 --p=2
     #+end_example

     In this program we use the tile data layout from PLASMA so that the call
     #+begin_example
     MORSE_Desc_Create_User(&descA, NULL, MorseRealDouble,
                            NB, NB, NB*NB, N, N,
                            0, 0, N, N,
                            GRID_P, GRID_Q,
                            morse_getaddr_ccrb,
                            morse_getblkldd_ccrb,
                            morse_getrankof_2d);
     #+end_example
     is equivalent to the following call

     #+begin_example
     MORSE_Desc_Create(&descA, NULL, MorseRealDouble,
                       NB, NB, NB*NB, N, N,
                       0, 0, N, N,
                       GRID_P, GRID_Q);
     #+end_example
     functions *morse_getaddr_ccrb*, *morse_getblkldd_ccrb*,
     *morse_getrankof_2d* being used in *Desc_Create*.  It is interesting
     to notice that the code is almost the same as Step5.  The only
     additional information to give is the way tiles are distributed
     through the third function given to *MORSE_Desc_Create_User*.
     Here, because we have made experiments only with a 2-D
     block-cyclic distribution, we have parameters P and Q in the
     interface of *Desc_Create* but they have sense only for 2-D
     block-cyclic distribution and then using *morse_getrankof_2d*
     function.  Of course it could be used with other distributions,
     being no more the parameters of a 2-D block-cyclic grid but of
     another distribution.

**** Step7

     <<sec:tuto_step7>>

     This program is a copy of step6 with some additional calls to
     build a matrix from within chameleon using a function provided by
     the user.  This can be seen as a replacement of the function like
     *MORSE_dplgsy_Tile()* that can be used to fill the matrix with
     random data, *MORSE_dLapack_to_Tile()* to fill the matrix with data
     stored in a lapack-like buffer, or *MORSE_Desc_Create_User()* that
     can be used to describe an arbitrary tile matrix structure.  In
     this example, the build callback function are just wrapper
     towards *CORE_xxx()* functions, so the output of the program step7
     should be exactly similar to that of step6.  The difference is
     that the function used to fill the tiles is provided by the user,
     and therefore this approach is much more flexible.

     The new function to understand is *MORSE_dbuild_Tile*, e.g.
     #+begin_example
     struct data_pl data_A={(double)N, 51, N};
     MORSE_dbuild_Tile(MorseUpperLower, descA, (void*)&data_A, Morse_build_callback_plgsy);
     #+end_example

     The idea here is to let Chameleon fill the matrix data in a
     task-based fashion (parallel) by using a function given by the
     user.  First, the user should define if all the blocks must be
     entirelly filled or just the upper/lower part with, /e.g./
     MorseUpperLower.  We still relies on the same structure
     *MORSE_desc_t* which must be initialized with the proper
     parameters, by calling for example *MORSE_Desc_Create*.  Then, an
     opaque pointer is used to let the user give some extra data used
     by his function.  The last parameter is the pointer to the user's
     function.

*** List of available routines
**** Linear Algebra routines

     We list the linear algebra routines of the form
     *MORSE_name[_Tile[_Async]]* (/name/ follows LAPACK naming scheme, see
     http://www.netlib.org/lapack/lug/node24.html) that can be used
     with the Chameleon library. For details about these functions
     please refer to the doxygen documentation. /name/ can be one of the
     following:

     * *BLAS 2/3 routines*
       * gemm: matrix matrix multiply and addition
       * hemm: gemm with A Hermitian
       * herk: rank k operations with A Hermitian
       * her2k: rank 2k operations with A Hermitian
       * lauum: computes the product U * U' or L' * L, where the
         triangular factor U or L is stored in the upper or lower
         triangular part of the array A
       * symm: gemm with A symmetric
       * syrk: rank k operations with A symmetric
       * syr2k: rank 2k with A symmetric
       * trmm: gemm with A triangular
     * *Triangular solving routines*
       * trsm: computes triangular solve
       * trsmpl: performs the forward substitution step of solving a
         system of linear equations after the tile LU factorization of
         the matrix
       * trsmrv:
       * trtri: computes the inverse of a complex upper or lower triangular matrix A
     * *LL' (Cholesky) routines*
       * posv: linear systems solving using Cholesky factorization
       * potrf: Cholesky factorization
       * potri: computes the inverse of a complex Hermitian positive
         definite matrix A using the Cholesky factorization A
       * potrimm:
       * potrs: linear systems solving using existing Cholesky
         factorization
       * sysv: linear systems solving using Cholesky decomposition with
         A symmetric
       * sytrf: Cholesky decomposition with A symmetric
       * sytrs: linear systems solving using existing Cholesky
         decomposition with A symmetric
     * *LU routines*
       * gesv_incpiv: linear systems solving with LU factorization and
         partial pivoting
       * gesv_nopiv: linear systems solving with LU factorization and
         without pivoting
       * getrf_incpiv: LU factorization with partial pivoting
       * getrf_nopiv: LU factorization without pivoting
       * getrs_incpiv: linear systems solving using existing LU
         factorization with partial pivoting
       * getrs_nopiv: linear systems solving using existing LU
         factorization without pivoting
     * *QR/LQ routines*
       * gelqf: LQ factorization
       * gelqf_param: gelqf with hqr
       * gelqs: computes a minimum-norm solution min || A*X - B || using
         the LQ factorization
       * gelqs_param: gelqs with hqr
       * gels: Uses QR or LQ factorization to solve a overdetermined or
         underdetermined linear system with full rank matrix
       * gels_param: gels with hqr
       * geqrf: QR factorization
       * geqrf_param: geqrf with hqr
       * geqrs: computes a minimum-norm solution min || A*X - B || using
         the RQ factorization
       * hetrd: reduces a complex Hermitian matrix A to real symmetric
         tridiagonal form S
       * geqrs_param: geqrs with hqr
       * tpgqrt: generates a partial Q matrix formed with a blocked QR
         factorization of a "triangular-pentagonal" matrix C, which is
         composed of a unused triangular block and a pentagonal block V,
         using the compact representation for Q. See tpqrt to
         generate V
       * tpqrt: computes a blocked QR factorization of a
         "triangular-pentagonal" matrix C, which is composed of a
         triangular block A and a pentagonal block B, using the compact
         representation for Q
       * unglq: generates an M-by-N matrix Q with orthonormal rows,
         which is defined as the first M rows of a product of the
         elementary reflectors returned by MORSE_zgelqf
       * unglq_param: unglq with hqr
       * ungqr: generates an M-by-N matrix Q with orthonormal columns,
         which is defined as the first N columns of a product of the
         elementary reflectors returned by MORSE_zgeqrf
       * ungqr_param: ungqr with hqr
       * unmlq: overwrites C with Q*C or C*Q or equivalent operations
         with transposition on conjugate on C (see doxygen
         documentation)
       * unmlq_param: unmlq with hqr
       * unmqr: similar to unmlq (see doxygen documentation)
       * unmqr_param: unmqr with hqr
     * *EVD/SVD*
       * gesvd: singular value decomposition
       * heevd: eigenvalues/eigenvectors computation with A Hermitian
     * *Extra routines*
       * *Norms*
         * lange: computes norm of a matrix (Max, One, Inf, Frobenius)
         * lanhe: lange with A Hermitian
         * lansy: lange with A symmetric
         * lantr: lange with A triangular
       * *Random matrices generation*
         * plghe: generates a random Hermitian matrix
         * plgsy: generates a random symmetrix matrix
         * plrnt: generates a random matrix
       * *Others*
         * geadd: general matrix matrix addition
         * lacpy: copy matrix into another
         * lascal: scales a matrix
         * laset: copy the triangular part of a matrix into another, set a
           value for the diagonal and off-diagonal part
         * tradd: trapezoidal matrices addition

**** Options routines
     Enable MORSE feature.
     #+begin_src
     int MORSE_Enable  (MORSE_enum option);
     #+end_src
     Feature to be enabled:
     * *MORSE_WARNINGS*:   printing of warning messages,
     * *MORSE_AUTOTUNING*: autotuning for tile size and inner block size,
     * *MORSE_PROFILING_MODE*:  activate kernels profiling,
     * *MORSE_PROGRESS*:  to print a progress status,
     * *MORSE_GEMM3M*: to enable the use of the /gemm3m/ blas bunction.

     Disable MORSE feature.
     #+begin_src
     int MORSE_Disable (MORSE_enum option);
     #+end_src
     Symmetric to *MORSE_Enable*.

     Set MORSE parameter.
     #+begin_src
     int MORSE_Set     (MORSE_enum param, int  value);
     #+end_src
     Parameters to be set:
     * *MORSE_TILE_SIZE*:        size matrix tile,
     * *MORSE_INNER_BLOCK_SIZE*: size of tile inner block,
     * *MORSE_HOUSEHOLDER_MODE*: type of householder trees (FLAT or TREE),
     * *MORSE_HOUSEHOLDER_SIZE*: size of the groups in householder trees,
     * *MORSE_TRANSLATION_MODE*: related to the *MORSE_Lapack_to_Tile*, see ztile.c.

     Get value of MORSE parameter.
     #+begin_src
     int MORSE_Get     (MORSE_enum param, int *value);
     #+end_src

**** Auxiliary routines

     Reports MORSE version number.
     #+begin_src
     int MORSE_Version        (int *ver_major, int *ver_minor, int *ver_micro);
     #+end_src

     Initialize MORSE: initialize some parameters, initialize the runtime and/or MPI.
     #+begin_src
     int MORSE_Init           (int nworkers, int ncudas);
     #+end_src

     Finalyze MORSE: free some data and finalize the runtime and/or MPI.
     #+begin_src
     int MORSE_Finalize       (void);
     #+end_src

     Suspend MORSE runtime to poll for new tasks, to avoid useless CPU consumption when
     no tasks have to be executed by MORSE runtime system.
     #+begin_src
     int MORSE_Pause          (void);
     #+end_src

     Symmetrical call to MORSE_Pause, used to resume the workers polling for new tasks.
     #+begin_src
     int MORSE_Resume         (void);
     #+end_src

     Return the MPI rank of the calling process.
     #+begin_src
     int MORSE_My_Mpi_Rank    (void);
     #+end_src

     Return the size of the distributed computation
     #+begin_src
     int MORSE_Comm_size( int *size )
     #+end_src

     Return the rank of the distributed computation
     #+begin_src
     int MORSE_Comm_rank( int *rank )
     #+end_src

     Prepare the distributed processes for computation
     #+begin_src
     int MORSE_Distributed_start(void)
     #+end_src

     Clean the distributed processes after computation
     #+begin_src
     int MORSE_Distributed_stop(void)
     #+end_src

     Return the number of CPU workers initialized by the runtime
     #+begin_src
     int MORSE_GetThreadNbr()
     #+end_src

     Conversion from LAPACK layout to tile layout.
     #+begin_src
     int MORSE_Lapack_to_Tile (void *Af77, int LDA, MORSE_desc_t *A);
     #+end_src

     Conversion from tile layout to LAPACK layout.
     #+begin_src
     int MORSE_Tile_to_Lapack (MORSE_desc_t *A, void *Af77, int LDA);
     #+end_src

**** Descriptor routines

     Create matrix descriptor, internal function.
     #+begin_src
     int MORSE_Desc_Create(MORSE_desc_t **desc, void *mat, MORSE_enum dtyp,
                           int mb, int nb, int bsiz, int lm, int ln,
                           int i, int j, int m, int n, int p, int q);
     #+end_src

     Create matrix descriptor, user function.
     #+begin_src
     int MORSE_Desc_Create_User(MORSE_desc_t **desc, void *mat, MORSE_enum dtyp,
                                int mb, int nb, int bsiz, int lm, int ln,
                                int i, int j, int m, int n, int p, int q,
                                void* (*get_blkaddr)( const MORSE_desc_t*, int, int),
                                int (*get_blkldd)( const MORSE_desc_t*, int ),
                                int (*get_rankof)( const MORSE_desc_t*, int, int ));
     #+end_src

     Create matrix descriptor for tiled matrix which may not fit
     memory.
     #+begin_src
     int MORSE_Desc_Create_OOC(MORSE_desc_t **descptr, MORSE_enum dtyp, int mb, int nb, int bsiz,
                               int lm, int ln, int i, int j, int m, int n, int p, int q);
     #+end_src

     User's function version of MORSE_Desc_Create_OOC.
     #+begin_src
     int MORSE_Desc_Create_OOC_User(MORSE_desc_t **descptr, MORSE_enum dtyp, int mb, int nb, int bsiz,
                                    int lm, int ln, int i, int j, int m, int n, int p, int q,
                                    int (*get_rankof)( const MORSE_desc_t*, int, int ));
     #+end_src

     Destroys matrix descriptor.
     #+begin_src
     int MORSE_Desc_Destroy (MORSE_desc_t **desc);
     #+end_src

     Ensures that all data of the descriptor are up-to-date.
     #+begin_src
     int MORSE_Desc_Acquire (MORSE_desc_t  *desc);
     #+end_src

     Release the data of the descriptor acquired by the
     application. Should be called if MORSE_Desc_Acquire has been
     called on the descriptor and if you do not need to access to its
     data anymore.
     #+begin_src