Using FLENS-BLAS through Overloaded Operators

Toy Example

We use the same example as before, i.e. we compute \(y = \beta y + \alpha\,A^T x + z\) where \(\alpha, \beta\) are scalars, \(x, y, z\) are (dense) vectors and \(A\) is a (general) matrix (with full storage).

This time we just code it the natural way, i.e. as y = beta*y + alpha*transpose(A)*x + z and hope the best.

However, afterwards we want to check how FLENS-BLAS was internally utilized for the evaluation of the linear algebra expression. We therefore log the evaluation.

Example Code

flens/examples/tut02-page03-example.cc

#ifndef FLENS_DEBUG_CLOSURES

#define FLENS_DEBUG_CLOSURES

#endif

#include <cxxstd/iostream.h>

#include <flens/flens.cxx>

using namespace flens;

using namespace std;

int

main()

{

    typedef double                               T;

    typedef DenseVector<Array<T> >               DEVector;

    typedef GeMatrix<FullStorage<T, ColMajor> >  GEMatrix;

    const T  alpha = 1.5,

             beta = 2.5;

    DEVector x(3), y(3), z(3);

    x = 1, 2, 3;

    y = 2, 3, 4;

    z = 3, 4, 5;

    GEMatrix A(3,3);

    A = 1, 2, 3,

        5, 6, 7,

        5, 4, 3;

    verbose::ClosureLog::start("mylogfile");

    y = beta*y + alpha*transpose(A)*x + z;

    cout << "y = " << y << endl;

    verbose::ClosureLog::stop();

    return 0;

}

Comments on Example Code

Define the macro for debugging closures

#ifndef FLENS_DEBUG_CLOSURES

#define FLENS_DEBUG_CLOSURES

#endif

We turn on logging of the closure evaluation, i.e. the evaluation of linear algebra expressions that are coded through overloaded operators.

verbose::ClosureLog::start("mylogfile");

Compute \(y = \beta y + \alpha A^T x + z\)

y = beta*y + alpha*transpose(A)*x + z;

Stop logging.

verbose::ClosureLog::stop();

Compile, Run and Examining the Log-File

Compiling the code becomes slightly more complex. But we hope the comments give enough glues to see what need to be done.

$shell> cd flens/examples                                                     
$shell> #                                                                     
$shell> # cleanup old object files and compile some stuff needed for logging  
$shell> #                                                                     
$shell> rm -f *.o                                                             
$shell> g++ -Wall -std=c++11 -I../.. -c ../../flens/debug/auxiliary/*.cc      
$shell> #                                                                     
$shell> # compile with -DFLENS_DEBUG_CLOSURES and link against the log stuff  
$shell> #                                                                     
$shell> g++ -Wall -std=c++11 -I../.. *.o tut02-page03-example.cc              
$shell> ./a.out                                                               
y = 
           47           50.5             54 
$shell> #                                                                     
$shell> # look what is in the log file                                        
$shell> #                                                                     
$shell> cat mylogfile                                                         
--------------------------------------------------------------------------------
x1 = (((2.5 * x1) + ((1.5 * (A1)^T) * x2)) + x3);
flens::assign((((2.5 * x1) + ((1.5 * (A1)^T) * x2)) + x3), x1);
    flens::blas::copy(??1, (((2.5 * x1) + ((1.5 * (A1)^T) * x2)) + x3), x1);
        flens::blas::copy(??2, ((2.5 * x1) + ((1.5 * (A1)^T) * x2)), x1);
            --> flens::blas::mv(Trans, 1.5, A1, x2, 2.5, x1);
        --> flens::blas::axpy(1, x3, x1);

In the log files you see a complete trace of function calls. If you compile with -DNDEBUG instead most of these functions get inlined and only the functions marked with the arrows --> actually get called. Not that this means that in non-debug mode the resulting code is equivalent to calling CXXBLAS directly.

Note: The logging mechanism in FLENS gives different matrix/vector objects unique names. The letter represents the matrix/vector types:

Letter	Matrix/Vector Type
`x`	`DenseVector`
`A`	`GeMatrix`
`T`	`TrMatrix`
`S`	`SyMatrix`

Further, vectors and matrices of same type receive subsequent numbers (like in this example vectors receive names x1, x2, x3).