makePositiveDefinite() not working on submatrices

[Mikhail Katliar]

Example:

#include <blaze/Math.h>

int main(int, char **)
{
    blaze::DynamicMatrix<double> Q(3, 3);
    makePositiveDefinite(Q); // OK
    makePositiveDefinite(submatrix(Q, 0, 0, 2, 2)); // <-- compilation error

    return 0;
}

As a user I would expectmakePositiveDefinite to work on submatrices the same way it works on full matrices.

[Klaus Iglberger]

Hi Mikhail!

Thanks for creating this issue. You are correct, submatrices currently don’t provide a makePositiveDefinite() function. However, since the makePositiveDefinite function is part of the Blaze internals (i.e. marked as BLAZE_INTERNAL) and not documented in the wiki, we don’t consider it a bug that the according overload is missing. For that reason we consider this issue a feature request instead of a bug and will integrate an according function with one of the next push operations. Till then, please use the following function that is very similar to the implementation we’ll provide:

template< typename MT       // Type of the matrix
        , AlignmentFlag AF  // Alignment flag
        , bool SO           // Storage order
        , bool DF           // Density flag
        , size_t... CSAs >  // Compile time submatrix arguments
void makePositiveDefinite( Submatrix<MT,AF,SO,DF,CSAs...>& matrix )
{
   using blaze::randomize;

   using ET = ElementType_t<MT>;

   BLAZE_CONSTRAINT_MUST_BE_SCALAR_TYPE( ET );

   if( !isSquare( matrix ) ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
   }

   const size_t n( matrix.rows() );

   randomize( matrix );
   matrix *= ctrans( matrix );

   for( size_t i=0UL; i<n; ++i ) {
      matrix(i,i) += ET(n);
   }

   BLAZE_INTERNAL_ASSERT( isHermitian( matrix ), "Non-symmetric matrix detected" );
}

Thanks again for creating this issue,

Best regards,

Klaus!