SchurTraitEval2 for Dynamic and Static matrices

[Bita HashemiNezhad]

Hey Klaus,

I was trying to figure out how traits work. My understanding is that having two different arrays (a matrix and a vector) we tend to use a Dynamic result array if either of the arrays is Dynamic (for example a dynamic vector resulted from dynamic matrix with static vector multiplication). And when both of them of static, the result array is static. Is this correct? Do we do that when the resulted dimensions are unknown? Would you please explain what the general rule is?

In this file: https://bitbucket.org/blaze-lib/blaze/src/08a5303d3312a9898c497da0fdd2514fd23dd9b1/blaze/math/dense/DynamicMatrix.h#lines-6564

Is there a particular reason that you used MultTrait_t instead of SchurTrait_t?

Thanks,

Bita

[Klaus Iglberger]

Hi Bita!

The resulting type depends on the operands and the operation. It all depends on whether you can determine the dimensions at compile time. The following gives a (very simplified) overview of several selected operations:

// Matrix/matrix addition
Dynamic + Dynamic -> Dynamic
Dynamic + Static  -> Static
Static  + Dynamic -> Static
Static  + Static  -> Static

// Matrix/matrix Schur product
Dynamic % Dynamic -> Dynamic
Dynamic % Static  -> Static
Static  % Dynamic -> Static
Static  % Static  -> Static

// Matrix/vector multiplication
Dynamic * Dynamic -> Dynamic
Dynamic * Static  -> Dynamic
Static  * Dynamic -> Dynamic
Static  * Static  -> Static

// Matrix/matrix multiplication
Dynamic * Dynamic -> Dynamic
Dynamic * Static  -> Dynamic
Static  * Dynamic -> Dynamic
Static  * Static  -> Static

A (very) complete overview of resulting types can be found in the according class tests of the traits (e.g. <blaze/blazetest/src/mathtest/traits/schurtrait/ClassTest.cpp>).

The Schur product is a special case. It is defined as componentwise multiplication of all elements. Thus the SchurTrait specialization for DynamicMatrix uses MultTrait to evaluate the resulting type of the elements. For instance:

DynamicMatrix< DynamicMatrix<int> > A;
StaticMatrix< DynamicVector<double>, 3UL, 5UL > x;
// ... Initialization

const auto y = evaluate( A * x );

decltype( y );  // ... is 'StaticMatrix<DynamicVector<double>, 3UL, 5UL>'

In this example, there is no Schur product between a matrix and a vector, so MultTrait is required to determine the type of the elements.

I hope this helps to understand the details,

Best regards,

Klaus!

[Bita HashemiNezhad]

That was really educational, thanks a lot.

Bita