Implementation of MSpM on CPU

[CoxyMielle]

Implementation of simple_mspm (AB = C) and mspm (aAB+bC = C) in the reference and omp executor and adding corresponding tests.

[ginkgo-bot]

Error: The following files need to be formatted:

omp/matrix/dense_kernels.cpp
reference/matrix/dense_kernels.cpp
reference/test/matrix/dense_kernels.cpp
test/matrix/dense_kernels.cpp

You can find a formatting patch under Artifacts here or run format! if you have write access to Ginkgo

[yhmtsai]

To make the code format fitting into Ginkgo requirement, please install pre-commit and run pre-commit install to install the ginkgo config.
after installing that, it should format your code when you try to commit something.
To apply it to the codes already in branch, you can use re-commit run --from-ref origin/develop --to-ref HEAD

[yhmtsai]

Suggested change

// TODO: implement c = alpha * a * b + beta * c with single thread

you can delete this, too

[yhmtsai]

Suggested change

// TODO: implement c = a * b with single thread

sorry for my wrong copy. you can delete this comment here

[yhmtsai]

Suggested change

// TODO: implement c = a * b with single thread

[yhmtsai]

Suggested change

// TODO: implement c = alpha * a * b + beta * c with single thread

[yhmtsai]

this is unnecessary because the kernel is working for uniform precision now.
Does it affect your performance?

[yhmtsai]

Suggested change

	for(IndexType idx_B=b_rowptrs[k]; idx_B<b_rowptrs[k+1]; idx_B++){
	for(auto idx_b=b_rowptrs[k]; idx_b<b_rowptrs[k+1]; idx_b++){

also for the name

[yhmtsai]

our variable name should be snake_case ref: https://github.com/ginkgo-project/ginkgo/wiki/Contributing-guidelines#variables

[yhmtsai]

Question: Maybe I missing that. Could you remind me why you need the accumulator array?
From the implementation, one thread handle a row, so you can directly operate on the output data without accumulator, right?

[yhmtsai]

Suggested change

	std::transform( //initialize the accumulator with c + beta
	begin_row_c_vals_ptr, begin_row_c_vals_ptr + acc_size,
	//initialize the accumulator with c + beta
	std::transform(
	begin_row_c_vals_ptr, begin_row_c_vals_ptr + acc_size,

I would move comment out of function call to let clang-format do format unless there is a good reason.

[yhmtsai]

Suggested change

	auto advanced_def_mult_operand = [a, alpha](IndexType row, IndexType k){
	return alpha->at(0, 0) * a->at(row, k); //multiply a(row,k) by alpha
	};
	auto advanced_def_mult_operand = [alpha](auto a_val, auto b_val){
	return alpha->at(0, 0) * a_val * b_val; //multiply a(row,k) by alpha
	};

from the name, I was expecting this form. also this will reduce the unclear data access from the function call, but I do not have strong opinion on this yet.