Ability to create a tensor from a lambda

[ryanmrichard]

TA provides the very useful TA::make_array which allows you to make a DistArray from a lambda. This issue is for adding a ctor to TensorWrapper which allows the user to write a lambda which fills in the tensor. I'm not 100% sure on what signature we want the lambda to have. A couple possibilities:

double(std::vector<int>); // Given an index return the value
void(std::vector<int> lo, std::vector<int> hi, double*); // Given the range of the block and the block's start fill it in

The first is more generalizable (to non-contiguous memory buffers, row- vs. column-major, etc.) and with modern compiler optimizations it may actually perform quite well.

[wavefunction91]

I think I get what you're saying viz the first (correct me if I'm wrong), but I think that rationale is limited to when lambdas can be inlined (and even then, it's iffy and very compiler dependent) - this is not the case here as we'd (presumably) need to store the lambda in a std::function, which is unable to be inlined (it uses RTTI to delegate operator()(...)). At the very least, going through std::vector for index manipulation would preclude SIMD in 99% of cases (no guarantee of contiguous access).

The latter is probably the way we want to go, especially when we're forming tensors over AOs (since things are computed at the shell level, element-wise construction would force recomputation unless you have some memoization, which I think is the wrong abstraction here).

At the very least, I don't think that it hurts to implement both interfaces, i.e. we can have

template <typename ValueType, typename IndexType>
using element_populator_t = std::function<ValueType(IndexType)>;

template <typename ValueType, typename IndexType>
using block_populator_t = std::function<void(IndexType,IndexType,ValueType*)>;

With the element_populator_t signature, we can form a block_populator_t that loops over the elements and calls the element-wise functor, that way we only need to provide one non-trivial implementation and then the rest can be delegated

[ryanmrichard]

This all sounds good to me.

[wavefunction91]

All of the mechanics of this issue were implemented in #61 , remainder to be implemented in #66 .

[twindus]

Does that mean that this issue should be closed?

[wavefunction91]

I think that's fine, technically it wasn't fulfilled, but I think we can view #66 as superseding.