Kronecker Product & Sum

[adenchfi]

Motivation

Implement the Kronecker product (sometimes known as tensor or direct product) for matrices. The equivalent functionality in numpy is numpy.kron.

Additionally, implement the Kronecker sum, A (kron) I_B + I_A (kron) B, which is one way someone would do it when say creating a N-dimensional Laplacian stencil out of 1D stencils.

The numpy.kron convention for ordering matrix elements would be used.

To discuss:

• Should the user allocate the resulting array beforehand, or just pass in an allocatable array to be allocated?
  • The former allows for a more performant routine (/function), but the latter means the user doesn't have to figure out the final array sizes themselves.

Prior Art

No response

Additional Information

numpy.kron

[jvdp1]

Thank you @adenchfi for the proposition. I support such an implementation, as it would have been useful for my work a few weeks ago ;)

Re: the resulting array, the default in stdlib is that the resulting array is not allocatable, if the dimensions can be easily derived from the arguments. See for example the diag function.
Even in this case the user doesn't have to figure out the final dimention. E.g. the following should work without an explicit allocation:

integer :: array(5,5)
integer, allocatable :: d(:)
...
d = diag(array)
...

[adenchfi]

Glad to hear the support @jvdp1. I took your feedback and made an appropriate implementation, using the outer_product as a template. I am working on making a PR now; I am trying to figure out all I need to add for the testing suite.

[tehami02]

@adenchfi @jvdp1 I think it is better for the user to allocate the resulting array beforehand for performance reasons. This allows the function to use memory more efficiently and reduces the overhead associated with dynamic memory allocation.
However, providing the option for the function to allocate the array itself can be useful in situations where the user may not know the final array size or wants to avoid the complexity of calculating it. In such cases, the function can allocate the array and return it to the user. This approach can be more convenient for the user, but may be less efficient.