Definition of `vecdot` is ambiguous in the complex case.

The function linalg.vecdot is defined as:

Computes the (vector) dot product of two arrays.

It is not clear what this means for complex vectors, as it could be \sum x_i y_i or it could be (as defined for a complex dot product) \sum \conj(x_i) y_i.

I am aware that the API does not cover complex tensors yet, but many of the libraries that are currently implementing this operation do support complex tensors, so it would be great to disambiguate the meaning of this operation now, so that libraries that implement it can safely implement the intended operation for complex tensors.

[kgryte]

This issue was discussed during the most recent consortium meeting (1-6-2021). Consensus there was that the definition of the vector dot product for complex number input should conjugate (i.e., x^H y; similar to NumPy’s vdot).

Implementors can begin their complex number vecdot implementations assuming that this will be added to the specification along with more general complex number guidance.

[lezcano]

You can indeed replicate the this behaviour resizing the inputs adding a dimension of size 1 in both inputs (see https://github.com/pytorch/pytorch/issues/18027) but this seems fairly clunky. There is no easy way to do this at the moment with the API.