Multik 0.1 released with complex numbers, new line...

# mathematics

[Pavel Gorgulov]

Multik 0.1 released with complex numbers, new linear algebra methods, improved performance and other features
https://blog.jetbrains.com/kotlin/2021/10/multik-0-1-is-out/
Slack Conversation

[altavir]

Looks nice. We can start connecting it to KMath tensor API.

I found an inconsistency though. You try to follow numpy broadcasting rules. but

a = numpy.array([[1, 2, 3],[1, 2, 3]])
b = numpy.array([1, 2, 3])
a + b

will work in numpy and won't work in multik. I am not a fan of implicit broadcasting (and do not like numpy ideology in general), but one needs to be clear about that. In KMath I insisted that broadcasting is not possible in default algebras.

[Pavel Gorgulov]

What makes you think that we are trying to comply with the numpy broadcasting rules?

a = numpy.array([[1, 2, 3],[1, 2, 3]])
b = numpy.array([1, 2, 3])
a + b

This code will not work for us even at the compilation stage, since the dimensions are different. We introduced Dimension right from the start for this kind of checks.

[altavir]

Broadcasting for single number obviously works. Therefor the question is how do you choose when to broadcast and when not to.

[altavir]

In my opinion, implicit broadcasting is one of the main problems in numpy. In Julia they do special broadcasting operation with ., but it solves the problem only for simple one-argument operations. When we started to think about how to apply specific broadcasting rules to specific cases, we came to the algebra-based model, we use now in KMath. We use different rules for different scopes.

[Pavel Gorgulov]

Yes, ndarray operations with scalars are allowed. For several reasons:
* these are quite frequent operations
* no internal transformations occur for this
* they are intuitive, unlike broadcasting two ndarrays
* is a different object, not ndarray. That is, if we take and create ndarray with one elements, then the operation with another ndarray will be impossible due to different shapes.

I agree that implicit broadcasting is a problem. Therefore, at the level of ndarrays, it is also impossible for us.

[altavir]

What about types? I can check myself but what will happen if we will try to add a compex number to a ndarray of doubles or vise versa?

[altavir]

OK, I did not expect this:

[altavir]

But it works for complex numbers

[Pavel Gorgulov]

Same type required

[altavir]

I mean that you can add any number to a Complex. And even sum different complex types

[Pavel Gorgulov]

Yes, it is possible for this to be consistent with the numeric operations in Kotlin.