Functional Linear Algebra in Scala

on YouTube ↗28m

" summary

Claims a type-safe, functional linear-algebra layer in Scala that prevents mixing dimensions at compile time, finds real bugs, and supports practical PCA and nonlinear Sammon-style embedding. Implements path-dependent vector spaces and matrices as morphisms with domain/codomain, represents vectors as either functions or Java arrays, and runs PCA then Sammon mapping on a 16,000-word cloud producing a ~256M-entry distance matrix (~0.5–1 GB). For speed, it pushes inner loops into a Java-backed array ops layer to avoid boxing, yielding multiple-times speedups versus naïve Scala while keeping a clean API.

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" chapters (19)

1. 0:00Introduction
2. 1:06The Paradise
3. 4:01How to represent vectors
4. 4:46Types of vectors
5. 5:24Path dependent types
6. 5:49Vector space
7. 6:44Vector implementation
8. 7:26Mixed dimensions
9. 8:11PCA principle
10. 9:02Component analysis
11. 10:35Matrix representation
12. 11:31Matrix method
13. 14:38Cross
14. 15:18Dimension Reduction
15. 16:52Algorithm
16. 18:53Mutability
17. 19:57Performance
18. 22:09Java
19. 23:32Questions

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