array programing
“collection-oriented programming”—
- precise programs with bulk operations over the whole collection—the iteration structures/accesses are spelt out much more explicitly (i.e. not to use general structures like for loops as a crutch): iteration patterns are baked into the language
- performance: leaving the details of parallelism to your hardware
array programmings are easy to optimize
Lifting for loops is hard; but: \(\qty(\text{map } f) \cdot \qty(\text{map } g) = \text{map } \qty(f \cdot g)\). This is, notably, not true if your functions \(f\) and \(g\) are not pure (i.e. they have state or can throw exceptions); for instance, \(f\) crashes up front and \(g\) crashes in the end, then, the crashed error is different between the first and second method of evaluation.
numpy
broadcasting
suppose you had a operation \(A \text{ op } B\),and yet they have different dimensions, numpy perform something called “broadcasting”, which:
for each dimension \(1\);
- if \(A\), \(B\) dimension \(u\) edge has the same size, be done
- if one of \(A\) or \(B\) has size \(1\) in direction \(i\), replace the data in that dimension with the same size as each other
- if both have the same size, and none of these is \(1\), then we throw an error.
sizing
Notice: slicing defines views (i.e. aliases) off subsets in the array
the slice shares storage with the full array
copying
copying occurs when boolean indexing happens, because Numpy has no way of telling what access order element follow
Takeaways
- combinator calculus (i.e.
map-y systems) are important for array/collection programming- …useful for parallel implementations
- important for program generation