In that direction, you will probably face the situation when a function only handles the empty use case and delegates the others, and you don't want to transform items into a Collection or a Sequence. Performance shall be handle as a daily task, not as a firemen task force. We will therefore, spend a little time on sequences as well. However, we also need to understand some of the basics of sequences in order to properly deal with series. In fact, this chapter will deal almost exclusively with series. Then it's the caller responsibility to transform data when necessary, such as: my_func_3(tuple(x**2 for x in range(100)))Īctually, all this is really about performance when scaling the length of items.Īlways prefer Iterator when possible. In this chapter we’ll be taking a look at sequences and (infinite) series. using a set when a Sequence is required). Don't forget that all this is only about typing, to help a static type checker to report incorrect calls (e.g. Hence use a Sequence: from typing import Sequenceĭef my_func_3(items: Sequence) -> None:Ĭonclusion: The strategy is: "use the most generic type that the function can handle". If the function algorithm ( my_func_3) has to access by index to specific items, then both Iterable and Collection will fail if the caller provides a set, a Mapping or a 'strict' Iterator. Hence use a Collection: from typing import Collectionĭef my_func_2(items: Collection) -> None: However if the function algorithm (say my_func_2) requires more than one iteration, then Iterable will fail if the caller provides a 'strict' Iterator because the first iteration exhausts it. set), and because the iteration breaks before StopIteration, it is also more performing if he provides an 'strict' Iterator. The Integral Test can be used on a infinite series provided the terms of the series are positive and decreasing. Integral Test In this section we will discuss using the Integral Test to determine if an infinite series converges or diverges. tuple, list) or as a non- Sequence Collection (e.g. We will examine Geometric Series, Telescoping Series, and Harmonic Series. In case the caller doesn't have data as a Sequence (e.g. The implicit message to a function caller is: transfer data "as-is", just don't transform it. My_func_1(x**2 for x in range(100)) # "strict' Iterator, i.e. My_func_1(range(10)) # range is Sequence, Collection, Iterator My_func_1(my_dict.keys()) # dict.keys() is MappingKeys, Set, Collection, Iterator ![]() My_func_1(my_dict) # dict is Mapping, Collection, Iterator My_func_1() # set is Collection, Iterator My_func_1() # list is MutableSequence, Sequence, Collection, Iterator Correct calls include: my_func_1((1, 2, 3)) # tuple is Sequence, Collection, Iterator Iterable offers the maximum possibilities to the caller. Say my_func_1 is: from typing import Iterableĭef my_func_1(items: Iterable) -> None: You can look at the sequence and see a pattern. Now that that's out of the way, on to the more difficult stuff. (1) is saying this is the first number in the sequence and 12 is saying that that number is 12. d is basically saying this is a arithmetic sequence. ![]() Keep in mind that despite the strange notation, a sequence can be thought of as an. Hereafter is why and I hope it will help understanding the difference. Since 12 is the starting number you have d(1)12. For example, the sequence 1, 1/2, 1/3, 1/4, 1/5. Here’s another way which highlights this particular type of divergence.When writing a function/method with an items argument, I often prefer Iterable to Sequence. This seems to have been rather more work than we should have to do for such a simple problem. So let \(ε = 1\), and let \(r ∈ R\) be given. That is, we must show that for every \(r ∈ R\) there is an \(ε > 0\) such that for every \(N ∈ R\), there is an \(n > N\) with \(|n-r|≥ ε\). ![]() To show divergence we must show that the sequence satisfies the negation of the definition of convergence. This is clearly a divergent sequence but it may not be clear how to prove this formally. ^\infty\) become arbitrarily large as \(n\) increases.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |