days_of_the_week[14 % 7] There ya go!
On Wed, Nov 25, 2020 at 12:51 PM Mathew M. Noel via Python-ideas < python-ideas@python.org> wrote: > If circular indexing is used then instead of using a double FOR loop to > go through a list M times we can iterate from 0 to M*N (where N is the > length of the list) !!! > > > Almost all Machine Learning (ML) algorithms iterate for some predefined > epochs over a large data-set. So a double FOR loop is extremely common in > ML. Using circular indexing gets rid of this extra FOR loop. If we have to > iterate 2 times you can iterate using range(-n,n) but in most cases you > need to iterate over 10 or more epochs in ML. > > > Most scientific applications of Python involve an outer FOR loop which > progressively refines an approximation with an inner FOR loop by going > through a list of items. So circular indexing is useful. In the following I > discuss increasingly compelling reasons for adopting a circular indexing > scheme in Python. > > > Python uses an index of -1 to index the last element in a list. Since -1 > occurs before 0 we might think of the elements of the linear list are being > bent into a circle making the last element occur before the 0th element. > Consider a list with n elements: it would be perfectly reasonable to > address the element 0 of the list using an index of n since n occurs after > n-1 (if we assume that the list is bent into a circle). This feature can > prove to be extremely useful. Consider the following example: > > > days_of_the_week = > ["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"] > > It would be nice if > > days_of_the_week[0] > > is the same as > > days_of_the_week[7] > > is the same as > > days_of_the_week[14] etc > > In other words use modular indexing. In other words if the index is outside > the range 0 to n-1, we simply take the remainder when the index is divided by > n as the index. > Because of the close relationship between finite length sequences and > periodic sequences this feature might simplify scientific computing(circular > convolution etc). > > If circular indexing is used then we don't need the arbitrary rule that -1 > is the index of the last element. Since -1 is the same as n-1 automatically > in modular arithmetic. > > > A trivial objection: "why not use list_name[i%n] whenever we need this > feature?" By the same token we could do away with negative indices and use > -1%n for example when we need to index with -1! > > Its unclear why that people have an irrational preference for indices > that lie to the left of 0 while strongly rejecting the idea of indices that > lie to the right of n-1! > > Python does not raise a "index out of bound" exception for negative > indices like other programming languages. If this negative indexing is a > "feature" (although it allows some fatal errors to slip) then indices above > n-1 can also be considered a feature! > > Are there any deep mathematical reasons for adopting circular convention? > Circular convolution is a most important operation in a wide variety of > scientific disciplines since the Discrete Fourier Transform (DFT) of the > circular convolution of two signals is the product of the transforms. > Because of the universal applicability of Fourier ideas in science and the > close mathematical relationship between finite length and periodic > sequences circular indexing is extensively used in signal processing and > mathematics. > > We can extend the idea of circular indexing to multidimensional arrays. A > 2D array can be folded into a cylinder for indexing. Further this cylinder > can be folded into a toroid to reduce a triple FOR loop to a single FOR > loop. A deep mathematical justification for cylindrical indexing of 2D and > in general nD arrays is offered by the fact that n-dimensional DFT reduces > n-dimensional circular convolution to element-wise multiplication. > > _______________________________________________ > Python-ideas mailing list -- python-ideas@python.org > To unsubscribe send an email to python-ideas-le...@python.org > https://mail.python.org/mailman3/lists/python-ideas.python.org/ > Message archived at > https://mail.python.org/archives/list/python-ideas@python.org/message/5TJYKFLBHB26WEFFQXMY6AGWS34XTIUR/ > Code of Conduct: http://python.org/psf/codeofconduct/ > -- CALVIN SPEALMAN SENIOR QUALITY ENGINEER cspea...@redhat.com M: +1.336.210.5107 [image: https://red.ht/sig] <https://red.ht/sig> TRIED. TESTED. TRUSTED. <https://redhat.com/trusted>
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