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I've seen regex patterns that use explicitly numbered repetition instead of ?, * and +, i.e.:
Explicit Shorthand
(something){0,1} (something)?
(something){1} (something)
(something){0,} (something)*
(something){1,} (something)+
The questions are:
Are these two forms identical? What if you add possessive/reluctant modifiers?
If they are identical, which one is more idiomatic? More readable? Simply "better"?
To my knowledge they are identical. I think there maybe a few engines out there that don't support the numbered syntax but I'm not sure which. I vaguely recall a question on SO a few days ago where explicit notation wouldn't work in Notepad++.
The only time I would use explicitly numbered repetition is when the repetition is greater than 1:
Exactly two: {2}
Two or more: {2,}
Two to four: {2,4}
I tend to prefer these especially when the repeated pattern is more than a few characters. If you have to match 3 numbers, some people like to write: \d\d\d but I would rather write \d{3} since it emphasizes the number of repetitions involved. Furthermore, down the road if that number ever needs to change, I only need to change {3} to {n} and not re-parse the regex in my head or worry about messing it up; it requires less mental effort.
If that criteria isn't met, I prefer the shorthand. Using the "explicit" notation quickly clutters up the pattern and makes it hard to read. I've worked on a project where some developers didn't know regex too well (it's not exactly everyone's favorite topic) and I saw a lot of {1} and {0,1} occurrences. A few people would ask me to code review their pattern and that's when I would suggest changing those occurrences to shorthand notation and save space and, IMO, improve readability.
I can see how, if you have a regex that does a lot of bounded repetition, you might want to use the {n,m} form consistently for readability's sake. For example:
/^
abc{2,5}
xyz{0,1}
foo{3,12}
bar{1,}
$/x
But I can't recall ever seeing such a case in real life. When I see {0,1}, {0,} or {1,} being used in a question, it's virtually always being done out of ignorance. And in the process of answering such a question, we should also suggest that they use the ?, * or + instead.
And of course, {1} is pure clutter. Some people seem to have a vague notion that it means "one and only one"--after all, it must mean something, right? Why would such a pathologically terse language support a construct that takes up a whole three characters and does nothing at all? Its only legitimate use that I know of is to isolate a backreference that's followed by a literal digit (e.g. \1{1}0), but there are other ways to do that.
They're all identical unless you're using an exceptional regex engine. However, not all regex engines support numbered repetition, ? or +.
If all of them are available, I'd use characters rather than numbers, simply because it's more intuitive for me.
They're equivalent (and you'll find out if they're available by testing your context.)
The problem I'd anticipate is when you may not be the only person ever needing to work with your code.
Regexes are difficult enough for most people. Anytime someone uses an unusual syntax, the question
arises: "Why didn't they do it the standard way? What were they thinking that I'm missing?"
I understand the use of ramda's complement function which inverts the return of a predicate. What I can't get my head around is why "complement" was used as a name.
const invertPredicate = R.complement(R.identity)
invertPredicate(false) //true
Could someone please give some insight into this?
“In set theory, the complement of a set A refers to elements not in A”
https://en.m.wikipedia.org/wiki/Complement_(set_theory)
So R.complement will produce a predicate for all values that don’t satisfy the provided predicate.
Adding to the answer from Scott Christopher, Ramda (disclaimer: both Scott Christopher and I are Ramda authors) has gone through several iterations of these basic functions. At one point we had and, or, and not for values as well as andFn, orFn, and notFn for functions. We got rid of the value ones and used the nicer names for combining predicate functions.
But those value versions were popular. We brought them back. And we gave them back the simpler names, as that is how people read the infix operators || and && and the prefix !. It was easy to name the others as both and either, but we struggled a bit before finding complement. Once we find that one, we were happy enough to rename again. The actual explanation of the name is exactly as Scott Christopher says. I still have some regrets, but this was the correct decision for the library.
Why does stringsAsFactors use capital letters to aid readability in R when most other commands seem to use . (e.g., as.factor)?
Is this an idiosyncrasy or part of a higher organizaton of the commands that I am not familiar with?
Is there any way to predict which commands will use capital letters and which will use .?
Thanks
It is obvious -- no standard has been established before it was too late ;-)
A lot of the idiosyncrasies arise because of the heritage from the S language and compatibility with the implementation in S-PLUS. There has been a tendency in recent years to avoid new functions with names that include a . as a separator to avoid confusion with S3 methods. This hasn't been change retrospectively because of backwards compatibility and a desire to be faithful to functions from S/S-PLUS days.
Since _ was deprecated as an alternative to <-, some authors have used it in function names; an example are packages of Hadley Wickham, but there are plenty of others.
The lack of a strictly adhered standard can be confusing, and certainly adds to the learning curve, but is something you have to live with.
The so-called 'camelCase' is a good choice.
Besides Hadley, few recommend underscores. See for example the Google R Style Guide which says:
Don't use underscores ( _ ) or hyphens ( - ) in identifiers.
R itself does not enforce a style, but (heuristically speaking) not too many new core libraries use a dot either as a separator in identifiers as this is also used for
S3 methods.
I'm maintaining code for a mathematical algorithm that came from a book, with references in the comments. Is it better to have variable names that are descriptive of what the variables represent, or should the variables match what is in the book?
For a simple example, I may see this code, which reflects the variable in the book.
A_c = v*v/r
I could rewrite it as
centripetal_acceleration = velocity*velocity/radius
The advantage of the latter is that anyone looking at the code could understand it. However, the advantage of the former is that it is easier to compare the code with what is in the book. I may do this in order to double check the implementation of the algorithms, or I may want to add additional calculations.
Perhaps I am over-thinking this, and should simply use comments to describe what the variables are. I tend to favor self-documenting code however (use descriptive variable names instead of adding comments to describe what they are), but maybe this is a case where comments would be very helpful.
I know this question can be subjective, but I wondered if anyone had any guiding principles in order to make a decision, or had links to guidelines for coding math algorithms.
I would prefer to use the more descriptive variable names. You can't guarantee everyone that is going to look at the code has access to "the book". You may leave and take your copy, it may go out of print, etc. In my opinion it's better to be descriptive.
We use a lot of mathematical reference books in our work, and we reference them in comments, but we rarely use the same mathematically abbreviated variable names.
A common practise is to summarise all your variables, indexes and descriptions in a comment header before starting the code proper. eg.
// A_c = Centripetal Acceleration
// v = Velocity
// r = Radius
A_c = (v^2)/r
I write a lot of mathematical software. IF I can insert in the comments a very specific reference to a book or a paper or (best) web site that explains the algorithm and defines the variable names, then I will use the SHORT names like a = v * v / r because it makes the formulas easier to read and write and verify visually.
IF not, then I will write very verbose code with lots of comments and long descriptive variable names. Essentially, my code becomes a paper that describes the algorithm (anyone remember Knuth's "Literate Programming" efforts, years ago? Though the technology for it never took off, I emulate the spirit of that effort). I use a LOT of ascii art in my comments, with box-and-arrow diagrams and other descriptive graphics. I use Jave.de -- the Java Ascii Vmumble Editor.
I will sometimes write my math with short, angry little variable names, easier to read and write for ME because I know the math, then use REFACTOR to replace the names with longer, more descriptive ones at the end, but only for code that is much more informal.
I think it depends almost entirely upon the audience for whom you're writing -- and don't ever mistake the compiler for the audience either. If your code is likely to be maintained by more or less "general purpose" programmers who may not/probably won't know much about physics so they won't recognize what v and r mean, then it's probably better to expand them to be recognizable for non-physicists. If they're going to be physicists (or, for another example, game programmers) for whom the textbook abbreviations are clear and obvious, then use the abbreviations. If you don't know/can't guess which, it's probably safer to err on the side of the names being longer and more descriptive.
I vote for the "book" version. 'v' and 'r' etc are pretty well understood as acronymns for velocity and radius and is more compact.
How far would you take it?
Most (non-greek :-)) keyboards don't provide easy access to Δ, but it's valid as part of an identifier in some languages (e.g. C#):
int Δv;
int Δx;
Anyone coming afterwards and maintaining the code may curse you every day. Similarly for a lot of other symbols used in maths. So if you're not going to use those actual symbols (and I'd encourage you not to), I'd argue you ought to translate the rest, where it doesn't make for code that's too verbose.
In addition, what if you need to combine algorithms, and those algorithms have conflicting usage of variables?
A compromise could be to code and debug as contained in the book, and then perform a global search and replace for all of your variables towards the end of your development, so that it is easier to read. If you do this I would change the names of the variables slightly so that it is easier to change them later.
e.g A_c# = v#*v#/r#
What is the smartest way to design a math parser? What I mean is a function that takes a math string (like: "2 + 3 / 2 + (2 * 5)") and returns the calculated value? I did write one in VB6 ages ago but it ended up being way to bloated and not very portable (or smart for that matter...). General ideas, psuedo code or real code is appreciated.
A pretty good approach would involve two steps. The first step involves converting the expression from infix to postfix (e.g. via Dijkstra's shunting yard) notation. Once that's done, it's pretty trivial to write a postfix evaluator.
I wrote a few blog posts about designing a math parser. There is a general introduction, basic knowledge about grammars, sample implementation written in Ruby and a test suite. Perhaps you will find these materials useful.
You have a couple of approaches. You could generate dynamic code and execute it in order to get the answer without needing to write much code. Just perform a search on runtime generated code in .NET and there are plenty of examples around.
Alternatively you could create an actual parser and generate a little parse tree that is then used to evaluate the expression. Again this is pretty simple for basic expressions. Check out codeplex as I believe they have a math parser on there. Or just look up BNF which will include examples. Any website introducing compiler concepts will include this as a basic example.
Codeplex Expression Evaluator
If you have an "always on" application, just post the math string to google and parse the result. Simple way but not sure if that's what you need - but smart in some way i guess.
I know this is old, but I came across this trying to develop a calculator as part of a larger app and ran across some issues using the accepted answer. The links were IMMENSELY helpful in understanding and solving this problem and should not be discounted. I was writing an Android app in Java and for each item in the expression "string," I actually stored a String in an ArrayList as the user types on the keypad. For the infix-to-postfix conversion, I iterated through each String in the ArrayList, then evaluated the newly arranged postfix ArrayList of Strings. This was fantastic for a small number of operands/operators, but longer calculations were consistently off, especially as the expressions started evaluating to non-integers. In the provided link for Infix to Postfix conversion, it suggests popping the Stack if the scanned item is an operator and the topStack item has a higher precedence. I found that this is almost correct. Popping the topStack item if it's precedence is higher OR EQUAL to the scanned operator finally made my calculations come out correct. Hopefully this will help anyone working on this problem, and thanks to Justin Poliey (and fas?) for providing some invaluable links.
The related question Equation (expression) parser with precedence? has some good information on how to get started with this as well.
-Adam
Assuming your input is an infix expression in string format, you could convert it to postfix and, using a pair of stacks: an operator stack and an operand stack, work the solution from there. You can find general algorithm information at the Wikipedia link.
ANTLR is a very nice LL(*) parser generator. I recommend it highly.
Developers always want to have a clean approach, and try to implement the parsing logic from ground up, usually ending up with the Dijkstra Shunting-Yard Algorithm. Result is neat looking code, but possibly ridden with bugs. I have developed such an API, JMEP, that does all that, but it took me years to have stable code.
Even with all that work, you can see even from that project page that I am seriously considering to switch over to using JavaCC or ANTLR, even after all that work already done.
11 years into the future from when this question was asked: If you don't want to re-invent the wheel, there are many exotic math parsers out there.
There is one that I wrote years ago which supports arithmetic operations, equation solving, differential calculus, integral calculus, basic statistics, function/formula definition, graphing, etc.
Its called ParserNG and its free.
Evaluating an expression is as simple as:
MathExpression expr = new MathExpression("(34+32)-44/(8+9(3+2))-22");
System.out.println("result: " + expr.solve());
result: 43.16981132075472
Or using variables and calculating simple expressions:
MathExpression expr = new MathExpression("r=3;P=2*pi*r;");
System.out.println("result: " + expr.getValue("P"));
Or using functions:
MathExpression expr = new MathExpression("f(x)=39*sin(x^2)+x^3*cos(x);f(3)");
System.out.println("result: " + expr.solve());
result: -10.65717648378352
Or to evaluate the derivative at a given point(Note it does symbolic differentiation(not numerical) behind the scenes, so the accuracy is not limited by the errors of numerical approximations):
MathExpression expr = new MathExpression("f(x)=x^3*ln(x); diff(f,3,1)");
System.out.println("result: " + expr.solve());
result: 38.66253179403897
Which differentiates x^3 * ln(x) once at x=3.
The number of times you can differentiate is 1 for now.
or for Numerical Integration:
MathExpression expr = new MathExpression("f(x)=2*x; intg(f,1,3)");
System.out.println("result: " + expr.solve());
result: 7.999999999998261... approx: 8
This parser is decently fast and has lots of other functionality.
Work has been concluded on porting it to Swift via bindings to Objective C and we have used it in graphing applications amongst other iterative use-cases.
DISCLAIMER: ParserNG is authored by me.