I am trying to solve a numerical equation in R but would want a method which perform similar to vpasolve in Matlab. I have a non linear equation (involving lot of log functions) which when solve in R with uniroot gives me complete different answer compared to what vpasolve gives in matlab.
First, a word of caution: it's often much more productive to learn that there's a better way to do something than the way you are used to doing.
edit
I went back to MATLAB and realized that the "vpa" collection is using extended precision. Is that absolutely necessary for your purposes? If not, then my suggestions below may suffice.
If you do require extended precision, then perhaps Rmpfr::unirootR function will suffice. I would like to point out that, since all these solvers are generating an approximate solution (as opposed to analytic), the use of extended precision operations seems a bit pointless.
Next, you need to determine whether MATLAB::vpasolve or uniroot is getting you the correct answer. Or maybe you simply are converging to a root that's not the one you want, in which case you need to read up on setting limits on the starting conditions or the search region.
Finally, in addition to uniroot, I recommend you learn to use the R packages BBsolve , nleqslv, rootsolve, and ktsolve (disclaimer: I am the owner and maintainer of ktsolve). These packages are pretty flexible and may lead you to better solutions to your original problem.
This is quite a general question, but I have not been able to find a solution so far.
I am trying to solve a problem of combinatorial optimization in which I have several objective functions to optimize, as well as several constraints to impose. I am thus trying to find some software (an R package preferably) that can solve this problem.
I have explored several options, but none of them seems to be useful for my purpose: lpSolveAPI is aimed for linear programming only, which is not the case; mco can minimize a multidimensional objective function, but does not seem to be able to manage binary (i.e. decision) variables, needed for combinatorial problems; adagio and CEGO can deal with combinatorial optimization problems, but as far as I can see they can only optimize a single unidimensional function.
Is there any other package I am not aware of that can handle this type of problem? Or any of the aforementioned may be useful, though I may be missing the way to the functionality I need?
Thank you so much in advance with this. It is being really a nightmare trying to find this out.
I am working with a very large dataset, typically dealing with a few millions of combinations.
I want to solve the assignment problem.(maximise the sum)
I had tried solving it on a small test set using adagio::assignment, clue::solve_LSAP
I wasnt able to successfully install the "lpSolve" package on my system, threw some segmentation fault
Wanted to know which of these is faster or any other method which does it faster.
Thanks....
An LP formulation is not a good way to solve the assignment problem, whichever library you use. You have to use the Hungarian algorithm, and it looks like solve_LSAP does exactly that.
No need to try anything else IMHO.
EDIT: An efficient implementation of the Hungarian method should be O(n^3), which is extremely fast for any optimization algorithm. If solve_LSAP is not fast enough for your problem (assumed it is implemented correctly), it is very unlikely that any exact method will work.
You will have to use some sort of heuristic to approximate the solution.
I am doing matrix operations on large matrices in my C++ program. I need to verify the results that I get, I used to use WolframAlpha for the task up until now. But my inputs are very large now, and the web interface does NOT accept such large values (textfield is limited).
I am looking for a better solution to quickly cross-check/do math problems.
I know there is Matlab but I have never used it and I don't know if thats what will suffice my needs and how steep the learning curve would be?
Is this the time to make the jump? or there are other solutions?
If you don't mind using python, numpy might be an option.
Apart from the license costs, MATLAB is the state of the art numerical math tool. There is octave as free open source alternative, with a similar syntax. The learning curve is for both tools absolutely smooth!
WolframAlpha is web interface to Wolfram Mathematica. The command syntax is exactly the same. If you have access to Mathematica at your university, it would be most smooth choice for you since you already have experience with WolframAlpha.
You may also try some packages to convert Mathematica commands to MATLAB:
ToMatlab
Mathematica Symbolic Toolbox for MATLAB 2.0
Let us know in more details what is your validation process. How your data look like and what commands have you used in WolframALpha? Then we can help you with MATLAB alternative.
I have a number of small algorithms that I would like to write up in a paper. They are relatively short, and concise. However, instead of writing them in pseudo-code (à la Cormen or even Knuth), I would like to write an algebraic representation of them (more linear and better LaTeX rendering) . However, I cannot find resources as to the best notation for this, if there is anything: e.g. how do I represent a loop? If? The addition of a tuple to a list?
Has any of you encountered this problem, and somehow solved it?
Thanks.
EDIT: Thanks, people. I think I did a poor job at phrasing the question. Here goes again, hoping I make it clearer: what is the common notation for talking about loops and if-then clauses in a mathematical notation? For instance, I can use $acc \leftarrow acc \cup \langle i,i+1 \rangle$ to represent the "add" method of a list.
Don't do this. You are deviating from what people expect to see when they read a paper about algorithms. You should follow expected practices; your ideas are more likely to get the attention that they deserve. When in Rome, do as the Romans do.
Formatting code (or pseudocode as it may be) in a LaTeXed paper is very easy. See, for example, Formatting code in LaTeX.
I see if-expressions in mathematical notation fairly often. The usual thing for a loop is a recurrence relation, or equivalently, a function defined recursively.
Here's how the Ackermann function is defined on Wikipedia, for instance:
This picture is nice because it feels mathematical in flavor and yet you could clearly type it in almost exactly as written and have an implementation. It is not always possible to achieve that.
Other mathematical notations that correspond to loops include ∑-notation for summation and set-builder notation.
I hope this answers your question! But if your aim is to describe how something is done and have someone understand, I think it is probably a mistake to assume that mathematicians would prefer to see equations. I don't think they're interchangeable tools (despite Turing equivalence). If your algorithm involves mutable data structures, procedural code is probably going to be better than equations for explaining it.
I'd copy Knuth. Few know how to communicate better than him in a computer science setting.
A symbol for general loops does not exist; usually you will use the summation operator. "if" is represented using implications, and to "add a tuple to a list" you would use union.
However, in general, a bit of verbosity is not necessarily a bad thing - sometimes, especially for complex algorithms, it is best to spell it out in plain English, using examples and diagrams. This is doubly-true for non-coders.
Think about it: when you read a math text-book on Euclid's algorithm for GCD, or the sieve of Eratosthenes, how is it written? Usually, the algorithm itself is in prose, while the proof of the algorithm is where the mathematical symbols lie.
You might take a look at Haskell. Haskell formats well in latex, has a nice algebraic syntax, and you can even compile a latex file with Haskell in it, provided the code is wrapped in \begin{code} and \end{code}. See here: http://www.haskell.org/haskellwiki/Literate_programming. There are probably literate programming tools for other languages.
Lisp started out as a mathematical notation of a computing model so that the lecturer would have a better tool than turing machines. By accident, it turns out that it can be implemented in assembly - thus lisp, the programming language was born.
But I don't think this is really what you are looking for since the computing model that lisp describes doesn't have loops: recursion is used instead. The syntax derives from algebra where braces denote evaluate-this-and-substitute-the-result. Indeed, lisp's model of computing is basically substitution - what algebra essentially is.
Indeed, most functional languages like Lisp, Haskell and Erlang are derived from mathematics. Haskell is actually a result of proving that lambda calculus can be used to implement type systems. So Haskell, like Lisp was born out of pure mathematics. But again, the syntax is not what you would probably be used to.
You can certainly explain Lisp and Haskell syntax to mathematicians and they would treat it as a "game". Language constructs like loops, recursion and conditionals can be proven out of the rules of the game rather than blindly implemented like in other languages. This would lead you into the realms of combinatronics, another branch of mathematics. Indeed, in combinatronics, even the concept of numbers can be constructed out of the rules of the game rather than being a native part of the language (google Church Numerals).
So have a look at Lisp/Scheme, Erlang and Haskell if you want. Erlang especially has syntax close to what you want:
add(a,b) -> a + b
But my recommendation is to write in C-like pseudocode. It's sort of the lowest common denominator in programming languages. Has a syntax that is fairly easy to understand and clean. And the function syntax even derives from functions in mathematics. Remember f(x)?
As a plus, mathematicians are used to writing C, statisticians are used to writing C (though generally they prefer R), physicists are used to writing C, programmers are used to at least looking at C (I know a few who've never touched C).
Actually, scratch that. You mention that your target audience are statisticians. Write in R
Something like this website describes?
APL? The only problem is that few people can read it.