I now have an idea, that I use the function as a string, and I calculate the real integral by hand, and ask a question to the user what the definite integral is, but that isn't a real solution.
I was wondering if there was a way to input a function and output an integral/derivative (depending on user choice). My initial step was to put it into an array somehow, but given the many types of functions, this wasn't happening.
I researched everywhere, and I haven't found a method that actually does this with no additional code, nor any code that actually does this, period.
Also, I want to see if there was a way to make a GUI interface and plot inputted functions on to that, if that's possible too.
Thanks :)
What you're describing is known as symbolic integration. There's currently no fully general way to implement it, but there are some techniques available. One such is the Risch algorithm.
Alternatively, an easier problem than symbolic integration is [symbolic differentiation -- and, if the differential of the user's input is equivalent* to the expression which they were asked to integrate, then their integral is probably correct.
You may also want to consider using an existing CAS**, such as Mathematica, to implement this. They've already implemented most of the tools you're after.
*: Keep in mind, though, that two mathematical expressions may be equivalent without being identical, either in trivial ways (e.g, terms in a different order), more complex ones (e.g, large expressions factored differently), or fundamentally (e.g, trig functions replaced with complex exponentials or vice versa).
**: Computer algebra system
Javacalculus is what you are looking for.
Good luck!
Related
I have several java classes which implements a quite complicated (non-linear) business logic. Basically the user provides several (numeric) input parameters, and the application computes a scalar.
I would like to do a parameter scan on the input data, that is I would like to know what parameter values create the maximum output value.
The easiest and most time-consuming method would be to create some simple loops with "small" steps on the input parameters, and constantly check the output one.
But as I said, this takes quite a long time; there are several mathematical solutions for this problem (e.g. Newton-method).
My question is; are there any free/open source JAVA libraries which provide this parameter scanning funcionality?
Thanks,
krisy
You might be able to adjust OptaPlanner for this. Call your business logic in a SimpleScoreCalculator and wrap the returned scalar in a Score instance.
Make sure you use at least 6.1.0.Beta2 as that supports IntValueRange and DoubleValueRange.
As for optimization algorithms: if the variables are few, integer and small in range, "Branch And Bound" can work, guaranteeing you the optimal solution (but much faster than Brute Force).
Otherwise, you'll need to go with a limited selection Construction Heuristic followed by Local Search with custom Move implementations.
I have some function (for example, double function(double value)), and some range (for example, from A to B). I need to calculate max value of function in this range. Are there existed libraries for it? Please, give me advice.
If the function needs to handle floating-point values, you're going to have to use something like Golden section search. Note that for this specific method, there are significant limitations regarding the functions that can be handled (specifically it must be unimodal). There are some adjustments you can make to the algorithm which extend it to more functions, specifically these modifications will allow it to work for continuous functions.
Is this a continuous function, or a set of discrete values? If discrete values, then you can either iterate over all values, and set max/min flags as 808sound suggests, or you can load all values into an array.
If it's a continuous function, then you can either populate an array with the function's value at discrete inputs, and find the max as above, or if it's differentiable, then you can use basic calculus to find the points at which df(x)/dx are 0. The latter case is a little more abstract, and probably more complicated than you want, though?
A quick google search led me to this:
http://code.google.com/p/javacalculus/
But I've never used it myself, so I don't know if that implements the required functionality. It does differential equations, though, so I assume they'd have "baby stuff" like basic differentiation.
I do not know if there are any librairies in Java for your problem.
But I know you can easily do that with MatLab (or Octave for the OpenSource equivalent).
If you do not have any indication of what the functions inner workings are (i.e. the function is a black box that accepts an input and produces an output), there is no "easy" way to find the global maximum.
There are an infinite number of points to choose for your input (technically) so "iterating over all possible inputs" is not feasible mathematically.
There are various algorithms that will give you estimated maximum values ina function like this:
The hill climbing algorithm, and the firefly algorithm are two, but there are many more. This is a fairly well documented/studied computer science problem and there is a lot of material online for you to look at. I suggest starting with the hill climbing algorithm, and maybe expanding out to other global optimization algorithms.
Note: These algorithms do not guarantee that the result is the maximum, but provide an estimate of its value.*
I was looking for lightweight library that'd allow me to feed it a bunch of words, and then ask it whether a given word would have any close matches.z
I'm not particularly concerned with the underlying algorithm (I reckon a simple hamming distance algorithm would probably suffice, were I to undertake the task myself).
I'm just in the development of a small language and I found it nifty to make suggestions to the user when an "Undefined class" error is detected (lots of times it's just a misspelled word). I don't want to lose much time on the issue though.
Thanks
Levenshtein distance is a common way of handling it. Just add all the words to a list and then brute-force iterate over it and return the smallest distance. Here's one library with a Levenschtein function: http://commons.apache.org/lang/api-2.4/org/apache/commons/lang/StringUtils.html
If you have a large number of words and you want it to run fast, then you'd have to use ngrams. Spilt each word into bigrams and then add (bigram, word) to a map. Use the map to look up the bigrams in the target word, and then iterate through the candidates. That's probably more work than you want to do, though.
not necessarily a library but i think this article may be really helpful. it mostly describes the general workings of how a spelling corrector works in python, but also has a link for a java implementation which you may use if that is what you are looking for specifically (note that I haven't specifically used the java one before)
I want to make a Java program to help people with basic discrete mathematics (that is to say, checking the truth values of statements). To do this, I need to be able to detect how many variables the user inputs, what operators there are, and what quantifiers there are, if any (∃ and ∀). Is there a good algorithm for being able to do all these things?
Just so you know, I don't just want a result; I want full control over their input, so I can show them the logical proof. (so doing something like passing it to JavaScript won't work).
Okay, so, your question is a bit vague, but I think I understand what you'd like to do: an educational aid that processes first-order logic formulas, showing the user step by step how to work with such formulas, right? I think the idea has merit, and it's perfectly doable, even as a one-man project, but it's not terribly easily, and you'll have to learn a lot of new things -- but they're all very interesting things, so even if nothing at all comes out of it, you'd certainly get yourself some valuable knowledge.
I'd suggest you to start small. I'd start by building a recursive descent parser to recognize zero-order logic formulas (a machine that would decide if a formula is valid, i.e. it'd accept "A ^ B" but it'd reject "^ A ^"). Next up you'd have to devise a way to store the formula, and then you'd be able to actually work on it. Then again, start small: a little machine that accepts valid zero-order logic formulas like TRUE AND NOT (TRUE AND FALSE), and successfully reduces it step by step to true is already something that people can learn from, and it's not too hard to write. If you're feeling adventurous, add variables and make equations: A AND TRUE = TRUE -- it's easy to work these out with reductions and truth tables.
Things get tricky with quantifiers that bind variables, that's where the Automated theorem proving may come into play; but then, it all depends on exactly what you'd like to do: implementing transformations into the various normal forms, and showing the process step by step to the student would be fairly easy, and rather useful.
At any rate, I think it's a decent personal project, and you could learn a lot from it. If you're in a university, you could even get some credit for it eventually.
The technique I have used is to parse the input string using a context free grammar. There are many frameworks to help you do this, I have personally used ANTLR in the past to parse an input string into a descrete logic tree. ANTLR allows you to define a CFG which you can map to Java types. This allows you to map to a data structure to store and evaluate the truth value of the expression. Of course, you would also be able to pull out the variables contained in the data structure.
Given the source code of a program, how do I analyze it and count the function points within it?
Thanks!
You might find this tutorial on FPA of interest. Personally, I don't put much stock in this estimation method. From my perspective it attempts to provide a precise estimate in for things that have been shown repeatedly to not be precisely measurable. I much prefer planning poker or something similar that tries to group things within a similar order of magnitude and provide an estimate based on your previous estimations for similarly sized stories.
If you're doing this for a class, simply follow the rules given in the text book and crank out the answer. If you're really intending to try this as a software development estimation method, my advice is to simplify the process rather than make it more complex. I would imagine that members of the International Function Point User Group (yes, there is one), will disagree.
With a code analysis tool. If you want to write one yourself, you might want to start with cglib or ASM.