In a Java program which has a variable t counting up the time (relative to the program start, not system time), how can I turn a user-input String into a math formula that can be evaluated efficiently when needed.
(Basically, the preparation of the formula can be slow as it happens Pre run-time, but each stored function may be called several times during run-time and then has to be evaluated efficiently)
As I could not find a Math parser that would keep a formula loaded for later reference instead of finding a general graph solving the equation of y=f(x), I was considering to instead have my Java program generate a script (JS, Python, etc) out of the input String and then call said script with the current t as input parameter.
-However I have been told that Scripts are rather slow and thus impractical for real-time applications.
Is there a more efficient way of doing this? (I would even consider making my Java application generate and compile C-code for every user input if this would be viable)
Edit: A tree construct does work to store expressions, but is still fairly slow to evaluate as from what I understand I would need to turn it into a chain of expressions again when evaluating (as in, traverse the tree object) which should need more calls than direct solving of an equation. Instead I will attempt the generation of additional java classes.
What I do is generate Java code at a runtime and compile it. There are a number of libraries to help you do this, one I wrote is https://github.com/OpenHFT/Java-Runtime-Compiler This way it can be as efficient as if you had hand written the Java code yourself and if called enough times will be compiled to native code.
Can you provide some information on assumed function type and requested performance? Maybe it will be enough just to use math parser library, which pre-compiles string containing math formula with variables just once, and then use this pre-compiled form of formula to deliver result even if variables values are changing? This kind of solutions are pretty fast as it typically do not require repeating string parsing, syntax checking and so on.
An example of such open-source math parser I recently used for my project is mXparser:
mXparser on GitHub
http://mathparser.org/
Usage example containing function definition
Function f = new Function("f(x,y) = sin(x) + cos(y)");
double v1 = f.calculate(1,2);
double v2 = f.calculate(3,4);
double v3 = f.calculate(5,6);
In the above code real string parsing will be done just once, before calculating v1. Further calculation v1, v2 (an possible vn) will be done in fast mode.
Additionally you can use function definition in string expression
Expression e = new Expression("f(1,2)+f(3,4)", f);
double v = e.calculate();
Related
I am trying to create a class that takes in a string input containing pseudocode and computes its' worst case runtime complexity. I will be using regex to split each line and analyze the worst-case and add up the complexities (based on the big-O rules) for each line to give a final worst-case runtime. The pseudocode written will follow a few rules for declaration, initilization, operations on data structures. This is something I can control. How should I go about designing a class considering the rules of iterative and recursive analysis?
Any help in C++ or Java is appreciated. Thanks in advance.
class PseudocodeAnalyzer
{
public:
string inputCode;
string performIterativeAnalysis(string line);
string performRecursiveAnalysis(string line);
string analyzeTotalComplexity(string inputCode);
}
An example for iterative algorithm: Check if number in a grid is Odd:
1. Array A = Array[N][N]
2. for i in 1 to N
3. for j in 1 to N
4. if A[i][j] % 2 == 0
5. return false
6. endif
7. endloop
8. endloop
Worst-case Time-Complexity: O(n*n)
The concept: "I wish to write a program that analyses pseudocode in order to print out the algorithmic complexity of the algorithm it describes" is mathematically impossible!
Let me try to explain why that is, or how you get around the inevitability that you cannot write this.
Your pseudocode has certain capabilities. You call it pseudocode, but given that you are now trying to parse it, it's still a 'real' language where terms have real meaning. This language is capable of expressing algorithms.
So, which algorithms can it express? Presumably, 'all of them'. There is this concept called a 'turing machine': You can prove that anything a computer can do, a turing machine can also do. And turing machines are very simple things. Therefore, if you have some simplistic computer and you can use that computer to emulate a turing machine, you can therefore use it to emulate a complete computer. This is how, in fundamental informatics, you can prove that a certain CPU or system is capable of computing all the stuff some other CPU or system is capable of computing: Use it to compute a turing machine, thus proving you can run it all. Any system that can be used to emulate a turing machine is called 'turing complete'.
Then we get to something very interesting: If your pseudocode can be used to express anything a real computer can do, then your pseudocode can be used to 'write'... your very pseudocode checker!
So let's say we do just that and stick the pseudocode that describes your pseudocode checker in a function we shall call pseudocodechecker. It takes as argument a string containing some pseudocode, and returns a string such as O(n^2).
You can then write this program in pseudocode:
1. if pseudocodechecker(this-very-program) == O(n^2)
2. If True runSomeAlgorithmThatIsO(1)
3. If False runSomeAlgorithmTahtIsO(n^2)
And this is self-defeating: We have 'programmed' a paradox. It's like "This statement is a lie", or "the set of all sets that do not contain themselves". If it's false it is true and if it is true it false. [Insert GIF of exploding computer here].
Thus, we have mathematically proved that what you want is impossible, unless one of the following is true:
A. Your pseudocode-based checker is incorrect. As in, it will flat out give a wrong answer sometimes, thus solving the paradox: If you feed your program a paradox, it gives a wrong answer. But how useful is such an app? An app where you know the answer it gives may be incorrect?
B. Your pseudocode-based checker is incomplete: The official definition of your pseudocode language is so incapable, you cannot even write a turing machine in it.
That last one seems like a nice solution; but it is quite drastic. It pretty much means that your algorithm can only loop over constant ranges. It cannot loop until a condition is true, for example. Another nice solution appears to be: The program is capable of realizing that an answer cannot be given, and will then report 'no answer available', but unfortunately, with some more work, you can show that you can still use such a system to develop a paradox.
The answer by #rzwitserloot and the ones given in the link are correct. Let me just add that it is possible to compute an approximation both to the halting problem as well as to finding the time complexity of a piece of code (written in a Turing-complete language!). (Compare that to the existence of automated theorem provers for arithmetic and other second order logics, which are undecidable!) A tool that under-approximated the complexity problem would output the correct time complexity for some inputs, and "don't know" for other inputs.
Indeed, the whole wide field of code analyzers, often built into the IDEs that we use every day, more often than not under-approximate decision problems that are uncomputable, e.g. reachability, nullability or value analyses.
If you really want to write such a tool: the basic idea is to identify heuristics, i.e., common patterns for which a solution is known, such as various patterns of nested for-loops with only very basic arithmetic operations manipulating the indices, or simple recursive functions where the recurrence relation can be spotted straight-away. It would actually be not too hard (though definitely not easy!) to write a tool that could solve most of the toy problems (such as the one you posted) that are given as homework to students, and that are often posted as questions here on SO, since they follow a rather small number of patterns.
If you wish to go beyond simple heuristics, the main theoretical concept underlying more powerful code analyzers is abstract interpretation. Applied to your use case, this would mean developing a mapping between code constructs in your language to code constructs in a different language (or simpler code constructs in the same language) for which it is easier to compute the time complexity. This mapping would have to conform to some constraints, in particular, the mapped constructs have have the same or worse time complexity as the original code. Actually, mapping a piece of code to a recurrence relation would be an example of abstract interpretation. So is replacing a line of code with something like "O(1)". So, the task is just to formalize some of the things that we do in our heads anyway when we are analyzing the time complexity of code.
There is a question with the same title like this on stackoverflow here, but I wanted to ask if it is possible to do something similar to this in Java.
I wanted to make something similar to desmos, just like that guy did in Javascript,but i want to make it in Java using lwjgl 2. I am new to Java and I'd like to know if it is possible to convert a piece of string into a method. Is it possible?
I have looked for possible options and I found out that your can make your own Java eval() method. But I don't want to replace the x in the string for every pixel of the window-width.
Thanks in advance.
What you need is an engine/library that can evaluate expressions, defined as string at execution time. If you wrap the evaluation code into function call (e.g. lambda function), you will get what you need.
Option 1: You can use exp4j. exp4j is a small footprint library, capable of evaluating expressions and functions at execution time. Here is an example:
Expression e = new ExpressionBuilder("3 * sin(y) - 2 / (x - 2)")
.variables("x", "y")
.build()
.setVariable("x", 2.3)
.setVariable("y", 3.14);
double result = e.evaluate();
Option 2: You can use the Java's script engine. You can use it to evaluate expressions defined, for example, in JavaScript:
ScriptEngineManager manager = new ScriptEngineManager();
ScriptEngine engine = manager.getEngineByName("js");
Object result = engine.eval("sin(1.25)");
Option 3: Compile to native Java. With this approach, you use template to generate .java file with a class that contains your expression. Than you call the Java compiler. This approach has the drawback that has some complexity in the implementation and some initial latency (until the class is compiled), but the performance is the best. Here are some links to explore:
Create dynamic applications with javax.tools
In particular javax.tools.Compiler
Note of Caution Whatever approach you chose, have in mind that you need to think about the security. Allowing the user to enter code which can be evaluated without security restrictions could be very dangerous.
I have to give the user the option to enter in a text field a mathematical formula and then save it in the DB as a String. That is easy enough, but I also need to retrieve it and use it to do calculations.
For example, assume I allow someone to specify the formula of employee salary calculation which I must save in String format in the DB.
GROSS_PAY = BASIC_SALARY - NO_PAY + TOTAL_OT + ALLOWANCE_TOTAL
Assume that terms such as GROSS_PAY, BASIC_SALARY are known to us and we can make out what they evaluate to. The real issue is we can't predict which combinations of such terms (e.g. GROSS_PAY etc.) and other mathematical operators the user may choose to enter (not just the +, -, ×, / but also the radical sigh - indicating roots - and powers etc. etc.). So how do we interpret this formula in string format once where have retrieved it from DB, so we can do calculations based on the composition of the formula.
Building an expression evaluator is actually fairly easy.
See my SO answer on how to write a parser. With a BNF for the range of expression operators and operands you exactly want, you can follow this process to build a parser for exactly those expressions, directly in Java.
The answer links to a second answer that discusses how to evaluate the expression as you parse it.
So, you read the string from the database, collect the set of possible variables that can occur in the expression, and then parse/evaluate the string. If you don't know the variables in advance (seems like you must), you can parse the expression twice, the first time just to get the variable names.
as of Evaluating a math expression given in string form there is a JavaScript Engine in Java which can execute a String functionality with operators.
Hope this helps.
You could build a string representation of a class that effectively wraps your expression and compile it using the system JavaCompiler — it requires a file system. You can evaluate strings directly using javaScript or groovy. In each case, you need to figure out a way to bind variables. One approach would be to use regex to find and replace known variable names with a call to a binding function:
getValue("BASIC_SALARY") - getValue("NO_PAY") + getValue("TOTAL_OT") + getValue("ALLOWANCE_TOTAL")
or
getBASIC_SALARY() - getNO_PAY() + getTOTAL_OT() + getALLOWANCE_TOTAL()
This approach, however, exposes you to all kinds of injection type security bugs; so, it would not be appropriate if security was required. The approach is also weak when it comes to error diagnostics. How will you tell the user why their expression is broken?
An alternative is to use something like ANTLR to generate a parser in java. It's not too hard and there are a lot of examples. This approach will provide both security (users can't inject malicious code because it won't parse) and diagnostics.
div(1, sum(1, exp(sum(div(5, product(100, .1)), -5))))
I'm using this in a Solr query, and want to verify that it is the same as :
Where x is 5.
Is this language Java?
If it is, why am I getting this output here:
http://ideone.com/LWYWtU
If it isn't, what language is this and how do I test it?
Thanks in advance for your help.
EDIT: To add more of the surrounding code, here is the full boost value I'm sending to Solr:
if(exists(query({!frange l=0 u=60 v=product(geodist(),0.621371)})),div(1, sum(1, exp(sum(div(product(5), product(100, .1)), -5)))),0)
The reason I think it might be Java is because in the docs, it says Most Java Math functions are now supported, including: and then lists the math functions I ended up using for code.
Solr is Java, but that's not relevant since this is a set of functions that Solr parses and evaluate itself (and not related to Java, except that the backing functions are implemented in Java).
As far as I can say from what you've mapped the functions correctly, as long as the 5 in product(5) is the same as X. You shouldn't need product there, as the value can be included in div directly as far as I can see.
A way to validate it would be to use debugQuery in Solr and see what the value is evaluated as, and then compare it to your own value. Remember that floating point evaluation can introduce a few uncertanities.
I want to write a java program to calculate integral with three-point Gauss.
How to calculate result of every function that is string?
For example want to calculate F(x) = x^4 + cos(x) + e^2x
Evaluating a string is not an easy task by itself.
You have to write your own Interpreter with Lexer and a Parser.
You can consider to use thirdparty libraries for mathematical functions parsing and execution. I've never used any one of them. Simple googling reveals this:
JbcParser
JepParser
I'm sure there are a couple of others around...
Hope this helps