How do I pass in a polynomial function in java? - java

For a programming project in Calculus we were instructed to code a program that models the Simpson's 1/3 and 3/8 rule.
We are supposed to take in a polynomial(i.e. 5x^2+7x+10) but I am struggling conceptualizing this. I have began by using scanner but is there a better way to correctly read the polynomial?
Any examples or reference materials will be greatly appreciated.

I'd suggest that you start with a Function interface that takes in a number of input values and returns an output value:
public interface Function {
double evaluate(double x);
}
Write a polynomial implementation:
public class Poly {
public static double evaluate(double x, double [] coeffs) {
double value = 0.0;
if (coeffs != null) {
// Use Horner's method to evaluate.
for (int i = coeffs.length-1; i >= 0; --i) {
value = coeffs[i] + (x*value);
}
}
return value;
}
}
Pass that to your integrator and let it do its thing.

A simple way (to get you started) is to use an array.
In your example: 5x^2 + 7x + 10 would be:
{10,7,5}
I.e. at index 0 is the factor 10 for x^0 at index 1 is 7 for x^1 at index 2 is 10 for x^2.
Of course this not the best approach. To figure out way figure out how you would represent x^20

In java it would be easiest to pre-format your input and just ask for constants--as in, "Please enter the X^2 term" (and then the X term, and then the constant).
If that's not acceptable, you are going to be quite vulnerable to input style differences. You can separate the terms by String.split[ting] on + and -, that will leave you something like:
[5x^2], [7x], [10]
You could then search for strings containing "x^2" and "x" to differentiate your terms
Remove spaces and .toLowerCase() first to counter user variances, of course.
When you split your string you will need to identify the - cases so you can negate those constants.
You could do two splits, one on + the other on -. You could also use StringTokenizer with the option to keep the "Tokens" which might be more straight-forward but StringTokenizer makes some people a little uncomfortable, so go with whatever works for you.
Note that this will succeed even if the user types "5x^2 + 10 + 7 x", which can be handy.

I believe parsing is my problem. I am somewhat new to java so this is troubling me.
You should use a parser generator.
A parser generator is a tool that reads a grammar specification and converts it to a Java program that can recognize matches to the grammar. In addition to the parser generator itself, JavaCC provides other standard capabilities related to parser generation such as tree building (via a tool called JJTree included with JavaCC), actions, debugging, etc.
JavaCC's FAQ answers How do I parse arithmetic expressions?
See the examples that come with JavaCC.
See any text on compiling.
See Parsing Epressions by Recursive Descent and a tutorial by Theodore Norvell.
Also, see JavaCC - Parse math expressions into a class structure

Related

How to store mathematical formula in MS SQL Server DB and interpret it using JAVA?

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.

Replacing Mathematical Operators with Variable Java

Currently trying to do a reverse polish calculator for one of my Uni homework tasks.
I have the program working fine when using a bunch of if/else statements to work out which operator was typed in and do the mathematical operation normally like num1+num2.
This is beyond the homework task we were set but what I'm trying to do now is replace the operator with a variable for example: "num1 + num2" would become "num1 variable num2" where variable equals "+" etc.
Is there a way to do this in Java?
Thanks in advance
Since you are interested in going beyond the scope of the training material, and assuming you've learned about interfaces already, I believe what you are looking for is a binary expression tree (that wikipedia article actually explains it good).
Basically, you create an interface Expression with a double compute() method. There will be two types of implementing classes:
Operand: Constant and Variable.
Operator: Plus, Minus, Multiply, Divide. Each will have two Expression fields: left and right.
Your text expression is then parsed into the expression tree:
// input: "num1 + num2 * 3"
// result expression tree will be built by parser using:
Expression a = new Variable("num1");
Expression b = new Variable("num2");
Expression c = new Constant(3);
Expression d = new Multiply(b, c);
Expression e = new Plus(a, d);
Map<String, Double> variables = /*defined elsewhere*/;
double result = e.compute(variables);
Your new assignment, should you choose to accept it, will be to write the expression classes and a parser to build the expression tree from a text expression.
Hope this will encourage you to go way beyond the training material, having some fun while playing.
First you can use a switch on String rather than if-then-else chain. Another way is to build a static final Map (E.g. HashMap) from String to Function. The strings are the operators. The Functions do the operation. In Java 8 you can give the functions as lambdas. I only have access through a phone right now so can't show code. Your question will be much better received if you add code showing what you mean.

Solving two algebraic equations in java

I have two equations that need to be evaluated in java
y=(x+1)*2-3
y=5
These equations are dynamic in nature
y= x*8x6-5*5
y= 3
y is known in these equations, I need to determine the value of x
What is the best and easy way to write a program in java?
It seems that there are a couple of ways to go about this. My first thought (as always is overly complex and most likely not worth doing except for fun), is to use a create a grammar to parse out the order of operations, things that can evaluate to variables vs constants, etc. Then programatically solve the equations. This however is not something easily done. If this is for a compiler class, this might be worth looking at otherwise ignore it.
My second thought was to just use brute force. Though you will need to figure out what to do with negative values of x.
public int solve(int y){
int x=0;
while(y>(x+1)*2-3)
x++;
}
Some years later, hope this helps someone, to make this a lot simplier i will use the library exp4j (https://www.objecthunter.net/exp4j/) and the IDE netbeans 8.2 (https://netbeans.org/).
Create a frame like this
Later on the button add the code:
try {
net.objecthunter.exp4j.Expression e = new ExpressionBuilder(txtFunc.getText())
.variables("x")
.build()
.setVariable("x", Double.parseDouble(txtVar.getText()));
double result = e.evaluate();
txtRes.setText("" + result);
} catch (Exception e) {
JOptionPane.showMessageDialog(null, "Revisa la función o la variable, Posibles errores de operación: División entre 0");
}
Note: this is intended to evaluate "x"
So doing specifically that way is going to be little bit complicated, so we are going to do some math, if 5 is the value of the function evaluated then we isolate the value of "x". x=(y+1)/2 then re-evaluate, x=(5+1)/2=3, x=3 and with the code verify that this is actually the answer.
Comprobation
Same thing goes with the other function. (sorry for my technical english)
If by saying the equations are "dynamic" we are to infer that you are trying to construct a program to solve for x in an arbitrary algebraic equation (or set of equations), that's well beyond the scope of this forum. There are entire software packages designed to do things like that.

program for A three-point Gauss integration

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

Why are most string manipulations in Java based on regexp?

In Java there are a bunch of methods that all have to do with manipulating Strings.
The simplest example is the String.split("something") method.
Now the actual definition of many of those methods is that they all take a regular expression as their input parameter(s). Which makes then all very powerful building blocks.
Now there are two effects you'll see in many of those methods:
They recompile the expression each time the method is invoked. As such they impose a performance impact.
I've found that in most "real-life" situations these methods are called with "fixed" texts. The most common usage of the split method is even worse: It's usually called with a single char (usually a ' ', a ';' or a '&') to split by.
So it's not only that the default methods are powerful, they also seem overpowered for what they are actually used for. Internally we've developed a "fastSplit" method that splits on fixed strings. I wrote a test at home to see how much faster I could do it if it was known to be a single char. Both are significantly faster than the "standard" split method.
So I was wondering: why was the Java API chosen the way it is now?
What was the good reason to go for this instead of having a something like split(char) and split(String) and a splitRegex(String) ??
Update: I slapped together a few calls to see how much time the various ways of splitting a string would take.
Short summary: It makes a big difference!
I did 10000000 iterations for each test case, always using the input
"aap,noot,mies,wim,zus,jet,teun"
and always using ',' or "," as the split argument.
This is what I got on my Linux system (it's an Atom D510 box, so it's a bit slow):
fastSplit STRING
Test 1 : 11405 milliseconds: Split in several pieces
Test 2 : 3018 milliseconds: Split in 2 pieces
Test 3 : 4396 milliseconds: Split in 3 pieces
homegrown fast splitter based on char
Test 4 : 9076 milliseconds: Split in several pieces
Test 5 : 2024 milliseconds: Split in 2 pieces
Test 6 : 2924 milliseconds: Split in 3 pieces
homegrown splitter based on char that always splits in 2 pieces
Test 7 : 1230 milliseconds: Split in 2 pieces
String.split(regex)
Test 8 : 32913 milliseconds: Split in several pieces
Test 9 : 30072 milliseconds: Split in 2 pieces
Test 10 : 31278 milliseconds: Split in 3 pieces
String.split(regex) using precompiled Pattern
Test 11 : 26138 milliseconds: Split in several pieces
Test 12 : 23612 milliseconds: Split in 2 pieces
Test 13 : 24654 milliseconds: Split in 3 pieces
StringTokenizer
Test 14 : 27616 milliseconds: Split in several pieces
Test 15 : 28121 milliseconds: Split in 2 pieces
Test 16 : 27739 milliseconds: Split in 3 pieces
As you can see it makes a big difference if you have a lot of "fixed char" splits to do.
To give you guys some insight; I'm currently in the Apache logfiles and Hadoop arena with the data of a big website. So to me this stuff really matters :)
Something I haven't factored in here is the garbage collector. As far as I can tell compiling a regular expression into a Pattern/Matcher/.. will allocate a lot of objects, that need to be collected some time. So perhaps in the long run the differences between these versions is even bigger .... or smaller.
My conclusions so far:
Only optimize this if you have a LOT of strings to split.
If you use the regex methods always precompile if you repeatedly use the same pattern.
Forget the (obsolete) StringTokenizer
If you want to split on a single char then use a custom method, especially if you only need to split it into a specific number of pieces (like ... 2).
P.S. I'm giving you all my homegrown split by char methods to play with (under the license that everything on this site falls under :) ). I never fully tested them .. yet. Have fun.
private static String[]
stringSplitChar(final String input,
final char separator) {
int pieces = 0;
// First we count how many pieces we will need to store ( = separators + 1 )
int position = 0;
do {
pieces++;
position = input.indexOf(separator, position + 1);
} while (position != -1);
// Then we allocate memory
final String[] result = new String[pieces];
// And start cutting and copying the pieces.
int previousposition = 0;
int currentposition = input.indexOf(separator);
int piece = 0;
final int lastpiece = pieces - 1;
while (piece < lastpiece) {
result[piece++] = input.substring(previousposition, currentposition);
previousposition = currentposition + 1;
currentposition = input.indexOf(separator, previousposition);
}
result[piece] = input.substring(previousposition);
return result;
}
private static String[]
stringSplitChar(final String input,
final char separator,
final int maxpieces) {
if (maxpieces <= 0) {
return stringSplitChar(input, separator);
}
int pieces = maxpieces;
// Then we allocate memory
final String[] result = new String[pieces];
// And start cutting and copying the pieces.
int previousposition = 0;
int currentposition = input.indexOf(separator);
int piece = 0;
final int lastpiece = pieces - 1;
while (currentposition != -1 && piece < lastpiece) {
result[piece++] = input.substring(previousposition, currentposition);
previousposition = currentposition + 1;
currentposition = input.indexOf(separator, previousposition);
}
result[piece] = input.substring(previousposition);
// All remaining array elements are uninitialized and assumed to be null
return result;
}
private static String[]
stringChop(final String input,
final char separator) {
String[] result;
// Find the separator.
final int separatorIndex = input.indexOf(separator);
if (separatorIndex == -1) {
result = new String[1];
result[0] = input;
}
else {
result = new String[2];
result[0] = input.substring(0, separatorIndex);
result[1] = input.substring(separatorIndex + 1);
}
return result;
}
Note that the regex need not be recompiled each time. From the Javadoc:
An invocation of this method of the form str.split(regex, n) yields the same result as the expression
Pattern.compile(regex).split(str, n)
That is, if you are worried about performance, you may precompile the pattern and then reuse it:
Pattern p = Pattern.compile(regex);
...
String[] tokens1 = p.split(str1);
String[] tokens2 = p.split(str2);
...
instead of
String[] tokens1 = str1.split(regex);
String[] tokens2 = str2.split(regex);
...
I believe that the main reason for this API design is convenience. Since regular expressions include all "fixed" strings/chars too, it simplifies the API to have one method instead of several. And if someone is worried about performance, the regex can still be precompiled as shown above.
My feeling (which I can't back with any statistical evidence) is that most of the cases String.split() is used in a context where performance is not an issue. E.g. it is a one-off action, or the performance difference is negligible compared to other factors. IMO rare are the cases where you split strings using the same regex thousands of times in a tight loop, where performance optimization indeed makes sense.
It would be interesting to see a performance comparison of a regex matcher implementation with fixed strings/chars compared to that of a matcher specialized to these. The difference might not be big enough to justify the separate implementation.
I wouldn't say most string manipulations are regex-based in Java. Really we are only talking about split and replaceAll/replaceFirst. But I agree, it's a big mistake.
Apart from the ugliness of having a low-level language feature (strings) becoming dependent on a higher-level feature (regex), it's also a nasty trap for new users who might naturally assume that a method with the signature String.replaceAll(String, String) would be a string-replace function. Code written under that assumption will look like it's working, until a regex-special character creeps in, at which point you've got confusing, hard-to-debug (and maybe even security-significant) bugs.
It's amusing that a language that can be so pedantically strict about typing made the sloppy mistake of treating a string and a regex as the same thing. It's less amusing that there's still no builtin method to do a plain string replace or split. You have to use a regex replace with a Pattern.quoted string. And you only even get that from Java 5 onwards. Hopeless.
#Tim Pietzcker:
Are there other languages that do the same?
JavaScript's Strings are partly modelled on Java's and are also messy in the case of replace(). By passing in a string, you get a plain string replace, but it only replaces the first match, which is rarely what's wanted. To get a replace-all you have to pass in a RegExp object with the /g flag, which again has problems if you want to create it dynamically from a string (there is no built-in RegExp.quote method in JS). Luckily, split() is purely string-based, so you can use the idiom:
s.split(findstr).join(replacestr)
Plus of course Perl does absolutely everything with regexen, because it's just perverse like that.
(This is a comment more than an answer, but is too big for one. Why did Java do this? Dunno, they made a lot of mistakes in the early days. Some of them have since been fixed. I suspect if they'd thought to put regex functionality in the box marked Pattern back in 1.0, the design of String would be cleaner to match.)
I imagine a good reason is that they can simply pass the buck on to the regex method, which does all the real heavy lifting for all of the string methods. Im guessing they thought if they already had a working solution it was less efficient, from a development and maintenance standpoint, to reinvent the wheel for each string manipulation method.
Interesting discussion!
Java was not originally intended as a batch programming language. As such the API out of the box are more tuned towards doing one "replace" , one "parse" etc. except on Application initialization when the app may be expected to be parsing a bunch of configuration files.
Hence optimization of these APIs was sacrificed in the altar of simplicity IMO. But the question brings up an important point. Python's desire to keep the regex distinct from the non regex in its API, stems from the fact that Python can be used as an excellent scripting language as well. In UNIX too, the original versions of fgrep did not support regex.
I was engaged in a project where we had to do some amount of ETL work in java. At that time, I remember coming up with the kind of optimizations that you have alluded to, in your question.
I suspect that the reason why things like String#split(String) use regexp under the hood is because it involves less extraneous code in the Java Class Library. The state machine resulting from a split on something like , or space is so simple that it is unlikely to be significantly slower to execute than a statically implemented equivalent using a StringCharacterIterator.
Beyond that the statically implemented solution would complicate runtime optimization with the JIT because it would be a different block of code that also requires hot code analysis. Using the existing Pattern algorithms regularly across the library means that they are more likely candidates for JIT compilation.
Very good question..
I suppose when the designers sat down to look at this (and not for very long, it seems), they came at it from a point of view that it should be designed to suit as many different possibilities as possible. Regular Expressions offered that flexibility.
They didn't think in terms of efficiencies. There is the Java Community Process available to raise this.
Have you looked at using the java.util.regex.Pattern class, where you compile the expression once and then use on different strings.
Pattern exp = Pattern.compile(":");
String[] array = exp.split(sourceString1);
String[] array2 = exp.split(sourceString2);
In looking at the Java String class, the uses of regex seem reasonable, and there are alternatives if regex is not desired:
http://java.sun.com/javase/6/docs/api/java/lang/String.html
boolean matches(String regex) - A regex seems appropriate, otherwise you could just use equals
String replaceAll/replaceFirst(String regex, String replacement) - There are equivalents that take CharSequence instead, preventing regex.
String[] split(String regex, int limit) - A powerful but expensive split, you can use StringTokenizer to split by tokens.
These are the only functions I saw that took regex.
Edit: After seeing that StringTokenizer is legacy, I would defer to Péter Török's answer to precompile the regex for split instead of using the tokenizer.
The answer to your question is that the Java core API did it wrong. For day to day work you can consider using Guava libraries' CharMatcher which fills the gap beautifully.
...why was the Java API chosen the way it is now?
Short answer: it wasn't. Nobody ever decided to favor regex methods over non-regex methods in the String API, it just worked out that way.
I always understood that Java's designers deliberately kept the string-manipulation methods to a minimum, in order to avoid API bloat. But when regex support came along in JDK 1.4, of course they had to add some convenience methods to String's API.
So now users are faced with a choice between the immensely powerful and flexible regex methods, and the bone-basic methods that Java always offered.

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