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iOS-Polynomial-Regression

Objective-C function for calculation the polynomial regression of a given dataset.

There are no mathematical data analysis functions in Objective-C and I couldn't find a suitable math framework for this task. For my thesis I require a function to calculate the polynomial regression of a give data set. Since this function didn't exist I had to write it myself. Problem was that other programming languages usually have this implemented by default as some kind of "polyfit" function so I dind't really had an example to base myself on.

So I had to go into the math and figure out how to turn it into an algorithm. A hellish job I wouldn't recommend to anyone. I programmed an Objective-C function for the calculation the polynomial regression of a given dataset which is extremely easy to use.

You have to give an array of NSNumber for the x values and y values and the desired degree of polynomial you would like to aquire. The function will return an NSMutableArray containing the polynomial constants.

Overview

Features

  • Can calculate any degree of polynomial
  • Easy to implement
  • Very compact, one line usage
  • Also contains a custom matrix class for this project which handles doubles

Example

NSMutableArray *x = [[NSMutableArray alloc] init];
[x addObject: [NSNumber numberWithDouble: 0]];
[x addObject: [NSNumber numberWithDouble: 9]];
[x addObject: [NSNumber numberWithDouble: 13]];
[x addObject: [NSNumber numberWithDouble: 15]];
[x addObject: [NSNumber numberWithDouble: 19]];
[x addObject: [NSNumber numberWithDouble: 20]];
[x addObject: [NSNumber numberWithDouble: 26]];
[x addObject: [NSNumber numberWithDouble: 26]];
[x addObject: [NSNumber numberWithDouble: 29]];
[x addObject: [NSNumber numberWithDouble: 30]];

NSMutableArray *y = [[NSMutableArray alloc] init];

[y addObject: [NSNumber numberWithDouble: 1]];
[y addObject: [NSNumber numberWithDouble: -7]];
[y addObject: [NSNumber numberWithDouble: 6]];
[y addObject: [NSNumber numberWithDouble: 12]];
[y addObject: [NSNumber numberWithDouble: -4]];
[y addObject: [NSNumber numberWithDouble: -12]];
[y addObject: [NSNumber numberWithDouble: -2]];
[y addObject: [NSNumber numberWithDouble: 13]];
[y addObject: [NSNumber numberWithDouble: 23]];
[y addObject: [NSNumber numberWithDouble: 30]];

int degree = 6;
NSMutableArray *regression = [PolynomialRegression regressionWithXValues: x AndYValues: y PolynomialDegree: degree];

NSLog(@"The result is the sum of");

for(int i = 0; i < [regression count]; i++) {
    double value = [[regression objectAtIndex: i] doubleValue];
    NSLog(@"%f * x^%d", value, i);
}

Generates the following output in console

2015-03-22 19:52:48.751 PolynomialRegression[2701:111554] The result is the sum of
2015-03-22 19:52:48.752 PolynomialRegression[2701:111554] 1.011300 * x^0
2015-03-22 19:52:48.752 PolynomialRegression[2701:111554] -23.964676 * x^1
2015-03-22 19:52:48.752 PolynomialRegression[2701:111554] 4.546635 * x^2
2015-03-22 19:52:48.752 PolynomialRegression[2701:111554] -0.236831 * x^3
2015-03-22 19:52:48.752 PolynomialRegression[2701:111554] -0.000581 * x^4
2015-03-22 19:52:48.753 PolynomialRegression[2701:111554] 0.000309 * x^5
2015-03-22 19:52:48.753 PolynomialRegression[2701:111554] -0.000005 * x^6

Implementation

Implementation is easy. Just add the classes to your project and import the PolynomialRegression.h file.

Donate

You can support contributors of this project individually. Every contributor is welcomed to add his/her line below with any content. Ordering shall be alphabetically by GitHub username.

Please consider a small donation if you use iOS Polynomial Regression in your projects. It would make me really happy.

License

The license for the code is MIT.

You're welcome to use it in commercial, closed-source, open source, free or any other kind of software, as long as you credit me appropriately and share any improvements to the code.

Warranty

The code comes with no warranty of any kind. I hope it'll be useful to you (it certainly is to me), but I make no guarantees regarding its functionality or otherwise.