Please write a program that can do regularized linear model regression (polynomial basis) and visualization.
You should do it by both LSE and Newton’s method. Input parameters:
1. the path and name of a file which consists of data points (comma seperated: x,y):
2. the number of polynomial bases n.
3. lambda (only for LSE case)
Program Behavior: For example, if the number of bases is set to 3, it means that the program is going to find a curve that best fits the data points by
Required functions: a. For LSE:
- Use LU decomposition to find the inverse of , Gauss-Jordan elimination won’t be accepted.(A is the design matrix).
- Print out the equation of the best fitting line and the error.
b. For Newton’s method:
1. Please use the method mentioned in the lesson.
2. Print out the equation of the best fitting line and the error, and compare to LSE. c. For visualization:
- Please visualize the data points which are the input of program, and the best fitting curve.
- It’s free to use any existing package.
NOTE:
Use whatever programming language you prefer.
You should use as few functions from any library as possible. That would be great if you implement all detail operations (like matrix operations) by yourself.
Time complexity is not what we care for now, but if you like to improve it in that regard,
1,12 122,34 -12,323 ...
it is always good for you.
Grading policy
You must implement matrix inverse operation by yourself. Please do not use the built in package or you’ll not get 100.
Sample input & output (for reference only)
Input: A file (here shows the content of the file)
$ cat testfile.txt -5.0,51.76405234596766 -4.795918367346939,45.42306433039972 -4.591836734693878,41.274448104888755 -3.979591836734694,26.636216497466364 -3.571428571428571,20.256806057008426 -2.9591836734693877,11.618429243797276 -2.7551020408163263,10.450525068812203 -1.7346938775510203,1.8480982318414874 -1.3265306122448979,-1.0405349639051173 -0.9183673469387754,-4.614630798757861 -0.7142857142857144,-1.3871977310902517 -0.3061224489795915,-1.9916444039966117 0.1020408163265305,-0.912924608376358 0.7142857142857144,6.63482003068499 1.1224489795918373,9.546867459016372 1.7346938775510203,15.72016146597016 1.9387755102040813,20.62251683859554 2.5510204081632653,33.48059725819715 2.959183673469388,40.76391965675495 3.979591836734695,66.8997605629381 4.387755102040817,78.44316465660981 4.591836734693878,86.99156782355371 5.0,99.78725971978604
Output
Case1:n=2, =0
LSE: Fitting line: 4.43295031008X^1 + 29.3064047061 Total error: 16335.123165
Newton's Method: Fitting line: 4.43295031008X^1 + 29.3064047061 Total error: 16335.123165
Case2:n=3, =0
LSE: Fitting line: 3.02385339349X^2 + 4.90619026386X^1
-0.231401756088 Total error: 26.5599594993
Newton's Method: Fitting line: 3.02385339349X^2 + 4.90619026386X^1
-0.231401756088 Total error: 26.5599594993
Case3:n=3, =10000
LSE: Fitting line: 0.8345332827X^2 + 0.0931481983192X^1
+ 0.0469506992735 Total error: 22649.738493
Newton's Method: Fitting line: 3.02385339349X^2 + 4.90619026386X^1
-0.231401756088 Total error: 26.5599594993
