Curve Fitting

curve-fitting.markdown

Curve Fitting

A Pen by Jaegyeom Kim on CodePen.

License.

script.js

let theta = 0.0; // Start angle at 0
let dx=0.0001; // Value for incrementing x
let noise = [];
let t= [];
let y = [];
let weight = [];
let regulated_weight = [];
let target = [];
let diff = [];
let N = 0; // size of point
let M = 0; // size of weight
let C = 0; // const of eq
let error = 0;
let lambda = 0;
function setup() {
  createCanvas(600, 500);
  
  noiseSlider = createSlider(1, 100,50,1);
  noiseSlider.position(0,height+10);
  noiseSlider.input(ChangeNoise);
  noiseButton = createButton('make noise');
  noiseButton.mousePressed(MakeNoise);
  noiseButton.position(noiseSlider.x + noiseSlider.width,noiseSlider.y)
  noiseDisplayer = createP()
  noiseDisplayer.position(noiseSlider.x,noiseSlider.y);
  N = noiseSlider.value();
  noiseDisplayer.html('N = '+noiseSlider.value());
  
  fittingSlider = createSlider(1, 10,5,1);
  fittingSlider.input(ChangeFitting);
  M = fittingSlider.value();
  fittingSlider.position(noiseButton.x + noiseButton.width,noiseButton.y);
  fittingButton = createButton('Fitting');
  fittingButton.position(fittingSlider.x + fittingSlider.width,fittingSlider.y)
  fittingButton.mousePressed(Fitting);
  fittingDisplayer = createP();
  fittingDisplayer.position(fittingSlider.x,fittingSlider.y);
  fittingDisplayer.html('M = '+fittingSlider.value());
  
  regularizationSlider = createSlider(-30, 0,-15,1);
  regularizationSlider.input(ChangeLambda);
  lambda = regularizationSlider.value();
  regularizationSlider.position(fittingButton.x + fittingButton.width,fittingButton.y);
  regularizationButton = createButton('regularization');
  regularizationButton.position(regularizationSlider.x +regularizationSlider.width,regularizationSlider.y)
  regularizationButton.mousePressed(RegularizationFitting);
  regularizationDisplayer = createP();
  regularizationDisplayer.position(regularizationSlider.x,regularizationSlider.y);
  regularizationDisplayer.html('ln(Lambda) = '+regularizationSlider.value());
  
 
}

function draw() {
  background(0);
  translate(50,height/2);
  calcWave();
  drawNoise();
  drawFitting();
  drawRegulatedFitting();
}

function drawNoise(){
  strokeWeight(3);
  stroke(0,120,0);
  noFill();
  for (let v of noise) {
    ellipse(v.x * 500,v.y * 150,10);
  }
}

function drawFitting(){
  let x = 0;
  strokeWeight(3);
  stroke(255,0,0);
  beginShape();
  noFill();
  while (x<=1) {
    let y = 0;
    for(let i =0;i<=M;i++){
      y+= weight[i]*pow(x,i);
    }
    vertex(x*500, 150*y);
    x += dx;
  }
  endShape();
}

function drawRegulatedFitting(){
  let x = 0;
  strokeWeight(3);
  stroke(255,100,100);
  beginShape();
  noFill();
  while (x<=1) {
    let y = 0;
    for(let i =0;i<=M;i++){
      y+= regulated_weight[i]*pow(x,i);
    }
    vertex(x*500, 150*y);
    x += dx;
  }
  endShape();
}

function calcWave() {
  let x = 0;
  strokeWeight(3);
  stroke(255);
  beginShape();
  noFill();
  while (x<=1) {
    vertex(x*500, 150*sin(2*PI*x));
    x += dx;
  }
  endShape();
}

function MakeNoise() {
  noise = [];
  target=[];
  N = noiseSlider.value();
  for(let i =0;i<=N;i++){
    x = i/N;
    let t = createVector(x,sin(2*PI*x) + random(-0.4,0.4));
    noise.push(t);
    target.push(t.y);
  }
  
}


function Fitting() {
 M = fittingSlider.value()
  error=0;
  let X=[];
  for(let i =0;i<=N;i++){
    x = i/N;
    let temp = [];
    for(let j = 0;j<=M;j++){
      temp.push(pow(x,j));
    }
    X.push(temp);
  }
  weight = math.multiply(math.multiply(math.inv(math.multiply(math.transpose(X),X)),math.transpose(X)),target)
}

function RegularizationFitting() {
  M = fittingSlider.value()
  lambda = Math.pow(Math.E,regularizationSlider.value())
  let X=[];
  for(let i =0;i<=N;i++){
    x = i/N;
    let temp = [];
    for(let j = 0;j<=M;j++){
      temp.push(pow(x,j));
    }
    X.push(temp);
  }
  Lambda = math.multiply(math.identity(M+1),lambda);
  regulated_weight = math.multiply(math.multiply(math.inv(math.add(math.multiply(math.transpose(X),X),Lambda)),math.transpose(X)),target)["_data"];
}

function ChangeFitting(){
  fittingDisplayer.html('M = '+fittingSlider.value());
}

function ChangeNoise(){
  noiseDisplayer.html('N = '+noiseSlider.value());
}

function ChangeLambda(){
  regularizationDisplayer.html('ln(Lambda) = '+regularizationSlider.value());
}

function normalDistribution(x,simga,mu){
  let result = 1/math.sqrt(2*math.PI*(sigma*sigma))*
math.pow(math.E,(-1/(2*sigma*sigma)*(x-mu)*(x-mu)))
  return result;
}

scripts

<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/1.4.0/p5.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/9.4.4/math.js"></script>