/**
 * PI 
 * Forms prediction intervals
 */

PFont fontA;
int level = 95;
int samplesize = 30;
boolean oversampleleftarrow = false;
boolean oversamplerightarrow = false;
boolean overlevelleftarrow = false;
boolean overlevelrightarrow = false;
boolean getSample = false;
String meanstr = "";
String sdstr = "";
String PIstr = "";
String predstr = "";
int[] x1 = new int[1000];
int[] x2 = new int[1000];
int[] xpred = new int[1000];
float[] avvec = new float[1000];
float[] sdvec = new float[1000];
float[] lvec = new float[1000];
float[] rvec = new float[1000];
float[] predvec = new float[1000];
int[] out = new int[1000];

float[][] ttable = { {1.173864, 1.170346, 1.167743, 1.165740, 1.164151, 1.162859, 1.161788, 1.160886, 1.160116, 1.159451, 1.158871, 1.158360, 1.157907, 1.157502},
  {1.311434, 1.306952, 1.303639, 1.301090, 1.299069, 1.297426, 1.296066, 1.294920, 1.293942, 1.293097, 1.292360, 1.291711, 1.291136, 1.290623},
  {1.478705, 1.472810, 1.468458, 1.465112, 1.462460, 1.460306, 1.458522, 1.457020, 1.455738, 1.454632, 1.453666, 1.452817, 1.452064, 1.451392},
  {1.699127, 1.690924, 1.684875, 1.680230, 1.676551, 1.673565, 1.671093, 1.669013, 1.667239, 1.665707, 1.664371, 1.663197, 1.662155, 1.661226},
  {2.045230, 2.032245, 2.022691, 2.015368, 2.009575, 2.004879, 2.000995, 1.997730, 1.994945, 1.992543, 1.990450, 1.988610, 1.986979, 1.985523}};

int count = 0;

void setup()
{
  size(700,450);
  smooth();
  fontA = loadFont("ArialMT-48.vlw");
  textFont(fontA, 30);
  SampleMe();
}

void draw()
{
  float yupper, ylower;
  background(200);
  strokeWeight(3);
  fill(0);
  text("Confidence Level",23,345);
  String tempstr = "0."+level;
  text(tempstr,290,345);
  triangle(270,333,280,343,280,323);
  triangle(368,333,358,343,358,323);
  text("Sample Size",420,345);
  text(str(samplesize),620,345);
  triangle(600,333,610,343,610,323);
  triangle(672,333,662,343,662,323);

  fill(255);
  rect(290,375,120,45,10);
  fill(0);
  text("Sample",300,408);
  ellipseMode(CENTER);
  
  fill(0,0,0);
  for (int i = 0; i < 50; i++)
  {
   stroke(0);
   line(x1[i],52+5*i,x2[i],52+5*i);
      if(out[i] == 0) 
      {
       stroke(0); 
      }
      else 
      {
        stroke(255,0,0);
      }
   ellipse(xpred[i],52+5*i,4,4);
  }
  
  stroke(0);
  
  textFont(fontA, 24);
  text("Count: " + count, 575,30);
  
  int mx = mouseX;
  int my = mouseY;
  
  meanstr = "";
  sdstr = "";
  PIstr = "";
  predstr = "";
  boolean bubble = false;
  
  for (int i = 0; i < 50; i++)
  {
   yupper = 52+5*i-1;
   ylower = 52+5*i+1;
   if (mx >= x1[i] && mx <= x2[i] && my >= yupper && my <= ylower)
   {
     meanstr = nf(avvec[i],1,3);
     sdstr = nf(sdvec[i],1,3);
     PIstr = "("+nf(lvec[i],1,3)+","+nf(rvec[i],1,3)+")";
     predstr = nf(predvec[i],1,3);
     
     if (mx <= 495)
     {
       fill(255);
       rect(mx+10,ylower+10,190,90,10);
       textFont(fontA,18);
       fill(0);
       text("Sample Mean: " + meanstr,mx+20, ylower+30);
       text("SD: " + sdstr,mx+20, ylower+50);
       text("PI: " + PIstr,mx+20, ylower+70);
       text("New obs: " + predstr,mx+20,ylower+90);
     }
     else
     {
       fill(255);
       rect(mx-10-190,ylower+10,190,90,10);
       textFont(fontA, 18);
       fill(0);
       text("Sample Mean: " + meanstr,mx-190, ylower+30);
       text("SD: " + sdstr,mx-190, ylower+50);
       text("PI: " + PIstr,mx-190, ylower+70);
       text("New obs: " + predstr,mx-190,ylower+90);
      }
     bubble = true;
     break;
   }  
  }

  if (bubble == false)
  {
  for (int i = 0; i < 50; i++)
  {
   yupper = 52+5*i-2;
   ylower = 52+5*i+2;
   if (mx >= (xpred[i]-2) && mx <= (xpred[i]+2) && my >= yupper && my <= ylower)
   {
     meanstr = nf(avvec[i],1,3);
     sdstr = nf(sdvec[i],1,3);
     PIstr = "("+nf(lvec[i],1,3)+","+nf(rvec[i],1,3)+")";
     predstr = nf(predvec[i],1,3);
     
     if (mx <= 495)
     {
       fill(255);
       rect(mx+10,ylower+10,190,90,10);
       textFont(fontA,18);
       fill(0);
       text("Sample Mean: " + meanstr,mx+20, ylower+30);
       text("SD: " + sdstr,mx+20, ylower+50);
       text("PI: " + PIstr,mx+20, ylower+70);
       text("New obs: " + predstr,mx+20,ylower+90);
     }
     else
     {
       fill(255);
       rect(mx-10-190,ylower+10,190,90,10);
       textFont(fontA, 18);
       fill(0);
       text("Sample Mean: " + meanstr,mx-190, ylower+30);
       text("SD: " + sdstr,mx-190, ylower+50);
       text("PI: " + PIstr,mx-190, ylower+70);
       text("New obs: " + predstr,mx-190,ylower+90);
      }
     break;
   }  
  }
  }
  
  textFont(fontA, 30);
}

void mousePressed()
{
  oversampleleftarrow = false;
  oversamplerightarrow = false;
  overlevelleftarrow = false;
  overlevelrightarrow = false;
  getSample = false;
  if (mouseX >= 270 && mouseX <= 280 && mouseY >= 323 && mouseY <= 343) overlevelleftarrow = true;
  if (mouseX >= 358 && mouseX <= 368 && mouseY >= 323 && mouseY <= 343) overlevelrightarrow = true;
  if (mouseX >= 600 && mouseX <= 610 && mouseY >= 323 && mouseY <= 343) oversampleleftarrow = true;
  if (mouseX >= 662 && mouseX <= 672 && mouseY >= 323 && mouseY <= 343) oversamplerightarrow = true;  
  if (mouseX >= 290 && mouseX <= 410 && mouseY >= 375 && mouseY <= 420) getSample=true;
 
  if (overlevelleftarrow) level -= 5;
  if (overlevelrightarrow) level += 5;
  if (level > 95) level = 95;
  if (level < 75) level = 75;
  if (oversampleleftarrow) samplesize -= 5;
  if (oversamplerightarrow) samplesize += 5;  
  if (samplesize < 30) samplesize = 30;
  if (samplesize > 95) samplesize = 95;
  
  if (getSample)
  {
    SampleMe();
  }
}

void SampleMe()
{
  float[] avec= new float[samplesize];
  float[] temppred = new float[1];
  float sum, sd, var,av,tempx,tempx2;
  int tx, ty;
  count = 0;

  for (int j = 0; j < 1000; j++)
  {
     getNormal(samplesize,avec);
     getNormal(1,temppred);
     predvec[j] = temppred[0];
     
     sum = 0;
     for (int i = 0; i < samplesize; i++) sum += avec[i];
     av = sum/samplesize;
     avvec[j] = av;
     sum = 0;
     for (int i = 0; i < samplesize; i++) sum += pow(avec[i]-av,2);     
     var = sum/(samplesize - 1);
     sd = sqrt(var);
     sdvec[j] = sd;
     
     tx = (level-75)/5;
     ty = (samplesize-30)/5; 
      
     tempx = av - sd*sqrt(1.0+1.0/float(samplesize))*ttable[tx][ty];     
     tempx2 = av + sd*sqrt(1.0+1.0/float(samplesize))*ttable[tx][ty];  
    
     lvec[j] = tempx;
     rvec[j] = tempx2;
  
     x1[j] = int((tempx-7)*700/7+50);
     x2[j] = int((tempx2-7)*700/7+50);
     xpred[j] = int((temppred[0]-7)*700/7+50);
  
      if (tempx < temppred[0] && tempx2 > temppred[0]) 
      { 
       count++;
       out[j] = 0;
      }
      else
      {
        out[j] = 1;
      }
    }
}

void getNormal(int number, float[] zvec)
{
  float uone ;
  float utwo ;
  for (int i = 0; i < number; i++)
  {
   uone = random(0,1);
   utwo = random(0,1);
   zvec[i] = sqrt(-2*log(uone))*cos(2*PI*utwo)*1+10;
  }
}