import papaya.*;

PFont myfont;
PFont myboldfont;

JakeSlider samplemeanslider, confidenceslider, smallsampleslider, largesampleslider;
JakeButton leftarrow, rightarrow;

PImage PIeqn;
PImage smallleft;
PImage smallup;
PImage smalldown;
PImage smallright;

String[] names = {
  "Neo", "Batman", "Mr. Anderson", "Lisa Simpson", "Bart Simpson", "Homer Simpson", "Ted Mosby", "Robin Scherbatsky", "Spiderman", "Felicia", "Carol", "Samantha", "Nathan", "Morpheus"
};
String[] gender = {
  "He", "He", "He", "She", "He", "He", "He", "She", "He", "She", "She", "She", "He", "He"
};
String[] obj = {
  "male height", "female height", "male weight", "female weight", "cat length", "male salary", "cat speed", "dog weight"
};
float[] lower = {
  5.5, 5, 150, 100, 15, 40000, 20, 40
};
float[] upper = {
  6.5, 6, 200, 150, 20, 60000, 30, 70
};
String[] units = {
  "ft", "ft", "pounds", "pounds", "inches", "dollars", "mi/hr", "pounds"
};
String[] nouns = {
  "males", "females", "males", "females", "cats", "males", "cats", "dogs"
};

int[] samplesize = {10, 20, 51, 61, 91};
int[] confidence = { 80, 90, 95, 99};
float[][] ttable = {
  {
    1.3830, 1.8331, 2.2622, 3.2498
  }
  , {
    1.3277, 1.7291, 2.0930, 2.8609
  }
  , {
    1.2987, 1.6759, 2.0086, 2.6778
  }
  , {
    1.2958, 1.6707, 2.0003, 2.6603
  }
  , {
    1.2910, 1.6620, 1.9867, 2.6316
  }
};

float[] zvalues;
float leftCI = 0, rightCI = 0;

int samplesizeslidervalue;
int confidenceslidervalue;
float samplemeanslidervalue;

int[] digits = {1, 1, 3, 3, 2, 5, 2, 2};

int page = 1;
int numtemplates = 2;
String[] problemText = new String[numtemplates];

int namerand;
int objrand;
int sizerand;
int confidencerand;
float numrand;
String numrandstr;
float sdrand;
String sdrandstr;
String pagetext;
int temprand;

void setup()
{
  size(700, 500);
  smooth();

  myfont = loadFont("ArialMT-24.vlw");
  myboldfont = loadFont("Arial-BoldMT-24.vlw");

  PIeqn = loadImage("predicteqn.gif");
  smallleft = loadImage("leftbluesmall.jpg");
  smallup = loadImage("bluesmallup.jpg");
  smalldown = loadImage("smalldown.jpg");
  smallright = loadImage("rightbluesmall.jpg");

  PImage[] lefts = {loadImage("leftblue.jpg"), loadImage("leftpurple.jpg")};
  leftarrow = new JakeButton(30,415,lefts[1],lefts[0],lefts[0]);

  PImage[] rights = {loadImage("rightblue.jpg"), loadImage("rightpurple.jpg")};
  rightarrow = new JakeButton(615,415,rights[1],rights[0],rights[0]);

  zvalues = new float[201];
  float xloc = -4;

  for (int i = 0; i < 201; i++)
  {
    zvalues[i] = 1.0/sqrt(2.0*PI)*exp(-1.0*xloc*xloc/2.0);  
    xloc += .04;
  }

  generateRandom();

  float tempfloat = Float.parseFloat(numrandstr);
  float tempsd = Float.parseFloat(sdrandstr);
  samplemeanslider = new JakeSlider(390,350,100,30,tempfloat,tempfloat-tempsd/5, tempfloat+tempsd/5,false,color(71, 145, 255),color(2,52,77),myfont,10,digits[objrand],2); 
  samplemeanslider.setVisible(false);

  confidenceslider = new JakeSlider(220,350,100,30,confidence[confidencerand],80,99,true,color(71, 145, 255),color(2,52,77),myfont,10,2,0); 
  confidenceslider.setVisible(false);

  smallsampleslider = new JakeSlider(50,350,100,30,samplesize[sizerand],10,25,true,color(71, 145, 255),color(2,52,77),myfont,10,2,0); 
  smallsampleslider.setVisible(false);

  largesampleslider = new JakeSlider(50,350,100,30,samplesize[sizerand],30,100,true,color(71, 145, 255),color(2,52,77),myfont,10,2,0); 
  largesampleslider.setVisible(false);
}

void generateRandom()
{
  namerand = int(random(names.length));
  objrand = int(random(obj.length));
  sizerand = int(random(samplesize.length));
  confidencerand = int(random(confidence.length));
  numrand = random(lower[objrand], upper[objrand]);
  numrandstr = nf(numrand, digits[objrand], 2);
  sdrand = random(lower[objrand]/10, upper[objrand]/10);
  sdrandstr = nf(sdrand, digits[objrand]-1, 2);
  temprand = int(random(numtemplates));

  samplesizeslidervalue = samplesize[sizerand];
  confidenceslidervalue = confidence[confidencerand];
  float tempfloat = Float.parseFloat(numrandstr);
  samplemeanslidervalue = tempfloat;
}

void draw()
{
  background(255);
  fill(0);

  problemText[0] = names[namerand] + " is interested in studying " + obj[objrand] + 
    " in the US. " +  gender[namerand] + " sampled " + samplesize[sizerand] + " " + nouns[objrand] + 
    " at random and found a sample mean of " + numrandstr + " " + units[objrand] +  " and sample standard deviation of " + sdrandstr + " "  + units[objrand] + "." + 
    " Find the " + confidence[confidencerand] + "% prediction interval for a new observation of " + obj[objrand] + ".";

  problemText[1] = names[namerand] + " is performing a study on " + obj[objrand] + 
    " in France. " +  gender[namerand] + " collected a sample of " + samplesize[sizerand] + " " + nouns[objrand] + 
    " at random and found the mean of the sample to be " + numrandstr + " " + units[objrand] +  " and found the standard deviation of the sample to be " + sdrandstr + " "  + units[objrand] + "." + 
    " What is the " + confidence[confidencerand] + "% prediction interval for a new observation of " + obj[objrand] + "?";

  switch(page)
  {
  case 1:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step one: Identify the problem type and formula to use";
    drawStrings(pagetext, 30, 194, 25, "bold");
    pagetext = "The type of problem we have here is to find the prediction " +
      "interval for a new observation. We use the formula: ";
    image(PIeqn, 350-72, 295);
    drawStrings(pagetext, 80, 244, 25);

    leftarrow.setVisible(false);
    rightarrow.setVisible(true);
    break;

  case 2:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step two: Identify variables";
    drawStrings(pagetext, 30, 194, 25, "bold");
    pagetext = "We want to identify each variable in our formula:";   
    drawStrings(pagetext, 80, 244, 25);

    image(PIeqn, 350-72, 256);

    pagetext = "Ybar represents our sample mean. In this problem, the sample mean is " +  numrandstr 
      + "." + " S is our sample standard deviation, which is " + sdrandstr + "." + " Our sample size is represented by n, which is " 
      + samplesize[sizerand] + "." + " Lastly, we have the confidence level, given by the variable L, as " + confidence[confidencerand] + "%.";   

    drawStrings(pagetext, 80, 319, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 3:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step two continued: ";
    drawStrings(pagetext, 30, 194, 25, "bold");

    pagetext = "In our formula: ";
    drawStrings(pagetext, 80, 244, 25);

    image(PIeqn, 350-72, 248);

    pagetext = "The t with the subscript n - 1, (1 + L)/2 represents (1 + L)/2*100 percentile of the n - 1 t curve. In this case, " +
      "we have L = ." + confidence[confidencerand] + " and n = " + samplesize[sizerand] + " so we are looking for the " + 
      (confidence[confidencerand]+100)/2.0 + " percentile of the " + (samplesize[sizerand] - 1) + "th t curve. ";

    drawStrings(pagetext, 80, 319, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 4:
    drawStrings(problemText[temprand], 30, 44, 25);
    pagetext = "Step three: Find a percentile";
    drawStrings(pagetext, 30, 194, 25, "bold");

    float tempfloat = ((float)confidence[confidencerand]/100+1)/2.0;

    pagetext = "Use the table A.4 to the find the percentile of the t curve. Find " +
      "the " + (samplesize[sizerand] - 1) +"th row (sample size - 1) and the " + tempfloat + " column. This gives us the " +
      (confidence[confidencerand]+100)/2.0 + " percentile as " +  nf(ttable[sizerand][confidencerand], 1, 4) + " (ie " +  (confidence[confidencerand]+100)/2.0 +
      "% of the area is to the left of this point).";

    drawStrings(pagetext, 80, 244, 25); 
    pagetext = nf(tempfloat, 1, 4);
    drawStrings(pagetext, 230, 294+45, 25);   
    image(smalldown, 245, 294+50);
    if (samplesize[sizerand] == 10) 
    { 
      pagetext = "9";
      drawStrings(pagetext, 178, 396, 25);
    }
    if (samplesize[sizerand] >  10)
    { 
      pagetext = nf(samplesize[sizerand]-1, 2);
      drawStrings(pagetext, 167, 396, 25);
    }
    image(smallright, 195, 372);
    pagetext = nf(ttable[sizerand][confidencerand], 1, 4);
    drawStrings(pagetext, 230, 395, 25);
    drawBellcurve(ttable[sizerand][confidencerand], 400, 308, 200, 88);

    //noFill();
    //rect(130,294+31,400,70);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 5:
    drawStrings(problemText[temprand], 30, 44, 25);

    pagetext = "Step four: Plug in values and interpret result";
    drawStrings(pagetext, 30, 194, 25, "bold");

    pagetext = "Now, plug in your values for the variables into: ";
    drawStrings(pagetext, 80, 244, 25);

    image(PIeqn, 350-72, 258);

    pagetext = "Plugging in, we get " + numrandstr + " plus or minus " + sdrandstr + " times the the square root of (1.0 + 1.0 divided by " + samplesize[sizerand] + ") times " +
      nf(ttable[sizerand][confidencerand], 1, 4)+".";

    leftCI = Float.parseFloat(numrandstr) - Float.parseFloat(sdrandstr)*sqrt(1.0+1.0/(float)samplesize[sizerand])*ttable[sizerand][confidencerand];
    rightCI = Float.parseFloat(numrandstr) + Float.parseFloat(sdrandstr)*sqrt(1.0+1.0/(float)samplesize[sizerand])*ttable[sizerand][confidencerand];

    pagetext += " This gives us the interval (" + nf(leftCI, digits[objrand], 2) + ", " + nf(rightCI, digits[objrand], 2)+ "). " + names[namerand] + " is " + 
      confidence[confidencerand] + "% confident that a new observation of " + obj[objrand] + " will be between " + nf(leftCI, digits[objrand], 2) + " " + units[objrand] +
      " and " + nf(rightCI, digits[objrand], 2) + " " + units[objrand] + ".";

    drawStrings(pagetext, 80, 319, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 6:
    drawStrings(problemText[temprand], 30, 44, 25);

    pagetext = "Step five: State your assumptions";
    drawStrings(pagetext, 30, 194, 25, "bold");

    pagetext = "In creating our prediction interval, we have assumed the C + E model is valid, that the " +
      "population variance is unknown, and that epsilon is from a normal density. ";

    drawStrings(pagetext, 80, 244, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  case 7:
    drawStrings(problemText[temprand], 30, 44, 25); 
    pagetext = "Exploring the prediction interval: ";
    drawStrings(pagetext, 30, 194, 25, "bold"); 

    pagetext = "What is the effect of the sample size on the prediction interval? What are the effects of the confidence level and sample mean? ";
    drawStrings(pagetext, 50, 244, 25); 

    pagetext = "Sample size";
    drawStrings(pagetext, 50, 294+25, 25); 

    pagetext = "Confidence Level";
    drawStrings(pagetext, 205, 294+25, 25); 

    pagetext = "Sample mean";
    drawStrings(pagetext, 385, 294+25, 25); 

    pagetext = "Your interval:";
    drawStrings(pagetext, 540, 294+25, 25); 

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);

    confidenceslider.setVisible(true);
    samplemeanslider.setVisible(true);

    float leftedge, rightedge;
    tempfloat = Float.parseFloat(numrandstr);
    float tempsd = Float.parseFloat(sdrandstr);

    if (samplesize[sizerand] < 30)
    {
      smallsampleslider.setVisible(true);
      float percentile = (float)Probability.tinv((1.0 + (float)confidenceslidervalue/100.0)/2.0, samplesizeslidervalue-1);
      leftCI = samplemeanslidervalue - tempsd*sqrt(1.0+1.0/(float)samplesizeslidervalue)*percentile;
      rightCI = samplemeanslidervalue + tempsd*sqrt(1.0+1.0/(float)samplesizeslidervalue)*percentile;
      leftedge = map(leftCI, tempfloat-tempsd/5-tempsd*sqrt(1.1)*3.25, tempfloat+tempsd/5+tempsd*sqrt(1.1)*3.25, 540, 640);
      rightedge = map(rightCI, tempfloat-tempsd/5-tempsd*sqrt(1.1)*3.25, tempfloat+tempsd/5+tempsd*sqrt(1.1)*3.25, 540, 640);
    }
    else
    {
      largesampleslider.setVisible(true);
      float percentile = (float)Probability.tinv((1.0 + (float)confidenceslidervalue/100.0)/2.0, samplesizeslidervalue-1);
      leftCI = samplemeanslidervalue - tempsd*sqrt(1.0+1.0/(float)samplesizeslidervalue)*percentile;
      rightCI = samplemeanslidervalue + tempsd*sqrt(1.0+1.0/(float)samplesizeslidervalue)*percentile;
      leftedge = map(leftCI, tempfloat-tempsd/5-tempsd*sqrt(1.0333)*2.76, tempfloat+tempsd/5+tempsd*sqrt(1.0333)*2.76, 540, 640);
      rightedge = map(rightCI, tempfloat-tempsd/5-tempsd*sqrt(1.0333)*2.76, tempfloat+tempsd/5+tempsd*sqrt(1.0333)*2.76, 540, 640);
    }

    pagetext = "("+nf(leftCI, digits[objrand], 2)+", "+nf(rightCI, digits[objrand], 2)+")";
    drawStrings(pagetext, 540, 294+100-5, 25); 

    fill(71, 145, 255);
    rect(leftedge, 294+57, rightedge-leftedge, 4);

    break;
  case 8:
    drawStrings(problemText[temprand], 30, 44, 25); 
    pagetext = "Exploring the prediction interval continued: ";
    drawStrings(pagetext, 30, 194, 25, "bold"); 

    pagetext = "The sample mean is the midpoint/center of the prediction interval. Varying it will move the prediction interval around. The sample size " +
      "alters the width of the prediction interval. As you increase your sample size, the width gets smaller. Lastly, if you increase your level of confidence, " +
      "the width of the prediction interval will increase. ";
    drawStrings(pagetext, 30, 194+50, 25); 

    pagetext = "To try another problem, click the right arrow.";
    drawStrings(pagetext, 30, 194+200, 25);

    leftarrow.setVisible(true);
    rightarrow.setVisible(true);
    break;
  }

  samplemeanslider.updateSlider();
  samplemeanslider.drawSlider();
  
  samplemeanslidervalue = samplemeanslider.getValue();
  samplemeanslidervalue = round(samplemeanslidervalue*100.0)/100.0;

  confidenceslider.updateSlider();
  confidenceslider.drawSlider();
  
  confidenceslidervalue = (int)confidenceslider.getValue();

  smallsampleslider.updateSlider();
  smallsampleslider.drawSlider();
  
  largesampleslider.updateSlider();
  largesampleslider.drawSlider();

  if (samplesize[sizerand] < 30) 
  {
    samplesizeslidervalue = (int)smallsampleslider.getValue();
  }
  else
  {
    samplesizeslidervalue = (int)largesampleslider.getValue();
  }
  
  leftarrow.updateButton();
  leftarrow.drawButton();

  if (leftarrow.clicked)
  {
    if (samplesize[sizerand] < 30) smallsampleslider.setVisible(false);
    else largesampleslider.setVisible(false);
    confidenceslider.setVisible(false);
    samplemeanslider.setVisible(false);

    page--;
  }
  
  rightarrow.updateButton();
  rightarrow.drawButton();
  
  if(rightarrow.clicked)
  {
    if (samplesize[sizerand] < 30) smallsampleslider.setVisible(false);
    else largesampleslider.setVisible(false);
    confidenceslider.setVisible(false);
    samplemeanslider.setVisible(false);

    if (page == 8) 
    {
      page = 0; 
      generateRandom();
      float tempfloat = Float.parseFloat(numrandstr);
      float tempsd = Float.parseFloat(sdrandstr);
      confidenceslider.setValue(confidenceslidervalue);
      samplemeanslider.setRange(tempfloat-tempsd/5, tempfloat+tempsd/5);
      samplemeanslider.setValue(tempfloat);
      samplemeanslider.setDigits(digits[objrand],2);
      smallsampleslider.setValue(samplesize[sizerand]);
      largesampleslider.setValue(samplesize[sizerand]);
    }
    if (page != 8) page++;
  }

}

void drawStrings(String astring, int startx, int starty, int yspacing)
{
  drawStrings(astring, startx, starty, yspacing, "plain");
}

void drawStrings(String astring, int startx, int starty, int yspacing, String boldtype)
{
  String[] theTokens = splitTokens(astring, " ");
  int x = startx;
  int y = starty;

  if (boldtype.equals("plain"))
    textFont(myfont, 18);
  else
    textFont(myboldfont, 18);

  for (int words = 0; words < theTokens.length; words++)
  {
    String currentword = theTokens[words];
    float wordwidth = textWidth(currentword + " ");
    if (x + wordwidth > 675)
    { 
      x = startx;
      y += yspacing;
    }
    text(currentword, x, y);
    x += wordwidth;
  }
}

void drawBellcurve(float loc, int xstart, int ystart, int bwidth, int bheight)
{
  int index = round(map(loc, -4, 4, 0, 200));
  float xscreen, yscreen;
  float xloc = -4.0;

  fill(255, 0, 0);
  beginShape();
  for (int i = 10; i <= index; i++)
  {
    xscreen = map(xloc, -4, 4, xstart, xstart+bwidth);
    yscreen = map(zvalues[i], 0, 0.5, ystart+bheight, ystart);
    vertex(xscreen, yscreen);
    xloc += .04;
  }
  xloc-=.04;
  xscreen = map(xloc, -4, 4, xstart, xstart+bwidth);
  yscreen = map(zvalues[0], 0, 0.5, ystart+bheight, ystart);
  vertex(xscreen, yscreen);
  endShape(CLOSE);

  float saveloc = xloc;

  fill(255, 255, 255);
  beginShape();
  for (int i = index; i < 191; i++)
  {
    xscreen = map(xloc, -4, 4, xstart, xstart+bwidth);
    yscreen = map(zvalues[i], 0, 0.5, ystart+bheight, ystart);
    vertex(xscreen, yscreen);
    xloc += .04;
  }
  xscreen = map(saveloc, -4, 4, xstart, xstart+bwidth);
  yscreen = map(zvalues[0], 0, 0.5, ystart+bheight, ystart);
  vertex(xscreen, yscreen);
  endShape(CLOSE);
}