▶ 展示 · 回索引

15-worked-example-g1589.html

<!doctype html><html lang="zh-Hant"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>KP16 15 Worked Example G1589</title>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css">
<style>
:root{--bg:#071521;--panel:#0f2637;--ink:#f7fbff;--muted:#a9bfd0}
*{box-sizing:border-box}html,body{margin:0;width:100%;height:100%;background:#02080d;color:var(--ink);font-family:Inter,"Noto Sans TC","Microsoft JhengHei",sans-serif}
.wrap{width:100vw;height:100vh;display:grid;place-items:center;background:radial-gradient(circle at 18% 0%,#10344d 0,#02080d 58%,#000 100%)}
.stage{position:relative;width:min(100vw,177.7778vh);height:min(56.25vw,100vh);aspect-ratio:16/9;background:var(--bg);overflow:hidden}
canvas{position:absolute;inset:0;width:100%;height:100%;touch-action:none}
#math-layer{position:absolute;left:0;top:0;width:1600px;height:900px;transform-origin:0 0;pointer-events:none}
.formula{position:absolute;transform:translateY(-50%);line-height:1.2}
.formula .katex-display{margin:0;text-align:inherit}
.formula .katex-display>.katex{display:inline-block;text-align:inherit;white-space:nowrap}
.hint{position:absolute;right:2.1%;top:1.9%;font-size:.8vw;color:#9ab4c7;background:#071521cc;border:1px solid #ffffff18;border-radius:999px;padding:.5em .75em;z-index:5}
.note{position:absolute;left:2.1%;bottom:2.2%;font-size:.68vw;color:#89a3b8;background:#071521b8;border:1px solid #ffffff12;border-radius:12px;padding:.4em .65em;z-index:5}
@media(max-width:900px){.hint,.note{font-size:1.4vw}}
</style>
</head><body><div class="wrap"><div class="stage" id="stage"><canvas id="c" width="1600" height="900"></canvas><div id="math-layer"></div><div class="hint">互動：點擊 / 拖曳 • Click / Drag</div></div></div>
<script src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js"></script>
<script>
/* ===== Shared helpers (Canvas 1600x900 logical space + KaTeX math layer) ===== */
const CW=1600,CH=900;
const c=document.getElementById('c'),ctx=c.getContext('2d');
const stage=document.getElementById('stage'),mathLayer=document.getElementById('math-layer');
const P={bg:'#071521',panel:'#0f2637',panel2:'#102c40',ink:'#f7fbff',muted:'#a9bfd0',cyan:'#4fd1c5',amber:'#f6c85f',coral:'#ff7b72',lime:'#8fd694',violet:'#b794f4',blue:'#63b3ed',grid:'#17384d'};
const FONT='Inter,"Noto Sans TC","Microsoft JhengHei","PingFang TC","Noto Sans CJK TC","WenQuanYi Zen Hei",sans-serif';
let zones=[],drag=null;
window.__boxes=[];
const REC=()=>window.__audit===true;

function reset(){zones=[];window.__boxes=[];ctx.clearRect(0,0,CW,CH);ctx.fillStyle=P.bg;ctx.fillRect(0,0,CW,CH);
  for(let x=0;x<CW;x+=80)line(x,0,x,CH,'#0b2434',1);for(let y=0;y<CH;y+=80)line(0,y,CW,y,'#0b2434',1)}
function line(x1,y1,x2,y2,color='#fff',lw=3,dash=[]){ctx.save();ctx.strokeStyle=color;ctx.lineWidth=lw;ctx.setLineDash(dash);ctx.beginPath();ctx.moveTo(x1,y1);ctx.lineTo(x2,y2);ctx.stroke();ctx.restore()}
function rr(x,y,w,h,r=20,fill=P.panel,stroke=null,lw=2){ctx.beginPath();ctx.roundRect(x,y,w,h,r);if(fill){ctx.fillStyle=fill;ctx.fill()}if(stroke){ctx.strokeStyle=stroke;ctx.lineWidth=lw;ctx.stroke()}}
function dot(x,y,r,color){ctx.fillStyle=color;ctx.beginPath();ctx.arc(x,y,r,0,Math.PI*2);ctx.fill()}
function setFont(size,weight){ctx.font=`${weight} ${size}px ${FONT}`}
function rec(x0,y0,x1,y1,label){if(REC())window.__boxes.push({x0,y0,x1,y1,label})}
function txt(t,x,y,size=30,color=P.ink,align='left',weight=700){
  t=String(t);ctx.fillStyle=color;setFont(size,weight);ctx.textAlign=align;ctx.textBaseline='middle';ctx.fillText(t,x,y);
  if(REC()){const w=ctx.measureText(t).width,l=align==='left'?x:align==='center'?x-w/2:x-w;rec(l,y-size*.55,l+w,y+size*.55,t.slice(0,24))}}
function wrap(t,x,y,maxw,lh=34,size=24,color=P.muted,weight=550,align='left'){
  t=String(t).replace(/\\n/g,'\n');setFont(size,weight);ctx.fillStyle=color;ctx.textBaseline='top';ctx.textAlign=align;
  const out=[];
  for(const para of t.split('\n')){
    const raw=para.match(/[一-鿿]|[^\s一-鿿　-〿＀-￯]+\s*|\s+|[　-〿＀-￯]/g)||[''];
    const toks=[];for(let i=0;i<raw.length;i++){if(/^[「『（《【“‘]$/.test(raw[i])&&i+1<raw.length){toks.push(raw[i]+raw[i+1]);i++}else toks.push(raw[i])}
    let ln='';
    for(const tk of toks){
      const q=ln+tk;
      const isPunct=/^[　-〿＀-￯]$/.test(tk);
      if(ctx.measureText(q.trimEnd()).width>maxw&&ln&&!isPunct){out.push(ln.trimEnd());ln=tk.trimStart()}else ln=q}
    out.push(ln.trimEnd());
  }
  let yy=y;
  for(const l of out){ctx.fillText(l,x,yy);
    if(REC()){const w=ctx.measureText(l).width,lx=align==='left'?x:align==='center'?x-w/2:x-w;rec(lx,yy,lx+w,yy+size*1.15,l.slice(0,24))}
    yy+=lh}
  return yy}
function wrapCenter(t,cx,y,maxw,lh=34,size=24,color=P.muted,weight=550){return wrap(t,cx,y,maxw,lh,size,color,weight,'center')}
function footer(n){txt('PR115 · Ch02 · KP-16  單純貝氏分類器 Naive Bayes Classifier',70,878,15,'#6f8da3','left',600);txt(`${n} / 15`,1530,878,15,'#6f8da3','right',700)}
function title(zh,en,no){txt(`${String(no).padStart(2,'0')}  ${zh}`,70,68,38,P.ink,'left',900);txt(en,72,111,21,P.cyan,'left',650);line(70,146,1530,146,P.grid,2);footer(no)}
function chip(t,x,y,w,color){rr(x,y,w,40,20,color+'20',color,2);txt(t,x+w/2,y+20,18,color,'center',800)}
function btn(label,x,y,w,h,onClick,active=false,color=P.cyan,size=19){rr(x,y,w,h,15,active?color+'28':'#ffffff0c',active?color:'#ffffff22',2);txt(label,x+w/2,y+h/2,size,active?color:P.ink,'center',800);zones.push({type:'button',x,y,w,h,onClick})}
function area(x,y,w,h,onClick){zones.push({type:'button',x,y,w,h,onClick})}
function slider(x,y,w,min,max,value,onChange,label,fmt=v=>v.toFixed(2),accent=P.amber){
  line(x,y,x+w,y,'#ffffff35',8);const t=(value-min)/(max-min),kx=x+t*w;line(x,y,kx,y,accent+'88',8);dot(kx,y,15,accent);
  txt(label,x,y-31,20,P.muted,'left',650);txt(fmt(value),x+w,y-31,22,accent,'right',850);
  zones.push({type:'slider',x:x-20,y:y-28,w:w+40,h:56,min,max,onChange})}
function arrow(x1,y1,x2,y2,color=P.cyan,lw=5){line(x1,y1,x2,y2,color,lw);const a=Math.atan2(y2-y1,x2-x1),s=14;ctx.fillStyle=color;ctx.beginPath();ctx.moveTo(x2,y2);ctx.lineTo(x2-s*Math.cos(a-.5),y2-s*Math.sin(a-.5));ctx.lineTo(x2-s*Math.cos(a+.5),y2-s*Math.sin(a+.5));ctx.closePath();ctx.fill()}
function card(x,y,w,h,color,active=true){rr(x,y,w,h,22,active?P.panel2:P.panel,active?color:'#ffffff14',3)}

function pos(e){const r=c.getBoundingClientRect();return{x:(e.clientX-r.left)*CW/r.width,y:(e.clientY-r.top)*CH/r.height}}
function sliderVal(z,p){const t=Math.max(0,Math.min(1,(p.x-(z.x+20))/(z.w-40)));return z.min+t*(z.max-z.min)}
c.addEventListener('pointerdown',e=>{const p=pos(e);
  for(let i=zones.length-1;i>=0;i--){const z=zones[i];
    if(p.x>=z.x&&p.x<=z.x+z.w&&p.y>=z.y&&p.y<=z.y+z.h){
      if(z.type==='button'){z.onClick(p);return}
      if(z.type==='slider'||z.type==='drag'){drag=z;z.onChange(sliderVal(z,p),p);return}}}});
c.addEventListener('pointermove',e=>{if(!drag)return;const p=pos(e);drag.onChange(sliderVal(drag,p),p)});
addEventListener('pointerup',()=>drag=null);
addEventListener('pointercancel',()=>drag=null);
window.__listZones=function(){return zones.map(function(z,i){return {i:i,type:z.type,x:z.x,y:z.y,w:z.w,h:z.h}})};
window.__clickZone=function(i){var z=zones[i];if(!z)return;if(z.type==='button'){z.onClick({x:z.x+z.w/2,y:z.y+z.h/2})}else if(z.type==='slider'){z.onChange((z.min+z.max)/2,{x:z.x+z.w/2,y:z.y+z.h/2})}};

const FM={};
function placeFormula(f){const s=f.el.style;s.width=f.w+'px';s.fontSize=f.size+'px';s.color=f.color;s.textAlign=f.align;
  let left=f.x+f.ox;if(f.align==='center')left-=f.w/2;else if(f.align==='right')left-=f.w;
  s.left=left+'px';s.top=(f.y+f.oy)+'px'}
function setTex(id,tex){const f=FM[id];if(f.cur===tex)return;f.cur=tex;
  if(window.katex)katex.render(tex,f.el,{displayMode:true,throwOnError:false,strict:'ignore'});else f.el.textContent=tex}
function addFormula(o){const el=document.createElement('div');el.className='formula';el.dataset.fid=o.id;mathLayer.appendChild(el);
  const f=Object.assign({el,align:'center',size:32,ox:0,oy:0,w:600,color:'#f7fbff'},o);FM[o.id]=f;placeFormula(f);setTex(o.id,o.tex);return f}
function moveFormula(id,o){Object.assign(FM[id],o);placeFormula(FM[id])}
function showF(ids){for(const k in FM)FM[k].el.style.display=ids.includes(k)?'block':'none'}
function syncMath(){const r=stage.getBoundingClientRect();mathLayer.style.transform=`scale(${r.width/CW},${r.height/CH})`}
new ResizeObserver(syncMath).observe(stage);addEventListener('resize',syncMath);syncMath();

function mapper(px,py,pw,ph,x0,x1,y0,y1){return{X:x=>px+(x-x0)/(x1-x0)*pw,Y:y=>py+ph-(y-y0)/(y1-y0)*ph,px,py,pw,ph,x0,x1,y0,y1}}
function axes(m,xticks,ytickVals,xfmt=v=>v,yfmt=v=>v.toFixed(2),xlabel=''){
  line(m.px,m.py+m.ph,m.px+m.pw,m.py+m.ph,'#ffffff55',2);line(m.px,m.py,m.px,m.py+m.ph,'#ffffff55',2);
  for(const v of ytickVals){const Y=m.Y(v);line(m.px,Y,m.px+m.pw,Y,'#ffffff12',1);txt(yfmt(v),m.px-12,Y,17,P.muted,'right',600)}
  for(const v of xticks){const X=m.X(v);line(X,m.py+m.ph,X,m.py+m.ph+8,'#ffffff55',2);txt(xfmt(v),X,m.py+m.ph+26,17,P.muted,'center',600)}
  if(xlabel)txt(xlabel,m.px+m.pw,m.py+m.ph+52,17,P.muted,'right',600)}
const rampAnim=(dur,fn)=>{const t0=performance.now();const tick=now=>{const t=Math.min(1,(now-t0)/dur);fn(1-Math.pow(1-t,3));if(t<1)requestAnimationFrame(tick)};requestAnimationFrame(tick)};
const SUPD={'0':'⁰','1':'¹','2':'²','3':'³','4':'⁴','5':'⁵','6':'⁶','7':'⁷','8':'⁸','9':'⁹','-':'⁻'};
const sup=n=>String(n).split('').map(ch=>SUPD[ch]||ch).join('');
function fmtInt(v){return v.toLocaleString('en-US')}
function fmtBig(v){return v>=1e6?(v/1e6).toFixed(2)+'M':fmtInt(v)}
const C1=P.blue, C2=P.coral; /* class omega_1 (blue) / omega_2 (coral) throughout this topic */
</script>
<script>
/* ===== Page script ===== */

const Wgiven=[1.792,-1.253,0.847], W0given=-1.050;
const NAMES=['x₁ 帶書','x₂ 戴眼鏡','x₃ 上課時間'];
let X=[1,0,1];
let step=4; /* how many of the 4 terms (w1x1,w2x2,w3x3,w0) are revealed; default fully revealed */

addFormula({id:'g',tex:String.raw`g(\boldsymbol{x})=\boldsymbol{w}^{T}\boldsymbol{x}+w_0=\sum_{i=1}^{3}w_i x_i+w_0`,x:800,y:196,w:1100,size:24,align:'center'});

function render(){
  reset();
  title('數值驗證：g(x) = 1.589 ⟹ 判為 ω₁','Worked Numeric Check: g(x) = 1.589 ⟹ Decide ω₁',15);

  /* ---------- given ---------- */
  rr(60,170,1480,120,22,P.panel,P.cyan,2);
  showF(['g']);
  txt(`已知 Given：x = (${X.join(', ')})ᵀ　w = (${Wgiven.join(', ')})　w₀ = ${W0given}`,90,262,16.5,P.ink,'left',750);

  /* ---------- stepwise terms ---------- */
  rr(60,306,1480,344,24,P.panel2,'#ffffff14',2);
  txt('逐項代入　Substitute term by term',90,334,18,P.ink,'left',800);
  btn('重播 Replay',1120,312,180,40,()=>{step=0;render()},step===0,P.coral,16);
  btn('下一步 Next',1316,312,220,40,()=>{step=Math.min(4,step+1);render()},false,P.lime,16);

  const rows=[
    {label:'w₁ × x₁', expr:`${Wgiven[0]} × ${X[0]}`, val: Wgiven[0]*X[0]},
    {label:'w₂ × x₂', expr:`${Wgiven[1]} × ${X[1]}`, val: Wgiven[1]*X[1]},
    {label:'w₃ × x₃', expr:`${Wgiven[2]} × ${X[2]}`, val: Wgiven[2]*X[2]},
    {label:'w₀ (常數 constant)', expr:`${W0given}`, val: W0given},
  ];
  const rowY0=372, rowH=66;
  let running=0;
  rows.forEach((r,i)=>{
    const y=rowY0+i*rowH;
    const revealed = i<step;
    rr(90,y,980,rowH-12,12,revealed?'#ffffff0c':'#ffffff06',revealed?(r.val>=0?P.lime:P.coral):'#ffffff14',2);
    txt(r.label,116,y+27,17,revealed?P.ink:'#5f7b8f','left',750);
    txt(revealed?`= ${r.expr} = ${r.val.toFixed(3)}`:'尚未顯示 not revealed yet',380,y+27,16,revealed?(r.val>=0?P.lime:P.coral):'#5f7b8f','left',650);
    if(revealed) running += r.val;
    const cumX=1120, cumW=420;
    rr(cumX,y,cumW,rowH-12,12,revealed?'#4fd1c514':'#ffffff06',revealed?P.cyan:'#ffffff14',2);
    txt(revealed?`累計 running sum = ${running.toFixed(3)}`:'—',cumX+20,y+27,16,revealed?P.cyan:'#5f7b8f','left',700);
  });

  /* ---------- decision ---------- */
  const gx = step===4 ? Wgiven.reduce((a,w,j)=>a+w*X[j],0)+W0given : null;
  const decided = gx!==null;
  const gcol = decided ? (gx>=0?C1:C2) : '#5f7b8f';
  rr(60,662,1480,110,24,decided?gcol+'1c':P.panel,gcol,2.5);
  txt(decided?`g(x) = ${gx.toFixed(3)}`:'g(x) = ?　(完成全部 4 步才會顯示 reveal all 4 steps)',90,696,28,gcol,'left',900);
  wrap(decided?(gx>=0?'g(x) ≥ 0 ⟹ 似然比 ≥ 1 ⟹ 判為 ω₁':'g(x) < 0 ⟹ 似然比 < 1 ⟹ 判為 ω₂'):'依序按「下一步」，逐項代入直到算出完整的 g(x)。',90,730,1420,24,16,P.ink,650);

  /* ---------- explore other x ---------- */
  rr(60,792,1480,54,20,P.panel,'#ffffff14',2);
  txt('試試其他 x：Try other bit patterns',90,819,16,P.muted,'left',700);
  const swX=[420,650,880];
  X.forEach((v,i)=>btn(`${NAMES[i]} = ${v}`,swX[i],798,210,42,()=>{X[i]=1-X[i];step=4;render()},true,v===1?P.lime:P.coral,16));
}
render();
</script></body></html>