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plane.html
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<html>
<head>
<meta charset="UTF-8">
<!--link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.1.1/css/bootstrap.min.css" integrity="sha384-WskhaSGFgHYWDcbwN70/dfYBj47jz9qbsMId/iRN3ewGhXQFZCSftd1LZCfmhktB" crossorigin="anonymous"-->
<link rel="stylesheet" type="text/css" href="style/bootstrap.min.css"/>
<link rel="stylesheet" type="text/css" href="style/style.css"/>
<link href="http://cdn.jsdelivr.net/gh/joungkyun/font-d2coding/d2coding.css" rel="stylesheet" type="text/css">
<style>
.relative3 {
position: relative;
top: -120px;
left: 60px;
}
</style>
</head>
<body>
<div class="container" style="border:0px solid #FF0000;">
<div class="row">
<div class="col-6" style="border:0px solid #FF0000;margin-top:5px;">
<div class="card" style="border:1px solid #CCCCCC;margin-top:5px;">
<div class="card-body">
<h4 class="card-title func-title">f(x,y) = ax + by + c</h4>
<div id="graph1" style="height:680px;border:0px solid #0000FF;margin-top:10px;"></div>
</div>
</div>
<div class="relative3">
<div class="form-group">
<div class="custom-control custom-switch">
<input type="checkbox" class="custom-control-input" id="check-opacity">
<label class="custom-control-label" for="check-opacity">Opacity</label>
</div>
<div class="custom-control custom-switch">
<input type="checkbox" class="custom-control-input" id="check-samples">
<label class="custom-control-label" for="check-samples">Sample</label>
</div>
</div>
<!-- -5,-4,-3,-2,-1,0,1,2,3,4,5-->
<div class="form-group">
<label for="xy-plane" class="form-label">f(x,y)=const.</label>
<input type="range" class="form-range" min="-3" max="3" step="1" value="0" id="xy-plane">
</div>
<div class="form-group">
<button type="button" class="btn btn-primary btn-sm" id="learn">Learn</button>
<button type="button" class="btn btn-danger btn-sm" id="stop">Stop</button>
</div>
</div>
</div>
<div class="col-6" style="border:0px solid #FF0000;margin-top:5px;">
<div class="row">
<div class="col-12" style="margin:0px;border:0px solid #AABB00;">
<div class="card" style="border:1px solid #CCCCCC;margin-top:5px;">
<div class="card-body">
<h4 class="card-title func-title">ax + by + c = <span id="fc_value">0</span></h4>
<div id="graph-dx" style="height:400px;border:0px solid #0000FF;margin-top:10px;"></div>
</div>
</div>
</div>
</div>
<div class="row">
<div class="col-12" style="margin:0px;border:0px solid #AABB00;">
<form class="customizing">
<div class="card" style="border:0px solid #FF0000;margin-top:5px;">
<div class="card-body">
<h4 class="card-title func-title-small">a = <span id="coef_a_value"></span></h4>
<input type="range" min="-100" max="100" value="0" class="slider" id="coef_a" style="width:100%;">
</div>
</div>
<div class="card" style="border:0px solid #FF0000;margin-top:5px;">
<div class="card-body">
<h4 class="card-title func-title-small">b = <span id="coef_b_value"></span></h4>
<input type="range" min="-100" max="100" value="0" class="slider" id="coef_b" style="width:100%;">
</div>
</div>
<div class="card" style="border:0px solid #FF0000;margin-top:5px;">
<div class="card-body">
<h4 class="card-title func-title-small">c = <span id="coef_c_value"></span></h4>
<input type="range" min="-200" max="200" value="0" class="slider" id="coef_c" style="width:100%;">
</div>
</div>
</form>
</div>
</div>
</div>
</div>
</div>
<script type="text/javascript" src="https://code.jquery.com/jquery-2.1.4.min.js"></script>
<script type="text/javascript" src="https://cdn.plot.ly/plotly-1.43.2.min.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML"></script>
<script>
if (!String.prototype.format) {
String.prototype.format = function() {
var args = arguments;
return this.replace(/{(\d+)}/g, function(match, number) {
return typeof args[number] != 'undefined'
? args[number]
: match
;
});
};
}
/*
* numpy.linspace() 함수의 구현
* https://gist.github.com/joates/6584908
*/
var linspace = function(a, b, n) {
if(typeof n === "undefined") n = Math.max(Math.round(b-a)+1,1);
if(n<2) { return n===1 ? [a] : []; }
var i,ret = Array(n);
n--;
for(i=n; i>=0; i--) { ret[i] = (i*b+(n-i)*a)/n; }
return ret;
}
/*
* cost : function
*
*/
var cost = function(x1, x2, params = [2, 1, 0]) {
/******************************************
* default function
******************************************/
var a = params[0];
var b = params[1];
var c = params[2];
return a*x1 + b*x2 + c;
/******************************************
* user define function
******************************************/
// return x1*x2
}
/*
* calc. surface function value Z for drawing cost function
*/
var draw_surface = function(f, X, Y, params) {
var i, j;
//console.log(params);
var grid_size_x = X.length;
var grid_size_y = Y.length;
var Z = new Array(grid_size_y);
for(i = 0; i < grid_size_y; i++) {
Z[i] = new Array(grid_size_x);
for(j = 0; j < grid_size_x; j++)
Z[i][j] = f(X[j], Y[i], params);
}
return Z;
}
$( document ).ready(function() {
var GRAPH1 = document.getElementById('graph1');
var GRAPH_DX = document.getElementById('graph-dx');
// 함수의 정의역을 설정
// 함수가 바뀌면 여기 정의역을 적당히 조정해주면 됨
var min_x = -5; var max_x = 5;
var min_y = -4; var max_y = 4;
// 샘플 (버튼에 따라 보였다 안보였다 하게 하기)
var sample_pos = [1,-1]
var sample_neg = [2,-2]
// 그림을 그릴 스탭을 설정 값이 크면 정밀하게 그려지나 속도 느려짐
var step = 2;
var scale = 50;
var a = parseFloat($('#coef_a').val()) / scale;
var b = parseFloat($('#coef_b').val()) / scale;
var c = parseFloat($('#coef_c').val()) / scale;
var X = linspace(min_x, max_x, step);
var Y = linspace(min_y, max_y, step);
var Z = draw_surface(cost, X, Y, [a, b, c]);
var timer_id = -1;
var surface = {
type: 'surface',
z: Z, x: X, y: Y,
showscale:false,
colorscale: 'Portland', opacity:1.0, hoverinfo:'x+y+z',
name: 'surface',
contours: { x:{ show:false, highlight:true, color:'#348ABD', width:1,
highlightcolor:'#348ABD', highlightwidth:5},
y:{ show:false, highlight:true, color:'#A60628', width:1,
highlightcolor:'#A60628', highlightwidth:5},
z:{ show:false, highlight:false, }
}
};
var xyplane = {
type: 'surface',
z: Z, x: X, y: Y,
showscale:false,
opacity:0.7, hoverinfo:'x+y+z',
name: 'surface',
contours: { x:{ show:false, highlight:true, color:'#348ABD', width:1,
highlightcolor:'#348ABD', highlightwidth:5},
y:{ show:false, highlight:true, color:'#A60628', width:1,
highlightcolor:'#A60628', highlightwidth:5},
z:{ show:false, highlight:false, }
}
};
z_zero = X.map( function(value, index) {return 0;} );
y = X.map( function(value, index) {return -(a/b)*value-(c/b);} );
var line_3d = {
type: 'scatter3d',
mode: 'lines',
x: X, y: y, z: z_zero,
opacity: 1,
line: {
width: 6,
color: '#313552',
reversescale: false
}
};
// https://colorhunt.co/
var positive_3d = {
x: [sample_pos[0]],
y: [sample_pos[1]],
z: [0],
name: 'pos',
mode: 'markers',
type: 'scatter3d',
visible: false,
marker: {
size: 5,
color: '#B8405E',
line: {
color: 'rgb(0, 0, 0)',
width: 1
},
}
}
var negative_3d = {
x: [sample_neg[0]],
y: [sample_neg[1]],
z: [0],
name: 'pos',
mode: 'markers',
type: 'scatter3d',
visible: false,
marker: {
size: 5,
color: '#2EB086',
line: {
color: 'rgb(0, 0, 0)',
width: 1
},
}
}
var f_pos_z = a*1 + b*(-1) + c
var pos_to_the_plane = {
x: [sample_pos[0], sample_pos[0]],
y: [sample_pos[1], sample_pos[1]],
z: [0, f_pos_z],
name: 'pos',
mode: 'lines',
type: 'scatter3d',
visible: false,
line: {
width: 4,
color: '#313552',
},
marker: {
size: 5,
color: '#B8405E',
}
}
var f_neg_z = a*2 + b*(-2) + c
var neg_to_the_plane = {
x: [sample_neg[0], sample_neg[0]],
y: [sample_neg[1], sample_neg[1]],
z: [0, f_neg_z],
name: 'neg',
mode: 'lines',
type: 'scatter3d',
visible: false,
line: {
width: 4,
color: '#313552',
},
marker: {
size: 5,
color: '#B8405E',
}
}
var line = {
x: X,
y: y,
name: 'f(x)',
mode: 'lines',
marker: {color:'#313552'},
};
var positive_2d = {
x: [sample_pos[0]],
y: [sample_pos[1]],
name: 'pos',
mode: 'markers',
type: 'scatter',
visible: false,
marker: {
size: 12,
color: '#B8405E',
line: {
color: 'rgb(0, 0, 0)',
width: 1
},
}
}
var negative_2d = {
x: [sample_neg[0]],
y: [sample_neg[1]],
name: 'neg',
mode: 'markers',
type: 'scatter',
visible: false,
marker: {
size: 12,
color: '#2EB086',
line: {
color: 'rgb(0, 0, 0)',
width: 1
},
}
}
var layouts = {
'3d-square' : {
hovermode:'closest',
spikedistance:-1,
margin: {
l: 33, r: 20, b: 33, t: 20, pad: 0
},
scene:{
xaxis:{showspikes:false, range: [-4, 4], title:'x Axis'},
yaxis:{showspikes:false, range: [-4, 4], title:'y Axis'},
zaxis:{showspikes:false, range: [-4, 4], title:'z Axis'},
aspectratio:{x:1, y:1, z:1},
},
showlegend: false
},
'2dx' : {
// 2차원 그래프의 높이 범위를 여기서 설정
// 함수에 맞게 적당한 범위를 적어준다.
xaxis: {range: [-5, 5], title:'x Axis'},
yaxis: {range: [-5, 5], title:'y Axis'},
margin: {
l: 33, r: 20, b: 33, t: 20, pad: 0
},
},
};
Plotly.plot(GRAPH1, [surface, line_3d, pos_to_the_plane, neg_to_the_plane,
xyplane, positive_3d, negative_3d, ],
layouts['3d-square']);
Plotly.plot(GRAPH_DX, [line, positive_2d, negative_2d], layouts['2dx']);
// 곡면의 투명도를 조정하는 이벤트 핸들러
$("#check-opacity").change(function () {
if ($(this).prop("checked")) {
Plotly.restyle(GRAPH1, 'opacity', 0.8, 0);
return;
}
Plotly.restyle(GRAPH1, 'opacity', 1.0, 0);
});
// 샘플 보이기를 조정하는 이벤트 핸들러
$("#check-samples").change(function () {
if ($(this).prop("checked")) {
var update = {
visible: [true, true, true, true],
}
Plotly.restyle(GRAPH1, update, [2, 3, 5, 6]);
update = {
visible: [true, true]
}
Plotly.restyle(GRAPH_DX, update, [1, 2]);
return;
}
var update = {
visible: [false, false, false, false],
}
Plotly.restyle(GRAPH1, update, [2, 3, 5, 6]);
update = {
visible: [false, false]
}
Plotly.restyle(GRAPH_DX, update, [1, 2]);
});
// xy-plane 높이를 조절하는 이벤트 핸들러
$('#xy-plane').on("change mousemove", function() {
fc = parseFloat($(this).val());
$('#fc_value').html(fc);
// GRAPH1에서 xy-plane, line_3d 업데이트
Z_fc = draw_surface(cost, X, Y, [0, 0, fc]);
z_zero = X.map( function(value, index) {return fc;} );
y = X.map( function(value, index) {return -(a/b)*value-((c-fc)/b);} );
var update = { y:[y, Y], z: [z_zero, Z_fc] };
Plotly.restyle(GRAPH1, update, [1, 4,]);
// GRAPH_DX에서 line 업데이트
update = { y: [y] }
Plotly.restyle(GRAPH_DX, update, 0);
});
$('#coef_a').on("change mousemove", function() {
a = parseFloat($(this).val()) / scale;
$('#coef_a_value').html(a);
fc = parseFloat($("#xy-plane").val());
// redraw
// surface, line_3d, xyplane
Z = draw_surface(cost, X, Y, [a, b, c]);
y = X.map( function(value, index) {return -(a/b)*value-((c-fc)/b);} );
// to_the_plane
f_pos_z = a*sample_pos[0] + b*sample_pos[1] + c
f_neg_z = a*sample_neg[0] + b*sample_neg[1] + c
var update = {
y: [Y, y, [sample_pos[1],sample_pos[1]], [sample_neg[1],sample_neg[1]]],
z: [Z, z_zero, [0,f_pos_z], [0,f_neg_z]]
}
Plotly.restyle(GRAPH1, update, [0, 1, 2, 3]);
update = { y: [y] }
Plotly.restyle(GRAPH_DX, update, 0);
});
$('#coef_b').on("change mousemove", function() {
b = parseFloat($(this).val()) / scale;
$('#coef_b_value').html(b);
fc = parseFloat($("#xy-plane").val());
// redraw
Z = draw_surface(cost, X, Y, [a, b, c]);
y = X.map( function(value, index) {return -(a/b)*value-((c-fc)/b);} );
// to_the_plane
f_pos_z = a*1 + b*(-1) + c
f_neg_z = a*2 + b*(-2) + c
var update = {
y: [Y, y, [sample_pos[1],sample_pos[1]], [sample_neg[1],sample_neg[1]]],
z: [Z, z_zero, [0,f_pos_z], [0,f_neg_z]]
}
Plotly.restyle(GRAPH1, update, [0,1,2,3]);
update = { y: [y] }
Plotly.restyle(GRAPH_DX, update, 0);
});
$('#coef_c').on("change mousemove", function() {
c = parseFloat($(this).val()) / scale;
$('#coef_c_value').html(c);
fc = parseFloat($("#xy-plane").val());
// redraw
Z = draw_surface(cost, X, Y, [a, b, c]);
y = X.map( function(value, index) {return -(a/b)*value-((c-fc)/b);} );
// to_the_plane
f_pos_z = a*1 + b*(-1) + c
f_neg_z = a*2 + b*(-2) + c
var update = {
y: [Y, y, [sample_pos[1],sample_pos[1]], [sample_neg[1],sample_neg[1]]],
z: [Z, z_zero, [0,f_pos_z], [0,f_neg_z]]
}
Plotly.restyle(GRAPH1, update, [0,1,2,3]);
update = { y: [y] }
Plotly.restyle(GRAPH_DX, update, 0);
});
$("#stop").click(function () {
console.log("stop");
if(timer_id != -1) {
clearInterval(timer_id);
}
});
$("#learn").click(function () {
console.log("learn");
train_x = [sample_pos, sample_neg];
train_y = [1, -1];
eta = 0.01;
epochs = 5000;
timer_id = setInterval( function (){
correct = true;
for(j=0; j < 2; j++) {
x_j = train_x[j][0]
y_j = train_x[j][1]
target_j = train_y[j]
score = a*x_j + b*y_j + c
// unit step
if(score > 0){
o_j = 1;
} else{
o_j = -1;
}
console.log(j, score, a, b, c)
if(o_j != target_j) correct = false;
dc = eta*(target_j - o_j) // const, c
da = eta*(target_j - o_j)*x_j // x, a
db = eta*(target_j - o_j)*y_j // y, b
c += dc;
a += da;
b += db;
// slider update
$('#coef_a').val(a*scale)
$('#coef_a_value').html(a.toPrecision(6));
$('#coef_b').val(b*scale)
$('#coef_b_value').html(b.toPrecision(6));
$('#coef_c').val(c*scale)
$('#coef_c_value').html(c.toPrecision(6));
}
fc = parseFloat($("#xy-plane").val());
// redraw
Z = draw_surface(cost, X, Y, [a, b, c]);
y = X.map( function(value, index) {return -(a/b)*value-((c-fc)/b);} );
// to_the_plane
f_pos_z = a*1 + b*(-1) + c
f_neg_z = a*2 + b*(-2) + c
var update = {
y: [Y, y, [sample_pos[1],sample_pos[1]], [sample_neg[1],sample_neg[1]]],
z: [Z, z_zero, [0,f_pos_z], [0,f_neg_z]]
}
Plotly.restyle(GRAPH1, update, [0,1,2,3]);
update = { y: [y] }
Plotly.restyle(GRAPH_DX, update, 0);
// stop criterion
if (correct == true) {
console.log('break')
clearInterval(timer_id);
}
}, 50);
});
});
</script>
</body>
</html>