数学 - Python - JavaScript - 線形代数学 - R^n におけるベクトル – 直線と平面(2点の中点、一般公式、n次元空間)

学習環境

ラング線形代数学(上)(S.ラング (著)、芹沢正三 (翻訳)、ちくま学芸文庫)の1章(R^n におけるベクトル)、5(直線と平面)、練習問題22.を取り組んでみる。

$\frac{P + Q}{2}$

コード(Emacs)

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, Matrix
import random
print('22.')


def middle_point(p, q):
    return (p + q) / 2


for n in range(2, 6):
    for _ in range(2):
        p = Matrix([random.randrange(-10, 11) for _ in range(n)])
        q = Matrix([random.randrange(-10, 11) for _ in range(n)])
        for m in [p, q, middle_point(p, q)]:
            pprint(m.T)
        print()
    print()

入出力結果(Terminal, Jupyter(IPython))

$ ./sample22.py
22.
[-9  5]
[-6  -7]
[-15/2  -1]

[6  -1]
[7  7]
[13/2  3]


[-7  -6  -8]
[-5  2  -2]
[-6  -2  -5]

[3  -4  -5]
[4  1  -10]
[7/2  -3/2  -15/2]


[4  3  -4  4]
[3  -5  8  9]
[7/2  -1  2  13/2]

[9  7  10  8]
[3  -9  6  9]
[6  -1  8  17/2]


[-9  -1  -5  -4  -8]
[9  -7  5  1  10]
[0  -4  0  -3/2  1]

[-10  6  -9  6  8]
[10  1  8  3  8]
[0  7/2  -1/2  9/2  8]


$

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="r0">r = </label>
<input id="r0" type="number" min="0" value="2">
<label for="dx">dx = </label>
<input id="dx" type="number" min="0" step="0.001" value="0.001">
<br>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-10">
<label for="x2">x2 = </label>
<input id="x2" type="number" value="10">
<br>
<label for="y1">y1 = </label>
<input id="y1" type="number" value="-10">
<label for="y2">y2 = </label>
<input id="y2" type="number" value="10">

<button id="draw0">draw</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>

<script src="sample22.js"></script>

JavaScript

let div0 = document.querySelector('#graph0'),
    pre0 = document.querySelector('#output0'),
    width = 600,
    height = 600,
    padding = 50,
    btn0 = document.querySelector('#draw0'),
    btn1 = document.querySelector('#clear0'),
    input_r = document.querySelector('#r0'),
    input_dx = document.querySelector('#dx'),
    input_x1 = document.querySelector('#x1'),
    input_x2 = document.querySelector('#x2'),
    input_y1 = document.querySelector('#y1'),
    input_y2 = document.querySelector('#y2'),
    inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2],
    p = (x) => pre0.textContent += x + '\n';

let fns = [];

let draw = () => {
    pre0.textContent = '';

    let r = parseFloat(input_r.value),
        dx = parseFloat(input_dx.value),
        x1 = parseFloat(input_x1.value),
        x2 = parseFloat(input_x2.value),
        y1 = parseFloat(input_y1.value),
        y2 = parseFloat(input_y2.value);

    if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) {
        return;
    }    

    let points = [],
        colors = ['green', 'blue', 'orange', 'brown', 'purple',
                  'brown', 'pink', 'yellow', 'skyblue', 'gray'],
        lines = colors.map(color => {
            let x1 = (Math.random() < 0.5 ? -1 : 1) * Math.random() * 10,
                y1 = (Math.random() < 0.5 ? -1 : 1) * Math.random() * 10,
                x2 = (Math.random() < 0.5 ? -1 : 1) * Math.random() * 10,
                y2 = (Math.random() < 0.5 ? -1 : 1) * Math.random() * 10;
            
            points.push([(x1 + x2) / 2, (y1 + y2) / 2, 'red']);
            
            return [x1, y1, x2, y2, color];
        });

    console.log(points);
    fns
        .forEach((o) => {
            let [f, color] = o;
            for (let x = x1; x <= x2; x += dx) {
                let y = f(x);

                points.push([x, y, color]);
            }
        });
    
    let xscale = d3.scaleLinear()
        .domain([x1, x2])
        .range([padding, width - padding]);
    let yscale = d3.scaleLinear()
        .domain([y1, y2])
        .range([height - padding, padding]);

    let xaxis = d3.axisBottom().scale(xscale);
    let yaxis = d3.axisLeft().scale(yscale);
    div0.innerHTML = '';
    let svg = d3.select('#graph0')
        .append('svg')
        .attr('width', width)
        .attr('height', height);

    svg.selectAll('line')
        .data([[x1, 0, x2, 0], [0, y1, 0, y2]].concat(lines))
        .enter()
        .append('line')
        .attr('x1', (d) => xscale(d[0]))
        .attr('y1', (d) => yscale(d[1]))
        .attr('x2', (d) => xscale(d[2]))
        .attr('y2', (d) => yscale(d[3]))
        .attr('stroke', (d) => d[4] || 'black');

    svg.selectAll('circle')
        .data(points)
        .enter()
        .append('circle')
        .attr('cx', (d) => xscale(d[0]))
        .attr('cy', (d) => yscale(d[1]))
        .attr('r', r)
        .attr('fill', (d) => d[2] || 'green');
    
    svg.append('g')
        .attr('transform', `translate(0, ${height - padding})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${padding}, 0)`)
        .call(yaxis);

    [fns].forEach((fs) => p(fs.join('\n')));
};

inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();

r = dx =
x1 = x2 =
y1 = y2 =

Kamimura's blog

2018年11月30日金曜日

数学 - Python - JavaScript - 線形代数学 - R^n におけるベクトル – 直線と平面(2点の中点、一般公式、n次元空間)

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