JavaScript - 数学 - ベクトル空間 - 線形結合 - 係数から線形結合へ

行列プログラマー
原著

開発環境

• macOS Sierra - Apple (OS)
• Emacs (Text Editor)
• JavaScript (プログラミング言語)
• Node.js, Safari(JavaScript エンジン)
• Learning JavaScript [邦訳](参考書籍)

行列プログラマー(Philip N. Klein (著)、 松田 晃一 (翻訳)、 弓林 司 (翻訳)、 脇本 佑紀 (翻訳)、 中田 洋 (翻訳)、 齋藤 大吾 (翻訳)、オライリージャパン)の3章(ベクトル空間)、3.1(線形結合)、3.1.3(係数から線形結合へ)のクイズ 3.1.7 を JavaScript で取り組んでみる。

クイズ 3.1.7

コード(Emacs)

HTML5

<pre id="output0"></pre>

<button id="run0">run</button>
<button id="clear0">clear</button>

<script src="sample1.js"></script>    

JavaScript

let div0 = document.querySelector('#graph0'),
    pre0 = document.querySelector('#output0'),
    btn0 = document.querySelector('#run0'),
    btn1 = document.querySelector('#clear0'),
    p = (x) => pre0.textContent += x + '\n';

let Vector = (labels, func={}) => {
    let that = {},
        d = labels,
        f = func,
        setItem = (d, val) => {
            f[d] = val;
        },
        getItem = (d) => {
            return f[d] === undefined ? 0 : f[d];
        },
        scalarMul = (a) => {
            let func = {};

            d.forEach((k) => {
                func[k] = that.getItem(k) * a;
            });
            return Vector(d, func);
        },
        add = (v) => {
            let func = {},
                d0 = d.concat(v.d().filter((x) => d.indexOf(x) === -1));

            d0.forEach((d) => {
                func[d] = that.getItem(d) + v.getItem(d);
            });
            return Vector(d0, func);
        },
        sub = (v) => that.add(v.scalarMul(-1)),
        neg = () => that.scalarMul(-1),
        dot = (v) => {
            return d.map((x) => that.getItem(x) * v.getItem(x))
                .reduce((x, y) => x + y);
        },
        isEqual = (v) => {
            return d.every((x) => that.getItem(x) === v.getItem(x));
        },
        toString = () => {
            return '{' +
                d.map((k) => `${k}: ${that.getItem(k)}`).join(', ') +
                '}';
        };

    that.d = () => d;
    that.f = () => f;    
    that.getItem = getItem;
    that.setItem = setItem;
    that.scalarMul = scalarMul;
    that.add = add;
    that.sub = sub;
    that.neg = neg;
    that.dot = dot;
    that.isEqual = isEqual;
    that.toString = toString;
            
    return that;
};
let arrayToVector = (a) => {
    let l = [],
        f = {};

    a.forEach((x, i) => {
        l.push(i);
        f[i] = x;
    });
    return Vector(l, f);
};

let linComb = (vlist, clist) =>
    vlist.reduce((prev, v, i) => prev.add(v.scalarMul(clist[i])),
                 arrayToVector([]));
                                          

let UnitTest = () => {
    let that = {},
        run = () => {            
            Object.keys(that).forEach((key) => {
                that.setUp();
                if (/^test/.test(key)) {
                    p(key);
                    that[key]();
                }
                that.tearDown();
            });        
        },
        assertEqual = (x, y) => {
            if (x === y) {
                p('ok');
            } else {
                p(`failure - ${x} !== ${y}`);
            }
        },
        assertTrue = (x) => {
            if (x) {
                p('ok');
            } else {
                p(`failure`);
            }
        },
        assertFalse = (x) => {
            if (x) {
                p('failure');
            } else {
                p(`ok`);
            }
        };

    that.run = run;
    that.assertEqual = assertEqual;
    that.assertTrue = assertTrue;
    that.assertFalse = assertFalse;

    return that;
};

let Test = () => {
    let that = UnitTest();
    
    that.setUp = () => {};
    that.tearDown = () => {};

    that.test0 = () => {
        let vlist = []
            clist = [];

        that.assertTrue(linComb(vlist, clist).isEqual(arrayToVector([])));

    };
    that.test1 = () => {
        let vlist = [arrayToVector([0, 1])],
            clist = [5];

        that.assertTrue(linComb(vlist, clist).isEqual(arrayToVector([0, 5])))
    };
    that.test2 = () => {
        let vlist = [arrayToVector([0, 1]),
                     arrayToVector([2, 3])],
            clist = [5, 10];

        that.assertTrue(linComb(vlist, clist).isEqual(arrayToVector([20, 35])));
    };
    that.test5 = () => {
        let vlist = [arrayToVector([0, 1]),
                     arrayToVector([2, 3]),
                     arrayToVector([4, 5]),
                     arrayToVector([6, 7]),
                     arrayToVector([8, 9])],
            clist = [5, 4, 3, 2, 1];

        that.assertTrue(linComb(vlist, clist).isEqual(
            arrayToVector([40, 55])));
    };
            
    
    return that;
};

let output = () => {
    Test().run();
};

btn0.onclick = output;
btn1.onclick = () => pre0.textContent = '';
output();