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4章(行列)、4.10(線形関数)、4.10.8(対角行列)、クイズ4.10.21を JavaScript で取り組んでみる。
クイズ4.10.21
コード(Emacs)
HTML5
<pre id="output0"></pre> <button id="run0">run</button> <button id="clear0">clear</button> <script src="sample10.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', pObj = (obj) => Object.keys(obj).forEach((k) => p(`${k}: ${obj[k]}`)); range = (start, end, step=1) => { let result = []; for (let i = start; i < end; i += step) { result.push(i); } return result; }; let Vector = (labels, func={}) => { let that = {}, d = labels, f = func, setItem = (d, val) => { f[d] = val; }, getItem = (d) => f[d] === undefined ? 0 : f[d], scalarMul = (a) => { let func = {}; d.forEach((k) => { func[k] = that.getItem(k) * a; }); return Vector(d, func); }, add = (v) => { let func = {}, d0 = d.concat(v.d().filter((x) => d.indexOf(x) === -1)); d0.forEach((d) => { func[d] = that.getItem(d) + v.getItem(d); }); return Vector(d0, func); }, sub = (v) => that.add(v.scalarMul(-1)), neg = () => that.scalarMul(-1), dot = (v) => { return d.map((x) => that.getItem(x) * v.getItem(x)) .reduce((x, y) => x + y); }, isEqual = (v) => { return d.every((x) => that.getItem(x) === v.getItem(x)); }, toString = () => { return `Vector([${d.join(', ')}], ` + '{' + d.map((k) => `${k}: ${that.getItem(k)}`).join(', ') + '})'; }; that.d = () => d; that.f = () => f; that.getItem = getItem; that.setItem = setItem; that.scalarMul = scalarMul; that.add = add; that.sub = sub; that.neg = neg; that.dot = dot; that.isEqual = isEqual; that.toString = toString; return that; }; let Matrix = (labels, fn) => { let that = {}, getDomain = () => labels, getMap = () => fn, getElement = (i, j) => fn[i] === undefined ? 0 : fn[i][j] === undefined ? 0 : fn[i][j], toString = () => { let [m, n] = labels, s = Object.keys(fn).map((k) => { let o = fn[k], s = Object.keys(o).map((k) => `${k}: ${o[k]}`).join(', '); return `${k}: {${s}}`; }); return `Matrix([[${m.join(', ')}], [${n.join(', ')}]], {${s}}`; }; that.getDomain = getDomain; that.getMap = getMap; that.getElement = getElement; that.toString = toString; return that; }; let identity = (d) => Matrix([d, d], d.map((x) => [[x, x], 1])); let matrixToRowObj = (A) => { let result = {}; A.getDomain()[0] .forEach((i) => { let o = {}; A.getDomain()[1].forEach((j) => o[j] = A.getElement(i, j)); result[i] = Vector(A.getDomain()[1], o); }); return result; }; let matrixToColObj = (A) => { let result = {}; A.getDomain()[1] .forEach((j) => { let o = {}; A.getDomain()[0].forEach((i) => o[i] = A.getElement(i, j)); result[j] = Vector(A.getDomain()[0], o); }); return result; }; let matrixToVector = (M) => { let domain = M.getDomain(), labels = domain[0] .map((i) => domain[1].map((j) => `(${i}, ${j})`)) .reduce((x, y) => x.concat(y), []), func = {}; console.log(M.getMap()); M.getMap() .forEach((x) => { func[`(${x[0][0]}, ${x[0][1]})`] = x[1]; }); console.log(func); return Vector(labels, func); }; let transpose = (M) => { let [m, n] = M.getDomain(), o = {}; n.forEach((j) => { let o0 = {}; m.forEach((i) => { o0[i] = M.getElement(i, j); }) o[j] = o0; }); return Matrix([n, m], o); }; let diag = (D, entries) => { let labels = [D, D], fn = {}; D.forEach((d) => { let o = {}; o[d] = entries[d]; fn[d] = o; }); return Matrix(labels, fn); }; let output = () => { [[['a'], {a:1}], [['a', 'b'], {a:1, b:2}]].forEach((o) => { let [D, entries] = o, M = diag(D, entries); p(M); }); }; btn0.onclick = output; btn1.onclick = () => pre0.textContent = ''; output();
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