![](\"https://raw.githubusercontent.com/genkuroki/msfd28/master/images/NameJupyter.jpg\")
\n",
"\n",
"このように, Jupyter という名前は **open languages of science** である Julia, Python, R に着想を得ているが, それらの先頭部分を繋げたものではないと書かれており, **すべてのプログラミング言語** を平等に扱うことが宣言されている. だから, Jupyterを一部のプログラミング言語(特にPython)専用の環境であるかのような印象を広めることは, Jupyterの作者たちの意向に反している. さらに **open science** を強調していることにも注目せよ."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Python 2.7だと小2開発者に馬鹿にされるので注意\n",
"\n",
"* [小2開発者「なんだ2.xか。3じゃないのか」](https://twitter.com/monotarosamurai/status/778846894575357952)\n",
"\n",
"![](\"https://raw.githubusercontent.com/genkuroki/msfd28/master/images/sho2kaihatsusha.png\")
\n",
"\n",
"**注意:** この節はジョークのつもりで入れた."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### 整形された数式を含む説明の例\n",
"\n",
"パラメーター $w$ 付きの $y$ に関する確率密度函数 $p(y|w)$ と**事前分布**と呼ばれる $w$ に関する確率密度函数 $\\varphi(w)$ とサンプル $Y_1,\\ldots,Y_n$ から得られるベイズ推測法における予測分布 $p^*(y)$ は以下のように定義される:\n",
"\n",
"$$\n",
"p^*(y) = \n",
"\\frac{Z(Y_1,\\ldots,Y_n,y|\\varphi)}{Z(Y_1,\\ldots,Y_n|\\varphi)} =\n",
"Z(y|\\psi).\n",
"$$\n",
"\n",
"ここで\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"&\n",
"Z(y_1,\\ldots,y_n|\\varphi) = \\int \\prod_{k=1}^n p(Y_k|w)\\cdot\\varphi(w)\\,dw,\n",
"\\\\ &\n",
"\\psi(w) = \\frac{\\prod_{k=1}^n p(Y_k|w)\\cdot\\varphi(w)}{\\int \\prod_{k=1}^n p(Y_k|w)\\cdot\\varphi(w)\\,dw}.\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"$Z(y_1,\\ldots,y_n|\\varphi)$ は**分配函数**と呼ばれ, $Z(Y_1,\\ldots,Y_n|\\varphi)$ は**周辺尤度**と呼ばれ, $\\psi(w)$ は**事後分布**と呼ばれる."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Julia言語\n",
"\n",
"[Julia言語](https://github.com/JuliaLang/julia)は最新のプログラミング言語.\n",
"\n",
"* [v1.0.0](https://github.com/JuliaLang/julia/releases/tag/v1.0.0)になったのは2018年8月. (2019-03-15現在は[v1.1.0](https://github.com/JuliaLang/julia/releases/tag/v1.1.0))\n",
"\n",
"* 無料. オープンソース.\n",
"\n",
"* [JuliaBox](https://juliabox.com/)を使えばブラウザさえあれば使える.\n",
"\n",
"* スクリプト言語のように気軽に使える.\n",
"\n",
"* 計算が速い. \n",
"\n",
"* 私の場合には(個人差あり!), Cで書いてgccでコンパイルするよりも速いことが多い.\n",
"\n",
"* [GNU Octave](https://www.gnu.org/software/octave/)や[scilab](https://www.scilab.org/)のような[MATLAB](https://jp.mathworks.com/)クローンのユーザーにはJulia言語に引っ越しすることを強く勧める.\n",
"\n",
"* [Python](https://www.python.org/), [R](https://www.r-project.org/), [Ruby](https://www.ruby-lang.org/ja/)などとは共存して行くことになるだろう.\n",
"\n",
"私によるWindows環境でのJulia言語環境の作り方の記録：\n",
"\n",
"* [WindowsへのJulia言語のインストール](https://nbviewer.jupyter.org/gist/genkuroki/81de23edcae631a995e19a2ecf946a4f?flush_cache=true)\n",
"\n",
"私によるJulia言語の使用例のギャラリー：\n",
"\n",
"* [twitterにおける長大なスレッド](https://twitter.com/genkuroki/status/974473336724967424)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### v1.0がリリースされてから急激に人気が高まる\n",
"\n",
"* [Newsletter January 2019 (04 Jan 2019 | Julia Computing)](https://juliacomputing.com/blog/2019/01/04/january-newsletter.html)\n",
"\n",
"**Heaviside函数**の成分が追加されたのは2018年8月頃すなわちv1.0がリリースされたときである.\n",
"\n",
"![](\"https://juliacomputing.com/assets/img/newsletters/juliagrowth.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Just-in-time でコンパイル\n",
"\n",
"Julia言語では\n",
"\n",
"* 函数を実行したときに, \n",
"\n",
"* 与えられた引数の型情報を使って, \n",
"\n",
"* その函数をネイティブコードにコンパイルしてから実行する.\n",
"\n",
"こういう仕組みなので高速に計算したいコードは函数の中に入れなければいけない.\n",
"\n",
"最初の実行時にはコンパイルにも時間が取られることに注意.\n",
"\n",
"以下は円周率のモンテカルロ計算で比較."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 1.418559 seconds (40.00 M allocations: 762.914 MiB, 10.46% gc time)\n"
]
},
{
"data": {
"text/plain": [
"3.1410228"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"### 函数にせずに実行\n",
"\n",
"@time begin\n",
" L = 10^7\n",
" c = 0\n",
" for i in 1:L\n",
" global c\n",
" c += ifelse(rand()^2+rand()^2 ≤ 1, 1, 0)\n",
" end\n",
" 4c/L\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.047364 seconds (36.00 k allocations: 1.967 MiB)\n"
]
},
{
"data": {
"text/plain": [
"3.141308"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"### 函数にして実行\n",
"\n",
"function simpi(L=10^7)\n",
" c = 0\n",
" for i in 1:L\n",
" c += ifelse(rand()^2+rand()^2 ≤ 1, 1, 0)\n",
" end\n",
" 4c/L\n",
"end\n",
"simpi(10^5) # simpi(::Int64)がコンパイルされる\n",
"\n",
"@time simpi()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"実行コードを函数の中に入れるだけで数十倍計算が速くなった.\n",
"\n",
"Julia言語では各函数が引数の型情報に基いて just-in-time でコンパイルされる."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### gccとの比較\n",
"\n",
"円周率のモンテカルロ計算(1億回)で比較."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Julia Version 1.1.0\n",
"Commit 80516ca202 (2019-01-21 21:24 UTC)\n",
"Platform Info:\n",
" OS: Windows (x86_64-w64-mingw32)\n",
" CPU: Intel(R) Core(TM) i7-4770HQ CPU @ 2.20GHz\n",
" WORD_SIZE: 64\n",
" LIBM: libopenlibm\n",
" LLVM: libLLVM-6.0.1 (ORCJIT, haswell)\n",
"Environment:\n",
" JULIA_CMDSTAN_HOME = C:\\CmdStan\n",
" JULIA_NUM_THREADS = 4\n",
" JULIA_PKGDIR = C:\\JuliaPkg\n"
]
}
],
"source": [
"versioninfo()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gcc (Rev3, Built by MSYS2 project) 6.3.0\r\n",
"Copyright (C) 2016 Free Software Foundation, Inc.\r\n",
"This is free software; see the source for copying conditions. There is NO\r\n",
"warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.\r\n",
"\r\n"
]
}
],
"source": [
"run(`gcc --version`); # ほとんど使っていないのでバージョンが古い"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 2.537506 seconds (1.94 k allocations: 116.293 KiB)\n"
]
},
{
"data": {
"text/plain": [
"3.14153524"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"### gcc\n",
"\n",
"C_code= raw\"\"\"\n",
"#include \n",
"
\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"37376-frame, 2-channel SampleBuf{FixedPointNumbers.Fixed{Int16,15}, 2}\n",
"0.8475283446712019s sampled at 44100.0Hz\n",
"▇▇▇▇▇▇▇▇▇▇▇▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▄▅▄▄▄▄▄▄▄▄▃▃▃▂▁▁\n",
"▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▆▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▅▄▄▄▄▄▄▄▄▃▃▃▂▁▁"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## downloaded from https://freewavesamples.com/casio-mt-600-harpsichord-c3\n",
"samplesound1 = load(\"sounds/Casio-MT-600-Harpsichord-C3.wav\")"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/html": [
"SampleBuf display requires javascript
\n", "To enable for the whole notebook select \"Trust Notebook\" from the\n", " \"File\" menu. You can also trust this cell by re-running it. You may\n", " also need to re-run `using SampledSignals` if the module is not yet\n", " loaded in the Julia kernel, or `SampledSignals.embed_javascript()`\n", " if the Julia module is loaded but the javascript isn't initialized.
\n", "\n",
"
\n",
"\n",
"\n",
"\n",
"\n",
"SampleBuf display requires javascript
\n", "To enable for the whole notebook select \"Trust Notebook\" from the\n", " \"File\" menu. You can also trust this cell by re-running it. You may\n", " also need to re-run `using SampledSignals` if the module is not yet\n", " loaded in the Julia kernel, or `SampledSignals.embed_javascript()`\n", " if the Julia module is loaded but the javascript isn't initialized.
\n", "