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hello.ipynb
{
"cells": [
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"cell_type": "code",
"execution_count": 1,
"id": "750b96e8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hello World!\n"
]
}
],
"source": [
"println(\"Hello World!\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "dfa83b41",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
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"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"x = 1\n",
"y = 2\n",
"x = y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "fe3c867c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = 1\n",
"y = 2\n",
"z = x + y"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1d6ec4c5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3"
]
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"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
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"source": [
"z"
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{
"cell_type": "code",
"execution_count": 5,
"id": "69861ec0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3\n"
]
}
],
"source": [
"println(z)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "46de657f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sin(π/2)"
]
},
{
"cell_type": "markdown",
"id": "5913c47f",
"metadata": {},
"source": [
"# マークダウンの例\n",
"\n",
"例えば加法定理は以下のように書く.\n",
"\n",
"$$\n",
" \\sin(\\alpha+\\beta) = \\sin\\alpha \\cdot \\cos\\beta + \\cos\\alpha \\cdot \\sin\\beta\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a6dffe92",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.1411200080598672\n",
"0.1411200080598673\n"
]
}
],
"source": [
"α = 1\n",
"β = 2\n",
"println( sin(α+β) )\n",
"println( sin(α)*cos(β)+cos(α)*sin(β) )"
]
},
{
"cell_type": "markdown",
"id": "d908ab57",
"metadata": {},
"source": [
"# グラフを描写する\n",
"\n",
"Juliaでは, Plots.jlというパッケージを用いて関数や配列をプロットすることができる. CSVファイルなどをプロットしたい場合は, CSV.jlなどを用いて,　データを配列に格納する必要がある."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "09c3e8f3",
"metadata": {},
"outputs": [],
"source": [
"# using Pkg\n",
"# Pkg.add(\"Plots\")\n",
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "5a265ecf",
"metadata": {},
"outputs": [
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" 1781.83,358.76 1800.37,409.793 1818.92,463.785 1836.1,516.028 1853.27,570.053 1870.44,625.476 1887.62,681.905 1921.48,794.552 1955.34,906.436 1971.78,959.55 \n",
" 1988.22,1011.41 2004.66,1061.68 2021.1,1110.02 2037.95,1157.26 2054.8,1201.83 2071.66,1243.43 2088.51,1281.76 2097.74,1301.28 2106.97,1319.7 2116.2,1336.99 \n",
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" 2242.83,1444.97 2256.24,1441.36 2269.65,1434.83 2275.15,1431.31 2280.65,1427.31 2286.15,1422.82 2291.66,1417.86 \n",
" \"/>\n",
"<path clip-path=\"url(#clip910)\" d=\"\n",
"M1988.5 198.898 L2280.8 198.898 L2280.8 95.2176 L1988.5 95.2176 Z\n",
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" \"/>\n",
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" \"/>\n",
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]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(sin)"
]
},
{
"cell_type": "markdown",
"id": "fed84385",
"metadata": {},
"source": [
"https://zenn.dev/ohno/articles/3101433fbe9231"
]
},
{
"cell_type": "markdown",
"id": "37b0d982",
"metadata": {},
"source": [
"# 最適化問題を解く\n",
"\n",
"Optim.jlでは様々な方法で最適化問題を解くことができる. 最急降下法を用いて $f(x) = (x+2)^2 + 1$ の最小値・最小点を求める."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "2ea4ffb3",
"metadata": {},
"outputs": [],
"source": [
"# using Pkg\n",
"# Pkg.add(\"Optim\")\n",
"using Optim"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "60b8b7bf",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" * Status: success\n",
"\n",
" * Candidate solution\n",
" Final objective value: 1.000000e+00\n",
"\n",
" * Found with\n",
" Algorithm: Gradient Descent\n",
"\n",
" * Convergence measures\n",
" |x - x'| = 7.00e+00 ≰ 0.0e+00\n",
" |x - x'|/|x'| = 3.50e+00 ≰ 0.0e+00\n",
" |f(x) - f(x')| = 4.90e+01 ≰ 0.0e+00\n",
" |f(x) - f(x')|/|f(x')| = 4.90e+01 ≰ 0.0e+00\n",
" |g(x)| = 9.17e-11 ≤ 1.0e-08\n",
"\n",
" * Work counters\n",
" Seconds run: 0 (vs limit Inf)\n",
" Iterations: 1\n",
" f(x) calls: 3\n",
" ∇f(x) calls: 3\n"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f(x) = (x[1] + 2.0)^2 + 1\n",
"x0 = [5.0]\n",
"optimize(f, x0, method=GradientDescent())"
]
},
{
"cell_type": "markdown",
"id": "548e9250",
"metadata": {},
"source": [
"https://zenn.dev/ohno/articles/2a1dc7d609e5bc"
]
},
{
"cell_type": "markdown",
"id": "2c672c48",
"metadata": {},
"source": [
"# 固有値問題を解く\n",
"\n",
"LinearAlgebra.jlを使えば簡単に行列の固有値や固有ベクトルを求めることができる. LAPACKが裏で動いているので, 安心感がある. LinearAlgebra.jlは最初からインストールされている."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "5c1a46f6",
"metadata": {},
"outputs": [],
"source": [
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c1a12724",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3×3 Matrix{Int64}:\n",
" -4 0 6\n",
" -3 2 3\n",
" -3 0 5"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = [-4 0 6;\n",
" -3 2 3;\n",
" -3 0 5]"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "65dc8544",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Eigen{Float64, Float64, Matrix{Float64}, Vector{Float64}}\n",
"values:\n",
"3-element Vector{Float64}:\n",
" -1.0\n",
" 2.0\n",
" 2.0\n",
"vectors:\n",
"3×3 Matrix{Float64}:\n",
" -0.816497 0.0 -0.6742\n",
" -0.408248 1.0 0.301511\n",
" -0.408248 0.0 -0.6742"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eigen(A)"
]
},
{
"cell_type": "markdown",
"id": "eb79df72",
"metadata": {},
"source": [
"https://zenn.dev/ohno/articles/cb10dc5b3f5bbc"
]
},
{
"cell_type": "markdown",
"id": "a1287075",
"metadata": {},
"source": [
"# 特殊関数を使う\n",
"\n",
"Juliaには様々な特殊関数を利用するためのパッケージが用意されている."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "8c84d1f2",
"metadata": {},
"outputs": [],
"source": [
"# using Pkg\n",
"# Pkg.add(\"SpecialFunctions\")\n",
"using SpecialFunctions"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "f5348e14",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.1415926535897936"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gamma(1/2)^2"
]
},
{
"cell_type": "markdown",
"id": "b4bc757b",
"metadata": {},
"source": [
"https://zenn.dev/ohno/articles/f352f354e5cf96"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "97e477fb",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.8.2",
"language": "julia",
"name": "julia-1.8"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.8.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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