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    "# Table of Contents\n",
    " <p>"
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    "<div style=\"text-align: center;\">\n",
    "  <font size=\"5\">行列の計算速度競争</font>\n",
    "</div>\n",
    "<div style=\"text-align: right;\">\n",
    "<font size=\"3\"> cc by Shigeto R. Nishitani, 2017-10-30\n",
    "</font>\n",
    "</div>\n",
    "\n",
    "* file: ~/python/jupyter_num_calc/notebooks_python/LA_speed_race.ipynb"
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    "\n",
    "Mapleと，C, pythonで競争させてみました．Cはそのままです．Mapleは\n",
    "``` octave\n",
    "with(LinearAlgebra):\n",
    "data:=[1000,2000,4000];\n",
    "for n in data do\n",
    "  A:=RandomMatrix(n,n,generator = 0..1.0):\n",
    "  b:=RandomVector(n,generator = 0..1.0):\n",
    "  st:=time();\n",
    "  LUDecomposition(<A|b>):\n",
    "  print(time()-st);\n",
    "end:\n",
    "```\n",
    "\n",
    "です．pythonのcodeは，lapackにあるdgesvを指定して\n",
    "呼び出すようにしています．scipy.laのsolveでは何を使っているかはよくわからないので．\n",
    "\n",
    "``` python\n",
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "import time\n",
    "\n",
    "sizes = [1000, 2000, 4000]\n",
    "for n in sizes:\n",
    "    A = np.random.random((n, n))\n",
    "    b = np.random.random((n))\n",
    "    start = time.time()\n",
    "    la.lapack.dgesv(A, b)\n",
    "    print('%s [dim], %10.5f [sec] # python' % (n,time.time()-start))\n",
    "```\n",
    "\n",
    "結果は，次の通りです．\n",
    "\n",
    "|size|Maple[sec]|C[sec]|python[sec]|\n",
    "|:----|-----:|-----:|------:|\n",
    "|1000 | 0.339|0.0589|0.04101\n",
    "|2000 | 1.384|0.3826|0.12682\n",
    "|4000 |45.482|3.0111|0.81373\n",
    "\n",
    "pythonの圧勝ですね．絶対値はあまり意味がありません．MacBook Air(13-inch, Early 2015/2.2GHz Core i7, ElCapitan 10.11.6)ですが，softのversionにもよります．\n",
    "\n",
    "ただし，どんなrandomを生成しているかで結果は大きく変わるので，ちょっと怪しいです．\n",
    "たとえば，MapleのRandomMatrixでgeneratorを指定しないと\n",
    "size=1000でも9.773[sec]ととんでもないぐらい時間がかかります．\n",
    "\n",
    "MapleではさらにRandomMatrixの生成にも時間がかかります．\n",
    "MapleではNAGのライブラリを使っているので．．．\n",
    "\n",
    "ちなみにrubyでは[SciRuby](https://github.com/SciRuby/nmatrix/wiki/Getting-started)\n",
    "に従ってnmatrixをinstallして，\n",
    "```ruby\n",
    "require 'nmatrix'\n",
    "require 'time'\n",
    "\n",
    "#n = NMatrix.new(3, [4,9,2,3,5,7,8,1,6], dtype: :float64)\n",
    "[1000,2000,4000].each do |size|\n",
    "  n = size\n",
    "  aa = NMatrix.random([n,n])\n",
    "  start = Time.now\n",
    "  lu = aa.factorize_lu\n",
    "  p Time.now - start\n",
    "end\n",
    "```\n",
    "\n",
    "素直に走らせると，\n",
    "\n",
    "|size|nmatrix[sec]|nmaxtrix/lapacke|\n",
    "|:----|-----:|-----:|\n",
    "|1000 | 0.2118|0.028607|\n",
    "|2000 | 1.9287|0.191315|\n",
    "|4000 |16.9059|1.313174|\n",
    "\n",
    "のnmatrixです．2017/10/28現在nmatrix-0.2.4です．\n",
    "やっぱ，Rubyは数値計算苦手なんかと諦めかけたんですが，\n",
    "\n",
    "```\n",
    "gem install nmatrix nmatrix-lapacke\n",
    "```\n",
    "\n",
    "して\n",
    "```\n",
    "Require 'nmatrix/lapacke'\n",
    "```\n",
    "\n",
    "すると前表のnmatrix/lapacke欄です．これだと，C版に遜色ないですね．\n",
    "nmatrix-lapacke-0.2.3がinstallされています．このあたりの解説が[sciruby](http://sciruby.com/nmatrix/)以外見当たらなくて．．．\n",
    "\n"
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