Julia/Cubature and Yeppp.ipynb

Cubature and Yeppp.ipynb

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    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Cubature and Yeppp\n\nhttps://github.com/stevengj/Cubature.jl\n数値積分\n\nhttps://github.com/JuliaMath/Yeppp.jl\nベクトルの高速数値計算"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "using Cubature\n\n# integrate(1/(1+x^2), (x, 0, ∞)) = pi/2\n# x = t/(1-t^2)\n# dx = (1+t^2)/(1-t^2)^2\n# x = 0～∞ ⇔ t = 0～1\n\na = pi/2\n@time b = hquadrature(x->1/(1+x^2),0,10^22)\n@time c = hquadrature(t->1/(1+(t/(1-t^2))^2)*(1+t^2)/(1-t^2)^2,0,1)\n@time d = hquadrature(t->(1+t^2)/(1-t^2+t^4),0,1)\n\ndisplay(a)\ndisplay(b)\ndisplay(c)\ndisplay(d)",
      "execution_count": 6,
      "outputs": [
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          "output_type": "display_data",
          "data": {
            "text/plain": "1.5707963267948966"
          },
          "metadata": {}
        },
        {
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          "data": {
            "text/plain": "(1.5707963267948966, 6.138518647513451e-12)"
          },
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        {
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          "data": {
            "text/plain": "(1.5707963267948966, 7.650730483975984e-10)"
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          "data": {
            "text/plain": "(1.5707963267948966, 7.650730442049322e-10)"
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        },
        {
          "output_type": "stream",
          "text": "  0.061307 seconds (12.19 k allocations: 688.093 KiB)\n  0.050534 seconds (13.24 k allocations: 748.005 KiB)\n  0.040982 seconds (12.77 k allocations: 718.796 KiB)\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# Yeppp.log! の方が log. より3倍以上速い\n\nusing Yeppp\n\nx = rand(10^8)\n@time ty = @elapsed Yeppp.log!(similar(x), x)\n@time t  = @elapsed log.(x)\nt/ty",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": "  0.458827 seconds (10 allocations: 762.940 MiB, 24.33% gc time)\n  1.607678 seconds (33 allocations: 762.941 MiB, 3.58% gc time)\n",
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": "3.5039294453769205"
          },
          "metadata": {}
        }
      ]
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        "trusted": true,
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      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
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      "display_name": "Julia 0.6.0",
      "language": "julia"
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        "description": "Julia/Cubature and Yeppp.ipynb",
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