SVM.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "using Plots\n",
        "plotlyjs(size=(600,400))\n",
        "plot(rand(3),rand(3))\n",
        "nothing"
      ],
      "outputs": [
        {
          "output_type": "display_data",
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          "metadata": {}
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      ],
      "execution_count": 1,
      "metadata": {
        "execution": {
          "iopub.status.busy": "2020-06-03T14:04:30.944Z",
          "iopub.execute_input": "2020-06-03T14:04:32.188Z",
          "iopub.status.idle": "2020-06-03T14:05:17.884Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "using Pkg\n",
        "pkg\"add Ipopt\""
      ],
      "outputs": [],
      "execution_count": null,
      "metadata": {
        "scrolled": true
      }
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt"
      ],
      "outputs": [],
      "execution_count": null,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using Random, LinearAlgebra\n",
        "\n",
        "Random.seed!(0)\n",
        "\n",
        "n = 30\n",
        "X = rand(n, 2)\n",
        "w_sol = [0.3; 0.7]\n",
        "b_sol = -0.5\n",
        "y = [dot(w_sol, X[i,:]) + b_sol > 0 ? 1 : -1 for i = 1:n]\n",
        "\n",
        "plot(leg=false)\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)"
      ],
      "outputs": [],
      "execution_count": null,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\"=>0))\n",
        "\n",
        "@variable(model, w[1:2])\n",
        "@variable(model, b)\n",
        "\n",
        "@objective(model, Min, dot(w, w) / 2)\n",
        "\n",
        "@constraint(model, restr[i=1:n], (dot(w, X[i,:]) + b) * y[i] ≥ 1)\n",
        "\n",
        "#print(model)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "w, b = value.(w), value(b)\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = dual.(restr)\n",
        "I = findall(α .> 1e-6)\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "plot!(x -> -(w[1] * x + b) / w[2], 0, 1, c=:magenta, lw=2)\n",
        "plot!(x -> -(w[1] * x + b - 1) / w[2], 0, 1, c=:blue, l=:dash)\n",
        "plot!(x -> -(w[1] * x + b + 1) / w[2], 0, 1, c=:red, l=:dash)\n",
        "\n"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
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            ]
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        }
      ],
      "execution_count": 83,
      "metadata": {
        "scrolled": false
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    },
    {
      "cell_type": "code",
      "source": [
        "findall(α .> 1e-6)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 77,
          "data": {
            "text/plain": [
              "3-element Array{Int64,1}:\n",
              "  4\n",
              " 20\n",
              " 25"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 77,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "dot(w, X[25,:]) + b, y[25]"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 81,
          "data": {
            "text/plain": [
              "(-0.9999999900262804, -1)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 81,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "w, b"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 6,
          "data": {
            "text/plain": [
              "([5.917754103276014, 13.376069868373918], -9.718277405139164)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 6,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "w ./ w_sol, b / b_sol"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": [
              "([19.72584701092005, 19.108671240534168], 19.436554810278327)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 7,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using Random, LinearAlgebra\n",
        "\n",
        "Random.seed!(0)\n",
        "n = 100\n",
        "X = randn(n, 2) * 2\n",
        "w_sol = [0.5; 0.4]\n",
        "b_sol = -0.5\n",
        "y = [dot(w_sol, X[i,:]) + b_sol > randn() * 0.5 ? 1 : -1 for i = 1:n]\n",
        "\n",
        "plot(leg=false)\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 84,
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          "metadata": {}
        }
      ],
      "execution_count": 84,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\"=>0))\n",
        "\n",
        "@variable(model, w[1:2])\n",
        "@variable(model, b)\n",
        "\n",
        "@objective(model, Min, dot(w, w) / 2)\n",
        "\n",
        "@constraint(model, restr[i=1:n], (dot(w, X[i,:]) + b) * y[i] ≥ 1)\n",
        "\n",
        "#print(model)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "w, b = value.(w), value(b)\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = dual.(restr)\n",
        "I = findall(α .> 1e-6)\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "plot!(x -> -(w[1] * x + b) / w[2], extrema(X[:,1])..., c=:magenta, lw=2)\n",
        "plot!(x -> -(w[1] * x + b - 1) / w[2], extrema(X[:,1])..., c=:blue, l=:dash)\n",
        "plot!(x -> -(w[1] * x + b + 1) / w[2], extrema(X[:,1])..., c=:red, l=:dash)\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 95,
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      ],
      "execution_count": 95,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "termination_status(model)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": [
              "LOCALLY_INFEASIBLE::TerminationStatusCode = 5"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "\n",
        "C = 1e3\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\"=>0))\n",
        "\n",
        "@variable(model, w[1:2])\n",
        "@variable(model, b)\n",
        "@variable(model, ξ[1:n] ≥ 0)\n",
        "\n",
        "@objective(model, Min, dot(w, w) / 2 + C * sum(ξ))\n",
        "\n",
        "@constraint(model, restr[i=1:n], (dot(w, X[i,:]) + b) * y[i] ≥ 1 - ξ[i])\n",
        "\n",
        "#print(model)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "w, b, ξ = value.(w), value(b), value.(ξ)\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = dual.(restr)\n",
        "I = findall(1e-4 .< α .< C - 1e-4)\n",
        "#I = findall(1e-4 .< α)\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "plot!(x -> -(w[1] * x + b) / w[2], extrema(X[:,1])..., c=:magenta, lw=2)\n",
        "plot!(x -> -(w[1] * x + b - 1) / w[2], extrema(X[:,1])..., c=:blue, l=:dash)\n",
        "plot!(x -> -(w[1] * x + b + 1) / w[2], extrema(X[:,1])..., c=:red, l=:dash)\n",
        "\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 104,
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          "metadata": {}
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      ],
      "execution_count": 104,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "sort(α, rev=true)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 102,
          "data": {
            "text/plain": [
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              " 999.9999999908825\n",
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              "   ⋮\n",
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          "metadata": {}
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      ],
      "execution_count": 102,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using Random, LinearAlgebra\n",
        "\n",
        "Random.seed!(0)\n",
        "\n",
        "n = 100\n",
        "X = randn(n, 2) * 2\n",
        "y = [X[i,1]^2 + X[i,2]^2 > 3.5 ? 1 : -1 for i = 1:n]\n",
        "\n",
        "plot(leg=false)\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 112,
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      ],
      "execution_count": 112,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "ϕX = [X X[:,1].^2 + X[:,2].^2] # (x₁, x₂) → (x₁, x₂, x₁²+x₂²)\n",
        "\n",
        "plot(leg=false)\n",
        "I = findall(y .== 1)\n",
        "scatter!(ϕX[I,1], ϕX[I,2], ϕX[I,3], c=:blue, m=:square, ms=1)\n",
        "I = findall(y .== -1)\n",
        "scatter!(ϕX[I,1], ϕX[I,2], ϕX[I,3], c=:red, m=:circle, ms=1)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 113,
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          "metadata": {}
        }
      ],
      "execution_count": 113,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "gr()\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\"=>0))\n",
        "\n",
        "ϕ(x) = [x[1], x[2], x[1]^2 + x[2]^2]\n",
        "p = 3\n",
        "\n",
        "@variable(model, w[1:p])\n",
        "@variable(model, b)\n",
        "@variable(model, ξ[1:n] ≥ 0)\n",
        "\n",
        "@objective(model, Min, dot(w, w) / 2)\n",
        "\n",
        "@constraint(model, restr[i=1:n], (dot(w, ϕ(X[i,:])) + b) * y[i] ≥ 1)\n",
        "\n",
        "#print(model)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "w, b = value.(w), value(b)\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = dual.(restr)\n",
        "#I = findall(1e-4 .< α .< C - 1e-4)\n",
        "I = findall(1e-4 .< α)\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "x1g = range(extrema(X[:,1])..., length=100)\n",
        "x2g = range(extrema(X[:,2])..., length=100)\n",
        "\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[0.0])\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[1.0], c=:blue, l=:dash)\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[-1.0], c=:red, l=:dash)\n",
        "\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 114,
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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 114,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using Random, LinearAlgebra\n",
        "\n",
        "Random.seed!(0)\n",
        "n = 100\n",
        "X = randn(n, 2)\n",
        "w_sol = [0.5; 0.4]\n",
        "b_sol = -0.5\n",
        "y = [dot(w_sol, X[i,:]) + b_sol > randn() * 0.3 ? 1 : -1 for i = 1:n]\n",
        "\n",
        "plot(leg=false)\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)"
      ],
      "outputs": [
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          "output_type": "execute_result",
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          "metadata": {}
        }
      ],
      "execution_count": 116,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "gr()\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\"=>0))\n",
        "\n",
        "ϕ(x) = [x[1], x[2], x[1]^2, x[2]^2, x[1] * x[2], x[1]^3, x[1]^2 * x[2], x[1] * x[2]^2, x[2]^3]\n",
        "p = 9\n",
        "C = 1.0e3\n",
        "\n",
        "@variable(model, w[1:p])\n",
        "@variable(model, b)\n",
        "@variable(model, ξ[1:n] ≥ 0)\n",
        "\n",
        "# p + 1 + n\n",
        "\n",
        "@objective(model, Min, dot(w, w) / 2 + C * sum(ξ))\n",
        "\n",
        "@constraint(model, restr[i=1:n], (dot(w, ϕ(X[i,:])) + b) * y[i] ≥ 1 - ξ[i])\n",
        "\n",
        "# n\n",
        "\n",
        "#print(model)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "w, b, ξ = value.(w), value(b), value.(ξ)\n",
        "\n",
        "print(termination_status(model))\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = dual.(restr)\n",
        "I = findall(1e-4 .< α .< C - 1e-4)\n",
        "#I = findall(1e-4 .< α)\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "x1g = range(extrema(X[:,1])..., length=400)\n",
        "x2g = range(extrema(X[:,2])..., length=400)\n",
        "\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[0.0], c=:magenta, lw=2)\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[1.0], c=:blue, l=:dash)\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[-1.0], c=:red, l=:dash)\n",
        "\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "LOCALLY_SOLVED"
          ]
        },
        {
          "output_type": "execute_result",
          "execution_count": 119,
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              "  2268.69,1162.61 2265.97,1159 2264.1,1156.51 2263.25,1155.39 2260.49,1151.78 2258.56,1149.24 2257.74,1148.17 2254.95,1144.56 2253.02,1142.06 2252.15,1140.95 \n",
              "  2249.33,1137.34 2247.48,1134.97 2246.5,1133.73 2243.64,1130.12 2241.93,1127.97 2240.77,1126.51 2237.88,1122.91 2236.39,1121.05 2234.97,1119.3 2232.04,1115.69 \n",
              "  2230.85,1114.22 2229.09,1112.08 2226.13,1108.47 2225.31,1107.46 2223.14,1104.86 2220.15,1101.25 2219.77,1100.79 2217.12,1097.64 2214.23,1094.19 2214.09,1094.03 \n",
              "  2211.02,1090.42 2208.69,1087.67 2207.94,1086.81 2204.84,1083.2 2203.15,1081.23 2201.72,1079.59 2198.59,1075.98 2197.61,1074.85 2195.42,1072.37 2192.26,1068.76 \n",
              "  2192.06,1068.54 2189.04,1065.15 2186.52,1062.31 2185.83,1061.54 2182.59,1057.93 2180.98,1056.14 2179.33,1054.32 2176.05,1050.71 2175.44,1050.04 2172.74,1047.1 \n",
              "  2169.9,1044 2169.43,1043.49 2166.08,1039.88 2164.36,1038.03 2162.71,1036.27 2159.34,1032.67 2158.82,1032.11 2155.92,1029.06 2153.28,1026.26 2152.5,1025.45 \n",
              "  2149.04,1021.84 2147.74,1020.47 2145.56,1018.23 2142.19,1014.73 2142.08,1014.62 2138.55,1011.01 2136.65,1009.06 2135.01,1007.4 2131.46,1003.79 2131.11,1003.44 \n",
              "  2127.86,1000.18 2125.57,997.874 2124.25,996.569 2120.63,992.959 2120.03,992.363 2116.96,989.35 2114.49,986.908 2113.29,985.74 2109.59,982.131 2108.95,981.503 \n",
              "  2105.85,978.521 2103.41,976.153 2102.1,974.911 2098.34,971.302 2097.87,970.85 2094.52,967.692 2092.33,965.602 2090.7,964.083 2086.86,960.473 2086.78,960.397 \n",
              "  2082.97,956.863 2081.24,955.249 2079.07,953.254 2075.7,950.143 2075.15,949.644 2071.19,946.035 2070.16,945.088 2067.2,942.425 2064.62,940.079 2063.2,938.815 \n",
              "  2059.18,935.206 2059.08,935.112 2055.11,931.596 2053.54,930.197 2051.01,927.987 2048,925.324 2046.9,924.377 2042.77,920.767 2042.46,920.493 2038.58,917.158 \n",
              "  2036.91,915.711 2034.37,913.548 2031.37,910.969 2030.15,909.939 2025.9,906.329 2025.83,906.268 2021.6,902.719 2020.29,901.615 2017.27,899.11 2014.75,897.002 \n",
              "  2012.92,895.5 2009.21,892.428 2008.55,891.891 2004.13,888.281 2003.67,887.897 1999.67,884.671 1998.13,883.409 1995.19,881.062 1992.59,878.96 1990.68,877.452 \n",
              "  1987.04,874.549 1986.14,873.843 1981.57,870.233 1981.5,870.176 1976.95,866.623 1975.96,865.849 1972.29,863.014 1970.42,861.56 1967.6,859.404 1964.88,857.308 \n",
              "  1962.88,855.795 1959.34,853.093 1958.12,852.185 1953.8,848.916 1953.34,848.575 1948.5,844.966 1948.26,844.779 1943.62,841.356 1942.72,840.682 1938.7,837.747 \n",
              "  1937.17,836.622 1933.74,834.137 1931.63,832.599 1928.74,830.527 1926.09,828.613 1923.7,826.918 1920.55,824.664 1918.62,823.308 1915.01,820.752 1913.49,819.699 \n",
              "  1909.47,816.877 1908.32,816.089 1903.93,813.038 1903.11,812.479 1898.39,809.237 1897.84,808.87 1892.85,805.472 1892.53,805.26 1887.31,801.744 1887.16,801.651 \n",
              "  1881.76,798.052 1881.75,798.041 1876.27,794.431 1876.22,794.398 1870.74,790.822 1870.68,790.781 1865.16,787.212 1865.14,787.2 1859.6,783.655 1859.52,783.603 \n",
              "  1854.06,780.148 1853.81,779.993 1848.52,776.678 1848.04,776.383 1842.98,773.245 1842.2,772.774 1837.44,769.848 1836.29,769.164 1831.89,766.489 1830.32,765.555 \n",
              "  1826.35,763.167 1824.27,761.945 1820.81,759.882 1818.15,758.335 1815.27,756.634 1811.96,754.726 1809.73,753.423 1805.68,751.116 1804.19,750.25 1799.33,747.507 \n",
              "  1798.65,747.115 1793.11,744.018 1792.88,743.897 1787.57,740.964 1786.31,740.287 1782.02,737.948 1779.64,736.678 1776.48,734.971 1772.87,733.068 1770.94,732.032 \n",
              "  1766.01,729.459 1765.4,729.133 1759.86,726.277 1759,725.849 1754.32,723.464 1751.85,722.239 1748.78,720.691 1744.58,718.63 1743.24,717.959 1737.7,715.27 \n",
              "  1737.16,715.02 1732.15,712.63 1729.53,711.411 1726.61,710.032 1721.76,707.801 1721.07,707.476 1715.53,704.971 1713.75,704.191 1709.99,702.513 1705.54,700.582 \n",
              "  1704.45,700.099 1698.91,697.738 1697.04,696.972 1693.37,695.428 1688.3,693.363 1687.83,693.166 1682.29,690.962 1679.14,689.753 1676.74,688.81 1671.2,686.714 \n",
              "  1669.62,686.143 1665.66,684.677 1660.12,682.696 1659.64,682.534 1654.58,680.781 1649.04,678.924 1649.04,678.924 1643.5,677.139 1637.96,675.416 1637.61,675.315 \n",
              "  1632.42,673.767 1626.87,672.188 1625.05,671.705 1621.33,670.687 1615.79,669.262 1610.95,668.095 1610.25,667.919 1604.71,666.661 1599.17,665.489 1594.01,664.486 \n",
              "  1593.63,664.409 1588.09,663.421 1582.55,662.529 1577,661.738 1571.46,661.048 1569.79,660.876 1565.92,660.459 1560.38,659.971 1554.84,659.587 1549.3,659.303 \n",
              "  1543.76,659.117 1538.22,659.021 1532.68,659.007 1527.13,659.064 1521.59,659.178 1516.05,659.332 1510.51,659.507 1504.97,659.681 1499.43,659.829 1493.89,659.927 \n",
              "  1488.35,659.948 1482.81,659.866 1477.27,659.656 1471.72,659.293 1466.18,658.758 1460.64,658.032 1456.09,657.267 1455.1,657.09 1449.56,655.864 1444.02,654.399 \n",
              "  1441.63,653.657 1438.48,652.617 1432.94,650.519 1431.84,650.047 1427.4,648.006 1424.34,646.438 1421.85,645.074 1418.17,642.828 1416.31,641.612 1413,639.219 \n",
              "  1410.77,637.475 1408.59,635.609 1405.23,632.46 1404.78,631.999 1401.6,628.39 1399.69,625.944 1398.85,624.78 1396.6,621.171 1394.7,617.561 1394.15,616.24 \n",
              "  1393.26,613.951 1392.21,610.342 1391.52,606.732 1391.19,603.123 1391.23,599.513 1391.64,595.903 1392.39,592.294 1393.49,588.684 1394.15,587.002 1394.95,585.075 \n",
              "  1396.77,581.465 1398.85,577.855 1399.69,576.558 1401.24,574.246 1403.86,570.636 1405.23,568.868 1406.68,567.027 1409.63,563.417 1410.77,562.067 1412.67,559.807 \n",
              "  1415.72,556.198 1416.31,555.508 1418.75,552.588 1421.7,548.979 1421.85,548.791 1424.54,545.369 1427.24,541.759 1427.4,541.549 1429.77,538.15 1432.15,534.54 \n",
              "  1432.94,533.308 1434.35,530.931 1436.39,527.321 1438.27,523.711 1438.48,523.307 1439.98,520.102 1441.55,516.492 1442.98,512.883 1444.02,510.065 1444.29,509.273 \n",
              "  1445.45,505.663 1446.51,502.054 1447.46,498.444 1448.32,494.835 1449.08,491.225 1449.56,488.727 1449.76,487.615 1450.34,484.006 1450.84,480.396 1451.28,476.787 \n",
              "  1451.65,473.177 1451.95,469.567 1452.2,465.958 1452.39,462.348 1452.52,458.739 1452.6,455.129 1452.64,451.519 1452.63,447.91 1452.58,444.3 1452.48,440.691 \n",
              "  1452.34,437.081 1452.17,433.471 1451.96,429.862 1451.72,426.252 1451.44,422.643 1451.13,419.033 1450.8,415.423 1450.43,411.814 1450.04,408.204 1449.62,404.595 \n",
              "  1449.56,404.116 1449.17,400.985 1448.69,397.375 1448.18,393.766 1447.66,390.156 1447.11,386.547 1446.54,382.937 1445.96,379.327 1445.35,375.718 1444.73,372.108 \n",
              "  1444.09,368.499 1444.02,368.138 1443.41,364.889 1442.72,361.279 1442.02,357.67 1441.3,354.06 1440.56,350.451 1439.81,346.841 1439.05,343.231 1438.48,340.565 \n",
              "  1438.27,339.622 1437.47,336.012 1436.65,332.403 1435.82,328.793 1434.99,325.183 1434.14,321.574 1433.28,317.964 1432.94,316.568 1432.4,314.355 1431.5,310.745 \n",
              "  1430.59,307.135 1429.68,303.526 1428.75,299.916 1427.82,296.307 1427.4,294.692 1426.87,292.697 1425.9,289.087 1424.93,285.478 1423.95,281.868 1422.96,278.259 \n",
              "  1421.97,274.649 1421.85,274.25 1420.95,271.039 1419.92,267.43 1418.89,263.82 1417.85,260.211 1416.81,256.601 1416.31,254.9 1415.75,252.991 1414.68,249.382 \n",
              "  1413.6,245.772 1412.52,242.163 1411.44,238.553 1410.77,236.364 1410.34,234.943 1409.23,231.334 1408.11,227.724 1406.99,224.115 1405.86,220.505 1405.23,218.495 \n",
              "  1404.73,216.895 1403.58,213.286 1402.42,209.676 1401.27,206.067 1400.11,202.457 1399.69,201.176 1398.93,198.847 1397.75,195.238 1396.56,191.628 1395.37,188.019 \n",
              "  1394.18,184.409 1394.15,184.309 1392.97,180.799 1391.76,177.19 1390.54,173.58 1389.32,169.971 1388.61,167.867 1388.1,166.361 1386.86,162.751 1385.61,159.142 \n",
              "  1384.37,155.532 1383.13,151.923 1383.07,151.747 1381.86,148.313 1380.6,144.703 1379.33,141.094 1378.07,137.484 1377.53,135.955 1376.79,133.875 1375.5,130.265 \n",
              "  1374.21,126.655 1372.93,123.046 1371.98,120.42 1371.63,119.436 1370.32,115.827 1369.02,112.217 1367.71,108.607 1366.44,105.122 1366.4,104.998 1365.07,101.388 \n",
              "  1363.74,97.7785 1362.42,94.1689 1361.09,90.5593 1360.9,90.0557 1359.75,86.9497 1358.4,83.3401 1357.06,79.7305 1355.71,76.1209 1355.36,75.1873 1354.35,72.5113 \n",
              "  1352.99,68.9017 1351.63,65.2921 1350.27,61.6825 1349.82,60.498 1348.9,58.0729 1347.52,54.4633 1346.14,50.8537 1344.77,47.2441 \n",
              "  \"/>\n",
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              "  2352.76,1362.88 2351.74,1361.14 2349.64,1357.53 2347.54,1353.92 2347.21,1353.36 2345.41,1350.31 2343.28,1346.7 2341.67,1343.99 2341.14,1343.09 2338.97,1339.48 \n",
              "  2336.8,1335.87 2336.13,1334.76 2334.61,1332.26 2332.41,1328.65 2330.59,1325.68 2330.2,1325.04 2327.96,1321.43 2325.72,1317.82 2325.05,1316.74 2323.46,1314.21 \n",
              "  2321.19,1310.6 2319.51,1307.93 2318.91,1306.99 2316.6,1303.39 2314.3,1299.78 2313.97,1299.26 2311.96,1296.17 2309.61,1292.56 2308.43,1290.73 2307.25,1288.95 \n",
              "  2304.87,1285.34 2302.89,1282.32 2302.49,1281.73 2300.07,1278.12 2297.66,1274.51 2297.35,1274.04 2295.2,1270.9 2292.75,1267.29 2291.8,1265.89 2290.28,1263.68 \n",
              "  2287.79,1260.07 2286.26,1257.86 2285.28,1256.46 2282.75,1252.85 2280.72,1249.95 2280.22,1249.24 2277.65,1245.63 2275.18,1242.15 2275.09,1242.02 2272.48,1238.41 \n",
              "  2269.88,1234.8 2269.64,1234.47 2267.23,1231.19 2264.59,1227.58 2264.1,1226.91 2261.92,1223.97 2259.24,1220.36 2258.56,1219.45 2256.53,1216.75 2253.81,1213.15 \n",
              "  2253.02,1212.09 2251.06,1209.54 2248.3,1205.93 2247.48,1204.85 2245.51,1202.32 2242.71,1198.71 2241.93,1197.7 2239.88,1195.1 2237.04,1191.49 2236.39,1190.66 \n",
              "  2234.17,1187.88 2231.29,1184.27 2230.85,1183.71 2228.38,1180.66 2225.46,1177.05 2225.31,1176.86 2222.5,1173.44 2219.77,1170.11 2219.54,1169.83 2216.53,1166.22 \n",
              "  2214.23,1163.45 2213.52,1162.61 2210.47,1159 2208.69,1156.88 2207.41,1155.39 2204.33,1151.78 2203.15,1150.4 2201.21,1148.17 2198.09,1144.56 2197.61,1144 \n",
              "  2194.92,1140.95 2192.06,1137.69 2191.75,1137.34 2188.53,1133.73 2186.52,1131.47 2185.31,1130.12 2182.05,1126.51 2180.98,1125.33 2178.76,1122.91 2175.47,1119.3 \n",
              "  2175.44,1119.27 2172.11,1115.69 2169.9,1113.29 2168.76,1112.08 2165.37,1108.47 2164.36,1107.39 2161.94,1104.86 2158.82,1101.56 2158.51,1101.25 2155.02,1097.64 \n",
              "  2153.28,1095.82 2151.52,1094.03 2148,1090.42 2147.74,1090.15 2144.42,1086.81 2142.19,1084.55 2140.83,1083.2 2137.22,1079.59 2136.65,1079.03 2133.55,1075.98 \n",
              "  2131.11,1073.58 2129.86,1072.37 2126.15,1068.76 2125.57,1068.2 2122.38,1065.15 2120.03,1062.89 2118.6,1061.54 2114.79,1057.93 2114.49,1057.65 2110.91,1054.32 \n",
              "  2108.95,1052.48 2107.02,1050.71 2103.41,1047.38 2103.1,1047.1 2099.12,1043.49 2097.87,1042.35 2095.11,1039.88 2092.33,1037.38 2091.06,1036.27 2086.99,1032.67 \n",
              "  2086.78,1032.48 2082.84,1029.06 2081.24,1027.65 2078.67,1025.45 2075.7,1022.89 2074.46,1021.84 2070.21,1018.23 2070.16,1018.18 2065.89,1014.62 2064.62,1013.55 \n",
              "  2061.53,1011.01 2059.08,1008.98 2057.12,1007.4 2053.54,1004.47 2052.68,1003.79 2048.18,1000.18 2048,1000.03 2043.61,996.569 2042.46,995.652 2038.99,992.959 \n",
              "  2036.91,991.339 2034.31,989.35 2031.37,987.088 2029.58,985.74 2025.83,982.9 2024.79,982.131 2020.29,978.776 2019.94,978.521 2015.01,974.911 2014.75,974.717 \n",
              "  2010.01,971.302 2009.21,970.723 2004.93,967.692 2003.67,966.792 1999.77,964.083 1998.13,962.925 1994.54,960.473 1992.59,959.123 1989.22,956.863 1987.04,955.385 \n",
              "  1983.82,953.254 1981.5,951.712 1978.32,949.644 1975.96,948.104 1972.71,946.035 1970.42,944.561 1967,942.425 1964.88,941.085 1961.18,938.815 1959.34,937.675 \n",
              "  1955.24,935.206 1953.8,934.332 1949.16,931.596 1948.26,931.056 1942.95,927.987 1942.72,927.849 1937.17,924.711 1936.57,924.377 1931.63,921.644 1930,920.767 \n",
              "  1926.09,918.647 1923.26,917.158 1920.55,915.72 1916.33,913.548 1915.01,912.864 1909.47,910.081 1909.18,909.939 1903.93,907.374 1901.72,906.329 1898.39,904.74 \n",
              "  1894,902.719 1892.85,902.181 1887.31,899.699 1885.94,899.11 1881.76,897.295 1877.48,895.5 1876.22,894.969 1870.68,892.723 1868.54,891.891 1865.14,890.558 \n",
              "  1859.6,888.473 1859.06,888.281 1854.06,886.473 1848.85,884.671 1848.52,884.554 1842.98,882.722 1837.71,881.062 1837.44,880.973 1831.89,879.312 1826.35,877.737 \n",
              "  1825.28,877.452 1820.81,876.25 1815.27,874.85 1811,873.843 1809.73,873.539 1804.19,872.315 1798.65,871.18 1793.63,870.233 1793.11,870.133 1787.57,869.171 \n",
              "  1782.02,868.297 1776.48,867.507 1770.94,866.802 1769.34,866.623 1765.4,866.177 1759.86,865.63 1754.32,865.159 1748.78,864.762 1743.24,864.435 1737.7,864.173 \n",
              "  1732.15,863.972 1726.61,863.828 1721.07,863.735 1715.53,863.687 1709.99,863.68 1704.45,863.707 1698.91,863.761 1693.37,863.838 1687.83,863.931 1682.29,864.033 \n",
              "  1676.74,864.138 1671.2,864.241 1665.66,864.336 1660.12,864.417 1654.58,864.478 1649.04,864.515 1643.5,864.523 1637.96,864.497 1632.42,864.433 1626.87,864.327 \n",
              "  1621.33,864.176 1615.79,863.976 1610.25,863.726 1604.71,863.422 1599.17,863.063 1598.52,863.014 1593.63,862.64 1588.09,862.155 1582.55,861.61 1577,861.003 \n",
              "  1571.46,860.334 1565.92,859.604 1564.54,859.404 1560.38,858.798 1554.84,857.925 1549.3,856.989 1543.76,855.991 1542.75,855.795 1538.22,854.912 1532.68,853.768 \n",
              "  1527.13,852.564 1525.49,852.185 1521.59,851.28 1516.05,849.93 1510.72,848.575 1510.51,848.521 1504.97,847.024 1499.43,845.473 1497.7,844.966 1493.89,843.843 \n",
              "  1488.35,842.15 1485.85,841.356 1482.81,840.384 1477.27,838.551 1474.92,837.747 1471.72,836.646 1466.18,834.677 1464.72,834.137 1460.64,832.63 1455.1,830.528 \n",
              "  1455.1,830.527 1449.56,828.336 1446.06,826.918 1444.02,826.087 1438.48,823.768 1437.41,823.308 1432.94,821.369 1429.17,819.699 1427.4,818.909 1421.85,816.379 \n",
              "  1421.24,816.089 1416.31,813.766 1413.65,812.479 1410.77,811.087 1406.29,808.87 1405.23,808.342 1399.69,805.52 1399.19,805.26 1394.15,802.616 1392.35,801.651 \n",
              "  1388.61,799.641 1385.7,798.041 1383.07,796.593 1379.23,794.431 1377.53,793.47 1372.94,790.822 1371.98,790.27 1366.82,787.212 1366.44,786.991 1360.9,783.631 \n",
              "  1360.86,783.603 1355.36,780.184 1355.06,779.993 1349.82,776.655 1349.4,776.383 1344.28,773.042 1343.88,772.774 1338.74,769.342 1338.48,769.164 1333.2,765.555 \n",
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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 119,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using Random, LinearAlgebra\n",
        "\n",
        "Random.seed!(0)\n",
        "n = 100\n",
        "X = randn(n, 2)\n",
        "w_sol = [0.5; 0.4]\n",
        "b_sol = -0.5\n",
        "y = [dot(w_sol, X[i,:]) + b_sol > randn() * 0.3 ? 1 : -1 for i = 1:n]\n",
        "\n",
        "plot(leg=false)\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)"
      ],
      "outputs": [
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          "metadata": {}
        }
      ],
      "execution_count": 136,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "\n",
        "C = 1e2\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\" => 0))\n",
        "\n",
        "@variable(model, 0 ≤ α[i=1:n] ≤ C)\n",
        "\n",
        "@objective(model, Max, sum(α) -\n",
        "    0.5 * sum(α[i] * α[j] * y[i] * y[j] * dot(X[i,:], X[j,:]) for i = 1:n, j = 1:n))\n",
        "@constraint(model, sum(α .* y) == 0)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = value.(α)\n",
        "I = findall(1e-4 .< α .< C - 1e-4)\n",
        "\n",
        "w = sum(α[i] * y[i] * X[i,:] for i = 1:n)\n",
        "k = I[1]\n",
        "b = y[k] - dot(w, X[k,:])\n",
        "\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "plot!(x -> -(w[1] * x + b) / w[2], extrema(X[:,1])..., c=:magenta, lw=2)\n",
        "plot!(x -> -(w[1] * x + b - 1) / w[2], extrema(X[:,1])..., c=:blue, l=:dash)\n",
        "plot!(x -> -(w[1] * x + b + 1) / w[2], extrema(X[:,1])..., c=:red, l=:dash)\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 137,
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      ],
      "execution_count": 137,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "\n",
        "ϕ(x) = [x[1], x[2], x[1]^2, x[2]^2, x[1] * x[2], x[1]^3, x[1]^2 * x[2], x[1] * x[2]^2, x[2]^3]\n",
        "C = 1e3\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\" => 0))\n",
        "\n",
        "@variable(model, 0 ≤ α[i=1:n] ≤ C)\n",
        "\n",
        "@objective(model, Max, sum(α) -\n",
        "    0.5 * sum(α[i] * α[j] * y[i] * y[j] * dot(ϕ(X[i,:]), ϕ(X[j,:])) for i = 1:n, j = 1:n))\n",
        "@constraint(model, sum(α .* y) == 0)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = value.(α)\n",
        "I = findall(1e-4 .< α .< C - 1e-4)\n",
        "J = findall(α .> 1e-4)\n",
        "\n",
        "w = sum(α[i] * y[i] * ϕ(X[i,:]) for i = J)\n",
        "k = I[1]\n",
        "b = y[k] - dot(w, ϕ(X[k,:]))\n",
        "\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "x1g = range(extrema(X[:,1])..., length=400)\n",
        "x2g = range(extrema(X[:,2])..., length=400)\n",
        "\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[0.0], c=:magenta, lw=2)\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[1.0], c=:blue, l=:dash)\n",
        "contour!(x1g, x2g, (x1, x2) -> dot(w, ϕ([x1; x2])) + b, levels=[-1.0], c=:red, l=:dash)\n",
        "\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
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          "output_type": "execute_result",
          "execution_count": 141,
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          "metadata": {}
        }
      ],
      "execution_count": 141,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "using JuMP, Ipopt\n",
        "\n",
        "σ = 1\n",
        "K(x1, x2) = exp(-norm(x1 - x2)^2 / 2σ^2)\n",
        "Kmat = [K(X[i,:], X[j,:]) for i = 1:n, j = 1:n]\n",
        "C = 1e6\n",
        "\n",
        "model = Model(optimizer_with_attributes(Ipopt.Optimizer, \"print_level\" => 0))\n",
        "\n",
        "@variable(model, 0 ≤ α[i=1:n] ≤ C)\n",
        "\n",
        "@objective(model, Max, sum(α) -\n",
        "    0.5 * sum(α[i] * α[j] * y[i] * y[j] * Kmat[i,j] for i = 1:n, j = 1:n))\n",
        "@constraint(model, sum(α .* y) == 0)\n",
        "\n",
        "optimize!(model)\n",
        "\n",
        "plot(leg=false)\n",
        "\n",
        "α = value.(α)\n",
        "I = findall(1e-4 .< α .< C - 1e-4)\n",
        "J = findall(α .> 1e-4)\n",
        "\n",
        "k = I[1]\n",
        "b = y[k] - sum(α[i] * y[i] * K(X[i,:], X[k,:]) for i = J)\n",
        "\n",
        "scatter!(X[I,1], X[I,2], c=:green, m=(:white,stroke(1,:green),10))\n",
        "\n",
        "I = findall(y .== 1)\n",
        "scatter!(X[I,1], X[I,2], c=:blue, m=:square)\n",
        "I = findall(y .== -1)\n",
        "scatter!(X[I,1], X[I,2], c=:red, m=:circle)\n",
        "\n",
        "x1g = range(extrema(X[:,1])..., length=400)\n",
        "x2g = range(extrema(X[:,2])..., length=400)\n",
        "\n",
        "F(x) = sum(α[i] * y[i] * K(x, X[i,:]) for i = J) + b\n",
        "contour!(x1g, x2g, (x1, x2) -> F([x1; x2]), levels=[0.0], c=:magenta, lw=2)\n",
        "contour!(x1g, x2g, (x1, x2) -> F([x1; x2]), levels=[1.0], c=:blue, l=:dash)\n",
        "contour!(x1g, x2g, (x1, x2) -> F([x1; x2]), levels=[-1.0], c=:red, l=:dash)\n",
        "\n",
        "xlims!(extrema(X[:,1])...)\n",
        "ylims!(extrema(X[:,2])...)"
      ],
      "outputs": [
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              "  2340.37,1122.91 2340.4,1119.3 2340.42,1115.69 2340.41,1112.08 2340.39,1108.47 2340.34,1104.86 2340.27,1101.25 2340.17,1097.64 2340.04,1094.03 2339.88,1090.42 \n",
              "  2339.68,1086.81 2339.44,1083.2 2339.17,1079.59 2338.85,1075.98 2338.48,1072.37 2338.06,1068.76 2337.59,1065.15 2337.06,1061.54 2336.47,1057.93 2336.13,1056.04 \n",
              "  2335.81,1054.32 2335.07,1050.71 2334.25,1047.1 2333.35,1043.49 2332.37,1039.88 2331.3,1036.27 2330.59,1034.09 2330.11,1032.67 2328.8,1029.06 2327.38,1025.45 \n",
              "  2325.85,1021.84 2325.05,1020.09 2324.16,1018.23 2322.3,1014.62 2320.3,1011.01 2319.51,1009.66 2318.1,1007.4 2315.7,1003.79 2313.97,1001.35 2313.09,1000.18 \n",
              "  2310.21,996.569 2308.43,994.469 2307.07,992.959 2303.62,989.35 2302.89,988.623 2299.79,985.74 2297.35,983.593 2295.57,982.131 2291.8,979.192 2290.89,978.521 \n",
              "  2286.26,975.319 2285.63,974.911 2280.72,971.893 2279.69,971.302 2275.18,968.845 2272.9,967.692 2269.64,966.12 2265.06,964.083 2264.1,963.671 2258.56,961.489 \n",
              "  2255.75,960.473 2253.02,959.526 2247.48,957.767 2244.35,956.863 2241.93,956.192 2236.39,954.791 2230.85,953.531 2229.49,953.254 2225.31,952.429 2219.77,951.456 \n",
              "  2214.23,950.601 2208.69,949.856 2206.86,949.644 2203.15,949.228 2197.61,948.703 2192.06,948.272 2186.52,947.931 2180.98,947.675 2175.44,947.502 2169.9,947.408 \n",
              "  2164.36,947.389 2158.82,947.444 2153.28,947.57 2147.74,947.764 2142.19,948.024 2136.65,948.349 2131.11,948.736 2125.57,949.185 2120.55,949.644 2120.03,949.694 \n",
              "  2114.49,950.276 2108.95,950.917 2103.41,951.617 2097.87,952.375 2092.33,953.19 2091.91,953.254 2086.78,954.086 2081.24,955.043 2075.7,956.061 2071.55,956.863 \n",
              "  2070.16,957.148 2064.62,958.323 2059.08,959.567 2055.21,960.473 2053.54,960.892 2048,962.323 2042.46,963.835 2041.56,964.083 2036.91,965.478 2031.37,967.23 \n",
              "  2029.94,967.692 2025.83,969.138 2020.29,971.193 2020,971.302 2014.75,973.468 2011.41,974.911 2009.21,975.965 2004.08,978.521 2003.67,978.747 1998.13,981.906 \n",
              "  1997.74,982.131 1992.59,985.544 1992.3,985.74 1987.6,989.35 1987.04,989.83 1983.52,992.959 1981.5,995.012 1980,996.569 1976.93,1000.18 1975.96,1001.46 \n",
              "  1974.21,1003.79 1971.81,1007.4 1970.42,1009.72 1969.66,1011.01 1967.67,1014.62 1965.89,1018.23 1964.88,1020.4 1964.21,1021.84 1962.61,1025.45 1961.1,1029.06 \n",
              "  1959.66,1032.67 1959.34,1033.48 1958.22,1036.27 1956.79,1039.88 1955.39,1043.49 1953.99,1047.1 1953.8,1047.6 1952.53,1050.71 1951.05,1054.32 1949.55,1057.93 \n",
              "  1948.26,1060.95 1948,1061.54 1946.35,1065.15 1944.65,1068.76 1942.91,1072.37 1942.72,1072.74 1941.02,1075.98 1939.06,1079.59 1937.17,1082.93 1937.02,1083.2 \n",
              "  1934.8,1086.81 1932.5,1090.42 1931.63,1091.72 1930.03,1094.03 1927.41,1097.64 1926.09,1099.38 1924.61,1101.25 1921.63,1104.86 1920.55,1106.1 1918.4,1108.47 \n",
              "  1915.01,1112.04 1914.97,1112.08 1911.18,1115.69 1909.47,1117.25 1907.08,1119.3 1903.93,1121.89 1902.61,1122.91 1898.39,1126.01 1897.64,1126.51 1892.85,1129.64 \n",
              "  1892.04,1130.12 1887.31,1132.84 1885.58,1133.73 1881.76,1135.64 1877.93,1137.34 1876.22,1138.07 1870.68,1140.14 1868.13,1140.95 1865.14,1141.87 1859.6,1143.26 \n",
              "  1854.06,1144.34 1852.47,1144.56 1848.52,1145.09 1842.98,1145.5 1837.44,1145.59 1831.89,1145.33 1826.35,1144.72 1825.45,1144.56 1820.81,1143.7 1815.27,1142.26 \n",
              "  1811.38,1140.95 1809.73,1140.36 1804.19,1137.9 1803.14,1137.34 1798.65,1134.76 1797.11,1133.73 1793.11,1130.79 1792.31,1130.12 1788.43,1126.51 1787.57,1125.62 \n",
              "  1785.25,1122.91 1782.54,1119.3 1782.02,1118.51 1780.36,1115.69 1778.56,1112.08 1777.08,1108.47 1776.48,1106.63 1775.96,1104.86 1775.15,1101.25 1774.61,1097.64 \n",
              "  1774.33,1094.03 1774.29,1090.42 1774.5,1086.81 1774.93,1083.2 1775.59,1079.59 1776.45,1075.98 1776.48,1075.88 1777.59,1072.37 1778.93,1068.76 1780.47,1065.15 \n",
              "  1782.02,1061.87 1782.19,1061.54 1784.2,1057.93 1786.37,1054.32 1787.57,1052.47 1788.76,1050.71 1791.38,1047.1 1793.11,1044.85 1794.19,1043.49 1797.24,1039.88 \n",
              "  1798.65,1038.28 1800.49,1036.27 1803.92,1032.67 1804.19,1032.4 1807.64,1029.06 1809.73,1027.06 1811.51,1025.45 1815.27,1022.08 1815.56,1021.84 1819.86,1018.23 \n",
              "  1820.81,1017.43 1824.34,1014.62 1826.35,1013.01 1828.98,1011.01 1831.89,1008.77 1833.76,1007.4 1837.44,1004.67 1838.67,1003.79 1842.98,1000.66 1843.67,1000.18 \n",
              "  1848.52,996.722 1848.74,996.569 1853.84,992.959 1854.06,992.802 1858.94,989.35 1859.6,988.859 1863.94,985.74 1865.14,984.831 1868.8,982.131 1870.68,980.647 \n",
              "  1873.45,978.521 1876.22,976.204 1877.81,974.911 1881.76,971.347 1881.81,971.302 1885.57,967.692 1887.31,965.792 1888.89,964.083 1891.81,960.473 1892.85,959.005 \n",
              "  1894.37,956.863 1896.55,953.254 1898.33,949.644 1898.39,949.521 1899.87,946.035 1901.08,942.425 1902.01,938.815 1902.7,935.206 1903.16,931.596 1903.43,927.987 \n",
              "  1903.52,924.377 1903.44,920.767 1903.23,917.158 1902.87,913.548 1902.39,909.939 1901.79,906.329 1901.08,902.719 1900.26,899.11 1899.35,895.5 1898.39,892.063 \n",
              "  1898.34,891.891 1897.26,888.281 1896.1,884.671 1894.85,881.062 1893.51,877.452 1892.85,875.766 1892.11,873.843 1890.64,870.233 1889.09,866.623 1887.47,863.014 \n",
              "  1887.31,862.665 1885.79,859.404 1884.03,855.795 1882.2,852.185 1881.76,851.363 1880.31,848.575 1878.35,844.966 1876.31,841.356 1876.22,841.208 1874.21,837.747 \n",
              "  1872.03,834.137 1870.68,831.984 1869.78,830.527 1867.46,826.918 1865.14,823.426 1865.06,823.308 1862.58,819.699 1860.03,816.089 1859.6,815.502 1857.39,812.479 \n",
              "  1854.67,808.87 1854.06,808.091 1851.85,805.26 1848.95,801.651 1848.52,801.133 1845.94,798.041 1842.98,794.59 1842.84,794.431 1839.61,790.822 1837.44,788.449 \n",
              "  1836.29,787.212 1832.84,783.603 1831.89,782.645 1829.25,779.993 1826.35,777.171 1825.53,776.383 1821.65,772.774 1820.81,772.011 1817.6,769.164 1815.27,767.15 \n",
              "  1813.38,765.555 1809.73,762.559 1808.96,761.945 1804.32,758.335 1804.19,758.238 1799.4,754.726 1798.65,754.186 1794.2,751.116 1793.11,750.381 1788.66,747.507 \n",
              "  1787.57,746.815 1782.73,743.897 1782.02,743.481 1776.48,740.374 1776.32,740.287 1770.94,737.499 1769.26,736.678 1765.4,734.837 1761.44,733.068 1759.86,732.38 \n",
              "  1754.32,730.135 1752.51,729.459 1748.78,728.094 1743.24,726.246 1741.92,725.849 1737.7,724.602 1732.15,723.145 1728.23,722.239 1726.61,721.874 1721.07,720.795 \n",
              "  1715.53,719.894 1709.99,719.169 1704.57,718.63 1704.45,718.618 1698.91,718.246 1693.37,718.04 1687.83,717.999 1682.29,718.119 1676.74,718.396 1673.75,718.63 \n",
              "  1671.2,718.829 1665.66,719.415 1660.12,720.146 1654.58,721.016 1649.04,722.021 1647.97,722.239 1643.5,723.164 1637.96,724.432 1632.42,725.817 1632.3,725.849 \n",
              "  1626.87,727.326 1621.33,728.938 1619.65,729.459 1615.79,730.659 1610.25,732.473 1608.52,733.068 1604.71,734.38 1599.17,736.366 1598.33,736.678 1593.63,738.434 \n",
              "  1588.8,740.287 1588.09,740.563 1582.55,742.759 1579.73,743.897 1577,745.004 1571.46,747.291 1570.95,747.507 1565.92,749.62 1562.4,751.116 1560.38,751.973 \n",
              "  1554.84,754.345 1553.96,754.726 1549.3,756.732 1545.58,758.335 1543.76,759.119 1538.22,761.502 1537.18,761.945 1532.68,763.875 1528.72,765.555 1527.13,766.224 \n",
              "  1521.59,768.547 1520.1,769.164 1516.05,770.837 1511.28,772.774 1510.51,773.083 1504.97,775.285 1502.14,776.383 1499.43,777.431 1493.89,779.517 1492.59,779.993 \n",
              "  1488.35,781.542 1482.81,783.492 1482.48,783.603 1477.27,785.375 1471.72,787.174 1471.6,787.212 1466.18,788.897 1460.64,790.531 1459.61,790.822 1455.1,792.08 \n",
              "  1449.56,793.536 1445.92,794.431 1444.02,794.899 1438.48,796.167 1432.94,797.336 1429.29,798.041 1427.4,798.405 1421.85,799.375 1416.31,800.239 1410.77,800.999 \n",
              "  1405.24,801.651 1405.23,801.652 1399.69,802.198 1394.15,802.635 1388.61,802.961 1383.07,803.173 1377.53,803.272 1371.98,803.254 1366.44,803.119 1360.9,802.863 \n",
              "  1355.36,802.485 1349.82,801.983 1346.9,801.651 1344.28,801.352 1338.74,800.591 1333.2,799.696 1327.66,798.664 1324.71,798.041 1322.11,797.489 1316.57,796.167 \n",
              "  1311.03,794.695 1310.13,794.431 1305.49,793.063 1299.95,791.269 1298.68,790.822 1294.41,789.301 1289.01,787.212 1288.87,787.158 1283.33,784.82 1280.65,783.603 \n",
              "  1277.79,782.285 1273.15,779.993 1272.25,779.54 1266.7,776.569 1266.38,776.383 1261.16,773.353 1260.22,772.774 1255.62,769.877 1254.55,769.164 1250.08,766.119 \n",
              "  1249.3,765.555 1244.54,762.053 1244.4,761.945 1239.85,758.335 1239,757.641 1235.59,754.726 1233.46,752.849 1231.58,751.116 1227.92,747.638 1227.78,747.507 \n",
              "  1224.25,743.897 1222.38,741.924 1220.89,740.287 1217.71,736.678 1216.83,735.651 1214.72,733.068 1211.87,729.459 1211.29,728.704 1209.19,725.849 1206.64,722.239 \n",
              "  1205.75,720.93 1204.24,718.63 1201.96,715.02 1200.21,712.123 1199.79,711.411 1197.76,707.801 1195.83,704.191 1194.67,701.923 1194,700.582 1192.29,696.972 \n",
              "  1190.67,693.363 1189.13,689.753 1189.13,689.752 1187.71,686.143 1186.36,682.534 1185.1,678.924 1183.92,675.315 1183.59,674.246 1182.82,671.705 1181.81,668.095 \n",
              "  1180.87,664.486 1180.01,660.876 1179.21,657.267 1178.49,653.657 1178.05,651.219 1177.84,650.047 1177.26,646.438 1176.75,642.828 1176.3,639.219 1175.92,635.609 \n",
              "  1175.6,631.999 1175.34,628.39 1175.14,624.78 1175,621.171 1174.93,617.561 1174.91,613.951 1174.95,610.342 1175.04,606.732 1175.2,603.123 1175.41,599.513 \n",
              "  1175.67,595.903 1175.99,592.294 1176.36,588.684 1176.79,585.075 1177.26,581.465 1177.79,577.855 1178.05,576.283 1178.38,574.246 1179.02,570.636 1179.71,567.027 \n",
              "  1180.45,563.417 1181.24,559.807 1182.08,556.198 1182.96,552.588 1183.59,550.166 1183.9,548.979 1184.89,545.369 1185.93,541.759 1187.02,538.15 1188.15,534.54 \n",
              "  1189.13,531.533 1189.33,530.931 1190.56,527.321 1191.84,523.711 1193.17,520.102 1194.54,516.492 1194.67,516.15 1195.96,512.883 1197.43,509.273 1198.94,505.663 \n",
              "  1200.21,502.71 1200.5,502.054 1202.11,498.444 1203.76,494.835 1205.45,491.225 1205.75,490.596 1207.2,487.615 1208.99,484.006 1210.81,480.396 1211.29,479.463 \n",
              "  1212.69,476.787 1214.62,473.177 1216.57,469.567 1216.83,469.09 1218.59,465.958 1220.64,462.348 1222.38,459.33 1222.72,458.739 1224.86,455.129 1227.04,451.519 \n",
              "  1227.92,450.073 1229.26,447.91 1231.52,444.3 1233.46,441.238 1233.81,440.691 1236.16,437.081 1238.53,433.471 1239,432.761 1240.95,429.862 1243.4,426.252 \n",
              "  1244.54,424.59 1245.9,422.643 1248.43,419.033 1250.08,416.686 1250.99,415.423 1253.59,411.814 1255.62,409.013 1256.22,408.204 1258.89,404.595 1261.16,401.541 \n",
              "  1261.59,400.985 1264.32,397.375 1266.7,394.243 1267.07,393.766 1269.87,390.156 1272.25,387.095 1272.68,386.547 1275.53,382.937 1277.79,380.077 1278.39,379.327 \n",
              "  1281.29,375.718 1283.33,373.171 1284.2,372.108 1287.14,368.499 1288.87,366.359 1290.09,364.889 1293.06,361.279 1294.41,359.625 1296.05,357.67 1299.04,354.06 \n",
              "  1299.95,352.954 1302.06,350.451 1305.07,346.841 1305.49,346.331 1308.11,343.231 1311.03,339.739 1311.13,339.622 1314.18,336.012 1316.57,333.15 1317.21,332.403 \n",
              "  1320.26,328.793 1322.11,326.561 1323.29,325.183 1326.32,321.574 1327.66,319.955 1329.34,317.964 1332.35,314.355 1333.2,313.314 1335.35,310.745 1338.32,307.135 \n",
              "  1338.74,306.616 1341.29,303.526 1344.22,299.916 1344.28,299.838 1347.14,296.307 1349.82,292.942 1350.02,292.697 1352.89,289.087 1355.36,285.905 1355.7,285.478 \n",
              "  1358.5,281.868 1360.9,278.692 1361.24,278.259 1363.95,274.649 1366.44,271.258 1366.61,271.039 1369.23,267.43 1371.79,263.82 1371.98,263.531 1374.31,260.211 \n",
              "  1376.75,256.601 1377.53,255.419 1379.15,252.991 1381.48,249.382 1383.07,246.835 1383.75,245.772 1385.95,242.163 1388.07,238.553 1388.61,237.585 1390.12,234.943 \n",
              "  1392.1,231.334 1393.98,227.724 1394.15,227.383 1395.8,224.115 1397.52,220.505 1399.15,216.895 1399.69,215.599 1400.69,213.286 1402.13,209.676 1403.48,206.067 \n",
              "  1404.71,202.457 1405.23,200.791 1405.85,198.847 1406.88,195.238 1407.8,191.628 1408.6,188.019 1409.28,184.409 1409.84,180.799 1410.27,177.19 1410.58,173.58 \n",
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          "metadata": {}
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      ],
      "execution_count": 148,
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [],
      "outputs": [],
      "execution_count": null,
      "metadata": {}
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