Nonlinear_gPC_SMPC.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Nonlinear_gPC_SMPC.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kJCBCvUXWeqZ",
        "outputId": "6406e02a-364a-436b-a900-8c47a62cc781"
      },
      "source": [
        "!pip install chaospy\n",
        "!pip install casadi"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: chaospy in /usr/local/lib/python3.7/dist-packages (4.3.3)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from chaospy) (1.4.1)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from chaospy) (1.21.2)\n",
            "Requirement already satisfied: numpoly<2.0.0,>=1.1.2 in /usr/local/lib/python3.7/dist-packages (from chaospy) (1.2.3)\n",
            "Collecting casadi\n",
            "  Downloading casadi-3.5.5-cp37-none-manylinux1_x86_64.whl (34.2 MB)\n",
            "\u001b[K     |████████████████████████████████| 34.2 MB 17 kB/s \n",
            "\u001b[?25hInstalling collected packages: casadi\n",
            "Successfully installed casadi-3.5.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TBov-kt1WNAX"
      },
      "source": [
        "import chaospy\n",
        "import numpy as np\n",
        "import casadi as ca\n",
        "from matplotlib import pyplot"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "twZyvCQDWd3g"
      },
      "source": [
        "import scipy.integrate as integrate\n"
      ],
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "14NIkbr-qmxS"
      },
      "source": [
        "Exploring gPC\n",
        "\n",
        "example system: $\\frac{d x(t)}{d t}=-\\theta x(t)+w(t), x(0)=1$, where $\\theta \\sim \\mathcal{N}(0,1)$ and $w(t) \\sim \\mathcal{N}(0,1)$\n",
        "\n",
        "From the paper \"An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems\" "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zkkDUxniF4re"
      },
      "source": [
        "coordinates = np.linspace(0, 1, 1000)"
      ],
      "execution_count": 115,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VZjuxvs70Zk2"
      },
      "source": [
        "def model_mu(theta):\n",
        "    return np.e**(-theta * coordinates)"
      ],
      "execution_count": 116,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k3Jzjd7Z0vmm"
      },
      "source": [
        "def model_V(theta):\n",
        "    return (1 - np.e**(-2 * theta * coordinates))/(2*theta)"
      ],
      "execution_count": 117,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4qjB8aYcm3DI"
      },
      "source": [
        "# mu_t = lambda t: np.exp(t**2/2)\n",
        "# sigma_int = lambda t,theta: (1-np.exp(-2*theta*t)/(2*theta))*np.exp(-theta**2/2)\n",
        "\n",
        "# result = integrate.quad(sigma_int(2), 0, 4.5) "
      ],
      "execution_count": 118,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vx2XMmfFuZm2"
      },
      "source": [
        "# result = integrate.quad(lambda x:x**2, 0, 1)"
      ],
      "execution_count": 119,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "es9g5hshz8Yu"
      },
      "source": [
        "Pseudo-spectral projection: [reference](https://chaospy.readthedocs.io/en/master/user_guide/main_usage/pseudo_spectral_projection.html)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hCb4XRUA1-Vy"
      },
      "source": [
        "normal = chaospy.Normal(0, 1)"
      ],
      "execution_count": 132,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SpunOdjw2J2z"
      },
      "source": [
        "gauss_quads = [\n",
        "    chaospy.generate_quadrature(order, normal, rule=\"gaussian\")\n",
        "    for order in range(1, 6)\n",
        "]"
      ],
      "execution_count": 158,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SFcPRKOWFA4k"
      },
      "source": [
        "gauss_evals = [\n",
        "    np.array([model_mu(node) for node in nodes.T])\n",
        "    for nodes, weights in gauss_quads\n",
        "]"
      ],
      "execution_count": 159,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XSuUOZ9lLX64",
        "outputId": "9680f241-402e-4c63-e2d6-934c832ac16e"
      },
      "source": [
        "nodes"
      ],
      "execution_count": 160,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-3.32425743, -1.88917588, -0.61670659,  0.61670659,  1.88917588,\n",
              "         3.32425743]])"
            ]
          },
          "metadata": {},
          "execution_count": 160
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "QbiHcv6rFEVH",
        "outputId": "f97ef95e-bf39-4aca-b3c1-b9c3b9258be6"
      },
      "source": [
        "pyplot.subplot(111)\n",
        "pyplot.plot(coordinates, gauss_evals[4].T, alpha=0.3)\n",
        "pyplot.title(\"Gaussian\")\n",
        "\n",
        "pyplot.show()"
      ],
      "execution_count": 168,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U1bdPrOG2V0W",
        "outputId": "6ab3e70b-9f7f-4941-9ce0-3e22d5c73dcc"
      },
      "source": [
        "expansions = [chaospy.generate_expansion(order, normal)\n",
        "              for order in range(1, 10)]\n",
        "expansions[0].round(10)"
      ],
      "execution_count": 169,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "polynomial([1.0, q0])"
            ]
          },
          "metadata": {},
          "execution_count": 169
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u20frsSy3Zrt"
      },
      "source": [
        "coordinates = np.linspace(0, 1, 1000)"
      ],
      "execution_count": 170,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zDrWCiLQ3Ug5"
      },
      "source": [
        ""
      ],
      "execution_count": 170,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "567FsGrl2i5m"
      },
      "source": [
        "gauss_model_approx = [\n",
        "    chaospy.fit_quadrature(expansion, nodes, weights, evals)\n",
        "    for expansion, (nodes, weights), evals in zip(expansions, gauss_quads, gauss_evals)\n",
        "]"
      ],
      "execution_count": 171,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vnjIdLFPOLYm",
        "outputId": "6d427456-1909-4dc2-d87e-98278042e6d7"
      },
      "source": [
        "gauss_model_approx[0].shape"
      ],
      "execution_count": 186,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1000,)"
            ]
          },
          "metadata": {},
          "execution_count": 186
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "fg5S9NVJGgsH",
        "outputId": "42866c79-cfcb-4386-f7cf-561902656ecc"
      },
      "source": [
        "model_approx = gauss_model_approx[4]\n",
        "nodes, _ = gauss_quads[4]\n",
        "evals = model_approx(*nodes)\n",
        "\n",
        "pyplot.subplot(111)\n",
        "pyplot.plot(coordinates, evals, alpha=0.3)\n",
        "pyplot.title(\"Gaussian\")\n",
        "\n",
        "pyplot.show()"
      ],
      "execution_count": 172,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_QYwtUnS3DAn"
      },
      "source": [
        "expected = chaospy.E(gauss_model_approx[-2], normal)\n",
        "std = chaospy.Std(gauss_model_approx[-2], normal)"
      ],
      "execution_count": 173,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uSot9DSK6uwG",
        "outputId": "f188b0b3-f99c-47bb-9e55-8016a26ae6bc"
      },
      "source": [
        "expected[:4].round(4), std[:4].round(4)"
      ],
      "execution_count": 174,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([1., 1., 1., 1.]), array([0.   , 0.001, 0.002, 0.003]))"
            ]
          },
          "metadata": {},
          "execution_count": 174
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "D5I_Jc9j6zYs",
        "outputId": "d399f2ee-33bc-4b97-a4f2-50ad4375cfa1"
      },
      "source": [
        "pyplot.rc(\"figure\", figsize=[6, 4])\n",
        "\n",
        "pyplot.xlabel(\"coordinates\")\n",
        "pyplot.ylabel(\"model approximation\")\n",
        "pyplot.fill_between(\n",
        "    coordinates, expected-2*std, expected+2*std, alpha=0.3)\n",
        "pyplot.plot(coordinates, expected)\n",
        "\n",
        "pyplot.show()"
      ],
      "execution_count": 175,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Swmdc3ioL4L0"
      },
      "source": [
        "_t = coordinates\n",
        "\n",
        "true_mean = np.hstack([\n",
        "    np.e**(_t**2/2)])"
      ],
      "execution_count": 176,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_7e68jYbLygB"
      },
      "source": [
        "def error_in_mean(predicted_mean, true_mean=true_mean):\n",
        "    return np.mean(np.abs(predicted_mean-true_mean))"
      ],
      "execution_count": 177,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3S-r5wb8MQaJ",
        "outputId": "8f72e97e-8e70-4d82-d73f-870814c30a72"
      },
      "source": [
        "error_in_mean(expected)"
      ],
      "execution_count": 178,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.6874133500355288e-06"
            ]
          },
          "metadata": {},
          "execution_count": 178
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vLRA6qvDMSNe"
      },
      "source": [
        "gauss_sizes = [len(weights) for _, weights in gauss_quads]\n",
        "eps_gauss_mean = [\n",
        "    error_in_mean(chaospy.E(model, normal))\n",
        "    for model in gauss_model_approx\n",
        "]"
      ],
      "execution_count": 179,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "btzEc4FhMZYj",
        "outputId": "272871e1-3a11-46c6-b28a-41df8c918f5b"
      },
      "source": [
        "pyplot.rc(\"figure\", figsize=[12, 4])\n",
        "\n",
        "pyplot.subplot(111)\n",
        "pyplot.title(\"Error in mean\")\n",
        "pyplot.loglog(gauss_sizes, eps_gauss_mean, \"o-\", label=\"Gaussian\")\n",
        "pyplot.legend()"
      ],
      "execution_count": 180,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb9b30b0c10>"
            ]
          },
          "metadata": {},
          "execution_count": 180
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ycnJ8XY5Ij1IvaBERkZ6nNcsiAaytXtA5RSfVC1pERKSLaM2ySABTL2gRERHfUFgWCVDqBS0iItL9tAxDpJdTL2gREZGz05plEWmmXtAiIiIfF1BhWd0wRHpeW72gdxdWcKSipvkY9YIWEZHeKqDCchPNLIv4Xlu9oHPLqpqfVy9oERHpDdQNQ0TOy5D+4cwfH8f88XHNY231gs7MLlIvaBER6XUUlkXknEVHhjJn7GDmjB3cPNZWL+jfv3XwnHpBv7C9gAfW7qWwvJrhMZHcsTiVa6cm9vj3JyIi0kRhWUS6RGd7QdfWN/Dc+wXUep8rKK/m7uc+BFBgFhERn1FYFpFucz69oFuqrmvggbV7FZZFRMRnFJZFpEeFBgeRNszTy/nz3rGGRkfK916jre3GBeXV/OiVPaSnJXDxqEGE6A6EIiLSgxSWRcTngoOM4TGRFJRXf+K58JAgVm/M5ZF3PiI6MpQFqXGkpyUwf3yc+j6LiEi367GwbGZpwH8CQ4BM59xve+raIuL/7licyt3PfUh13b+WY0SGBnPv8gtYODGBd3JKyMgqZl12MS/uKCQkyJg5Opb0tAQWpsWTPDjKh9WLiEhv1aE+y2b2GLAUKHbOTW4xvgT4BRAMPOKcu68D5woCVjvnvnS2Y9VnWaRv6Ug3jIZGx46842RkFZOZVcS+okoAUuL7k54Wz6K0BKaOHPSxLhsiIiJn06mbkpjZPKAST8id7B0LBvYBi4B8YAtwPZ7gfG+rU9zknCs2s08D3wDWOOf+fLbrKiyLyNkcLqsiI6uIzOwi3jt4jPpGR2xUGAtS41iYlsC88XH0D9eKMxERObNO38HPzEYBr7QIy3OA/3HOLfY+vhvAOdc6KLd1rledc1ef7TiFZRE5Fydq6tiwr4RM73KNiuo6woKDmDUmloVpCaSnxZM0qJ+vyxQRET/UHXfwSwTyWjzOB2adoYAFwHIgHHjtDMfdCtwKMHLkyE6UJyJ9zcCIUJZeOJylFw6nvqGRbbnHycwuJiOriHte2s09L+1mwtABzcF5SlIMQVquISIiZ9CZmeXPAUucc1/zPl4BzHLOreyq4jSzLCJd5WBJJZlZnuC8Nfc4DY2OIf3DuWKCp7vGZeOG0C9MyzVERPqq7phZLgBGtHic5B3rNDNbBixLSUnpitOJiDAmrj9j4vpzy7wxlFed5q19Jbyxp4jXdx3lma35hIUEMXfsYNK9s87DoiN9XbKIiPiBzswsh+DZ4JeOJyRvAW5wzu3uquI0sywi3a2uoZEtHx0jwzvrfPhYFQCTEweSPiGBhWkJTE4ciJmWa4iI9Gad7YbxFLAAT4/kIuAe59yjZvYp4CE8HTAec879uIuKbZpZviUnJ6crTikiclbOOfYXVza3pdt2+DjOQcLAcK6YkMCiifFcMnYIEaHBvi5VRES6WKe7YfiCZpZFxJfKKmtZv7eEzKwiNuwr4dTpBiJCg7g0JY6FafFckRZP/IAIX5cpIiJdIKDCsmaWRcTf1NY38N7BY56ezlnFzbfmnjIihoUT4klPSyBt2AAt1xARCVABFZabaGZZRPyRc47soyfJzCrijaxiduaVA5AYE0l6mic4zx4TS3iIlmuIiASKgArLmlkWkUBSfLKG9dnFZGQV805OKdV1DUSFBXPZuDgWTkzg8tQ4BvcP93WZIiJyBgEVlptoZllEAk1NXQPvHiht3iRYdKIWM5g2chDpafEsTEtgXHx/LdcQEfEzCssiIj3MOcfuwhO8saeIzOwidhWcAGBkbL/m4DxzdCyhwUE+rlRERAIqLGsZhoj0RkcrasjMLiJjTxH/PFDG6fpGBoSHMD81joVpCSxIjSOmX5ivyxQR6ZMCKiw30cyyiPRWVafreSenlMysYjKziymtrCU4yJiePIhF3rsIjonr7+syRUT6DIVlERE/1djo2JlfTqb3LoLZR08CMGZIVHN3jRnJgwjRcg0RkW6jsCwiEiDyj1c1B+dNB8uoa3BER4ZyeWoc6WkJzE+NY2BEqK/LFBHpVQIqLGvNsoiIR2VtPW/vKyEjq5j1e4s5duo0IUHGzNGxLExLYGFaAiMH9/N1mSIiAS+gwnITzSyLiPxLQ6Nj++HjzW3pcoorARgX35/0tAQWTYznohGDCA5SWzoRkXOlsCwi0svklp1qDs6bPzpGfaMjNiqMy1PjWZgWz2Xj4+gfHuLrMkVEAoLCsohIL1ZRXceGfSVkZBXx5t4SKqrrCAsOYvbYwSz0bhJMjIn0dZkiIn5LYVlEpI+ob2hka+5xMrOKyMgq5qPSUwBMGDqARRMTSE9L4MLEaIK0XENEpFlAhWVt8BMR6ToHSiqbg/PWQ8dodBA3IJwrUuNJT4vn0nFD6Bem5Roi0rcFVFhuopllEZGudfzUad7cV0xGVjEb9pZwsrae8JAg5qYM8fR0npDA0OgIX5cpItLjFJZFRORjTtc3suXQMd7YU0RmdhF5x6oBuCAxmvS0eBamJTBp+EDMtFxDRHo/hWUREWmXc46c4koysorIzCrm/cPHcQ6GDozgirR4FqUlMGfsYCJCg31dqohIt1BYFhGRDiutrGV9djGZWcVsyCmh6nQDkaHBXDpuCAvT4rl8QjzxA7RcQ0R6D4VlERE5LzV1DWw6WEamt6dzYUUNABeNiGluSzdh6AAt1xCRgKawLCIineacI+vISW93jSJ25lcAkBgT2RycZ42JJTxEyzVEJLAEVFhW6zgRkcBQfKKGddme7hrv7C+hpq6RqLBg5o2PIz0tgctT4xjcP9zXZYqInFVAheUmmlkWEQkcNXUN/HN/KRlZxazLLqLoRC1BBtNGDiI9LYGFafGkxPfXcg0R8UsKyyIi0mMaGx27C0/wRlYRmVlF7C48AUDy4H6kT/AE54tHxxIaHOTjSkVEPBSWRUTEZ45UVJOZVUxGVhHvHijjdH0jAyJCmD8+jkUTE1gwPp7ofqG+LlNE+jCFZRER8Qunaut5Z38pmVlFrMsuprTyNMFBxozkQSxMS2DhxARGD4nydZki0scoLIuIiN9pbHTsyC8n03szlOyjJwEYExfFwrQE0ifEMz15ECFariEi3UxhWURE/F7esSpPcM4uZtPBMuoaHDH9Qrk8NZ70tHjmjY9jYISWa4hI1/OLsGxmUcBbwP8451452/EKyyIifdfJmjreziklY08R6/cWc7yqjpAgY9aYWM9yjbQERsT283WZItJLdCosm9ljwFKg2Dk3ucX4EuAXQDDwiHPuvrOc54dAJbBHYVlERDqqodHx/uHjZGQVkbGniAMlpwAYn9C/uS3dRSMGERyktnQicn46G5bn4Qm5q5vCspkFA/uARUA+sAW4Hk9wvrfVKW4CpgCDgQigVGFZRETO16HSU2R41zlvPnSMhkbH4KgwLp8Qz8K0eC4bF0dUeIivyxSRANLpZRhmNgp4pUVYnoNnOcVi7+O7AZxzrYNy0+t/DEQBE4Fq4DPOucYzXVNhWUREzqaiqo439xWTmVXMm3uLOVFTT1hwELPHDmZRWjxXpCWQGBPp6zJFxM91R1j+HLDEOfc17+MVwCzn3MqznOcrnGFm2cxuBW4FGDly5PTc3NwO1SciIlLX0MjWQ8fJzCoiI6uIQ2VVAKQNG8jCtHgWpiVwQWI0QVquISKt+E1YPheaWRYRkfPlnONAyanmtnRbc4/R6CBuQDjpE+JJT0vg0pQhRIYF88L2Ah5Yu5fC8mqGx0Ryx+JUrp2a6OtvQUR6UHthuTMLugqAES0eJ3nHOs3MlgHLUlJSuuJ0IiLSB5kZKfH9SYnvz7/PH8vxU6dZv9ezXOOVD47w9JY8wkOCGBsXRU5xJXUNnsmjgvJq7n7uQwAFZhHp1MxyCJ4Nful4QvIW4Abn3O6uKk4zyyIi0h1O1zey+aNjZGQVsWZTLg2Nn/xvYWJMJP+86wofVCcivtDezHKHbolkZk8BG4FUM8s3s5udc/XASmAtkAU801VB2cyWmdmqioqKrjidiIjIx4SFBHHpuCH8z6cn0dhGUAbPDPP+4soerkxE/I3u4CciIn3a3PvWUVBe3f7zKYNZMTuZhWkJuu22SC/WqZnlnqaZZRER6Sl3LE4lMjT4Y2ORocH88JpJ3H7leA6WnOLrT7zPZfev51eZORSfrPFRpSLiC5pZFhGRPu9M3TDqGxrJzC5mzcZc3tlfSmiwsWTyMFbMTubiUYMwUxs6kd6g063jfEFhWURE/MmBkkqe2JTLs9vyOVlTz4ShA/jS7GQ+MzVRdwwUCXABFZZbtI67JScnx9fliIiIfEzV6Xpe3FHI6o25ZB05wYDwED47PYkvzR5JSvwAX5cnIuchoMJyE80si4iIP3PO8f7h46zemMtrHx6hrsFxyVjPhsBFE7UhUCSQKCyLiIh0o9LKWv6yJY8nN+VSWFHD0IERXD9zJNfPHEH8wAhflyciZxFQYVnLMEREJFDVNzSyLruYNZtyeTunlJAgY8nkoayYnczM0bHaECjipwIqLDfRzLKIiASygyWVPLHpMH/dlvexDYHXTk2kvzYEivgVhWUREREfqTpdz0veDYF7jpygf3gIn52WyJdmJzMuQRsCRfyBwrKIiIiPeTYElvPEplxe/eAIpxsamTNmMCvmeDYEhmpDoIjPBFRY1pplERHp7Uora3lmax5PbjpMQXk1CQPDuWFmsjYEivhIQIXlJppZFhGR3q6h0bE+u5jVm3LZsK+EkCBjsXdD4CxtCBTpMe2FZe0uEBER8aHgIGPhxAQWTkzgUOkpntiUyzNb83j1gyOMT+jPitnJfGZakjYEiviIZpZFRET8TPXpBl7eWcjqTYfYVXCCqLBglk9LYsWcZMZrQ6BItwioZRhasywiIuLZELgjr5w1G3N5xbshcPaYWFbMHsWVk7QhUKQrBVRYbqKZZREREY+yylqe2ZrPE5tyKSivJn5AONfPHMkNs0aSoA2BIp2msCwiItILNDQ63txbzOqNuby1r4TgIGPxpARWzB7F7DHaEChyvrTBT0REpBcIDjLS0xJIT0sgt6xpQ2A+r314lHHx/VkxJ5nPTE1kQESor0sV6RU0sywiIhLgauoaeGlnIWs25vJhQQVRYcF8ZloiK2aPInWoNgSKdISWYYiIiPQBTRsCX/6gkNP1jcwcHcuX5ySzeNJQbQgUOQOFZRERkT7k2KnTPLM1jyc25ZJ/vJq4pg2BM0cyNFobAkVaC6iwrNZxIiIiXaOh0fHWvmLWbMzlzX0lBJlx5cQEVsxJZs6YwdoQKOIVUGG5iWaWRUREuk5u2Sn+/N5h/rI1j/KqOlLiPXcIXD5NGwJFFJZFREQE8GwIfHlnIU9symVnfgX9woL5zNREVsxJZsLQgb4uT8QnFJZFRETkE3bmlbNmUy4v7fRuCBwVywrvhsCwEG0IlL5DYVlERETadfzUaf66LY8nNh3m8LEqz4bAi0dw/ayRDIuO9HV5It1OYVlERETOqrHR8VZOCWs25rJ+bzFBZixK82wIvGSsNgRK76U7+ImIiMhZBQUZl6fGc3lqPIfLqnhycy7PbMnj77uPMjYuyrMhcHoSA7UhUPoIzSyLiIjIGdXUNfDqB0dYvSmXnXnl9AsL5tqpiayYnUzaMG0IlN7B58swzGwB8H+B3cDTzrk3z/YahWURERH/8kG+5w6BL+0spLa+kYtHDeJLs5O5avIwbQiUgNZeWO7Qu9rMHjOzYjPb1Wp8iZntNbP9ZnbXWU7jgEogAsjvaOEiIiLiPy5MiuGBz09h093p/Pen0ig+Wct/Pr2DS+5bx8/+sZfC8mpflyjSpTo0s2xm8/AE3dXOucnesWBgH7AIT/jdAlwPBAP3tjrFTUCpc67RzBKAnzvnvni262pmWURExL81Njo2eDcErttbjAGLJiawYvYo5qZoQ6AEjk5t8HPObTCzUa2GZwL7nXMHvRd4GrjGOXcvsPQMpzsOhHfkuiIiIuLfgoKMBanxLEiNJ+9YFU++d5i/bDnM2t1FjImL4kuzkvns9CSiI7UhUAJTZxYXJQJ5LR7ne8faZGbLzez3wBrg4TMcd6uZbTWzrSUlJZ0oT0RERHrSiNh+3HXVBDbenc7Pr5vCwIhQfvjKHmb/v0zufpI5nfYAABJQSURBVO4D9hSe8HWJIuesx1rHOeeeA57rwHGrgFXgWYbR3XWJiIhI14oIDWb5tCSWT0viw/wK1mw6xHPvF/DU5jxmJA9ixZxklkweSnhIsK9LFTmrzswsFwAjWjxO8o51mpktM7NVFRUVXXE6ERER8ZELkqK5/3NTeO976fzvq9MorfRsCJx73zoeWJtNgTYEip/rcOs475rlV1ps8AvBs8EvHU9I3gLc4Jzb3VXFaYOfiIhI79LY6Hh7fylrNh4iM9uzITA9LYEvz0lm7tghBAVpQ6D4Rqc2+JnZU8ACYIiZ5QP3OOceNbOVwFo8HTAe66qgbGbLgGUpKSldcToRERHxE0FBxvzxccwfH0fesSr+vPkwf9mSxxt7ihgzJIovzk7mc9oQKH5Ed/ATERERn6qtb+C1D4+wZmMu7x8uJyI0iGsvSmTFnGQmDY/2dXnSR/j8Dn7nosXM8i05OTm+LkdERER6yK6CCp7YlMsLOwqoqWtk2sgYvjxnFFddoA2B0r0CKiw30cyyiIhI31RRVcdft+XxxKZcDpVVMTgqjH+7eARfnJ1MYkykr8uTXiigwrJmlkVERAQ8GwLf2V/Kmk25ZGYVAXDFBM+GwEtTtCFQuk5AheUmmlkWERGRJvnHq3hq82Ge3pxH2anTjB4SxRdnjeTz00cQ3U8bAqVzFJZFRESkV6itb+D1D4+yZlMu23KPExEaxDVTPBsCJydqQ6Ccn4AKy1qGISIiIh2xu9C7IXB7IdV1DUwdGcOX5yRz1eRhRIRqQ6B0XECF5SaaWRYREZGOqKiu42/b8nliUy4HS08R690QeMPMkYyI7efr8iQAKCyLiIhIr9fY6Hj3QBmrNx4iI6sIB6RPiOdLs5OZNy6OoCDjhe0FPLB2L4Xl1QyPieSOxalcOzXR16WLj3XqDn4iIiIigSAoyLh03BAuHTeEgvJqnnrvME9vOUxGVjGjBvfjohEx/H33UWrqGgEoKK/m7uc+BFBgljb55cyy1iyLiIhIV6mtb+Dvu46yZmMuW3OPt3lMYkwk/7zrih6uTPxJezPLQb4o5myccy87526NjtaOVhEREemc8JBgrrkokWe/cQntdWUuLK/u0ZokcPhlWBYRERHpDsPbuftfv/BgSitre7gaCQQKyyIiItJn3LE4lchWLeWCg4yq2gbm37+ehzL2UVlb76PqxB8pLIuIiEifce3URO5dfgGJMZEYnrXKP/v8FDK+O5954+N4KCOHBQ+s50/vHuJ0faOvyxU/oA1+IiIiIl7bDx/nvtezee+jY4yM7cfti1NZesEwgoLaW+0svYX6LIuIiIh0gHOON/eV8JPXs8k+epJJwwdy11UTuGxcnK9Lk24UUN0wRERERHzFzLg8NZ7XvnUZD/7bFMqr6ljx6Ga++MgmPsgv93V50sMUlkVERETaEBRkfGZqEutun8//WTqRPYUn+PTD/+Sbf36fj0pP+bo86SFahiEiIiLSASdr6vjDhoP84e2PqGto5AszR/Ct9HHED4jwdWnSBbRmWURERKQLFJ+s4VeZ+3lq82FCg4O45bLR3DJvDAMiQn1dmnSCwrKIiIhIF/qo9BQ//cdeXv3gCLFRYay8PIUvzh5JeEjw2V8sfiegwrJax4mIiEig+CC/nJ/8PZt/7i8jaVAk371yPNdMSVS7uQATUGG5iWaWRUREJFC8nVPCfa9ns7vwBBOGDuC/rprAgvFxmCk0BwK1jhMRERHpRpeNi+PllZfyy+unUnW6ga/+cQtfWLWJ7YeP+7o06QSFZREREZEuEhRkfHrKcDL+13x+eM0kDpRU8pnfvMs3ntjGgZJKX5cn50HLMERERES6SWVtPY++/RGrNhygpr6R62aM4NsLx5EwUO3m/I3WLIuIiIj4SGllLQ+v28+T7+USHGTcNHc0/z5/LNGRajfnLxSWRURERHzscFkVP3tjLy/uKCSmXyjfXJDCijnJRISq3Zyv+Twsm1kQ8H+BgcBW59yfzvYahWURERHpjXYVVHD/2r1s2FfC8OgIvrNoPMunJRGsdnM+06luGGb2mJkVm9muVuNLzGyvme03s7vOcpprgCSgDsjvaOEiIiIivc3kxGhW3zSTP39tFkMGhHPHsx9w1S82kJlVhD//q39f1KGZZTObB1QCq51zk71jwcA+YBGe8LsFuB4IBu5tdYqbvH+OO+d+b2bPOuc+d7bramZZREREejvnHK99eJSf/mMvH5We4uJRg7jrqglMT471dWl9SnszyyEdebFzboOZjWo1PBPY75w76L3A08A1zrl7gaVtFJAPnPY+bOh46SIiIiK9l5lx9YXDuHJSAs9szeOhjBw++9uNLJqYwJ2LUxmXMMDXJfZpnemznAjktXic7x1rz3PAYjP7FbChvYPM7FYz22pmW0tKSjpRnoiIiEjgCA0O4ouzknnrjgXcfuV4Nh4oY/FDG7jz2Z0Ullf7urw+q0Mzy13BOVcF3NyB41YBq8CzDKO76xIRERHxJ/3CQlh5xThumJXMr9fvZ83GXF7cUchXLhnFNxaMJaZfmK9L7FM6M7NcAIxo8TjJO9ZpZrbMzFZVVFR0xelEREREAk5sVBjfXzqRdbfP5+oLh7Hq7YPMu389v3vrADV1WtHaUzrcOs67ZvmVFhv8QvBs8EvHE5K3ADc453Z3VXHa4CciIiLikXXkBA+s3cu67GKGDozg2wvH8bnpSYQEd2buU5p0tnXcU8BGINXM8s3sZudcPbASWAtkAc90VVDWzLKIiIjIx6UNG8hjX7mYv9w6m2ExEdz13IcsfmgDa3cfVbu5bqQ7+ImIiIgEGOcca3cXcf/abA6WnGLayBj+a8kEZo0Z7OvSApbP7+B3LsxsGbAsJSXllpycHF+XIyIiIuKX6hsaeXZbPg9m7KPoRC1XTIjnziWpTBg60NelBZyACstNNLMsIiIicnbVpxt4/N1D/ObN/VTW1rN8ahLfWTSOpEH9fF1awFBYFhEREenlyqtO89s3D/DHdw+Bgy/PSeabl6cwKErt5s4moMKylmGIiIiInL/C8moeytjHs9vyiQoL4esLxvLVuaPoF9Zjt9gIOAEVlptoZllERETk/O0rOsn9f99LRlYRcQPC+fbCcVw3YwShajf3CZ1qHSciIiIigWd8wgAeuXEGz359Dsmx/fjv53dx5YMbeO3DI2o310F+GZbVZ1lERESk68wYFctfvz6HR748g5Ag4z+efJ9rf/Mu7x4o9XVpfk/LMERERET6kIZGx3Pv5/PgG/sorKhh/vg47lySyqTh0b4uzae0ZllEREREmtXUNbBmYy4Pr99PRXUd1140nO9emcqI2L7Zbk5hWUREREQ+oaK6jt+9dYA//vMjGhodX5yVzG1XpDC4f7ivS+tRARWW1TpOREREpGcVnajhoYwcntmaR0RIELfOG8vXLhtNVHjfaDcXUGG5iWaWRURERHrW/uJKfrp2L3/ffZQh/cP4Vvo4vnDxSMJC/LIvRJdR6zgREREROauU+P78bsV0nvuPSxgb15//8+JuFj34Fi/tLKSx0X8nWbuLwrKIiIiIfMK0kYN4+tbZ/PGrFxMZGsy3ntrOp3/9Du/k9K12c365DENrlkVERET8R0Oj48UdBfzsH/soKK/m0pQh/NeSCVyQ1HvazWnNsoiIiIh0Sm19A09sOszD63I4XlXH0guHcfuVqYwaEuXr0jpNYVlEREREusSJmjr+sOEgj7z9EXUNjVw/cyTfSh9H3IDAbTensCwiIiIiXar4RA2/XJfD05vzCAsJ4muXjuaWeWMYEBHq69LOmcKyiIiIiHSLj0pP8dN/7OXVD44QGxXGbVekcMOskYSHBPu6tA5T6zgRERER6Rajh0Tx6xum8dLKuUwYOoAfvLyH9J+9xfPb8wO+3ZzCsoiIiIh0iQuTYnjya7NYfdNMoiND+c5fdnL1r97hzb3F+PNqhjPxy7BsZsvMbFVFRYWvSxERERGRc2BmzBsfx8srL+UXX7iIyto6vvLHLVz/h03syCv3dXnnTGuWRURERKTbnK5v5KnNh/llZg5lp07zqQuGcvuVqYyJ6+/r0j5GG/xERERExGcqa+t55O2D/GHDQWrqG/m3i0fw7fRxxA+M8HVpgMKyiIiIiPiB0spaHl63nyffyyU4yLj50tEkDYrk4XUHKCyvZnhMJHcsTuXaqYk9WpfCsoiIiIj4jcNlVfzsjb28uKPwE89FhgZz7/ILejQwq3WciIiIiPiNkYP78YsvTG3zrn/VdQ08sHavD6r6JIVlEREREfGZ0pO1bY4Xllf3cCVtU1gWEREREZ8ZHhN5TuM9rcfCspldZma/M7NHzOzdnrquiIiIiPivOxanEhn68dtiR4YGc8fiVB9V9HEdCstm9piZFZvZrlbjS8xsr5ntN7O7znQO59zbzrmvA68Afzr/kkVERESkt7h2aiL3Lr+AxJhIDEiMiezxzX1n0qFuGGY2D6gEVjvnJnvHgoF9wCIgH9gCXA8EA/e2OsVNzrli7+ueAW52zp0823XVDUNEREREekJ73TBCOvJi59wGMxvVangmsN85d9B7gaeBa5xz9wJL2yliJFDRkaAsIiIiIuJrnVmznAjktXic7x07k5uBP57pADO71cy2mtnWkpKSTpQnIiIiItI5HZpZ7irOuXs6cMwqMzsCLAsLC5veA2WJiIiIiLSpMzPLBcCIFo+TvGOd5px72Tl3a3R0dFecTkRERETkvHQmLG8BxpnZaDMLA74AvNQVRZnZMjNbVVFR0RWnExERERE5Lx3thvEUsAAYAhQB9zjnHjWzTwEP4emA8Zhz7sddWpxZCZDblefsoGhASV3Ed/QZFF/Re69v0c/b//jyZ5LsnItrPdihsNzXmNkq59ytvq5DpK/SZ1B8Re+9vkU/b//jjz8T3e66bS/7ugCRPk6fQfEVvff6Fv28/Y/f/Uw0sywiIiIi0g7NLIuIiIiItENhWURERESkHQrLIiIiIiLt6NE7+PV2ZhYF/AY4DbzpnHvSxyWJ9Bn6/Ikv6f0n4jvd/fnrdTPLZjbCzNab2R4z221m/9mJcz1mZsVmtquN55aY2V4z229md3mHlwPPOuduAT59vtcVCVRmFmFmm81sp/fz94NOnEufPzkvZhZsZtvN7JVOnEPvP5FzZGYxZvasmWWbWZaZzTnP8/jV56/XhWWgHviuc24iMBv4pplNbHmAmcWb2YBWYyltnOtxYEnrQTMLBn4NXAVMBK73XiMJyPMe1tDJ70MkENUCVzjnpgAXAUvMbHbLA/T5kx7wn0BWW0/o/SfSrX4B/N05NwGYQqvPYaB+/npdWHbOHXHOve/9+iSeH1Riq8PmAy+YWTiAmd0C/KqNc20AjrVxmZnAfufcQefcaeBp4BogH88PDHrh363I2TiPSu/DUO+f1v0p9fmTbmNmScDVwCPtHKL3n0g3MLNoYB7wKIBz7rRzrrzVYQH5+evVH2gzGwVMBd5rOe6c+yuwFviLmX0RuAn4/DmcOpF//QYDnh9SIvAc8Fkz+y1+2FRbpCd4/wl8B1AMvOGc0+dPetJDwJ1AY1tP6v0n0m1GAyXAH73LoB7xriVuFqifv167wc/M+gN/A77tnDvR+nnn3P1m9jTwW2Bsi9mw8+acOwV8tbPnEQlkzrkG4CIziwGeN7PJzrldrY7R50+6nJktBYqdc9vMbEF7x+n9J9ItQoBpwG3OuffM7BfAXcD3Wx4UiJ+/XjmzbGaheILyk86559o55jJgMvA8cM85XqIAGNHicZJ3TES8vP/8tp62153p8yfdYS7waTM7hOefZ68wsydaH6T3n0i3yAfyW/xr4rN4wvPHBOLnr9eFZTMzPOtlspxzP2/nmKnAKjzrXL4KDDazH53DZbYA48xstJmFAV8AXupc5SKBz8zivDPKmFkksAjIbnWMPn/SLZxzdzvnkpxzo/C8L9Y5577U8hi9/0S6h3PuKJBnZqneoXRgT8tjAvXz1+vCMp6ZhRV4ZhR2eP98qtUx/YDrnHMHnHONwJeB3NYnMrOngI1Aqpnlm9nNAM65emAlnnU3WcAzzrnd3fctiQSMYcB6M/sAz/+pveGca92+S58/8SW9/0S6z23Ak97/BlwE/L9Wzwfk58+ca71RXUREREREoHfOLIuIiIiIdAmFZRERERGRdigsi4iIiIi0Q2FZRERERKQdCssiIiIiIu1QWBYRERERaYfCsoiIiIhIOxSWRURERETaobAsIiIiItKO/w8rFLrzq2v1RgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1onyS_GmOl_w"
      },
      "source": [
        "Point collocation: [reference](https://chaospy.readthedocs.io/en/master/user_guide/main_usage/point_collocation.html)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NweCNdiMMeBS"
      },
      "source": [
        "gauss_nodes = [nodes for nodes, _ in gauss_quads]"
      ],
      "execution_count": 187,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UTolgyeKO2JH"
      },
      "source": [
        "sobol_samples = normal.sample(10000, rule=\"sobol\")"
      ],
      "execution_count": 189,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eK5Kn7KSO7He"
      },
      "source": [
        "sobol_nodes = [sobol_samples[:nodes.shape[1]] for nodes in gauss_nodes]"
      ],
      "execution_count": 193,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TD891Q7mQByN"
      },
      "source": [
        "sobol_evals = [\n",
        "    np.array([model_mu(node) for node in nodes.T])\n",
        "    for nodes in sobol_nodes\n",
        "]"
      ],
      "execution_count": 204,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "xhNqn8gHQGtt",
        "outputId": "90a9615a-ffd7-4f2e-b941-6d87c5de5258"
      },
      "source": [
        "pyplot.subplot(111)\n",
        "pyplot.plot(coordinates, sobol_evals[4].T, alpha=0.3)\n",
        "pyplot.title(\"Sobol evaluations\")\n"
      ],
      "execution_count": 205,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Sobol evaluations')"
            ]
          },
          "metadata": {},
          "execution_count": 205
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AEj3UiN0PPVj",
        "outputId": "82b69aaf-abf5-4a02-870f-201c90a50c32"
      },
      "source": [
        "expansions = [chaospy.generate_expansion(order, normal)\n",
        "              for order in range(1, 10)]\n",
        "expansions[0].round(10)"
      ],
      "execution_count": 195,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "polynomial([1.0, q0])"
            ]
          },
          "metadata": {},
          "execution_count": 195
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "urVfY5e5PX0w"
      },
      "source": [
        "gauss_model_approx = [\n",
        "    chaospy.fit_regression(expansion, samples, evals)\n",
        "    for expansion, samples, evals in zip(expansions, gauss_nodes, gauss_evals)\n",
        "]"
      ],
      "execution_count": 196,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sXuYe43zQNpF"
      },
      "source": [
        "sobol_model_approx = [\n",
        "    chaospy.fit_regression(expansion, samples, evals)\n",
        "    for expansion, samples, evals in zip(expansions, sobol_nodes, sobol_evals)\n",
        "]"
      ],
      "execution_count": 206,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "SXV1_IS1Pa6Y",
        "outputId": "c2b681a4-aa7b-43d6-b11f-29e153b5e14c"
      },
      "source": [
        "pyplot.subplot(121)\n",
        "model_approx = gauss_model_approx[4]\n",
        "evals = model_approx(*gauss_nodes[1])\n",
        "pyplot.plot(coordinates, evals, alpha=0.3)\n",
        "pyplot.title(\"Gaussian approximation\")\n",
        "\n",
        "pyplot.subplot(122)\n",
        "model_approx = sobol_model_approx[1]\n",
        "evals = model_approx(*sobol_nodes[1])\n",
        "pyplot.plot(coordinates, evals, alpha=0.3)\n",
        "pyplot.title(\"Sobol approximation\")\n",
        "\n",
        "pyplot.show()"
      ],
      "execution_count": 207,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fyuigDljPdHU"
      },
      "source": [
        "expected = chaospy.E(gauss_model_approx[-2], normal)"
      ],
      "execution_count": 199,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "IQlUUqIsPfVY",
        "outputId": "0fdbc0ee-8795-41cd-916a-27f723bd3ebc"
      },
      "source": [
        "pyplot.rc(\"figure\", figsize=[6, 4])\n",
        "\n",
        "pyplot.xlabel(\"coordinates\")\n",
        "pyplot.ylabel(\"model approximation\")\n",
        "pyplot.fill_between(\n",
        "    coordinates, expected-2*std, expected+2*std, alpha=0.3)\n",
        "pyplot.plot(coordinates, expected)\n",
        "\n",
        "pyplot.show()"
      ],
      "execution_count": 200,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zsBRMF5NPmu7"
      },
      "source": [
        "eps_sobol_mean = [\n",
        "    error_in_mean(chaospy.E(model, normal))\n",
        "    for model in sobol_model_approx\n",
        "]"
      ],
      "execution_count": 208,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "yZYLMifPQkvc",
        "outputId": "7a047b22-13d7-4547-90e0-8302a2f2cbf8"
      },
      "source": [
        "sizes = [nodes.shape[1] for nodes in gauss_nodes]\n",
        "\n",
        "pyplot.rc(\"figure\", figsize=[12, 4])\n",
        "\n",
        "pyplot.subplot(121)\n",
        "pyplot.title(\"Error in mean\")\n",
        "pyplot.loglog(sizes, eps_gauss_mean, \"-\", label=\"Gaussian\")\n",
        "pyplot.loglog(sizes, eps_sobol_mean, \"--\", label=\"Sobol\")\n",
        "pyplot.legend()"
      ],
      "execution_count": 211,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb9aeb35650>"
            ]
          },
          "metadata": {},
          "execution_count": 211
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}