shaabhishek/contour-plot-experiments.ipynb

## contour-plot-experiments.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "contour plot experiments",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyM4QyWFkd3n7KbNt8x5Wcqt",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/shaabhishek/7df10eddd699f7c0f32a13de8afe3278/contour-plot-experiments.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FupenEW807rx"
      },
      "source": [
        "import numpy as np\n",
        "import torch\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vFviWO2G1Bz1"
      },
      "source": [
        "x = np.linspace(0, 1, 5)\n",
        "y = np.linspace(0, 1, 5)\n",
        "\n",
        "X, Y = np.meshgrid(x, y)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zE-IlsRY1NrL"
      },
      "source": [
        "def f(x, y):\n",
        "    return (x-.5) ** 2 + (y-.5) ** 2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vuD9aHvP9mDX"
      },
      "source": [
        "F = lambda x: f(*x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "id": "e2NeN9DU1HgR",
        "outputId": "e2a08aea-3deb-44db-caeb-e60c054b1cab"
      },
      "source": [
        "fig, ax = plt.subplots(1, 1, figsize=(6, 6))\n",
        "mappable = ax.contourf(X, Y, f(X,Y));\n",
        "ax.scatter(*minimize(F, np.zeros(2)).x, marker='x', c='red')\n",
        "fig.colorbar(mappable, ax=ax)\n",
        "f(X,Y).shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(5, 5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xIgmJAX81nHc",
        "outputId": "66c0f993-bc08-4f24-9910-2891a8b0967c"
      },
      "source": [
        "np.mgrid[0:1.1:.25, 0:1.1:.25]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[0.  , 0.  , 0.  , 0.  , 0.  ],\n",
              "        [0.25, 0.25, 0.25, 0.25, 0.25],\n",
              "        [0.5 , 0.5 , 0.5 , 0.5 , 0.5 ],\n",
              "        [0.75, 0.75, 0.75, 0.75, 0.75],\n",
              "        [1.  , 1.  , 1.  , 1.  , 1.  ]],\n",
              "\n",
              "       [[0.  , 0.25, 0.5 , 0.75, 1.  ],\n",
              "        [0.  , 0.25, 0.5 , 0.75, 1.  ],\n",
              "        [0.  , 0.25, 0.5 , 0.75, 1.  ],\n",
              "        [0.  , 0.25, 0.5 , 0.75, 1.  ],\n",
              "        [0.  , 0.25, 0.5 , 0.75, 1.  ]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y1w3Ug_V2qf1",
        "outputId": "788753c2-125f-402e-f65a-eeacce9d1070"
      },
      "source": [
        "np.mgrid[0:1.1:.25, 0:1.1:.25].reshape(2, -1).T#.reshape(2, 5, 5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.  , 0.  ],\n",
              "       [0.  , 0.25],\n",
              "       [0.  , 0.5 ],\n",
              "       [0.  , 0.75],\n",
              "       [0.  , 1.  ],\n",
              "       [0.25, 0.  ],\n",
              "       [0.25, 0.25],\n",
              "       [0.25, 0.5 ],\n",
              "       [0.25, 0.75],\n",
              "       [0.25, 1.  ],\n",
              "       [0.5 , 0.  ],\n",
              "       [0.5 , 0.25],\n",
              "       [0.5 , 0.5 ],\n",
              "       [0.5 , 0.75],\n",
              "       [0.5 , 1.  ],\n",
              "       [0.75, 0.  ],\n",
              "       [0.75, 0.25],\n",
              "       [0.75, 0.5 ],\n",
              "       [0.75, 0.75],\n",
              "       [0.75, 1.  ],\n",
              "       [1.  , 0.  ],\n",
              "       [1.  , 0.25],\n",
              "       [1.  , 0.5 ],\n",
              "       [1.  , 0.75],\n",
              "       [1.  , 1.  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dz0dd6Ni4uJu",
        "outputId": "2b81f039-bfc4-4e7e-a6d2-63279cb661e9"
      },
      "source": [
        "phi_grid = np.mgrid[0:1.1:.25, 0:1.1:.25].reshape(2, -1).T\n",
        "# torch.from_numpy(phi_grid)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.0000, 0.0000],\n",
              "        [0.0000, 0.2500],\n",
              "        [0.0000, 0.5000],\n",
              "        [0.0000, 0.7500],\n",
              "        [0.0000, 1.0000],\n",
              "        [0.2500, 0.0000],\n",
              "        [0.2500, 0.2500],\n",
              "        [0.2500, 0.5000],\n",
              "        [0.2500, 0.7500],\n",
              "        [0.2500, 1.0000],\n",
              "        [0.5000, 0.0000],\n",
              "        [0.5000, 0.2500],\n",
              "        [0.5000, 0.5000],\n",
              "        [0.5000, 0.7500],\n",
              "        [0.5000, 1.0000],\n",
              "        [0.7500, 0.0000],\n",
              "        [0.7500, 0.2500],\n",
              "        [0.7500, 0.5000],\n",
              "        [0.7500, 0.7500],\n",
              "        [0.7500, 1.0000],\n",
              "        [1.0000, 0.0000],\n",
              "        [1.0000, 0.2500],\n",
              "        [1.0000, 0.5000],\n",
              "        [1.0000, 0.7500],\n",
              "        [1.0000, 1.0000]], dtype=torch.float64)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2r5XdoAUAvNv"
      },
      "source": [
        "elbos = np.random.rand(len(phi_grid))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "75m_J0xoAcK2"
      },
      "source": [
        "elbo_xi = {str(phi.astype(int)): elbo for phi, elbo in zip(phi_grid, elbos) if tuple(phi) in [(0,0), (0,1), (1,0), (1,1)]}\n",
        "sorted_phi = sorted(elbo_xi.keys(), key=lambda phi: elbo_xi[phi])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "YZsk8zgBA2uB",
        "outputId": "2b678010-44c6-4285-cc22-5ce45bd8342f"
      },
      "source": [
        "# print(\"ELBO order: \")\n",
        "\" < \".join(sorted_phi)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'[0 1] < [1 1] < [1 0] < [0 0]'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5YCFpbD8BVIC",
        "outputId": "952cc1be-c17b-4161-aba3-fcb018880378"
      },
      "source": [
        "np.mgrid[0:1.01:.2, 0:1.01:.2].shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 6, 6)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 110
        }
      ]
    }
  ]
}
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"name": "contour plot experiments",
	"provenance": [],
	"collapsed_sections": [],
	"authorship_tag": "ABX9TyM4QyWFkd3n7KbNt8x5Wcqt",
	"include_colab_link": true
	},
	"kernelspec": {
	"name": "python3",
	"display_name": "Python 3"
	}
	},
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "view-in-github",
	"colab_type": "text"
	},
	"source": [
	"<a href=\"https://colab.research.google.com/gist/shaabhishek/7df10eddd699f7c0f32a13de8afe3278/contour-plot-experiments.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "FupenEW807rx"
	},
	"source": [
	"import numpy as np\n",
	"import torch\n",
	"import matplotlib.pyplot as plt\n",
	"from scipy.optimize import minimize"
	],
	"execution_count": null,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "vFviWO2G1Bz1"
	},
	"source": [
	"x = np.linspace(0, 1, 5)\n",
	"y = np.linspace(0, 1, 5)\n",
	"\n",
	"X, Y = np.meshgrid(x, y)"
	],
	"execution_count": null,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "zE-IlsRY1NrL"
	},
	"source": [
	"def f(x, y):\n",
	" return (x-.5) 2 + (y-.5) 2"
	],
	"execution_count": null,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "vuD9aHvP9mDX"
	},
	"source": [
	"F = lambda x: f(*x)"
	],
	"execution_count": null,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 392
	},
	"id": "e2NeN9DU1HgR",
	"outputId": "e2a08aea-3deb-44db-caeb-e60c054b1cab"
	},
	"source": [
	"fig, ax = plt.subplots(1, 1, figsize=(6, 6))\n",
	"mappable = ax.contourf(X, Y, f(X,Y));\n",
	"ax.scatter(*minimize(F, np.zeros(2)).x, marker='x', c='red')\n",
	"fig.colorbar(mappable, ax=ax)\n",
	"f(X,Y).shape"
	],
	"execution_count": null,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"(5, 5)"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 20
	},
	{
	"output_type": "display_data",
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x432 with 2 Axes>"
	]
	},
	"metadata": {
	"tags": [],
	"needs_background": "light"
	}
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "xIgmJAX81nHc",
	"outputId": "66c0f993-bc08-4f24-9910-2891a8b0967c"
	},
	"source": [
	"np.mgrid[0:1.1:.25, 0:1.1:.25]"
	],
	"execution_count": null,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"array([[[0. , 0. , 0. , 0. , 0. ],\n",
	" [0.25, 0.25, 0.25, 0.25, 0.25],\n",
	" [0.5 , 0.5 , 0.5 , 0.5 , 0.5 ],\n",
	" [0.75, 0.75, 0.75, 0.75, 0.75],\n",
	" [1. , 1. , 1. , 1. , 1. ]],\n",
	"\n",
	" [[0. , 0.25, 0.5 , 0.75, 1. ],\n",
	" [0. , 0.25, 0.5 , 0.75, 1. ],\n",
	" [0. , 0.25, 0.5 , 0.75, 1. ],\n",
	" [0. , 0.25, 0.5 , 0.75, 1. ],\n",
	" [0. , 0.25, 0.5 , 0.75, 1. ]]])"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 47
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "Y1w3Ug_V2qf1",
	"outputId": "788753c2-125f-402e-f65a-eeacce9d1070"
	},
	"source": [
	"np.mgrid[0:1.1:.25, 0:1.1:.25].reshape(2, -1).T#.reshape(2, 5, 5)"
	],
	"execution_count": null,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"array([[0. , 0. ],\n",
	" [0. , 0.25],\n",
	" [0. , 0.5 ],\n",
	" [0. , 0.75],\n",
	" [0. , 1. ],\n",
	" [0.25, 0. ],\n",
	" [0.25, 0.25],\n",
	" [0.25, 0.5 ],\n",
	" [0.25, 0.75],\n",
	" [0.25, 1. ],\n",
	" [0.5 , 0. ],\n",
	" [0.5 , 0.25],\n",
	" [0.5 , 0.5 ],\n",
	" [0.5 , 0.75],\n",
	" [0.5 , 1. ],\n",
	" [0.75, 0. ],\n",
	" [0.75, 0.25],\n",
	" [0.75, 0.5 ],\n",
	" [0.75, 0.75],\n",
	" [0.75, 1. ],\n",
	" [1. , 0. ],\n",
	" [1. , 0.25],\n",
	" [1. , 0.5 ],\n",
	" [1. , 0.75],\n",
	" [1. , 1. ]])"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 49
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "dz0dd6Ni4uJu",
	"outputId": "2b81f039-bfc4-4e7e-a6d2-63279cb661e9"
	},
	"source": [
	"phi_grid = np.mgrid[0:1.1:.25, 0:1.1:.25].reshape(2, -1).T\n",
	"# torch.from_numpy(phi_grid)"
	],
	"execution_count": null,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"tensor([[0.0000, 0.0000],\n",
	" [0.0000, 0.2500],\n",
	" [0.0000, 0.5000],\n",
	" [0.0000, 0.7500],\n",
	" [0.0000, 1.0000],\n",
	" [0.2500, 0.0000],\n",
	" [0.2500, 0.2500],\n",
	" [0.2500, 0.5000],\n",
	" [0.2500, 0.7500],\n",
	" [0.2500, 1.0000],\n",
	" [0.5000, 0.0000],\n",
	" [0.5000, 0.2500],\n",
	" [0.5000, 0.5000],\n",
	" [0.5000, 0.7500],\n",
	" [0.5000, 1.0000],\n",
	" [0.7500, 0.0000],\n",
	" [0.7500, 0.2500],\n",
	" [0.7500, 0.5000],\n",
	" [0.7500, 0.7500],\n",
	" [0.7500, 1.0000],\n",
	" [1.0000, 0.0000],\n",
	" [1.0000, 0.2500],\n",
	" [1.0000, 0.5000],\n",
	" [1.0000, 0.7500],\n",
	" [1.0000, 1.0000]], dtype=torch.float64)"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 61
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "2r5XdoAUAvNv"
	},
	"source": [
	"elbos = np.random.rand(len(phi_grid))"
	],
	"execution_count": null,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "75m_J0xoAcK2"
	},
	"source": [
	"elbo_xi = {str(phi.astype(int)): elbo for phi, elbo in zip(phi_grid, elbos) if tuple(phi) in [(0,0), (0,1), (1,0), (1,1)]}\n",
	"sorted_phi = sorted(elbo_xi.keys(), key=lambda phi: elbo_xi[phi])"
	],
	"execution_count": null,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 34
	},
	"id": "YZsk8zgBA2uB",
	"outputId": "2b678010-44c6-4285-cc22-5ce45bd8342f"
	},
	"source": [
	"# print(\"ELBO order: \")\n",
	"\" < \".join(sorted_phi)"
	],
	"execution_count": null,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"application/vnd.google.colaboratory.intrinsic+json": {
	"type": "string"
	},
	"text/plain": [
	"'[0 1] < [1 1] < [1 0] < [0 0]'"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 105
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "5YCFpbD8BVIC",
	"outputId": "952cc1be-c17b-4161-aba3-fcb018880378"
	},
	"source": [
	"np.mgrid[0:1.01:.2, 0:1.01:.2].shape"
	],
	"execution_count": null,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"(2, 6, 6)"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 110
	}
	]
	}
	]
	}