2_1_ML_tutorial_FittingBasics.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mlexchange/als_ml_tutorial/blob/main/2_1_ML_tutorial_FittingBasics.ipynb)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a7b4d677",
      "metadata": {
        "id": "a7b4d677"
      },
      "source": [
        "In this tutorial we will go over how to build an object that can be used to fit data.\n",
        "\n",
        "We will be exploring some of the functionality in pytorch aimed at providing basic insights in the underlying funcationality of the machinery that make pytorch do it's job.\n",
        "\n",
        "The example used is a simple polynomial fitting exersize, but many of the issues we encounter directly translate to fitting neural networks."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "id": "05a9374c",
      "metadata": {
        "id": "05a9374c",
        "outputId": "e641349d-85e6-4974-b718-c72b5bd65ccb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<torch._C.Generator at 0x7eadccb5b910>"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "#Basic numpy for arrays etc\n",
        "import numpy as np\n",
        "# we want to plot stuff\n",
        "import matplotlib.pyplot as plt\n",
        "# we will use torch\n",
        "import torch\n",
        "# nn contains a lot of useful things\n",
        "from torch import nn\n",
        "# we need optim to get optimize stuff\n",
        "from torch import optim\n",
        "\n",
        "# fix random seed\n",
        "torch.manual_seed(42)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "53afb00a",
      "metadata": {
        "id": "53afb00a"
      },
      "source": [
        "\n",
        "Torch libraries contain a large number of tools that overlap with numpy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "id": "df155c4d",
      "metadata": {
        "id": "df155c4d",
        "outputId": "4654e797-0c96-4ad0-a1a4-214b068207dc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Values\n",
            "[0.  0.5 1. ]\n",
            "tensor([0.0000, 0.5000, 1.0000])\n",
            "\n",
            "Sin of values\n",
            "[0.         0.47942554 0.84147098]\n",
            "tensor([0.0000, 0.4794, 0.8415])\n",
            "\n",
            "Types\n",
            "<class 'numpy.ndarray'>\n",
            "<class 'torch.Tensor'>\n"
          ]
        }
      ],
      "source": [
        "some_values_numpy = np.linspace(0,1,3)\n",
        "some_values_torch = torch.linspace(0,1,3)\n",
        "print()\n",
        "print(\"Values\")\n",
        "print(some_values_numpy)\n",
        "print(some_values_torch)\n",
        "print()\n",
        "print(\"Sin of values\")\n",
        "print(np.sin(some_values_numpy))\n",
        "print(torch.sin(some_values_torch))\n",
        "print()\n",
        "print(\"Types\")\n",
        "print(type(some_values_numpy))\n",
        "print(type(some_values_torch))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8f81e94f",
      "metadata": {
        "id": "8f81e94f"
      },
      "source": [
        "pytorch handles data in tensors. They feel a lot like numpy arrays."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "id": "a9d21c86",
      "metadata": {
        "id": "a9d21c86",
        "outputId": "4bac7f07-2543-4437-d0bb-9b269dbd1ee4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.5\n",
            "tensor(1.5000)\n"
          ]
        }
      ],
      "source": [
        "sum_numpy = np.sum(some_values_numpy)\n",
        "sum_torch = torch.sum(some_values_torch)\n",
        "\n",
        "print(sum_numpy)\n",
        "print(sum_torch)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Tensors in pytorch are different from a numpy array: they can have gradients, and they can live on different devices.\n",
        "\n",
        "Because machine learning can be accelerated by using GPU's we need to be able to send stuff back and forth."
      ],
      "metadata": {
        "id": "zYxcI3MB1dTR"
      },
      "id": "zYxcI3MB1dTR"
    },
    {
      "cell_type": "code",
      "source": [
        "this_tensor = torch.rand(2,3, requires_grad=True, device=\"cpu\")\n",
        "print(\"It has gradients and lives on the CPU\")\n",
        "print(this_tensor)\n",
        "print(\"And now we push it to the GPU\")\n",
        "print(this_tensor.to('cuda:0'))\n",
        "print()\n",
        "print(\" This **grad_fn=<ToCopyBackward0>** indicates that the gradient computation \\ninvolves a copy part\")\n",
        "print()\n",
        "print()\n",
        "print(\"This tensor lives on the GPU\")\n",
        "that_tensor = torch.rand(1,2, requires_grad=True, device=\"cuda:0\")\n",
        "print(that_tensor)\n",
        "print(\"And now we move it to the cpu\")\n",
        "print(that_tensor.cpu())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zQ-RGHHj1ue0",
        "outputId": "bd1d43f2-375a-4fdf-8986-c2e78acb3580"
      },
      "id": "zQ-RGHHj1ue0",
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "It has gradients and lives on the CPU\n",
            "tensor([[0.8823, 0.9150, 0.3829],\n",
            "        [0.9593, 0.3904, 0.6009]], requires_grad=True)\n",
            "And now we push it to the GPU\n",
            "tensor([[0.8823, 0.9150, 0.3829],\n",
            "        [0.9593, 0.3904, 0.6009]], device='cuda:0', grad_fn=<ToCopyBackward0>)\n",
            "\n",
            " This **grad_fn=<ToCopyBackward0>** indicates that the gradient computation \n",
            "involves a copy part\n",
            "\n",
            "\n",
            "This tensor lives on the GPU\n",
            "tensor([[0.6130, 0.0101]], device='cuda:0', requires_grad=True)\n",
            "And now we move it to the cpu\n",
            "tensor([[0.6130, 0.0101]], grad_fn=<ToCopyBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ec39cd01",
      "metadata": {
        "id": "ec39cd01"
      },
      "source": [
        "The biggest feature of pytorch tensors is the auto differentiation.\n",
        "\n",
        "\n",
        "\n",
        "Lets say we have the function\n",
        "\n",
        "$\n",
        "y = x^2 + 4\n",
        "$\n",
        "\n",
        "its derivative is\n",
        "\n",
        "$\n",
        "y' = \\frac{d y}{ d x} = 2 x\n",
        "$\n",
        "\n",
        "so when x is 2, y=8 and y'=4\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "id": "9d25055a",
      "metadata": {
        "id": "9d25055a",
        "outputId": "c767341b-30e2-4fca-a362-3ce60aab7b1f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradient:  tensor(4.)\n"
          ]
        }
      ],
      "source": [
        "# define a tensor, make sure we state that we will need to compute a derivative on it\n",
        "x = torch.tensor(2.0, requires_grad=True)\n",
        "# define the function\n",
        "y = x*x + 4  # Define a simple mathematical operation\n",
        "# compute the gradient and print it\n",
        "y.backward()\n",
        "print(\"Gradient: \", x.grad)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a8e8e28d",
      "metadata": {
        "id": "a8e8e28d"
      },
      "source": [
        "This is neat. We can get to the second derivative as well, but this requieres a bit more poking around.  Ask chatGPT how to do this.\n",
        "\n",
        "Lets build a class that describes a function for polynomial fitting\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "id": "d2b1f5f2",
      "metadata": {
        "id": "d2b1f5f2"
      },
      "outputs": [],
      "source": [
        "class MyFunction(nn.Module): # we inherit from nn.Module\n",
        "    def __init__(self, coefs): # put in initial guesses for polynomial coefficients\n",
        "        super().__init__() # do the super thing\n",
        "        self.coefs = nn.Parameter(coefs) #\n",
        "\n",
        "    def forward(self, x):\n",
        "        result = self.coefs[0]\n",
        "        tmp = torch.ones_like(x)\n",
        "        for this_coef in self.coefs[1:]:\n",
        "            tmp = tmp * x # x**something\n",
        "            result = result + tmp*this_coef\n",
        "        return result\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9d545c80",
      "metadata": {
        "id": "9d545c80"
      },
      "source": [
        "The **super().\\__init__()** line is commonly used in the constructor method (__init__) of a subclass to call the constructor of its parent (superclass). This is important for object-oriented programming in Python, especially when you're working with inheritance. Doing so ensures that the subclass is initialized based on the behavior defined in the parent class's constructor, in addition to any new behavior you define in the subclass.\n",
        "\n",
        "\n",
        "The .forward method allows you to do this:\n",
        "\n",
        "my_output = myclass(my_data)\n",
        "\n",
        "It is tied to the \\__call__ method, which defines the behavoir of the class when called (like above)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "id": "deeb5718",
      "metadata": {
        "id": "deeb5718"
      },
      "outputs": [],
      "source": [
        "funct = MyFunction(torch.rand(4))\n",
        "\n",
        "x = torch.linspace(-1,1,100)\n",
        "f = funct(x)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e925d61e",
      "metadata": {
        "id": "e925d61e"
      },
      "source": [
        "Let's look at this"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "id": "6797075c",
      "metadata": {
        "id": "6797075c",
        "outputId": "b172ea55-0b15-40b5-e1cb-ebe394274d71",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 197
        }
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "RuntimeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-61-44cf989e500b>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mRuntimeError\u001b[0m: Can't call numpy() on Tensor that requires grad. Use tensor.detach().numpy() instead."
          ]
        }
      ],
      "source": [
        "plt.plot(x.numpy(),f.numpy())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7fed5af7",
      "metadata": {
        "id": "7fed5af7"
      },
      "source": [
        "Oh! The tensor we have is still a tensor that can be used to compute a gradient on, and we can't get a numpy version of this. We can do two things:\n",
        "\n",
        " - get rid of the need for gradients\n",
        " - 'detach' it\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "id": "0d130d87",
      "metadata": {
        "id": "0d130d87"
      },
      "outputs": [],
      "source": [
        "# DETACH\n",
        "f_detach = f.detach().numpy()\n",
        "\n",
        "# no gradients computed\n",
        "with torch.no_grad():\n",
        "    f_no_grad = funct(x).numpy()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "id": "76640e31",
      "metadata": {
        "id": "76640e31",
        "outputId": "be976501-a999-4ff9-c01f-853e41275c74",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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qtwCoNOhFnmsbaWk5nsKSdUa2bNlCnTp1rHhrERGRklv2b8jNgHpdoM2tVlfjMYp9ZOTs2bPs3bs3/3FCQgJbtmyhRo0aNGjQgHHjxnH48GE++eQTAN566y0aN25MmzZtOHfuHB988AFLlixh4cKFpdcLERGRspYSD5vzvtsY8C+w2aytx4MUO4xs3LiRPn365D8eM2YMAKNGjWL69OkcPXqUxMTE/NdzcnJ4+umnOXz4MIGBgbRv355FixYV+BkiIiKu7sScZwkxTlLqDyC0QQ+ry/EoVzWAtbwUdQCMiIhIWdi09Bs6L7+HXONNdM6rPD/iRg1aLYKifn/r2jQiIiKX43RQf/0/AfjUEc0h6mhdkVKmMCIiInI5mz8hNGsfZ0xl3nbchsMYrStSyiyZ2isiIuIWzqXB0n8BkNzxSW7xaUuPiJo6RVPKFEZEREQuZeXrkHEcajal5ZCnGO/ta3VFHkmnaURERApz+gCsfSfvfv9/goJImVEYERERKUzMRHDkQONe0Hyg1dV4NIURERGRC2xYPg/i52JsXjDg31rgrIwpjIiIiPxOzI6j+C0eD8AXub2JOVXL4oo8n8KIiIjI72Su/5QOXvtJN5V4y3G71hQpBwojIiIi551LY2DKFAAmO27hmAnWmiLlQFN7RUREzlv5Ov7nTpBZpSHO5g8ytWkdrSlSDhRGREREAE7uy5/KGzjkFZ5rEWltPRWITtOIiIgALByfN5W3yQ2aylvOFEZERET2LYHdP4DNGwZM0lTecqYwIiIiFdqi7Yc5NmtM3oNuD0DtltYWVAEpjIiISIUVE5/Cyi9eofa5BE6ZKiytc6/VJVVICiMiIlJhbd21lzE+swF40/4nVh2yW1xRxaQwIiIiFdYd6R8RbMtgh7Mhnzlu0JoiFtHUXhERqZgOb6Z+Qt5RkfWtxvFeh25aU8QiCiMiIlLxOJ0w/xnAQPth3HPrcKsrqtB0mkZERCqerV/A4Y3gVwX6vWh1NRWewoiIiFQs51Jh0cS8+72ehaph1tYjCiMiIlKxHPx6AmQcJ6NqY+j+kNXlCAojIiJSgayJXUm9Xz4B4KGTw4j55bTFFQkojIiISEVhDPVWP4+PzckCR1fWmA6s3X/S6qoEhREREakofv6Khme3kGX8+Kd9JA5jtK6Ii9DUXhER8XxZZ2Dh8wAcav8oA/y70COiptYVcREKIyIi4vmWTYKMY1CzGc1uHsd4Hz+rK5Lf0WkaERHxbEd/hvXv593/w6ugIOJyFEZERMRjxew4StKnD4NxQptboEkfq0uSQiiMiIiIR4qJT2Hh528QnrGNDOPPisZPWV2SXILCiIiIeKQtu/czzudzAP7ruI3lyb4WVySXojAiIiIe6c60D6hhO8tuZzgf2gdoGq8L02waERHxPIlrqZcwG4A1rf7Oux16aBqvC1MYERERz+LIhXm/jg/pNJJ7bhpubT1yRTpNIyIinmXtO3AsHgJrQvQLVlcjRaAwIiIinuNMIix7Oe9+v5cgsIa19UiRKIyIiIjHOPbVk5CbyelaXSHyTqvLkSJSGBEREY+wZeEMah9ZTK7x5vZDtxOz85jVJUkRKYyIiIj7O5dGxIa88SHvOwaTQDhr95+0uCgpKoURERFxf0teIij3OAnOUCY7/ojDGK0r4kY0tVdERNxb0gZYPxWAU31eYXhGc3pE1NS6Im5EYURERNyXIxe+fwIw0GE4nfvcQmera5Ji02kaERFxX2vehmM7oFIN6P8vq6uRElIYERERt7Rq/QZyl0zKezDg31BZY0TclcKIiIi4nZgdyZjvn8TX5LDK0YYY3z5WlyRXQWFERETcTub6GVznvZ1zxpcJ9vtZm3DK6pLkKiiMiIiIe0lP4Q9H3wbg/xy3sd+Eahqvm9NsGhERcS8/PoNvTipp1duQG/EwU5uEahqvm1MYERER97FzHsR/CzZvgv40hefrtLe6IikFOk0jIiLuIesM/PB03v1rHgcFEY+hMCIiIm7h0Kxn4GwyGVUaQa9nrS5HSpHCiIiIuLyNy76l/v6vALjn5Ahi9qRZXJGUJoURERFxbTkZNFkzFoDP7H3ZRGtdkdfDKIyIiIhrW/wi1XOOcNjU5D+OO3VFXg+k2TQiIuK6DsbCuvcASOn1H27LbK0r8noghREREXFNOZnw7SOAgY530emG2+hkdU1SJnSaRkREXNPSf8GpfVC1jq7I6+EURkRExOWsX/kTzth38h4M+T+oVM3SeqRsKYyIiIhLWbwtkeoxT+GFk68d1xJjj7S6JCljCiMiIuJSKq2aRDOvwxwz1fiXfZSm8VYACiMiIuI6EtcSlfIFAM/ZR3PKVNY03gpAs2lERMQ15GTA3L9gw3C40a00DLmVqZrGWyEojIiIiGtY9AKc2g9B9ah3x1uMDwi2uiIpJzpNIyIi1ktYAevzFjfjprdBQaRCURgRERFrZaeTNeshAA5FDIOmfS0uSMqbwoiIiFjq0MynqJR5mCRTiwHx/YmJT7G6JClnCiMiImKd3T9SP2EWTmPjmdwHOWcL1FTeCkhhRERErJFxAr57DIAPHYPYYNroirwVlGbTiIhI+TMGvn8CMo5DrVZEXP8Kdx88qyvyVlAKIyIiUv62fgG75oGXL9z6Hn3rNKBvO6uLEqsU+zTNihUrGDJkCHXr1sVmszF37twrbrNs2TI6deqEv78/TZs2Zfr06SUoVUREPMHKDZvJ/u7pvAe9x0KdDtYWJJYrdhjJyMigQ4cOTJ48uUjtExISGDx4MH369GHLli08+eST3H///fz000/FLlZERNxbzI6j+Hz3CP7OTDY5m7GoxnCrSxIXUOzTNIMGDWLQoEFFbj9lyhQaN27M66+/DkCrVq1YtWoVb775JgMGDCju24uIiDtb8zZR3vFkGn+eyX2YPgdSiW5bz+qqxGJlPpsmNjaW6OjoAs8NGDCA2NjYS26TnZ1NWlpagZuIiLi5o1vpe/R9AF6yj2S/CdXMGQHKIYwkJycTGlpwZHRoaChpaWlkZWUVus2kSZMIDg7Ov4WHh5d1mSIiUpZyMuHr+/Fy5nKsXjSBPe5h6sgumjkjgIuuMzJu3DhSU1Pzb0lJSVaXJCIiVyNmPJz4BaqEUfvO9xk/pI2CiOQr86m9YWFhpKQUXNo3JSWFoKAgKlWqVOg2/v7++Pv7l3VpIiJSHn75CTZ8kHf/lnehsk7NSEFlfmQkKiqKxYsXF3guJiaGqKiosn5rERGx2PLNOzj71YN5D3o8DE1usLYgcUnFDiNnz55ly5YtbNmyBciburtlyxYSExOBvFMsI0eOzG//0EMPsX//fv72t7+xa9cu3nnnHb766iueeuqp0umBiIi4pJgdR3HO+QtV7KfZ6Qxncb2/WF2SuKhih5GNGzfSsWNHOnbsCMCYMWPo2LEjEyZMAODo0aP5wQSgcePG/PDDD8TExNChQwdef/11PvjgA03rFRHxcM7Yd+njvZVzxpcx9sdYc/Cs1SWJi7IZY4zVRVxJWloawcHBpKamEhQUZHU5IiJyJUe24PwgGi9nLuNz72WGI1qzZyqgon5/69o0IiJSurLPwtf35U/j9Qu7n6lNQhRE5JIURkREpHQteBZO7oWgetT+81TGB9awuiJxcS65zoiIiLinnxd8CHGfYrDBre+DgogUgcKIiIiUilXrN9Ao9u8A/Nc+lJjMZhZXJO5CYURERK6ePYfGyx4jyJbFRmdzJjv+yNr9J62uStyEwoiIiFy9Rf+gXuZOTpsqPJn7ODnGSxfBkyLTAFYREbk6u+bD2skAHLjuNQac60CPiJqaPSNFpjAiIiIldyYJ5v66smrUo3SMHk5HaysSN6TTNCIiUiKLth8iaeodcO4M1OsMfSdaXZK4KYUREREptpj4FPbOHEt4xnbSTCArO/wHfPysLkvclMKIiIgU28lNc3nI53sAxtofYNmxQIsrEnemMCIiIsVz+gB/TPwnAB/ZBzLf0U0zZ+SqaACriIgUnT0bvhqFb24aZ2pGcqThc0xtGqaZM3JVFEZERKToFoyDo1ugUg2qjfiUv1cLt7oi8QA6TSMiIkWy7ccPYOOHv153ZiooiEgpURgREZErWhO7moi1zwHwtv1mYnLbWVyReBKFERERubxzaTRf9hCVbdmsdrThbcftuu6MlCqFERERuTRj4NuHCclO5IipwVP2x8g1Ns2ekVKlAawiInJpq/8Pdn4P3n4k9X6PIan1dd0ZKXUKIyIiUrj9y2HxC3n3B71C9y796W5tReKhdJpGREQusmLjFjI+HwnGCZF/hs73WF2SeDCFERERKWDxtkSCvruXyvYzbHc2YnHEs2CzWV2WeDCFERER+Y0x1Fw2lkivfZw2VXgk9ynWJGZYXZV4OIURERH5zfqpRJ78AYex8Xju4xw0tTRzRsqcBrCKiEieA6tgwVgA9kX+jea+QxipmTNSDhRGREQEziTBV6PAOKDd7TQfOo7xGici5USnaUREKrrcLNI+HgaZJ0ir1hqG/FcDVqVcKYyIiFRkxnB0xv0End7BSVOVQckPErM33eqqpIJRGBERqchWvk6dxHnkGm8eyX2CZFttXXdGyp3CiIhIRbXrB1jyEgAT7XezwbTBYYxmz0i50wBWEZGKKHk7fD067363B+jT6K9U2n9S150RSyiMiIhUMMs27yRywR+plpsBjXvBgEn08/ZRCBHL6DSNiEgFsmhbEpXm3k21nGQSnKEsbf8qeOv/S8VaCiMiIhWFMdRa+gzdvXaRZirxoP0ZVh12WF2ViMKIiEiFsfJ1Opz6Ebvx4rHcJ/nFWVeDVcUl6NiciEhFsGNO/syZPZ0n0NRrAHdpsKq4CIUREREPt27lQjoteQBfgO5/odWgpxhvdVEiv6PTNCIiHmzlhjgiFt2Pr8lhsaMjMeGPW12SyEUURkREPFXWGVosvpdatlR2OhvwlP0x1h44Y3VVIhdRGBER8UT2HPhqBLXP7SfFVGN07jOkmQANWBWXpDEjIiKexhj47jFIWAF+VUjoNZ0Bp0O1uqq4LIURERFPs2wS/DwTbN5w+8f0aNaHHlbXJHIZOk0jIuJBdvzwDix/Je/BjW9As2hrCxIpAoUREREPsXnxLJqvfx6A/9lvJqbSIIsrEikahREREU9weBNtVz+Gr83BHMc1vOkYxtr9J62uSqRIFEZERNzdyX3w2Z/wc2axwtGOcfaHcBg0c0bchgawioi4s7PH4NNbIfME1OmAvcdH/DkpWzNnxK0ojIiIuKklW/fR8qfh1M08ANUbwZ9nc0OV2tzQwerKRIpHp2lERNzQom1J+M0eQd3M3ZwwQazu8T5UqW11WSIlojAiIuJunA7qLn6Ma713kGH8uT/3byw5XtXqqkRKTGFERMSdGAPznqL1maVkGx8eyn2aLc4IDVYVt6YxIyIi7mTxC7D5Y7B5savnmzTP6cJIDVYVN6cwIiLiJn6Z82+ab30z78GNb9Gh80g0VlU8gU7TiIi4gfjv/0vzrXnLvL+cewcxlQZaXJFI6VEYERFxdT/PotWmCQBMsd/IVOdNWl1VPIrCiIiIK9v1A8x5EBuGGfZoXnXcqdVVxeNozIiIiAuKiU8hJe5H7tz3V7yMAzoMJ6z5RO5OOK3VVcXjKIyIiLiYmPgU3pvxKTP8XsbLlktK/QGE3vQ/+nn70K9NHavLEyl1Ok0jIuJiErcuZ7rff6hky2GZI5IPav8dvPX/juK5FEZERFzJ4U2M3P8UVWznWONsw4O5T9KtaZjVVYmUKUVtERFXcWQLzLgF39yznK7VlRX1X+F/zeprfIh4PIUREREXELtmGR0WjyDQkQbhPah+19eM9a9idVki5UKnaURELBa7ZgXNf7qLQEcam51NWdLlHVAQkQpEYURExErJ2+iw+C5q2tLZ6ozg3tyxrE7KtroqkXKlMCIiYpWjW+HjIQQ6UtnijGBU7nOcMYFa0EwqHI0ZERGxwpE4+GQonDsD9bpwuut7/PFQjhY0kwpJYUREpJytW7WI9kvvppIjHep3g7u+pk9AEH0ira5MxBo6TSMiUo7Wr5hPq5i7qORIZ4OzOUu6ToGAIKvLErGUwoiISHnZv5zIZfcQZMtinbMl92mwqgig0zQiIuXjl5/gyxH4ObNZ4WjHX+xPk2H8NFhVBIUREZEyt3XhJ7SNfQpvY4cWg8lp+wp3HEzXYFWRX5XoNM3kyZNp1KgRAQEBdO/enfXr11+y7fTp07HZbAVuAQEBJS5YRMSdbJ8/hbarH8fb2PnOEcWidv8hul04429srSAi8qtih5Evv/ySMWPGMHHiRDZv3kyHDh0YMGAAx44du+Q2QUFBHD16NP928ODBqypaRMQtxL5D2/XP4m0zfGXvxdP2R4k9kGZ1VSIup9hh5I033mD06NHcc889tG7dmilTphAYGMi0adMuuY3NZiMsLCz/Fhqq/xsQEQ9mDCz5J/w0DoCp9j/wnOMBco1NY0REClGsMSM5OTls2rSJcePG5T/n5eVFdHQ0sbGxl9zu7NmzNGzYEKfTSadOnfj3v/9NmzZtLtk+Ozub7OzfRpinpen/JETEPcTsOEq1Zc/R9fg3eU/cMJ5GNe9iVMIpjRERuYRiHRk5ceIEDofjoiMboaGhJCcnF7pNixYtmDZtGt9++y2ffvopTqeTnj17cujQoUu+z6RJkwgODs6/hYeHF6dMERFLLNqWRNbMe+h6/BucxsbOTi/A9X+lX5swjRERuYwyX2ckKiqKkSNHEhkZSa9evfjmm2+oVasW77333iW3GTduHKmpqfm3pKSksi5TROTqnEsjYuHd3OQdS67x5kn7Y8z26m91VSJuoVinaUJCQvD29iYlJaXA8ykpKYSFhRXpZ/j6+tKxY0f27t17yTb+/v74+/sXpzQREeukJ8NntxGRvo2zJoBHcp9iubMdUzU+RKRIinVkxM/Pj86dO7N48eL855xOJ4sXLyYqKqpIP8PhcLBt2zbq1KlTvEpFRFzQ6rWxnH67NyRvg8q12N7/C5r2vImpI7votIxIERV70bMxY8YwatQounTpQrdu3XjrrbfIyMjgnnvuAWDkyJHUq1ePSZMmAfDiiy/So0cPmjZtypkzZ3j11Vc5ePAg999/f+n2RESknK1f+ROtFt1LddtZEpyhHO71Gdd260oPqwsTcTPFDiPDhg3j+PHjTJgwgeTkZCIjI1mwYEH+oNbExES8vH474HL69GlGjx5NcnIy1atXp3PnzqxZs4bWrVuXXi9ERMpb/Ld0XHI/vrYctjgjeCD3bww5Vplrra5LxA3ZjDHG6iKuJC0tjeDgYFJTUwkK0tUtRcRCxkDs/2DheMCwyNGRp+yPk278dWpG5AJF/f7WtWlERIpo0fbDBC9//rc1RLqOxjQcw58OnNEaIiJXQWFERKQIlmzdh232fXT1jsNpbOyJHEuLPzxLP5uNfm3rWl2eiFsr83VGRETc3umDtPnxNvp6x3HO+PKI/Um+8r0JbDarKxPxCAojIiKXk7gWpt5A6Ln9HDPVGJ47gR8dXXWNGZFSpNM0IiKFiIlPIWP9DG5KfBkvZy6EtWdXl//RKdmXhzU+RKRUKYyIiFwgZvsR9s18hod85gGQUq8/oaOmc71fZa63uDYRT6QwIiLye1mniVh4N/181gHwjn0oJ8OeYbxfZYsLE/FcCiMiIucd2wlfDKdJWgJZxo9n7Q/xnaMHU5vUsroyEY+mMCIiAmyJ+ZRWsc/g78yE4AZs6f42tU7VZqrGh4iUOYUREanYnA4SvhpH5K73AFjjaE1O72n07tiKol3+U0Sulqb2ikjFlXECZtxC41+DyDT7QO6xj2PlYZe/SoaIR9GRERGpcGLiU0j8eQV/Pvg8AVnJ2H0CeSrzXuaba3AYozVERMqZwoiIVCgxO5JZ8fkkxvvMwM/mIKNqYyqP+IKbTtSg9v6TusaMiAUURkSk4jiXSr2Yh3jJdykACxzd2Nr03zxbuxX9aqMQImIRhRERqRiOxMGsu2l95gC5xptXHHfygX0gU5s1sLoykQpPYUREPJsx7PruNZpueQUfkwvBDdjc5XVMan1N2xVxEQojIuK5Mk5y/LP7aXlkCQA/Obrg1+dd+kQ2p7vFpYnIbzS1V0Q8076l8G5Pah1ZQrbx4YXcETxsH8OqQ3arKxORC+jIiIh4lEXbkghcNYmeKZ8BcDaoCbcfv59faKRpuyIuSmFERDzGmtjVhP74MO28DgCQ1GQ44cPeYMzedNZq2q6Iy1IYERH353TCunfptvAf+HjlcNpU4Tn7A9Stfjvj/QLp1zpQIUTEhSmMiIhbW7lhM+HLn6bR2c34AEsdHRhnf5BkU42pOiUj4hYURkTEPRnDjh8m02HDPwmyZZFp/DnQ5e/YI4YxOOGUTsmIuBGFERFxP2eS4PvHabNvCdhgk7MZz+Q+TB9bD8a3CaNfmzCrKxSRYlAYERG3EbMjmex10xh45H/42DNwePvz8rk/Mt05mFxjY5xOy4i4JYUREXELq9atJ3Dek/Tz3gHAmZqdqDb8fbodC8KpmTIibk1hRERcmyMX1vyX7ktextc7hyzjx2uOYdgaPcjzIc3oF6IL3Im4O4UREXFZ61YupNGasYRm7cMXWOloywT7/SSY2kxtUtvq8kSklCiMiIjryTpN0uzn6Lr3C7xshlOmCke6T+Bcw5u5QTNlRDxOhQ4j61YtYldiMnUj++kPm4grMAa2fgELxxOeeQJs8I3jWibZR3CTs71myoh4qAobRmLiU6i68HlGee1k3a6WbOwzji69bwabzerSRCqk2DUrqLfmeRqc3QrkXVNm9Ik7WG/a6poyIh6uwoaRdXuSaWTq0dHsobvXLlg+Cvb3YFPjB/jhbEuimoboaIlIecg8ReI3z9Ntz+d42wyZxp9DHR6n+U1/495fTtNaM2VEPJ7NGGOsLuJK0tLSCA4OJjU1laCgoFL5mTHxKYz+ZCP1bKe43/t7RvotxduZA0CcsymT7Tcz7M+j6demTqm8n4j8JiY+hXV7U7jN/ETLnf+Dc2cAmO/oxr/tIxhwTRfG39ja2iJF5KoV9fu7wh4Z6dc6lKkju7B2/0nqR/THO9ywdsZEOqR8Q0evvXzg9zrH5s1hW+IjzM3tRo+mofo/M5FSELMjmU8/m8bffT6luddhANKDW/DA8dt0SkakgqqwR0YKExOfwthPFnOfzwLu8l5IkC0LgIOmNlPtg+kz7Cn6tm9YZu8v4vGO/sz+z8cQkb4BgFOmCrEN/8LgUWOJ2X2StTolI+JRivr9rTBygZj4FNbuP8m19X0x66fS4fDn1LSlA5DhU53K1z3MsqCbWHHISVQT/dEUKYoVG7cQvOZl2p9agA1DtvFhhqM//7UP5fWRvfU5EvFQCiOlICY+hcc/WcUw7xXc5/0D4V7HAcg0/sxy9OZDx0DGjxisP6Qil5JxgoPfvkTY7s/wt+UCkBw+mD3txrDsWKCOgoh4OIWRUnL+SElUo2CiTSxH579CnaxfAHAaG79Uv570jg/wY2pjzcARIe8zs/mXg9yeM5eIvR9DzlkA1jpb8bL9z3Tu2VeDU0UqCA1gLSX9Wv9+4OptbPe6lr9+Np3R3j/S23sLLc8sh6XL8XdGMG3tQGzDHya6XbilNYtYZcnWfcR99QoP+syjmi0DgLTqbXg05UZWmw44DDyiwakicgEdGSmB80dL+oacxn/je7Q5Pp+AXw9Bn/WpTpVrHmB50BCWH/HWuBKpGM6lwfr3yFz+XwIdaQDsddYlrtmj3H7Xw8TsPKbBqSIVkE7TlJOY+BSe/WQJd/ks5k7vRYTZTgOQa7xZ4OzGDHs0o++6S0tYi2fKOs3eeW9Sb9c0KjnyBnrvc9bhHcctzHH05L2R3RQ+RCowhZFy9Nu4kiCiWU/ij2/SIOPn/NePBURQu89fWOp/AyuTcnS0RNxf2hGInYx9w0f42PNOx+x11iUr6mmSw//A2gNndBRERBRGrBQTn8JbM2Yz0ieGIV5rCLRlA3mzcOY5o/jC3oeH77pDR0vE7axeG0ulDZOJPL0AL2feqcldznAm229mgYli5DURGpwqIvkURiz223olfvTJXsKxpe9Q+1xC/uvHKkVwqsVwvjPX0bFFhP4PUlyXMZCwnOMxb1Lr6LL8p0+HdOFAqwe4JaYy3jYvHMYwdWQX/VsWkXwKIy4mZkcy73/6GcN9lvIHr7X5A16zjQ8xzi7U7X0fnXrfCt6a4CQuIvcc2xd+RMj2DwjL2gvkTWdf7OzIVMdNtOs5gPE3ts4P3jotIyIXUhhxQb9f3TVr00waHpxFG6+DvzWoEkZCvSEs8O5N07Zd9YddrHH6AGycRs6Gj/HLOQPknWLcFXYTYxJ7kERdHQURkSJRGHFx568a3NbrILd6Leeuyuvwyz6d/3q8syE+kcNIbnAjy476atCrlC2Hnbils6m87WOapcZiI+/PwmETwgx7NF86+3LrNW3pEVFTR0FEpMgURtxAgcPbzavz5RcfUuOX2fTyisPP5gDyDouvM6343hFF/9tG07tjK4urFk8RE5/Czvht3OhYTN0DXxOQlZL/2onQaznU9M/curgqNpu3joSISIkojLih80dLatgyGOi1lrurrKd59rb8151449WkFzuqR/NDbicNfJWSyclg2+LPOLPmY67z3p7/9ClThW8c1/GFsx+9e0ZpPIiIXDWFETf1+z/+AC/M+JEh3mv5g1cs7bwO5LezGy9ina0J6Xobx+pFa7VXuayY7UdI2bqQG3KWUPfIIsjNyH9tpbMdO0Jv5o2kZjhsfjoKIiKlRmHEQxT4P9PQsyz5+j3qHppPS6+k/DZOYyPONGOhozO9hoygZ/eeYLNZWLW4BKcTDq0nccWn+O/5nlDbmfyXMqs04L3TXZnj7EWiCWHqyC4AOgoiIqVKYcRDnT+V08QrmWjbBv5UJY4m2bsKNqoRwcGQ61luOlO3fR9duK8icTpYv+onnNu/JTJ9GQFZyfkvnTZV+MHZg5w2f+LeYX/S9WJEpMwpjHiwC0/ljP/kJ/p7b+YGr81c7xufvzImwFkTQGa9azgZdj0Lc9rRunVbffF4mMXbEjm29Seuc6yj1pEl+GefzH8t17cKx+tG8/c9zYg17TlnvHUKRkTKjcJIBVLgVE6TQL76cgbee37keq+t1LKlFmi73xmGb7MbCO88kKXZLVl5yKGxJm4kJj6F2H0n6RN2juuI43jcPCofXp1/yQGANBPIYmdHFjh70LD7EJ67qaMGooqIJRRGKrDzp3J8bIYWHOC+sH2En1xNR9sefGzO/HZOYyPeNGKtsyVdeg0h8ppBxBzIJXbfSQUUF3E+fFzbwJ/qxzewedlcrvP6meZehwu0O2pqEOPswvF6fXn3QB2MzVcDUUXEcgojFdyFp3JGf7KRYFsWXW3xTGh9jIBDqwpcKwfAYGOXM5xNpjkbHc25beitZFUOJ3b/KYWT8pZ9lk2rF7JqyXdc67WD9rZ9+P669gyAw9g4XLU92Y1u4IlNtdhNIxwGDUQVEZeiMCIFXHiYPiY+hb9/EkNP7510te3k5uoJVEnff9F2x00wW5zN2OKM4Ia+A+nco4+OnpQ2YyD1EFvXLSFr3xpa5W4n+MxOMI4CzY751GXRuZbEmrYsd7Tl9ZG98/elwoeIuCKFEbmiC7/Elm/ewczZX9LZaw+dvH6hvdcBfLBftN0BZyg7TCN2OBvSr09f0qu1YtkRH6KahujL8BLOn26JalKTfuFA8s/s2boaR9ImGmfvxP/c8Yu2yQqsx4/pjVnvbM0qZxsmjhgE6KiHiLgPhREpkd8HFC9HNu9+PouO3vtpZ9tHdPBhAs8mFrrdKVOFPaY+dZt1JLx5JzZm1mbFqeq0a9mCfm3CyrkX1ouJT2HjL0ncEHKayml7WbVmNa28EmltO3DRoGIAB17sdDYgztmUTaYljTtH88StfXTUQ0TcmsKIlIoLvwyXxu3mw1lzaOt1kBa2g3QLOExoTmKBgbG/l2H8cVZvTGaVRuyx16ZGvWa0bt0WqjVk0RE/1hxId6vTPQWOcLQOhXNprInbSuLeeDpVOUlz3+OcTNpFVvIv1LedKPRnGGycCGjA2oy6bHFGsM00I6RZF+bvTsPbZtPAUxHxGAojUmYuHBz76CdraO51hCYc4on2DnKOxhNw5hfqcwxv2+X/eR03waSY6oTWa0x2pVD2ZlUhtE44rZo2hsAQ1iTDmiMQ2axB/uJtFwaCiwLCVbbp2TiI6Eb+kHWa9Tv3knDgAO2rZeN/7jhrf44nzHaGOraTNPU/jW9u+mX7d8IEcbxSBOvP1mKvCWe7syGPDr8Zp08goz/ZWCB8gE7BiIhnURiRclPY4NjRn2wkwOagLikMbXCOtMO7aUAy9W0naFs5lWo5R/BznivW+zi8K2H3rUpipi9Z+JOFH7Vq1GDXSTs5+GLHmx5NQzFevizafRIvwGBoXy+Y7YfP4GNz4mtyuTYiGC9nDtsOHqOyLZtAzlG/spOczDSqkEVVW1ax6jptqnDYhHDQhBFUvyXV67fkH6syOUA9TpiqlwwaOgUjIp5OYUQsVdjU4gJHAYzh2RlLqed1ihBO06dOLmdSEqnFaUJs6bQMyibQfgbfcycJsmVa0ocs76ocswdywgRxwlTDr1oYcaf8OUE1DpuaPHhTL85VqsO9X+y86PSKgoaIiMKIuJjCvpyvGFh+fc7XZqhkMph8axN8c9N564eNVLZl42+yubFVNdbsSqKSLRcv4+D2jmHYjJ35W5PwAhxAl4Y12XDwNE68yDY+3NKlMU5vPz5ad4RsAkg3/vSPbMKncSfJsgVyyhnIf+7qBV7eRTqVouAhIlI4hRFxO1cKLJd6rjzbiIhI0SmMiIiIiKWK+v3tVY41iYiIiFxEYUREREQspTAiIiIillIYEREREUspjIiIiIilShRGJk+eTKNGjQgICKB79+6sX7/+su1nzZpFy5YtCQgIoF27dsyfP79ExYqIiIjnKXYY+fLLLxkzZgwTJ05k8+bNdOjQgQEDBnDs2LFC269Zs4bhw4dz3333ERcXx9ChQxk6dCjbt2+/6uJFRETE/RV7nZHu3bvTtWtX/ve//wHgdDoJDw/nscceY+zYsRe1HzZsGBkZGcybNy//uR49ehAZGcmUKVOK9J5aZ0RERMT9lMk6Izk5OWzatIno6OjffoCXF9HR0cTGxha6TWxsbIH2AAMGDLhke4Ds7GzS0tIK3ERERMQzFSuMnDhxAofDQWhowWWxQ0NDSU5OLnSb5OTkYrUHmDRpEsHBwfm38PDw4pQpIiIibsQlZ9OMGzeO1NTU/FtSUpLVJYmIiEgZ8SlO45CQELy9vUlJSSnwfEpKCmFhYYVuExYWVqz2AP7+/vj7+xenNBEREXFTxQojfn5+dO7cmcWLFzN06FAgbwDr4sWLefTRRwvdJioqisWLF/Pkk0/mPxcTE0NUVFSR3/f8GFuNHREREXEf57+3rzhXxhTTzJkzjb+/v5k+fbqJj483DzzwgKlWrZpJTk42xhgzYsQIM3bs2Pz2q1evNj4+Pua1114zO3fuNBMnTjS+vr5m27ZtRX7PpKQkA+imm2666aabbm54S0pKuuz3fLGOjEDeVN3jx48zYcIEkpOTiYyMZMGCBfmDVBMTE/Hy+m0oSs+ePfn88895/vnnee6552jWrBlz586lbdu2RX7PunXrkpSURNWqVbHZbMUt+ZLS0tIIDw8nKSnJY6cMe3of1T/35+l9VP/cn6f3sSz7Z4whPT2dunXrXrZdsdcZ8SQVYf0ST++j+uf+PL2P6p/78/Q+ukL/XHI2jYiIiFQcCiMiIiJiqQodRvz9/Zk4caJHTyP29D6qf+7P0/uo/rk/T++jK/SvQo8ZEREREetV6CMjIiIiYj2FEREREbGUwoiIiIhYSmFERERELOXxYeRf//oXPXv2JDAwkGrVqhVpG2MMEyZMoE6dOlSqVIno6Gj27NlToM2pU6f485//TFBQENWqVeO+++7j7NmzZdCDyytuHQcOHMBmsxV6mzVrVn67wl6fOXNmeXSpgJL8nnv37n1R7Q899FCBNomJiQwePJjAwEBq167NM888g91uL8uuXFJx+3jq1Ckee+wxWrRoQaVKlWjQoAGPP/44qampBdpZtQ8nT55Mo0aNCAgIoHv37qxfv/6y7WfNmkXLli0JCAigXbt2zJ8/v8DrRfk8lrfi9HHq1Klcd911VK9enerVqxMdHX1R+7vvvvuifTVw4MCy7sYlFad/06dPv6j2gICAAm1cbR8Wp3+F/T2x2WwMHjw4v40r7b8VK1YwZMgQ6tati81mY+7cuVfcZtmyZXTq1Al/f3+aNm3K9OnTL2pT3M91sRXvyjTuZ8KECeaNN94wY8aMMcHBwUXa5uWXXzbBwcFm7ty5ZuvWreamm24yjRs3NllZWfltBg4caDp06GDWrl1rVq5caZo2bWqGDx9eRr24tOLWYbfbzdGjRwvcXnjhBVOlShWTnp6e3w4wH330UYF2v+9/eSnJ77lXr15m9OjRBWpPTU3Nf91ut5u2bdua6OhoExcXZ+bPn29CQkLMuHHjyro7hSpuH7dt22ZuvfVW891335m9e/eaxYsXm2bNmpk//vGPBdpZsQ9nzpxp/Pz8zLRp08yOHTvM6NGjTbVq1UxKSkqh7VevXm28vb3Nf/7zHxMfH2+ef/75i65dVZTPY3kqbh/vvPNOM3nyZBMXF2d27txp7r77bhMcHGwOHTqU32bUqFFm4MCBBfbVqVOnyqtLBRS3fx999JEJCgoqUPv5a5Wd50r7sLj9O3nyZIG+bd++3Xh7e5uPPvoov40r7b/58+ebv//97+abb74xgJkzZ85l2+/fv98EBgaaMWPGmPj4ePP2228bb29vs2DBgvw2xf2dlYTHh5HzPvrooyKFEafTacLCwsyrr76a/9yZM2eMv7+/+eKLL4wxxsTHxxvAbNiwIb/Njz/+aGw2mzl8+HCp134ppVVHZGSkuffeews8V5R/xGWtpP3r1auXeeKJJy75+vz5842Xl1eBP5jvvvuuCQoKMtnZ2aVSe1GV1j786quvjJ+fn8nNzc1/zop92K1bN/PII4/kP3Y4HKZu3bpm0qRJhbb/05/+ZAYPHlzgue7du5sHH3zQGFO0z2N5K24fL2S3203VqlXNxx9/nP/cqFGjzM0331zapZZIcft3pb+trrYPr3b/vfnmm6Zq1arm7Nmz+c+50v77vaL8Dfjb3/5m2rRpU+C5YcOGmQEDBuQ/vtrfWVF4/Gma4kpISCA5OZno6Oj854KDg+nevTuxsbEAxMbGUq1aNbp06ZLfJjo6Gi8vL9atW1dutZZGHZs2bWLLli3cd999F732yCOPEBISQrdu3Zg2bdqVLwFdyq6mf5999hkhISG0bduWcePGkZmZWeDntmvXLv/ijgADBgwgLS2NHTt2lH5HLqO0/i2dv6aEj0/Ba1+W5z7Myclh06ZNBT47Xl5eREdH5392LhQbG1ugPeTti/Pti/J5LE8l6eOFMjMzyc3NpUaNGgWeX7ZsGbVr16ZFixb85S9/4eTJk6Vae1GUtH9nz56lYcOGhIeHc/PNNxf4HLnSPiyN/ffhhx9yxx13ULly5QLPu8L+K4krfQZL43dWFMW+aq+nS05OBijwRXX+8fnXkpOTqV27doHXfXx8qFGjRn6b8lAadXz44Ye0atWKnj17Fnj+xRdf5IYbbiAwMJCFCxfy8MMPc/bsWR5//PFSq/9KStq/O++8k4YNG1K3bl1+/vlnnn32WXbv3s0333yT/3ML27/nXytPpbEPT5w4wUsvvcQDDzxQ4Pny3ocnTpzA4XAU+rvdtWtXodtcal/8/rN2/rlLtSlPJenjhZ599lnq1q1b4I/7wIEDufXWW2ncuDH79u3jueeeY9CgQcTGxuLt7V2qfbickvSvRYsWTJs2jfbt25Oamsprr71Gz5492bFjB/Xr13epfXi1+2/9+vVs376dDz/8sMDzrrL/SuJSn8G0tDSysrI4ffr0Vf+bLwq3DCNjx47llVdeuWybnTt30rJly3KqqHQVtX9XKysri88//5zx48df9Nrvn+vYsSMZGRm8+uqrpfJFVtb9+/2Xcrt27ahTpw59+/Zl3759NGnSpMQ/tzjKax+mpaUxePBgWrduzT/+8Y8Cr5XlPpSSefnll5k5cybLli0rMMjzjjvuyL/frl072rdvT5MmTVi2bBl9+/a1otQii4qKIioqKv9xz549adWqFe+99x4vvfSShZWVvg8//JB27drRrVu3As+78/5zFW4ZRp5++mnuvvvuy7aJiIgo0c8OCwsDICUlhTp16uQ/n5KSQmRkZH6bY8eOFdjObrdz6tSp/O2vRlH7d7V1zJ49m8zMTEaOHHnFtt27d+ell14iOzv7qq9fUF79O6979+4A7N27lyZNmhAWFnbRSPCUlBSAUtl/UD59TE9PZ+DAgVStWpU5c+bg6+t72faluQ8LExISgre3d/7v8ryUlJRL9iUsLOyy7YvyeSxPJenjea+99hovv/wyixYton379pdtGxERQUhICHv37i3XL7Or6d95vr6+dOzYkb179wKutQ+vpn8ZGRnMnDmTF1988YrvY9X+K4lLfQaDgoKoVKkS3t7eV/1vokhKbfSJiyvuANbXXnst/7nU1NRCB7Bu3Lgxv81PP/1k2QDWktbRq1evi2ZgXMo///lPU7169RLXWhKl9XtetWqVAczWrVuNMb8NYP39SPD33nvPBAUFmXPnzpVeB4qgpH1MTU01PXr0ML169TIZGRlFeq/y2IfdunUzjz76aP5jh8Nh6tWrd9kBrDfeeGOB56Kioi4awHq5z2N5K24fjTHmlVdeMUFBQSY2NrZI75GUlGRsNpv59ttvr7re4ipJ/37PbrebFi1amKeeesoY43r7sKT9++ijj4y/v785ceLEFd/Dyv33exRxAGvbtm0LPDd8+PCLBrBezb+JItVaaj/JRR08eNDExcXlT1+Ni4szcXFxBaaxtmjRwnzzzTf5j19++WVTrVo18+2335qff/7Z3HzzzYVO7e3YsaNZt26dWbVqlWnWrJllU3svV8ehQ4dMixYtzLp16wpst2fPHmOz2cyPP/540c/87rvvzNSpU822bdvMnj17zDvvvGMCAwPNhAkTyrw/Fypu//bu3WtefPFFs3HjRpOQkGC+/fZbExERYa6//vr8bc5P7e3fv7/ZsmWLWbBggalVq5alU3uL08fU1FTTvXt3065dO7N3794C0wntdrsxxrp9OHPmTOPv72+mT59u4uPjzQMPPGCqVauWP3NpxIgRZuzYsfntV69ebXx8fMxrr71mdu7caSZOnFjo1N4rfR7LU3H7+PLLLxs/Pz8ze/bsAvvq/N+g9PR089e//tXExsaahIQEs2jRItOpUyfTrFmzcg/HJenfCy+8YH766Sezb98+s2nTJnPHHXeYgIAAs2PHjvw2rrQPi9u/86699lozbNiwi553tf2Xnp6e/z0HmDfeeMPExcWZgwcPGmOMGTt2rBkxYkR++/NTe5955hmzc+dOM3ny5EKn9l7ud1YaPD6MjBo1ygAX3ZYuXZrfhl/XYzjP6XSa8ePHm9DQUOPv72/69u1rdu/eXeDnnjx50gwfPtxUqVLFBAUFmXvuuadAwCkvV6ojISHhov4aY8y4ceNMeHi4cTgcF/3MH3/80URGRpoqVaqYypUrmw4dOpgpU6YU2rasFbd/iYmJ5vrrrzc1atQw/v7+pmnTpuaZZ54psM6IMcYcOHDADBo0yFSqVMmEhISYp59+usC02PJU3D4uXbq00H/TgElISDDGWLsP3377bdOgQQPj5+dnunXrZtauXZv/Wq9evcyoUaMKtP/qq69M8+bNjZ+fn2nTpo354YcfCrxelM9jeStOHxs2bFjovpo4caIxxpjMzEzTv39/U6tWLePr62saNmxoRo8eXap/6IurOP178skn89uGhoaaP/zhD2bz5s0Ffp6r7cPi/hvdtWuXAczChQsv+lmutv8u9ffhfJ9GjRplevXqddE2kZGRxs/Pz0RERBT4Pjzvcr+z0mAzppzna4qIiIj8jtYZEREREUspjIiIiIilFEZERETEUgojIiIiYimFEREREbGUwoiIiIhYSmFERERELKUwIiIiIpZSGBERERFLKYyIiIiIpRRGRERExFIKIyIiImKp/wcgpbp2zYaLXAAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.plot(x.numpy(),f_no_grad, '.', markersize=4)\n",
        "plt.plot(x.numpy(),f_detach)\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d3155967",
      "metadata": {
        "id": "d3155967"
      },
      "source": [
        "Note this:\n",
        "\n",
        "    self.coefs = nn.Parameter(coefs)\n",
        "   \n",
        "The nn.Parameter call is the notification that we want pytorch to use this tensor as parameters we want to optimize.\n",
        "\n",
        "Lets give this a try, but on a more simple system for fitting purposes.\n",
        "We first have to define a scoring function, and lets use something the torch has predefined"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 65,
      "id": "6820c45c",
      "metadata": {
        "id": "6820c45c"
      },
      "outputs": [],
      "source": [
        "# lets use a mean squared error\n",
        "loss_1 = nn.MSELoss()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7d3974a3",
      "metadata": {
        "id": "7d3974a3"
      },
      "source": [
        "Lets build a function and define some values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 66,
      "id": "69d976f2",
      "metadata": {
        "id": "69d976f2"
      },
      "outputs": [],
      "source": [
        "#we intialize a polynomial with 1's\n",
        "funct = MyFunction(torch.Tensor([1,1]))\n",
        "\n",
        "# the ideal polynomial has slope 2 and intercept 3\n",
        "x = torch.Tensor([-1, 1])\n",
        "y_obs = torch.Tensor([-2+3,2+3])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "43b76a86",
      "metadata": {
        "id": "43b76a86"
      },
      "source": [
        "Now we use the gradient calculations via a 'backward' call"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "id": "cfeefb12",
      "metadata": {
        "id": "cfeefb12",
        "outputId": "57678f3c-e6b2-409a-ab20-d4cc5ede5e3f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([-4., -2.])\n"
          ]
        }
      ],
      "source": [
        "# gradients are accumulated, so make sure that we have a zero-array when we start\n",
        "if funct.coefs.grad is not None:\n",
        "    funct.coefs.grad.zero_()\n",
        "\n",
        "y_pred = funct(x) # compute the function\n",
        "loss_actual = loss_1(y_pred, y_obs)\n",
        "loss_actual.backward()\n",
        "\n",
        "print(funct.coefs.grad)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3ecbc019",
      "metadata": {
        "id": "3ecbc019"
      },
      "source": [
        "Lets minimize the function.\n",
        "\n",
        "We will use first derivatives only, so we will need to guess a step size. Here we will simply multiple the gradient by a small number and use that as a step size.\n",
        "\n",
        "Here is what we will do in a loop\n",
        "\n",
        "- Get the loss function\n",
        "- compute the gradient\n",
        "- scale them by a factor\n",
        "- get the new coefficients\n",
        "- make new coefficients\n",
        "- make a new object\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 68,
      "id": "477129f6",
      "metadata": {
        "scrolled": false,
        "id": "477129f6",
        "outputId": "30f006b7-a851-457a-bfd0-88c27d0f7dfc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 coef-a: 1.20 coef-b: 0.80 loss function 13.000\n",
            "iteration 0002 coef-a: 1.85 coef-b: 1.23 loss function 5.325\n",
            "iteration 0004 coef-a: 2.26 coef-b: 1.51 loss function 2.181\n",
            "iteration 0006 coef-a: 2.53 coef-b: 1.69 loss function 0.893\n",
            "iteration 0008 coef-a: 2.70 coef-b: 1.80 loss function 0.366\n",
            "iteration 0010 coef-a: 2.81 coef-b: 1.87 loss function 0.150\n",
            "iteration 0012 coef-a: 2.88 coef-b: 1.92 loss function 0.061\n",
            "iteration 0014 coef-a: 2.92 coef-b: 1.95 loss function 0.025\n",
            "iteration 0016 coef-a: 2.95 coef-b: 1.97 loss function 0.010\n",
            "iteration 0018 coef-a: 2.97 coef-b: 1.98 loss function 0.004\n",
            "iteration 0020 coef-a: 2.98 coef-b: 1.99 loss function 0.002\n",
            "iteration 0022 coef-a: 2.99 coef-b: 1.99 loss function 0.001\n",
            "iteration 0024 coef-a: 2.99 coef-b: 1.99 loss function 0.000\n",
            "iteration 0026 coef-a: 2.99 coef-b: 2.00 loss function 0.000\n",
            "iteration 0028 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0030 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0032 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0034 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0036 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0038 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0040 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0042 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0044 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0046 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n",
            "iteration 0048 coef-a: 3.00 coef-b: 2.00 loss function 0.000\n"
          ]
        }
      ],
      "source": [
        "funct = MyFunction(torch.Tensor([0,0]))\n",
        "step_size = 0.1\n",
        "\n",
        "for ii in range(50):\n",
        "    y_pred = funct(x) # coimpute function\n",
        "    loss_actual = loss_1(y_pred, y_obs) # get the loss\n",
        "    loss_actual.backward() # compute gradients\n",
        "    step = funct.coefs.grad*step_size # scale the gradients\n",
        "    funct = MyFunction(funct.coefs - step) # make a new function\n",
        "    #-------------- Printing stuff --------------\n",
        "    tmp = funct.coefs.detach().numpy() - step.numpy() #for printing\n",
        "    new_a = funct.coefs.detach()[0].item() - step[0].item()\n",
        "    new_b = funct.coefs.detach()[1].item() - step[1].item()\n",
        "    if ii%2==0:\n",
        "        print( f\"iteration {ii:04} coef-a: {new_a:3.2f} coef-b: {new_b:3.2f} loss function {loss_actual.item():4.3f}\")\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fe927570",
      "metadata": {
        "id": "fe927570"
      },
      "source": [
        "While this works, this is far from optimal.\n",
        "Here are some issues with how we do things\n",
        "\n",
        "- *What is a good step size?*\n",
        "\n",
        "When we have a very large model, computing second derivatives isn't really an option. Also, Machine Learning is not optimizing a function per se, it's finding some function that has properties you desire, such as being able to predict values.\n",
        "\n",
        "Instead of using our silly gradients $\\times$ step, we can use an optimizer that takes care of some details\n",
        "(we still need to define a learning rate though)\n",
        "\n",
        "- *Why do we need to make a new model?*\n",
        "\n",
        "We don't, but we can't just change the self.coefs values either, because they are nn.Parameter objects and other steops are involved. blabla gradients blabla computational graph most likely. This is actually taken care of by the optimizer as shown in a bit.\n",
        "\n",
        "\n",
        "- *Why is the multiplier fixed? Shouldn't it vary like when we have newtons method?*\n",
        "\n",
        "Yes it should. We actually can have it slowly / rapidly change over the course of our optimization. This is called a scheduler. There are many of those available. Some dynamic behavoir is availavble within various optimizers, like SGD or Adam and its cousins.\n",
        "\n",
        "- *Even when we scale things down, my functions can have a so-called exploding gradient, i.e. things can go get very large and go to infinity, and I will get NaNs.*\n",
        "\n",
        "That is indeed a problem. To combat this, we can use gradient clipping, i.e. do not allow any element with the gradient to be above a certain value in the absolute sense.\n",
        "\n",
        "\n",
        "Let incorporate this and make our data a little more complicated"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 69,
      "id": "67daff92",
      "metadata": {
        "id": "67daff92",
        "outputId": "da1ee249-cac3-4312-a5c6-b8beb0611420",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "SIGMA=.25 # noise levels\n",
        "N_obs = 10 # number of observations\n",
        "\n",
        "# train data\n",
        "x = torch.linspace(-1,1,N_obs)\n",
        "y_obs = 2*x*x - x + 3 + torch.normal(0, SIGMA, x.shape)\n",
        "\n",
        "# test data\n",
        "x_test = torch.linspace(-1.1,1.1,N_obs-3)\n",
        "y_test = 2*x_test*x_test - x_test + 3 + torch.normal(0, SIGMA, x_test.shape)\n",
        "\n",
        "plt.plot(x.numpy(), y_obs.numpy(), '.')\n",
        "plt.plot(x_test.numpy(), y_test.numpy(), '.')\n",
        "plt.show()\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 70,
      "id": "c2d34c68",
      "metadata": {
        "scrolled": false,
        "id": "c2d34c68",
        "outputId": "7910dac7-4f9f-4fc8-bdd0-641f499e08a5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 coef-a: 0.89 coef-b: 0.49 coef-c: 0.85  loss function 8.262\n",
            "iteration 0010 coef-a: 1.85 coef-b: -0.46 coef-c: 1.81  loss function 1.898\n",
            "iteration 0020 coef-a: 2.61 coef-b: -1.06 coef-c: 2.52  loss function 0.195\n",
            "iteration 0030 coef-a: 2.96 coef-b: -1.11 coef-c: 2.72  loss function 0.294\n",
            "iteration 0040 coef-a: 2.96 coef-b: -0.89 coef-c: 2.50  loss function 0.194\n",
            "iteration 0050 coef-a: 2.86 coef-b: -0.78 coef-c: 2.19  loss function 0.090\n",
            "iteration 0060 coef-a: 2.85 coef-b: -0.84 coef-c: 1.99  loss function 0.080\n",
            "iteration 0070 coef-a: 2.93 coef-b: -0.89 coef-c: 1.93  loss function 0.065\n",
            "iteration 0080 coef-a: 3.01 coef-b: -0.88 coef-c: 1.89  loss function 0.056\n",
            "iteration 0090 coef-a: 3.05 coef-b: -0.86 coef-c: 1.83  loss function 0.053\n",
            "iteration 0100 coef-a: 3.06 coef-b: -0.86 coef-c: 1.76  loss function 0.050\n",
            "iteration 0110 coef-a: 3.07 coef-b: -0.87 coef-c: 1.72  loss function 0.050\n",
            "iteration 0120 coef-a: 3.09 coef-b: -0.87 coef-c: 1.70  loss function 0.049\n",
            "iteration 0130 coef-a: 3.10 coef-b: -0.87 coef-c: 1.69  loss function 0.049\n",
            "iteration 0140 coef-a: 3.10 coef-b: -0.87 coef-c: 1.68  loss function 0.049\n",
            "iteration 0150 coef-a: 3.10 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0160 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0170 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0180 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0190 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0200 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0210 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0220 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0230 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0240 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n"
          ]
        }
      ],
      "source": [
        "# lets make a random polynomial with 3 terms\n",
        "funct = MyFunction(torch.rand(3))\n",
        "\n",
        "\n",
        "n_epochs = 250 # we train 250 epochs\n",
        "learning_rate=.1 # learning rate is 0.1\n",
        "max_norm = 100 # gradient clipping!\n",
        "\n",
        "# choose your minimizer\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.AdamW(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "# our scheduler\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.9995)  # Reduce LR every 10 steps\n",
        "\n",
        "# our loss function\n",
        "criterion = nn.MSELoss()\n",
        "#criterion = nn.L1Loss()\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs)  # Get the loss\n",
        "\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "\n",
        "    # Gradient Clipping\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "\n",
        "    optimizer.step()  # Update parameters\n",
        "\n",
        "    # Learning rate scheduling\n",
        "    scheduler.step()\n",
        "\n",
        "    new_a = funct.coefs.detach()[0].item()\n",
        "    new_b = funct.coefs.detach()[1].item()\n",
        "    new_c = funct.coefs.detach()[2].item()\n",
        "    if not ii%10 :\n",
        "        print(f\"iteration {ii:04} coef-a: {new_a:3.2f} coef-b: {new_b:3.2f} coef-c: {new_c:3.2f}  loss function {loss_actual.item():4.3f}\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6cf8ed0e",
      "metadata": {
        "id": "6cf8ed0e"
      },
      "source": [
        "We can use other optimizers, like l-BFGS, that provide approximate second order accelration. The training loop needs to be modified slightly though."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 71,
      "id": "4ce0abea",
      "metadata": {
        "scrolled": false,
        "id": "4ce0abea",
        "outputId": "26254864-b36e-40f9-e7ae-697ba54d2029",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0001 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0002 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0003 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n",
            "iteration 0004 coef-a: 3.11 coef-b: -0.87 coef-c: 1.67  loss function 0.049\n"
          ]
        }
      ],
      "source": [
        "funct = MyFunction(torch.rand(3))\n",
        "optimizer = optim.LBFGS(funct.parameters(), lr=0.1, max_iter=200, history_size=100)  # Using L-BFGS optimizer\n",
        "criterion = nn.MSELoss()\n",
        "#criterion = nn.L1Loss()\n",
        "\n",
        "# Function for closure, required for LBFGS\n",
        "def closure():\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    #print(\"in closure\")\n",
        "    return loss_actual\n",
        "\n",
        "# Training loop\n",
        "for ii in range(5):\n",
        "    optimizer.step(closure)  # Optimizer step\n",
        "    loss_actual = closure()\n",
        "\n",
        "    new_a = funct.coefs.detach()[0].item()\n",
        "    new_b = funct.coefs.detach()[1].item()\n",
        "    new_c = funct.coefs.detach()[2].item()\n",
        "\n",
        "    print(f\"iteration {ii:04} coef-a: {new_a:3.2f} coef-b: {new_b:3.2f} coef-c: {new_c:3.2f}  loss function {loss_actual.item():4.3f}\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 72,
      "id": "9e599171",
      "metadata": {
        "id": "9e599171",
        "outputId": "e595dc36-6134-4bc4-a29a-4fa2e38eeac0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "x_for_plotting = torch.linspace(-1,1,1000)\n",
        "with torch.no_grad():\n",
        "    y_pred = funct(x_for_plotting)\n",
        "plt.plot(x.numpy(), y_obs.numpy(), '.')\n",
        "plt.plot(x_for_plotting.numpy(), y_pred.numpy())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This is the end of this tutorial, at least, the basic part. Below, we will do some more advanced things, like regularizing our model to make sure we don't overfit. These issues will pop up in general machine learning tasks, and are explored in a more simplified environment here.\n",
        "\n"
      ],
      "metadata": {
        "id": "OU1OnPMuXKJ7"
      },
      "id": "OU1OnPMuXKJ7"
    },
    {
      "cell_type": "markdown",
      "source": [
        "-------------------------------------------------------------------------"
      ],
      "metadata": {
        "id": "w1WJFT3aXkeq"
      },
      "id": "w1WJFT3aXkeq"
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Are you sure you want to continue? Be warned, I might have overdone things a bit.....**"
      ],
      "metadata": {
        "id": "zd2eoIZFXkl2"
      },
      "id": "zd2eoIZFXkl2"
    },
    {
      "cell_type": "code",
      "source": [
        "# we need two extra imports\n",
        "!pip install einops\n",
        "import einops\n",
        "import tqdm"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KMlnpONoZMN8",
        "outputId": "dc41e57e-b42a-4138-ca7b-18c983398172"
      },
      "id": "KMlnpONoZMN8",
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: einops in /usr/local/lib/python3.10/dist-packages (0.6.1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4365ded1",
      "metadata": {
        "id": "4365ded1"
      },
      "source": [
        "Lets do some overfitting! We only have 10 data points, but lets fit a 15 parameter polynomial."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "id": "de2656ee",
      "metadata": {
        "scrolled": false,
        "id": "de2656ee",
        "outputId": "fd6130d5-91b7-41db-c00b-91be5019bfc8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000  loss function 19.727\n",
            "iteration 0100  loss function 0.026\n",
            "iteration 0200  loss function 0.024\n",
            "iteration 0300  loss function 0.023\n",
            "iteration 0400  loss function 0.023\n"
          ]
        }
      ],
      "source": [
        "K=15\n",
        "funct = MyFunction(torch.ones(K))\n",
        "\n",
        "n_epochs = 500\n",
        "learning_rate=0.1\n",
        "max_norm = 100\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=5, gamma=0.995)  # Reduce LR every 10 steps\n",
        "criterion = nn.MSELoss()\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs)  # Get the loss\n",
        "\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "\n",
        "    # Gradient Clipping\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "\n",
        "    optimizer.step()  # Update parameters\n",
        "\n",
        "    # Learning rate scheduling\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%100 :\n",
        "        print(f\"iteration {ii:04}  loss function {loss_actual.item():4.3f}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "id": "3ffd4f64",
      "metadata": {
        "id": "3ffd4f64",
        "outputId": "db9f715c-5199-4899-a3a0-e74b29d5dd35",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 914
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Parameter containing:\n",
            "tensor([ 2.9946, -0.9536,  2.1419, -0.0266,  0.5412,  0.0196, -0.1843,  0.0240,\n",
            "        -0.2902,  0.0387, -0.2504,  0.0538, -0.1966,  0.0653, -0.1556],\n",
            "       requires_grad=True)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "with torch.no_grad():\n",
        "    y_pred = funct(x_for_plotting)\n",
        "plt.plot(x.numpy(), y_obs.numpy(), '.')\n",
        "plt.plot(x_for_plotting.numpy(), y_pred.numpy())\n",
        "plt.show()\n",
        "print(funct.coefs)\n",
        "plt.bar(np.arange(len(funct.coefs)), funct.coefs.detach().numpy())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1877d689",
      "metadata": {
        "id": "1877d689"
      },
      "source": [
        "As you can see, the results are all over the place and the polynomial we have fits really nicely, but is obviously overfitting the data.\n",
        "\n",
        "Lets define some way to constrain out polynomial coefficients. We build a function that close to 0 when inpout if close to zero, rises rapidly to 1 when not.\n",
        "\n",
        "We can then use this as an added term during minimization on top of the MSE or L1 loss.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "id": "8c006d0a",
      "metadata": {
        "id": "8c006d0a",
        "outputId": "c94ecc71-3bf4-478d-e513-0d33681fb9ba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "t = torch.linspace(-1.25, 1.25, 10000)\n",
        "ft = t*10\n",
        "ft = (ft**2/(1+ft**2))**.5\n",
        "plt.plot(t,ft)\n",
        "ft = t*100\n",
        "ft = (ft**2/(1+ft**2))**.5\n",
        "plt.plot(t,ft)\n",
        "plt.legend(['delta=10','delta=100'])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "id": "96bd52d6",
      "metadata": {
        "id": "96bd52d6"
      },
      "outputs": [],
      "source": [
        "# our well function that encourages stuff to be zero / small\n",
        "def well_function(coefs, delta, power=.5):\n",
        "    tmp = coefs*delta\n",
        "    tmp = (tmp**2/(1+tmp**2))**power\n",
        "    return torch.sum(tmp)/len(coefs)\n",
        "\n",
        "# here we combine our custom well function with a standard loss\n",
        "class CustomLoss(nn.Module): # we inherit from nn.Module\n",
        "    def __init__(self, base_loss, weight, delta):\n",
        "        super().__init__()\n",
        "        self.base_loss = base_loss\n",
        "        self.weight = weight\n",
        "        self.delta = delta\n",
        "\n",
        "    def forward(self, y_pred, y_obs, params):\n",
        "        part1 = self.base_loss(y_pred, y_obs)\n",
        "        part2 = well_function(params, self.delta)\n",
        "        return part1 + self.weight*part2\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e1b9dd79",
      "metadata": {
        "id": "e1b9dd79"
      },
      "source": [
        "Lets give this a try. for now, we set the weight of the added term to 1 and the delta (determining the width) to 10."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 78,
      "id": "7677c096",
      "metadata": {
        "scrolled": false,
        "id": "7677c096",
        "outputId": "514c8d23-5a94-416c-cf04-8dd1ae73ecd7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 loss function 20.722\n",
            "iteration 0100 loss function 0.435\n",
            "iteration 0200 loss function 0.372\n",
            "iteration 0300 loss function 0.369\n",
            "iteration 0400 loss function 0.366\n"
          ]
        }
      ],
      "source": [
        "K = 15\n",
        "funct = MyFunction(torch.ones(K))\n",
        "\n",
        "n_epochs = 500\n",
        "learning_rate=.1\n",
        "max_norm = 100\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=100, gamma=0.9)  # Reduce LR every 10 steps\n",
        "\n",
        "criterion = CustomLoss(nn.MSELoss(),\n",
        "                       weight = 1,\n",
        "                       delta = 10.0)\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs, funct.coefs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%100:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "id": "614ec540",
      "metadata": {
        "id": "614ec540",
        "outputId": "5ce72232-18f4-4d6d-b8f5-2137735a3e1d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 932
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Parameter containing:\n",
            "tensor([ 2.9825e+00, -8.7202e-01,  2.2899e+00,  1.3666e-02, -1.3804e-02,\n",
            "        -1.0997e-02,  6.1613e-03,  2.7837e-03, -3.0754e-03,  9.4529e-03,\n",
            "         1.2995e-02,  1.4468e-02, -1.7551e-02, -9.5420e-03, -6.9327e-01],\n",
            "       requires_grad=True)\n"
          ]
        }
      ],
      "source": [
        "xx = torch.linspace(-1,1,1000)\n",
        "with torch.no_grad():\n",
        "    y_pred = funct(xx)\n",
        "plt.plot(x.numpy(), y_obs.numpy(), '.')\n",
        "plt.plot(xx.numpy(), y_pred.numpy())\n",
        "plt.show()\n",
        "\n",
        "plt.bar(np.arange(len(funct.coefs)), funct.coefs.detach().numpy())\n",
        "plt.show()\n",
        "print(funct.coefs)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cc5ffc5c",
      "metadata": {
        "id": "cc5ffc5c"
      },
      "source": [
        "This is less wild! We however need to make a decision on the hyper parameters of the constraint function. Lets check this out with a cross validation approach.\n",
        "\n",
        "We optimize on the train data, using our custom loss function, and we do validation on our base loss / MSE value. Our modified loss function tightens the space of our model, similar to choosing the number of polynomials. We are principally interested in how well we can predict observations in an MSE / L1 norm, so that is what we judge our model choice by.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 80,
      "id": "1a1f7847",
      "metadata": {
        "id": "1a1f7847"
      },
      "outputs": [],
      "source": [
        "def optimize_me(x,y,x_test,y_test, weight, delta):\n",
        "\n",
        "    funct = MyFunction(torch.rand(K)*2-1)\n",
        "    n_epochs = 500\n",
        "    learning_rate=1e-1\n",
        "    max_norm = 100\n",
        "    optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "    scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.99)  # Reduce LR every 10 steps\n",
        "    base_loss = nn.MSELoss()\n",
        "    criterion = CustomLoss(base_loss, weight, delta)\n",
        "\n",
        "\n",
        "    # Training loop\n",
        "    for ii in range(n_epochs):\n",
        "        optimizer.zero_grad()  # Zero out gradients\n",
        "        y_pred = funct(x)  # Compute function\n",
        "        loss_actual = criterion(y_pred, y_obs, funct.coefs)  # Get the loss\n",
        "        loss_actual.backward()  # Compute gradients\n",
        "        torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "        optimizer.step()  # Update parameters\n",
        "        scheduler.step()\n",
        "\n",
        "    with torch.no_grad():\n",
        "        tmp = funct(x_test)\n",
        "        test_loss = base_loss(tmp,y_test)\n",
        "    return test_loss.item(), funct.coefs\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 81,
      "id": "e0eb9c0f",
      "metadata": {
        "id": "e0eb9c0f",
        "outputId": "66a17197-d2d3-4062-a793-4954b0f1017c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 4/4 [00:29<00:00,  7.48s/it]\n"
          ]
        }
      ],
      "source": [
        "# just try a couple of combinations\n",
        "weights = [1,2,3,4]\n",
        "deltas = [0.01, 0.1, 1]\n",
        "params = []\n",
        "means = []\n",
        "stds = []\n",
        "coefs = []\n",
        "this_one = 0\n",
        "this_score = 1e90\n",
        "count = 0\n",
        "for w in tqdm.tqdm(weights):\n",
        "    for d in deltas:\n",
        "        vals = []\n",
        "        coefs_ens = []\n",
        "        params.append((w,d))\n",
        "        for ii in range(3): # because there is randomization going on, we can't really rely on a single trial\n",
        "            tmp,tmp_coefs = optimize_me(x,y_obs, x_test, y_test, w, d)\n",
        "            vals.append(tmp)\n",
        "            coefs_ens.append(tmp_coefs.detach().clone())\n",
        "        means.append(np.mean(np.array(vals)))\n",
        "        stds.append(np.std(np.array(vals)))\n",
        "        coefs.append(coefs_ens)\n",
        "        if means[-1] < this_score:\n",
        "            this_score = means[-1]\n",
        "            this_one = count\n",
        "        count += 1"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b9725ec8",
      "metadata": {
        "id": "b9725ec8"
      },
      "source": [
        "Now that we have explored a number of optiosn, lets plots them. We need to take the loss values and reshape the array. the einops library is really usefull. It retains gradients and you can use this as part of your networks if desired."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 82,
      "id": "8b18b1a9",
      "metadata": {
        "id": "8b18b1a9",
        "outputId": "424b84f4-af98-4c5a-a8f7-65e8a8d315d9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(12,) (4, 3)\n"
          ]
        }
      ],
      "source": [
        "means_s = einops.rearrange(np.array(means), \"(Y X) -> Y X\", Y=4, X=3)\n",
        "print(np.array(means).shape, means_s.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6e05444b",
      "metadata": {
        "id": "6e05444b"
      },
      "source": [
        "Plot this thing"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 83,
      "id": "8a879df5",
      "metadata": {
        "id": "8a879df5",
        "outputId": "0231458d-a9ab-44fa-e802-e13d26dc569f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 455
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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mmP65FQ0NDTddg7lVLX+3HjNl4rZ+/h6NddXejL9O2t6p8XYVVkZERALw1G45lhNERCQcKyMiIgHc3Q3X3hi+gsmIiEgATtPJ+U5aJSKiHouVERGRAD8/W86TMXwFkxERkQCcppPjNB0REQnHyoiISABWRnJMRkREAjAZyXGajoiIhGNlREQkACsjOSYjIiIBJHi+NbvHnnLdBiYjIiIBWBnJcc2IiIiEY2VERCQAKyM5JiMiIgGYjOQ4TUdERMKxMiIiEoCVkRyTERGRAJKkgORhMvH0/u6E03RERCQcKyMiIgH4PCM5JiMiIgG4ZiTHaToiIhKOlRERkQDcwCDHZEREJACn6eSYjIiIBGBlJMc1IyIiEo6VERGRAJIXpul8qTJiMiIiEkACIHn4dDxfergep+mIiEg4VkZERAI4oYCCJzC4MBkREQnA3XRynKYjIupFCgsLERkZCZVKhZSUFJSXl7fb97333kNSUhL69++Pfv36ISEhATt27JD1eeKJJ6BQKGQtIyPD7bhYGRERCeCUFFB08Ydei4uLYTAYUFRUhJSUFBQUFCA9PR3Hjx/HoEGDWvUfMGAAXnzxRcTExMDf3x8ffvghsrOzMWjQIKSnp7v6ZWRk4M0333R9HRAQ4PZ7YWVERCSAJHmnuWP9+vXIyclBdnY2YmNjUVRUhL59+2LLli1t9p8wYQIeeeQR/OpXv8KwYcOwcOFCxMXF4eDBg7J+AQEB0Ol0rhYSEuL2z4PJiIioh7PZbLLW1NTUqk9zczMqKiqg1+td15RKJfR6PUpLS2/6GpIkwWQy4fjx4xg3bpzse2azGYMGDcKoUaMwf/58XLx40e33wGRERCRAywYGTxsAREREQKPRuJrRaGz1ehcuXIDD4YBWq5Vd12q1sFgs7cbZ0NCAoKAg+Pv7Y+rUqXjttdfwwAMPuL6fkZGB7du3w2QyYc2aNThw4ACmTJkCh8Ph1s+Da0ZERAJ4czddTU0N1Gq16/qtrNm0Jzg4GFVVVWhsbITJZILBYEB0dDQmTJgAAJg1a5ar79133424uDgMGzYMZrMZkyZN6vDrMBkREQngzQ0MarValozaEhoaCj8/P1itVtl1q9UKnU7X7n1KpRLDhw8HACQkJODYsWMwGo2uZPRL0dHRCA0NxYkTJ9xKRkKn6TZu3Ii4uDjXDzI1NRV79+4VGRIRkU/y9/dHYmIiTCaT65rT6YTJZEJqamqHx3E6nW2uSbU4c+YMLl68iLCwMLfiE1oZDRkyBKtXr8aIESMgSRK2bduGhx9+GF988QXuvPNOkaEREXWqW9kN19YY7jAYDMjKykJSUhKSk5NRUFAAu92O7OxsAEBmZiYGDx7sWnMyGo1ISkrCsGHD0NTUhD179mDHjh3YuHEjAKCxsRErVqzAjBkzoNPpcPLkSSxZsgTDhw+Xbf3uCKHJaNq0abKvf/vb32Ljxo04dOgQkxER+bTrycjTNSP3+s+cORN1dXXIy8uDxWJBQkICSkpKXJsaqquroVT+e8LMbrfj6aefxpkzZxAYGIiYmBj8+c9/xsyZMwEAfn5++Oqrr7Bt2zbU19cjPDwckydPxsqVK91et+o2a0YOhwN//etfYbfb2y0Zm5qaZOWhzWbrqvCIiHxCbm4ucnNz2/ye2WyWfb1q1SqsWrWq3bECAwOxb98+r8QlPBkdOXIEqampuHLlCoKCgvD+++8jNja2zb5GoxErVqzo4giJiLyPZ9PJCf+c0ahRo1BVVYWysjLMnz8fWVlZ+Oabb9rsu3TpUjQ0NLhaTU1NF0dLROQdkpearxBeGfn7+7u2DSYmJuLw4cP4wx/+gE2bNrXqGxAQ4NX980RE1D0IT0a/dLNtg0REvoDTdHJCk9HSpUsxZcoU3HHHHbh06RLefvttmM1mry2IERF1W96YZ/OheTqhyai2thaZmZk4f/48NBoN4uLisG/fPtm5R0REPskLlRFYGXnHG2+8IfLliYiom+h2a0ZERL2BiBMYujMmIyIiAbiBQU7454yIiIhYGRERiSApPN+A4EOVEZMREZEAXDOS4zQdEREJx8qIiEgEfuhVhsmIiEgA7qaT4zQdEREJx8qIiEgUH5pm8xSTERGRAJymk2MyIiISgRsYZLhmREREwrEyIiISQvFT83QM3+B2ZbRt2zbs3r3b9fWSJUvQv39/jBkzBj/88INXgyMi8lmSl5qPcDsZvfLKKwgMDAQAlJaWorCwEGvXrkVoaCieffZZrwdIRES+z+1pupqaGgwfPhwAsGvXLsyYMQPz5s3DfffdhwkTJng7PiIi38QNDDJuV0ZBQUG4ePEiAOCjjz5yPSJcpVLhxx9/9G50RES+quXUbk+bj3C7MnrggQcwd+5cjB49Gt999x0efPBBAMDRo0cRGRnp7fiIiKgXcLsyKiwsRGpqKurq6vDuu+9i4MCBAICKigrMnj3b6wESEfmilkdIeNp8hduVkc1mw4YNG6BUyvPY8uXLUVNT47XAiIh8GteMZNyujKKionDhwoVW1//5z38iKirKK0EREVHv4nZlJLVTFzY2NkKlUnkcEBFRr8DHjst0OBkZDAYAgEKhQF5eHvr27ev6nsPhQFlZGRISErweIBGRL1JI15unY/iKDiejL774AsD1yujIkSPw9/d3fc/f3x/x8fFYvHix9yMkIvJFXDOS6XAy2r9/PwAgOzsbf/jDH6BWqzstKCIi6l3c3sDw5ptvMhEREXlK0IdeCwsLERkZCZVKhZSUFJSXl7fb97333kNSUhL69++Pfv36ISEhATt27JC/DUlCXl4ewsLCEBgYCL1ej++//97tuNxORna7HcuWLcOYMWMwfPhwREdHyxoREXWAgINSi4uLYTAYkJ+fj8rKSsTHxyM9PR21tbVt9h8wYABefPFFlJaW4quvvkJ2djays7Oxb98+V5+1a9diw4YNKCoqQllZGfr164f09HRcuXLFrdjc3k03d+5cHDhwAI8//jjCwsKgUPjObg4iIl+2fv165OTkIDs7GwBQVFSE3bt3Y8uWLXjhhRda9f/leaMLFy7Etm3bcPDgQaSnp0OSJBQUFOCll17Cww8/DADYvn07tFotdu3ahVmzZnU4NreT0d69e7F7927cd9997t5KREQtvLiBwWazyS4HBAQgICBAdq25uRkVFRVYunSp65pSqYRer0dpaenNX0qS8Mknn+D48eNYs2YNAODUqVOwWCzQ6/WufhqNBikpKSgtLXUrGbk9TRcSEoIBAwa4exsREf2cF6fpIiIioNFoXM1oNLZ6uQsXLsDhcECr1cqua7VaWCyWdsNsaGhAUFAQ/P39MXXqVLz22muuA7Jb7nN3zLa4XRmtXLkSeXl52LZtm+yzRkREJEZNTY1sY9kvqyJPBAcHo6qqCo2NjTCZTDAYDIiOjvb6I4M6lIxGjx4tWxs6ceIEtFotIiMjcdttt8n6VlZWejVAIiKf5MUTGNRq9U13OYeGhsLPzw9Wq1V23Wq1QqfTtXufUql0PcMuISEBx44dg9FoxIQJE1z3Wa1WhIWFycZ09xCEDiWj6dOnuzUoERHdWFefwODv74/ExESYTCbX33Sn0wmTyYTc3NwOj+N0OtHU1ATg+lmlOp0OJpPJlXxsNhvKysowf/78jgeHDiaj/Px8twYlIqLux2AwICsrC0lJSUhOTkZBQQHsdrtrd11mZiYGDx7sWnMyGo1ISkrCsGHD0NTUhD179mDHjh3YuHEjgOvHwy1atAirVq3CiBEjEBUVhWXLliE8PNztIsbtNSMiIvICAccBzZw5E3V1dcjLy4PFYkFCQgJKSkpcGxCqq6tljwey2+14+umncebMGQQGBiImJgZ//vOfMXPmTFefJUuWwG63Y968eaivr8fYsWNRUlLi9sHZCqm9Y7jbERIS0uZnixQKBVQqFYYPH44nnnjClWk7k81mg0ajwb++i4Y62O2NgXSL8uvuFB1Cr3J4ovbmncgrrjmbYfrnVjQ0NHTaSTMtf7fuWLMKykDPnnTg/PEKqp9/qVPj7SpuV0Z5eXn47W9/iylTpiA5ORkAUF5ejpKSEixYsACnTp3C/Pnzce3aNeTk5Hg9YCIiX6CAF9aMvBJJ9+B2Mjp48CBWrVqF//mf/5Fd37RpEz766CO8++67iIuLw4YNG5iMiIioQ9xORvv27XN9+vbnJk2ahN/85jcAgAcffLDNoyXIN6y4/ajoEHqVDFs/0SH0Gk7pate9GB+uJ+P2QsuAAQPw97//vdX1v//9766TGex2O4KDgz2PjojIVwk4KLU7c7syWrZsGebPn4/9+/e71owOHz6MPXv2oKioCADw8ccfY/z48d6NlIiIfJbbySgnJwexsbF4/fXX8d577wEARo0ahQMHDmDMmDEA4JquIyKidvBJrzK39Dmj++67j6d2ExF5oKtPYOjuOpSMbDabaw/7L48q/6WevtediIi6XoeSUUhICM6fP49Bgwahf//+bX7oVZIkKBQKOBwOrwdJRORzOE0n06Fk9Mknn7h2yu3fv79TAyIi6hWYjGQ6lIx+vjOOu+SIiMjbbulAt3/84x/47//+b4wZMwZnz54FAOzYsQMHDx70anBERL6qZQODp81XuJ2M3n33XaSnpyMwMBCVlZWu51o0NDTglVde8XqAREQ+qeUEBk+bj3A7Ga1atQpFRUXYvHmz7Cmv9913H5/ySkTUUTyBQcbtZHT8+HGMGzeu1XWNRoP6+npvxERERL2M28lIp9PhxIkTra4fPHgQ0dHRXgmKiMjXcc1Izu1klJOTg4ULF6KsrAwKhQLnzp3DW2+9hcWLF7v9zHMiol6L03QyHT4O6NSpU4iKisILL7wAp9OJSZMm4fLlyxg3bhwCAgKwePFiPPPMM50ZKxER+agOJ6Nhw4Zh6NChSEtLQ1paGo4dO4ZLly6hsbERsbGxCAoK6sw4iYh8izem2XpjZfTJJ5/AbDbDbDbjnXfeQXNzM6KjozFx4kRMnDgREyZMgFar7cxYiYh8B09gkOlwMpowYQImTJgAALhy5Qo+++wzV3Latm0brl69ipiYGBw9yqeAEhGRe27pERIqlQoTJ07E2LFjkZaWhr1792LTpk349ttvvR0fEZFvYmUk41Yyam5uxqFDh7B//36YzWaUlZUhIiIC48aNw+uvv85z64iIOojPM5LrcDKaOHEiysrKEBUVhfHjx+Opp57C22+/jbCwsM6Mj4iIeoEOJ6N//OMfCAsLc21WGD9+PAYOHNiZsRERUS/R4Q+91tfX449//CP69u2LNWvWIDw8HHfffTdyc3Pxt7/9DXV1dZ0ZJxGRb+GHXmU6XBn169cPGRkZyMjIAABcunQJBw8exP79+7F27VrMmTMHI0aMwNdff91pwRIR+QquGcnd0vOMgOvJacCAARgwYABCQkLQp08fHDt2zJuxERFRL9HhysjpdOLzzz+H2WzG/v378X//93+w2+0YPHgw0tLSUFhYiLS0tM6MlYjIt/hQZeOpDiej/v37w263Q6fTIS0tDb///e8xYcIEDBs2rDPjIyLyTfyckUyHk9Grr76KtLQ0jBw5sjPjISKiXqjDyeipp57qzDiIiHoVbmCQu6XjgIiIyEOcppO55d10RETU8xQWFiIyMhIqlQopKSkoLy9vt+/mzZtx//33IyQkBCEhIdDr9a36P/HEE1AoFLLW8hEgdzAZEREJIOKx48XFxTAYDMjPz0dlZSXi4+ORnp6O2traNvubzWbMnj0b+/fvR2lpKSIiIjB58mScPXtW1i8jIwPnz593tXfeecftnweTERGRCAJOYFi/fj1ycnKQnZ2N2NhYFBUVoW/fvtiyZUub/d966y08/fTTSEhIQExMDP70pz/B6XTCZDLJ+gUEBECn07laSEiIe4GByYiIqMez2Wyy1tTU1KpPc3MzKioqoNfrXdeUSiX0ej1KS0s79DqXL1/G1atXMWDAANl1s9mMQYMGYdSoUZg/fz4uXrzo9ntgMiIiEsGLlVFERAQ0Go2rGY3GVi934cIFOByOVk/k1mq1sFgsHQr5+eefR3h4uCyhZWRkYPv27TCZTFizZg0OHDiAKVOmwOFwdPhHAXA3HRGREN7c2l1TUwO1Wu26HhAQ4NnAbVi9ejV27twJs9kMlUrluj5r1izXv++++27ExcVh2LBhMJvNmDRpUofHZ2VERCSCFysjtVota20lo9DQUPj5+cFqtcquW61W6HS6G4a6bt06rF69Gh999BHi4uJu2Dc6OhqhoaE4ceLEDfv9EpMREVEv4O/vj8TERNnmg5bNCKmpqe3et3btWqxcuRIlJSVISkq66eucOXMGFy9edPvBq0xGREQiCNhNZzAYsHnzZmzbtg3Hjh3D/PnzYbfbkZ2dDQDIzMzE0qVLXf3XrFmDZcuWYcuWLYiMjITFYoHFYkFjYyMAoLGxEc899xwOHTqE06dPw2Qy4eGHH8bw4cORnp7uVmxcMyIiEkDEcUAzZ85EXV0d8vLyYLFYkJCQgJKSEtemhurqaiiV/65RNm7ciObmZjz66KOycfLz87F8+XL4+fnhq6++wrZt21BfX4/w8HBMnjwZK1eudHvdismIiKgXyc3NRW5ubpvfM5vNsq9Pnz59w7ECAwOxb98+r8QldJrOaDTi3nvvRXBwMAYNGoTp06fj+PHjIkMiIuoafOy4jNBkdODAASxYsACHDh3Cxx9/jKtXr2Ly5Mmw2+0iwyIi6nQijgPqzoRO05WUlMi+3rp1KwYNGoSKigqMGzdOUFRERNTVutWaUUNDAwC0OmqiRVNTk+yYC5vN1iVxERF5nTem2XyoMuo2W7udTicWLVqE++67D3fddVebfYxGo+zIi4iIiC6OkojIS7hmJNNtktGCBQvw9ddfY+fOne32Wbp0KRoaGlytpqamCyMkIqLO0i2m6XJzc/Hhhx/i008/xZAhQ9rtFxAQ0ClnLhERdTXFT83TMXyF0GQkSRKeeeYZvP/++zCbzYiKihIZDhFR1+GakYzQZLRgwQK8/fbb+OCDDxAcHOw6xlyj0SAwMFBkaEREnUrECQzdmdA1o40bN6KhoQETJkxAWFiYqxUXF4sMi4iIupjwaToiol6J03Qy3WIDAxFRr+RDycRT3WZrNxER9V6sjIiIBOAGBjkmIyIiEbhmJMNpOiIiEo6VERGRAJymk2MyIiISgdN0MpymIyIi4VgZEREJwGk6OSYjIiIROE0nw2RERCQCk5EM14yIiEg4VkZERAJwzUiOyYiISARO08lwmo6IiIRjZUREJIBCkqDw8Jlunt7fnTAZERGJwGk6GU7TERGRcKyMiIgE4G46OSYjIiIROE0nw2k6IiISjpUREZEAnKaTY2VERCSC5KXmpsLCQkRGRkKlUiElJQXl5eXt9t28eTPuv/9+hISEICQkBHq9vlV/SZKQl5eHsLAwBAYGQq/X4/vvv3c7LiYjIiIBWiojT5s7iouLYTAYkJ+fj8rKSsTHxyM9PR21tbVt9jebzZg9ezb279+P0tJSREREYPLkyTh79qyrz9q1a7FhwwYUFRWhrKwM/fr1Q3p6Oq5cueJWbExGRES9xPr165GTk4Ps7GzExsaiqKgIffv2xZYtW9rs/9Zbb+Hpp59GQkICYmJi8Kc//QlOpxMmkwnA9aqooKAAL730Eh5++GHExcVh+/btOHfuHHbt2uVWbExGREQieHGazmazyVpTU1Orl2tubkZFRQX0er3rmlKphF6vR2lpaYdCvnz5Mq5evYoBAwYAAE6dOgWLxSIbU6PRICUlpcNjumJxqzcREXmNt6boIiIioNFoXM1oNLZ6rQsXLsDhcECr1cqua7VaWCyWDsX7/PPPIzw83JV8Wu7zZMwW3E1HRNTD1dTUQK1Wu74OCAjw+musXr0aO3fuhNlshkql8vr4rIyIiESQJO80AGq1WtbaSkahoaHw8/OD1WqVXbdardDpdDcMdd26dVi9ejU++ugjxMXFua633HcrY/4SkxERkQBdvZvO398fiYmJrs0HAFybEVJTU9u9b+3atVi5ciVKSkqQlJQk+15UVBR0Op1sTJvNhrKyshuO2RZO0xER9RIGgwFZWVlISkpCcnIyCgoKYLfbkZ2dDQDIzMzE4MGDXWtOa9asQV5eHt5++21ERka61oGCgoIQFBQEhUKBRYsWYdWqVRgxYgSioqKwbNkyhIeHY/r06W7FxmRERCSCgLPpZs6cibq6OuTl5cFisSAhIQElJSWuDQjV1dVQKv89YbZx40Y0Nzfj0UcflY2Tn5+P5cuXAwCWLFkCu92OefPmob6+HmPHjkVJSYnb60oKSeq5T2ey2WzQaDT413fRUAdzxpF8U8bQZNEh9BrXpKvYf/WvaGhokG0I8KaWv1v3PrIKfW7zbCPAtatXcPj9lzo13q7Cv+BERCQcp+mIiETgIyRkmIyIiATgqd1yTEZERCL87HNCHo3hI7hmREREwrEyIiISgNN0ckxGREQicAODDJMRUTcnXW0WHUKvIUlXRYfQazEZEREJwGk6OSYjIiIRuJtOhrvpiIhIOFZGREQCcJpOjsmIiEgE7qaT4TQdEREJx8qIiEgATtPJMRkREYnglK43T8fwEUxGREQicM1IhmtGREQkHCsjIiIBFPDCmpFXIukemIyIiETgCQwynKYjIiLhWBkREQnArd1yTEZERCJwN50Mp+mIiEg4VkZERAIoJAkKDzcgeHp/d8JkREQkgvOn5ukYPoLTdEREJBwrIyIiAThNJ8dkREQkAnfTyTAZERGJwBMYZLhmREREwrEyIiISgCcwyDEZERGJwGk6GU7TERH1IoWFhYiMjIRKpUJKSgrKy8vb7Xv06FHMmDEDkZGRUCgUKCgoaNVn+fLlUCgUshYTE+N2XExGREQCKJzeae4oLi6GwWBAfn4+KisrER8fj/T0dNTW1rbZ//Lly4iOjsbq1auh0+naHffOO+/E+fPnXe3gwYPuBQYmIyIiMVqm6Txtbli/fj1ycnKQnZ2N2NhYFBUVoW/fvtiyZUub/e+99168+uqrmDVrFgICAtodt0+fPtDpdK4WGhrqVlwAkxERUa/Q3NyMiooK6PV61zWlUgm9Xo/S0lKPxv7+++8RHh6O6OhozJkzB9XV1W6PwWRERCSC5KUGwGazyVpTU1Orl7tw4QIcDge0Wq3sularhcViueW3kZKSgq1bt6KkpAQbN27EqVOncP/99+PSpUtujcNkREQkQMtxQJ42AIiIiIBGo3E1o9HYZe9jypQpeOyxxxAXF4f09HTs2bMH9fX1+Mtf/uLWONzaTUTUw9XU1ECtVru+bmt9JzQ0FH5+frBarbLrVqv1hpsT3NW/f3+MHDkSJ06ccOs+VkZERCJ4cQODWq2WtbaSkb+/PxITE2EymVzXnE4nTCYTUlNTvfa2GhsbcfLkSYSFhbl1HysjIiIRJHj+PCI3P/NqMBiQlZWFpKQkJCcno6CgAHa7HdnZ2QCAzMxMDB482DXN19zcjG+++cb177Nnz6KqqgpBQUEYPnw4AGDx4sWYNm0ahg4dinPnziE/Px9+fn6YPXu2W7ExGRERCSDiERIzZ85EXV0d8vLyYLFYkJCQgJKSEtemhurqaiiV/54wO3fuHEaPHu36et26dVi3bh3Gjx8Ps9kMADhz5gxmz56Nixcv4vbbb8fYsWNx6NAh3H777W7FxmRERNSL5ObmIjc3t83vtSSYFpGRkZBukvB27tzplbiYjIiIRJDghbPpvBJJt8BkREQkAg9KleFuOiIiEo6VERGRCE4ACi+M4SOEVkaffvoppk2bhvDwcCgUCuzatUtkOEREXcabJzD4AqHJyG63Iz4+HoWFhSLDICIiwYRO002ZMgVTpkwRGQIRkRjcwCDDNSMiIhGYjGR6VDJqamqSHY1us9kERkNERN7So7Z2G41G2THpERERokMiIro1Ap702p31qGS0dOlSNDQ0uFpNTY3okIiIbo3TS81H9KhpuoCAgBs+h52IqKcQcVBqdyY0GTU2NsoewHTq1ClUVVVhwIABuOOOOwRGRkREXUloMvr888+Rlpbm+tpgMAAAsrKysHXrVkFRERF1Ae6mkxGajCZMmHDT48mJiHySUwIUHv79c/rO388etYGBiIh8U4/awEBE5DM4TSfDZEREJIQ3PifkO8mI03RERCQcKyMiIhE4TSfDZEREJIJTgsfTbNxNR0RE5D2sjIiIRJCc15unY/gIJiMiIhG4ZiTDZEREJALXjGS4ZkRERMKxMiIiEoHTdDJMRkREIkjwQjLySiTdAqfpiIhIOFZGREQicJpOhsmIiEgEpxOAh58TcvrO54w4TUdERMKxMiIiEoHTdDKsjIiIRGhJRp42NxUWFiIyMhIqlQopKSkoLy9vt+/Ro0cxY8YMREZGQqFQoKCgwOMx28NkRETUSxQXF8NgMCA/Px+VlZWIj49Heno6amtr2+x/+fJlREdHY/Xq1dDpdF4Zsz1MRkREIjgl7zQ3rF+/Hjk5OcjOzkZsbCyKiorQt29fbNmypc3+9957L1599VXMmjULAQEBXhmzPUxGREQCSJLTK62jmpubUVFRAb1e77qmVCqh1+tRWlp6S+/Bm2NyAwMRkQiS+5VNm2MAsNlssssBAQGtKpkLFy7A4XBAq9XKrmu1Wnz77be39PLeHJOVERFRDxcREQGNRuNqRqNRdEhuY2VERCSC5IVHSPxUGdXU1ECtVrsut7W+ExoaCj8/P1itVtl1q9Xa7uaEm/HmmKyMiIhEcDq90wCo1WpZaysZ+fv7IzExESaT6WchOGEymZCamnpLb8GbY7IyIiLqJQwGA7KyspCUlITk5GQUFBTAbrcjOzsbAJCZmYnBgwe7pvmam5vxzTffuP599uxZVFVVISgoCMOHD+/QmB3FZEREJIIXp+k6aubMmairq0NeXh4sFgsSEhJQUlLi2oBQXV0NpfLfE2bnzp3D6NGjXV+vW7cO69atw/jx42E2mzs0ZkcpJKnnnidhs9mg0Wjwr++ioQ7mjCP5pvTwBNEh9BrXpKsw4wM0NDTI1mC8qeXv1sS+s9BH4e/RWNekZnxyeWenxttV+BeciIiE4zQdEZEIAqbpujMmIyIiEZwSoGAyasFpOiIiEo6VERGRCJIEj5/06kOVEZMREZEAklOC5OE0XQ/eDN0KkxERkQiSE55XRh7e341wzYiIiIRjZUREJACn6eSYjIiIROA0nUyPTkYt/1dga/SdXwjRL12TrooOode4hus/666oOK7hqsefeW2J1xf06GR06dIlAMDQe06LDYSoU/0/0QH0OpcuXYJGo+mUsf39/aHT6XDQsscr4+l0Ovj7e3bGXXfQow9KdTqdOHfuHIKDg6FQKESH02E2mw0RERGtHohFnYc/867VU3/ekiTh0qVLCA8Pl51e7W1XrlxBc3OzV8by9/eHSqXyylgi9ejKSKlUYsiQIaLDuGUtD8KirsOfedfqiT/vzqqIfk6lUvlEAvEmbu0mIiLhmIyIiEg4JiMBAgICkJ+f3+Zz6qlz8GfetfjzJnf16A0MRETkG1gZERGRcExGREQkHJMREREJx2RERETCMRl5SWFhISIjI6FSqZCSkoLy8vIb9v/rX/+KmJgYqFQq3H333dizR340yHvvvYfJkydj4MCBUCgUqKqq6sTofYM7v4OjR49ixowZiIyMhEKhQEFBQdcF6sM+/fRTTJs2DeHh4VAoFNi1a5fokKiHYDLyguLiYhgMBuTn56OyshLx8fFIT09HbW1tm/0/++wzzJ49G08++SS++OILTJ8+HdOnT8fXX3/t6mO32zF27FisWbOmq95Gj+bu7+Dy5cuIjo7G6tWrodPpujha32W32xEfH4/CwkLRoVBPI5HHkpOTpQULFri+djgcUnh4uGQ0Gtvs/1//9V/S1KlTZddSUlKkp556qlXfU6dOSQCkL774wqsx+xp3fwc/N3ToUOn3v/99J0bXOwGQ3n//fdFhUA/ByshDzc3NqKiogF6vd11TKpXQ6/UoLS1t857S0lJZfwBIT09vtz/d2K38Doioe2Ey8tCFCxfgcDig1Wpl17VaLSwWS5v3WCwWt/rTjd3K74CIuhcmIyIiEo7JyEOhoaHw8/OD1WqVXbdare0ujOt0Orf6043dyu+AiLoXJiMP+fv7IzExESaTyXXN6XTCZDIhNTW1zXtSU1Nl/QHg448/brc/3dit/A6IqHvp0Q/X6y4MBgOysrKQlJSE5ORkFBQUwG63Izs7GwCQmZmJwYMHw2g0AgAWLlyI8ePH43e/+x2mTp2KnTt34vPPP8cf//hH15j//Oc/UV1djXPnzgEAjh8/DuB6VcX/22/N3d9Bc3MzvvnmG9e/z549i6qqKgQFBWH48OHC3kdP19jYiBMnTri+PnXqFKqqqjBgwADccccdAiOjbk/0dj5f8dprr0l33HGH5O/vLyUnJ0uHDh1yfW/8+PFSVlaWrP9f/vIXaeTIkZK/v7905513Srt375Z9/80335QAtGr5+fld8G56Jnd+By1b5n/Zxo8f3/WB+5D9+/e3+XP95X//RL/ER0gQEZFwXDMiIiLhmIyIiEg4JiMiIhKOyYiIiIRjMiIiIuGYjIiISDgmIyIiEo7JiHza8uXLkZCQIDoMIroJJiPqlp544gkoFAooFArcdttt0Gq1eOCBB7BlyxY4nU6Pxp0+fbr3AiUir2Ayom4rIyMD58+fx+nTp7F3716kpaVh4cKF+PWvf41r166JDo+IvIjJiLqtgIAA6HQ6DB48GPfccw/+93//Fx988AH27t2LrVu3AgDq6+sxd+5c3H777VCr1Zg4cSK+/PLLNsdbvnw5tm3bhg8++MBVdZnNZgDA888/j5EjR6Jv376Ijo7GsmXLcPXqVde9X375JdLS0hAcHAy1Wo3ExER8/vnnnf0jIOo1eGo39SgTJ05EfHw83nvvPcydOxePPfYYAgMDsXfvXmg0GmzatAmTJk3Cd999hwEDBsjuXbx4MY4dOwabzYY333wTAFx9goODsXXrVoSHh+PIkSPIyclBcHAwlixZAgCYM2cORo8ejY0bN8LPzw9VVVW47bbbuvbNE/kwJiPqcWJiYvDVV1/h4MGDKC8vR21tLQICAgAA69atw65du/C3v/0N8+bNk90XFBSEwMBANDU1tXoMx0svveT6d2RkJBYvXoydO3e6klF1dTWee+45xMTEAABGjBjRmW+RqNdhMqIeR5IkKBQKfPnll2hsbMTAgQNl3//xxx9x8uRJt8YsLi7Ghg0bcPLkSTQ2NuLatWtQq9Wu7xsMBsydOxc7duyAXq/HY489hmHDhnnl/RAR14yoBzp27BiioqLQ2NiIsLAwVFVVydrx48fx3HPPdXi80tJSzJkzBw8++CA+/PBDfPHFF3jxxRfR3Nzs6rN8+XIcPXoUU6dOxSeffILY2Fi8//77nfH2iHolVkbUo3zyySc4cuQInn32WQwZMgQWiwV9+vRBZGRkh+739/eHw+GQXfvss88wdOhQvPjii65rP/zwQ6t7R44ciZEjR+LZZ5/F7Nmz8eabb+KRRx7x6P0Q0XVMRtRtNTU1wWKxwOFwwGq1oqSkBEajEb/+9a+RmZkJpVKJ1NRUTJ8+HWvXrsXIkSNx7tw57N69G4888giSkpJajRkZGYl9+/bh+PHjGDhwIDQaDUaMGIHq6mrs3LkT9957L3bv3i2ren788Uc899xzePTRRxEVFYUzZ87g8OHDmDFjRlf+OIh8GpMRdVslJSUICwtDnz59EBISgvj4eGzYsAFZWVlQKq/PMO/ZswcvvvgisrOzUVdXB51Oh3HjxkGr1bY5Zk5ODsxmM5KSktDY2Ij9+/fjoYcewrPPPovc3Fw0NTVh6tSpWLZsGZYvXw4A8PPzw8WLF5GZmQmr1YrQ0FD853/+J1asWNFVPwoin8fHjhMRkXDcwEBERMIxGRERkXBMRkREJByTERERCcdkREREwjEZERGRcExGREQkHJMREREJx2RERETCMRkREZFwTEZERCQckxEREQn3/wF4bSQx1txjigAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "\n",
        "# Create the plot\n",
        "fig, ax = plt.subplots()\n",
        "cax = ax.imshow((means_s), cmap='viridis', interpolation='None', origin='lower', vmax=0.5)\n",
        "\n",
        "# Add color bar\n",
        "cbar = fig.colorbar(cax, orientation='vertical')\n",
        "\n",
        "# Set axis labels\n",
        "ax.set_xticks(np.arange(len(deltas)))\n",
        "ax.set_yticks(np.arange(len(weights)))\n",
        "ax.set_xticklabels(deltas)\n",
        "ax.set_yticklabels(weights)\n",
        "\n",
        "# Label the axes\n",
        "ax.set_xlabel('Deltas')\n",
        "ax.set_ylabel('Weights')\n",
        "\n",
        "# Show the plot\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1ce8ed1d",
      "metadata": {
        "id": "1ce8ed1d"
      },
      "source": [
        "Find the best one"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 84,
      "id": "fc9d2a73",
      "metadata": {
        "id": "fc9d2a73"
      },
      "outputs": [],
      "source": [
        "selected_coefs = einops.rearrange( coefs[this_one], \"N C -> N C\")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "bcb6463b",
      "metadata": {
        "id": "bcb6463b"
      },
      "source": [
        "Because we have 5 of them, we can get some population statistics.\n",
        "\n",
        "Do not over interpret this! If the minimizer is ideal / if you are lucky, you will always converge to the lowest point and all your coefficients are the same...."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 85,
      "id": "55d70228",
      "metadata": {
        "id": "55d70228",
        "outputId": "c614278f-c806-4058-b8f8-41323a23d2f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 843
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.bar( np.arange(K), torch.mean(selected_coefs, dim=0))\n",
        "plt.show()\n",
        "plt.bar( np.arange(K), torch.std(selected_coefs, dim=0))\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c360de65",
      "metadata": {
        "id": "c360de65"
      },
      "source": [
        "Lets plot every model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 86,
      "id": "45601cd8",
      "metadata": {
        "id": "45601cd8",
        "outputId": "a66966bc-292e-41a8-d4fa-89867f8f56f4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "x_for_plotting = torch.linspace(-1,1,1000)\n",
        "for cc in selected_coefs:\n",
        "    ff = MyFunction(cc)\n",
        "    with torch.no_grad():\n",
        "        yy = ff(x_for_plotting)\n",
        "    plt.plot(x_for_plotting, yy)\n",
        "plt.plot(x, y_obs, '.')\n",
        "plt.show()\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0980c8a4",
      "metadata": {
        "id": "0980c8a4"
      },
      "source": [
        "Lets take all our data and put it together now that we have decided on what model to fit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 87,
      "id": "a2213e1a",
      "metadata": {
        "id": "a2213e1a",
        "outputId": "46d577f4-a2bd-4dd9-db12-713cdcbb1f47",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([17]) torch.Size([17])\n"
          ]
        }
      ],
      "source": [
        "x_all = torch.concatenate([x, x_test])\n",
        "y_all = torch.concatenate([y_obs, y_test])\n",
        "print(x_all.shape, y_all.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7ca0939e",
      "metadata": {
        "id": "7ca0939e"
      },
      "source": [
        "Pick the best weight and delta"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "id": "9f3c8612",
      "metadata": {
        "scrolled": false,
        "id": "9f3c8612",
        "outputId": "9dd66f33-6877-435c-e37f-a1c215af3046",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Weight 1.00e+00 Delta 1.00e+00\n",
            "iteration 0000 loss function 20.434\n",
            "iteration 0010 loss function 1.796\n",
            "iteration 0020 loss function 0.610\n",
            "iteration 0030 loss function 0.414\n",
            "iteration 0040 loss function 0.270\n",
            "iteration 0050 loss function 0.240\n",
            "iteration 0060 loss function 0.233\n",
            "iteration 0070 loss function 0.226\n",
            "iteration 0080 loss function 0.221\n",
            "iteration 0090 loss function 0.220\n",
            "iteration 0100 loss function 0.219\n",
            "iteration 0110 loss function 0.217\n",
            "iteration 0120 loss function 0.217\n",
            "iteration 0130 loss function 0.216\n",
            "iteration 0140 loss function 0.217\n"
          ]
        }
      ],
      "source": [
        "this_w, this_d = params[this_one]\n",
        "print(f'Weight {this_w:3.2e} Delta {this_d:3.2e}')\n",
        "\n",
        "funct = MyFunction(torch.ones(K))\n",
        "n_epochs = 150\n",
        "learning_rate=.1\n",
        "max_norm = 1\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.999)  # Reduce LR every 10 steps\n",
        "criterion = CustomLoss(nn.MSELoss(),this_w, this_d)\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs, funct.coefs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%10:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 89,
      "id": "f1cf152b",
      "metadata": {
        "scrolled": false,
        "id": "f1cf152b",
        "outputId": "adbe4ab1-cd75-45f4-8f8b-29a300bcff5e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 843
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "x_for_plotting = torch.linspace(-1.1,1.1,1000)\n",
        "with torch.no_grad():\n",
        "    y_for_plotting = funct(x_for_plotting)\n",
        "\n",
        "plt.plot(x_for_plotting.numpy(), y_for_plotting.numpy(), '--', c='black')\n",
        "plt.plot(x_all, y_all, '.')\n",
        "plt.show()\n",
        "plt.bar( np.arange(K), funct.coefs.detach())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c07557b9",
      "metadata": {
        "id": "c07557b9"
      },
      "source": [
        "Instead of using a custom loss function, we can instead try and use other tools. L1 minimization is know to induce sparsity."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "id": "1fc37f3c",
      "metadata": {
        "id": "1fc37f3c",
        "outputId": "cadbf282-ed8b-4df2-e387-763e1bdcb9c9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 loss function 3.367\n",
            "iteration 0010 loss function 1.482\n",
            "iteration 0020 loss function 0.494\n",
            "iteration 0030 loss function 0.349\n",
            "iteration 0040 loss function 0.216\n",
            "iteration 0050 loss function 0.128\n",
            "iteration 0060 loss function 0.142\n",
            "iteration 0070 loss function 0.104\n",
            "iteration 0080 loss function 0.098\n",
            "iteration 0090 loss function 0.110\n",
            "iteration 0100 loss function 0.106\n",
            "iteration 0110 loss function 0.102\n",
            "iteration 0120 loss function 0.110\n",
            "iteration 0130 loss function 0.115\n",
            "iteration 0140 loss function 0.101\n",
            "iteration 0150 loss function 0.140\n",
            "iteration 0160 loss function 0.140\n",
            "iteration 0170 loss function 0.109\n",
            "iteration 0180 loss function 0.089\n",
            "iteration 0190 loss function 0.126\n",
            "iteration 0200 loss function 0.105\n",
            "iteration 0210 loss function 0.094\n",
            "iteration 0220 loss function 0.096\n",
            "iteration 0230 loss function 0.101\n",
            "iteration 0240 loss function 0.094\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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qqlJERIR69OjR5D5Op1NOpzMQ4wEAgA6gQ115SU5OVlFRUaN1hYWFSk5ODtJEAACgo7E1Xk6cOKGysjKVlZVJ+u6j0GVlZaqoqJD03Vs+GRkZ/u1vvfVWffLJJ7rrrrv0wQcf6E9/+pOee+453XHHHXaOCQAADGJrvOzbt0+jRo3SqFGjJEk5OTkaNWqUFi1aJEk6cuSIP2QkKSEhQa+88ooKCwuVlJSkZcuW6amnnuJj0gAAwM/We14mTpwoy7Kafb6pb8+dOHGi9u/fb+NUAADAZB3qnhcAAIAzIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGCUg8bJy5UoNGDBAYWFhGjdunPbs2dPstvn5+XI4HI2WsLCwQIwJAAAMYHu8rFu3Tjk5Obr33ntVWlqqpKQkpaWl6ejRo83uExERoSNHjviXw4cP2z0mAAAwhO3x8sgjj2jOnDmaNWuWhg4dqry8PPXs2VNr1qxpdh+HwyG32+1foqOj7R4TAAAYwtZ4OXXqlEpKSpSamvr9DwwJUWpqqoqLi5vd78SJE+rfv7/i4uJ07bXX6t13321229raWvl8vkYLAADovGyNl6+++kr19fU/uHISHR0tr9fb5D6DBw/WmjVrtHHjRj3zzDNqaGhQSkqKPvvssya393g8crlc/iUuLq7dzwMAAHQcHe7TRsnJycrIyNDIkSM1YcIEvfjii+rTp4+efPLJJrfPzc1VdXW1f6msrAzwxAAAIJC623nw3r17q1u3bqqqqmq0vqqqSm63u1XHOOusszRq1CgdPHiwyeedTqecTudPnhUAAJjB1isvoaGhGj16tIqKivzrGhoaVFRUpOTk5FYdo76+Xu+8845iYmLsGhMAABjE1isvkpSTk6OZM2dqzJgxGjt2rJYvX66amhrNmjVLkpSRkaG+ffvK4/FIkhYvXqxLLrlEAwcO1LFjx7R06VIdPnxYN998s92jAgAAA9geL9OmTdOXX36pRYsWyev1auTIkdq8ebP/Jt6KigqFhHx/Aeibb77RnDlz5PV6de6552r06NHauXOnhg4daveoAADAAA7LsqxgD9GefD6fXC6XqqurFRER0e7HH7DglXY/5n/79KHJth7/x+iK5wwACKy2/P7ucJ82AgAAaAnxAgAAjEK8AAAAoxAvAADAKMQLAAAwCvECAACMQrwAAACjEC8AAMAotn/DLmAivpgPADourrwAAACjEC8AAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAo/ANuwAA2IBv6rYPV14AAIBRiBcAAGAU4gUAABiFeAEAAEbhhl0AgO24eRXtiSsvAADAKMQLAAAwCvECAACMQrwAAACjEC8AAMAoxAsAADAKH5UGgADjY8PAT8OVFwAAYJSAXHlZuXKlli5dKq/Xq6SkJK1YsUJjx45tdvvnn39eCxcu1KeffqpBgwZpyZIluuaaawIxKgAARrP7yp4U/Kt7tl95WbdunXJycnTvvfeqtLRUSUlJSktL09GjR5vcfufOnZo+fbpmz56t/fv3Kz09Xenp6Tpw4IDdowIAAAPYHi+PPPKI5syZo1mzZmno0KHKy8tTz549tWbNmia3f+yxx3T11Vfrzjvv1JAhQ3T//ffroosu0hNPPGH3qAAAwAC2xsupU6dUUlKi1NTU739gSIhSU1NVXFzc5D7FxcWNtpektLS0Zrevra2Vz+drtAAAgM7L1ntevvrqK9XX1ys6OrrR+ujoaH3wwQdN7uP1epvc3uv1Nrm9x+PRfffd1z4Dt0Kw3ucL5nuYnHPgBPOcg/UJmK54zsG8X6CrnXNXfB0J9v0ogWD8p41yc3NVXV3tXyorK4M9EgAAsJGtV1569+6tbt26qaqqqtH6qqoqud3uJvdxu91t2t7pdMrpdLbPwAAAoMOz9cpLaGioRo8eraKiIv+6hoYGFRUVKTk5ucl9kpOTG20vSYWFhc1uDwAAuhbbv+clJydHM2fO1JgxYzR27FgtX75cNTU1mjVrliQpIyNDffv2lcfjkSTNnTtXEyZM0LJlyzR58mStXbtW+/bt0+rVq+0eFUAQdIX35wG0L9vjZdq0afryyy+1aNEieb1ejRw5Ups3b/bflFtRUaGQkO8vAKWkpKigoED33HOP7r77bg0aNEgbNmzQsGHD7B4VANDJEMedU0C+YTcrK0tZWVlNPrd169YfrJs6daqmTp1q81QAAMBExn/aCAAAdC3ECwAAMEpA3jYCfgzeqwYANIUrLwAAwCjECwAAMApvGwEdCG+VAcCZceUFAAAYhXgBAABGIV4AAIBRuOcFALoQ7qtCZ8CVFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAUvmEXgCS+eRWAOYgXAF0WwQaYibeNAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBRb4+Xrr7/WjBkzFBERoV69emn27Nk6ceJEi/tMnDhRDoej0XLrrbfaOSYAADCIrX/baMaMGTpy5IgKCwtVV1enWbNm6ZZbblFBQUGL+82ZM0eLFy/2P+7Zs6edYwIAAIPYFi/vv/++Nm/erL1792rMmDGSpBUrVuiaa67RH//4R8XGxja7b8+ePeV2u+0aDQAAGMy2t42Ki4vVq1cvf7hIUmpqqkJCQrR79+4W93322WfVu3dvDRs2TLm5ufr222+b3ba2tlY+n6/RAgAAOi/brrx4vV5FRUU1/mHduysyMlJer7fZ/X7zm9+of//+io2N1dtvv6358+ervLxcL774YpPbezwe3Xfffe06OwAA6LjaHC8LFizQkiVLWtzm/fff/9ED3XLLLf7/PXz4cMXExOiKK67Qxx9/rAsuuOAH2+fm5ionJ8f/2OfzKS4u7kf/fAAA0LG1OV7mzZunG2+8scVtzj//fLndbh09erTR+v/7v//T119/3ab7WcaNGydJOnjwYJPx4nQ65XQ6W308AABgtjbHS58+fdSnT58zbpecnKxjx46ppKREo0ePliRt2bJFDQ0N/iBpjbKyMklSTExMW0cFAACdkG037A4ZMkRXX3215syZoz179uitt95SVlaWrr/+ev8njT7//HMlJiZqz549kqSPP/5Y999/v0pKSvTpp5/qpZdeUkZGhi677DKNGDHCrlEBAIBBbP2SumeffVaJiYm64oordM011+jSSy/V6tWr/c/X1dWpvLzc/2mi0NBQvfHGG7rqqquUmJioefPm6Ve/+pVefvllO8cEAAAGsfVL6iIjI1v8QroBAwbIsiz/47i4OG3bts3OkQAAgOH420YAAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAoxAvAADAKMQLAAAwCvECAACMQrwAAACjEC8AAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAoxAvAADAKN2DPQBa59OHJgd7BAAAOgSuvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAoxAvAADAKMQLAAAwCvECAACMQrwAAACjEC8AAMAotsXLAw88oJSUFPXs2VO9evVq1T6WZWnRokWKiYlRjx49lJqaqo8++siuEQEAgIFsi5dTp05p6tSpuu2221q9z8MPP6zHH39ceXl52r17t84++2ylpaXp5MmTdo0JAAAM47Asy7LzB+Tn5ys7O1vHjh1rcTvLshQbG6t58+bpd7/7nSSpurpa0dHRys/P1/XXX9+qn+fz+eRyuVRdXa2IiIifOj4AAAiAtvz+7jD3vBw6dEher1epqan+dS6XS+PGjVNxcXGz+9XW1srn8zVaAABA59Vh4sXr9UqSoqOjG62Pjo72P9cUj8cjl8vlX+Li4mydEwAABFf3tmy8YMECLVmypMVt3n//fSUmJv6kodoiNzdXOTk5/sfV1dWKj4/nCgwAAAY5/Xu7NXeztCle5s2bpxtvvLHFbc4///y2HNLP7XZLkqqqqhQTE+NfX1VVpZEjRza7n9PplNPp9D8+ffJcgQEAwDzHjx+Xy+VqcZs2xUufPn3Up0+fnzRUcxISEuR2u1VUVOSPFZ/Pp927d7fpE0uxsbGqrKxUeHi4HA6HLbO2ls/nU1xcnCorK7vMzcOcM+fcWXHOnHNn1VHO2bIsHT9+XLGxsWfctk3x0hYVFRX6+uuvVVFRofr6epWVlUmSBg4cqHPOOUeSlJiYKI/Ho1/84hdyOBzKzs7WH/7wBw0aNEgJCQlauHChYmNjlZ6e3uqfGxISon79+tlwRj9eREREl/mP4DTOuWvgnLsGzrlr6AjnfKYrLqfZFi+LFi3SX/7yF//jUaNGSZLefPNNTZw4UZJUXl6u6upq/zZ33XWXampqdMstt+jYsWO69NJLtXnzZoWFhdk1JgAAMIxt8ZKfn6/8/PwWt/nfm3IcDocWL16sxYsX2zUWAAAwXIf5qHRn5HQ6de+99za6obiz45y7Bs65a+CcuwYTz9n2b9gFAABoT1x5AQAARiFeAACAUYgXAABgFOIFAAAYhXix0cqVKzVgwACFhYVp3Lhx2rNnT7BHso3H49HFF1+s8PBwRUVFKT09XeXl5cEeK2Aeeugh/xctdmaff/65fvvb3+q8885Tjx49NHz4cO3bty/YY9mmvr5eCxcuVEJCgnr06KELLrhA999/f6v+9ooptm/frilTpig2NlYOh0MbNmxo9LxlWVq0aJFiYmLUo0cPpaam6qOPPgrOsO2kpXOuq6vT/PnzNXz4cJ199tmKjY1VRkaGvvjii+AN3A7O9O/832699VY5HA4tX748YPO1FfFik3Xr1iknJ0f33nuvSktLlZSUpLS0NB09ejTYo9li27ZtyszM1K5du1RYWKi6ujpdddVVqqmpCfZottu7d6+efPJJjRgxItij2Oqbb77R+PHjddZZZ+m1117Te++9p2XLluncc88N9mi2WbJkiVatWqUnnnhC77//vpYsWaKHH35YK1asCPZo7aampkZJSUlauXJlk88//PDDevzxx5WXl6fdu3fr7LPPVlpamk6ePBngSdtPS+f87bffqrS0VAsXLlRpaalefPFFlZeX6+c//3kQJm0/Z/p3Pm39+vXatWtXq76iP6gs2GLs2LFWZmam/3F9fb0VGxtreTyeIE4VOEePHrUkWdu2bQv2KLY6fvy4NWjQIKuwsNCaMGGCNXfu3GCPZJv58+dbl156abDHCKjJkydbN910U6N1v/zlL60ZM2YEaSJ7SbLWr1/vf9zQ0GC53W5r6dKl/nXHjh2znE6n9fe//z0IE7a//z3npuzZs8eSZB0+fDgwQ9msuXP+7LPPrL59+1oHDhyw+vfvbz366KMBn621uPJig1OnTqmkpESpqan+dSEhIUpNTVVxcXEQJwuc03/2ITIyMsiT2CszM1OTJ09u9G/dWb300ksaM2aMpk6dqqioKI0aNUp//vOfgz2WrVJSUlRUVKQPP/xQkvTvf/9bO3bs0KRJk4I8WWAcOnRIXq+30f+/XS6Xxo0b12Vey6TvXs8cDod69eoV7FFs09DQoBtuuEF33nmnLrzwwmCPc0a2/XmAruyrr75SfX29oqOjG62Pjo7WBx98EKSpAqehoUHZ2dkaP368hg0bFuxxbLN27VqVlpZq7969wR4lID755BOtWrVKOTk5uvvuu7V3717dfvvtCg0N1cyZM4M9ni0WLFggn8+nxMREdevWTfX19XrggQc0Y8aMYI8WEF6vV5KafC07/Vxnd/LkSc2fP1/Tp08P+h8ttNOSJUvUvXt33X777cEepVWIF7S7zMxMHThwQDt27Aj2KLaprKzU3LlzVVhY2GX+cGhDQ4PGjBmjBx98UNJ3f2z1wIEDysvL67Tx8txzz+nZZ59VQUGBLrzwQpWVlSk7O1uxsbGd9pzxvbq6Ol133XWyLEurVq0K9ji2KSkp0WOPPabS0lI5HI5gj9MqvG1kg969e6tbt26qqqpqtL6qqkputztIUwVGVlaWNm3apDfffFP9+vUL9ji2KSkp0dGjR3XRRRepe/fu6t69u7Zt26bHH39c3bt3V319fbBHbHcxMTEaOnRoo3VDhgxRRUVFkCay35133qkFCxbo+uuv1/Dhw3XDDTfojjvukMfjCfZoAXH69aorvpadDpfDhw+rsLCwU191+de//qWjR48qPj7e/3p2+PBhzZs3TwMGDAj2eE0iXmwQGhqq0aNHq6ioyL+uoaFBRUVFSk5ODuJk9rEsS1lZWVq/fr22bNmihISEYI9kqyuuuELvvPOOysrK/MuYMWM0Y8YMlZWVqVu3bsEesd2NHz/+Bx9///DDD9W/f/8gTWS/b7/9ViEhjV8mu3XrpoaGhiBNFFgJCQlyu92NXst8Pp92797daV/LpO/D5aOPPtIbb7yh8847L9gj2eqGG27Q22+/3ej1LDY2Vnfeeadef/31YI/XJN42sklOTo5mzpypMWPGaOzYsVq+fLlqamo0a9asYI9mi8zMTBUUFGjjxo0KDw/3vx/ucrnUo0ePIE/X/sLDw39wP8/ZZ5+t8847r9Pe53PHHXcoJSVFDz74oK677jrt2bNHq1ev1urVq4M9mm2mTJmiBx54QPHx8brwwgu1f/9+PfLII7rpppuCPVq7OXHihA4ePOh/fOjQIZWVlSkyMlLx8fHKzs7WH/7wBw0aNEgJCQlauHChYmNjlZ6eHryhf6KWzjkmJka//vWvVVpaqk2bNqm+vt7/ehYZGanQ0NBgjf2TnOnf+X8D7ayzzpLb7dbgwYMDPWrrBPvjTp3ZihUrrPj4eCs0NNQaO3astWvXrmCPZBtJTS5PP/10sEcLmM7+UWnLsqyXX37ZGjZsmOV0Oq3ExERr9erVwR7JVj6fz5o7d64VHx9vhYWFWeeff771+9//3qqtrQ32aO3mzTffbPK/3ZkzZ1qW9d3HpRcuXGhFR0dbTqfTuuKKK6zy8vLgDv0TtXTOhw4davb17M033wz26D/amf6d/1dH/6i0w7I60VdFAgCATo97XgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEb5f4ihP1VcwMKbAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "funct = MyFunction(torch.ones(K))\n",
        "n_epochs = 250\n",
        "learning_rate=.1\n",
        "max_norm = 10\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.999)  # Reduce LR every 10 steps\n",
        "criterion = nn.L1Loss()\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%10:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n",
        "x_for_plotting = torch.linspace(-1.1,1.1,1000)\n",
        "with torch.no_grad():\n",
        "    y_for_plotting = funct(x_for_plotting)\n",
        "\n",
        "plt.plot(x_for_plotting.numpy(), y_for_plotting.numpy(), '--', c='black')\n",
        "plt.plot(x_all, y_all, '.')\n",
        "plt.show()\n",
        "plt.bar( np.arange(K), funct.coefs.detach())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fa05dc9b",
      "metadata": {
        "id": "fa05dc9b"
      },
      "source": [
        "Nope.\n",
        "\n",
        "We can use __weight decay__. This adds in an L2 penalty on coefficients we refine, i.e.\n",
        "\n",
        "the loss term + sum(coefs**2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "id": "53c2d515",
      "metadata": {
        "scrolled": false,
        "id": "53c2d515",
        "outputId": "54353138-3ebc-4da0-bb9b-541ba717afc5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 loss function 3.787\n",
            "iteration 0010 loss function 3.505\n",
            "iteration 0020 loss function 3.227\n",
            "iteration 0030 loss function 2.952\n",
            "iteration 0040 loss function 2.680\n",
            "iteration 0050 loss function 2.419\n",
            "iteration 0060 loss function 2.185\n",
            "iteration 0070 loss function 2.130\n",
            "iteration 0080 loss function 2.053\n",
            "iteration 0090 loss function 1.978\n",
            "iteration 0100 loss function 1.906\n",
            "iteration 0110 loss function 1.834\n",
            "iteration 0120 loss function 1.768\n",
            "iteration 0130 loss function 1.701\n",
            "iteration 0140 loss function 1.635\n",
            "iteration 0150 loss function 1.566\n",
            "iteration 0160 loss function 1.499\n",
            "iteration 0170 loss function 1.434\n",
            "iteration 0180 loss function 1.367\n",
            "iteration 0190 loss function 1.301\n",
            "iteration 0200 loss function 1.236\n",
            "iteration 0210 loss function 1.170\n",
            "iteration 0220 loss function 1.109\n",
            "iteration 0230 loss function 1.043\n",
            "iteration 0240 loss function 0.979\n",
            "iteration 0250 loss function 0.918\n",
            "iteration 0260 loss function 0.855\n",
            "iteration 0270 loss function 0.794\n",
            "iteration 0280 loss function 0.732\n",
            "iteration 0290 loss function 0.671\n",
            "iteration 0300 loss function 0.611\n",
            "iteration 0310 loss function 0.552\n",
            "iteration 0320 loss function 0.504\n",
            "iteration 0330 loss function 0.467\n",
            "iteration 0340 loss function 0.434\n",
            "iteration 0350 loss function 0.404\n",
            "iteration 0360 loss function 0.374\n",
            "iteration 0370 loss function 0.345\n",
            "iteration 0380 loss function 0.320\n",
            "iteration 0390 loss function 0.291\n",
            "iteration 0400 loss function 0.264\n",
            "iteration 0410 loss function 0.234\n",
            "iteration 0420 loss function 0.209\n",
            "iteration 0430 loss function 0.183\n",
            "iteration 0440 loss function 0.155\n",
            "iteration 0450 loss function 0.130\n",
            "iteration 0460 loss function 0.107\n",
            "iteration 0470 loss function 0.099\n",
            "iteration 0480 loss function 0.099\n",
            "iteration 0490 loss function 0.094\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "funct = MyFunction(torch.zeros(K))\n",
        "n_epochs = 500\n",
        "learning_rate=.01\n",
        "max_norm = 100\n",
        "weight_decay_parameter=2e-2\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate, weight_decay=weight_decay_parameter)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.99)  # Reduce LR every 10 steps\n",
        "criterion = nn.L1Loss()\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%10:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n",
        "\n",
        "\n",
        "x_for_plotting = torch.linspace(-1.1,1.1,1000)\n",
        "with torch.no_grad():\n",
        "    y_for_plotting = funct(x_for_plotting)\n",
        "\n",
        "plt.plot(x_for_plotting.numpy(), y_for_plotting.numpy(), '--', c='black')\n",
        "plt.plot(x_all, y_all, '.')\n",
        "plt.show()\n",
        "plt.bar( np.arange(K), funct.coefs.detach())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "59b51903",
      "metadata": {
        "id": "59b51903"
      },
      "source": [
        "Note that it is very easy to get creative and perhap overboard.\n",
        " Because we don't need to derive derivatives ourselves, we can try weird stuff very easely\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "id": "3e4ca52b",
      "metadata": {
        "id": "3e4ca52b"
      },
      "outputs": [],
      "source": [
        "# our well function that encourages stuff to be zero / small\n",
        "def targeted_well_function(coefs, delta, power=.5, target = 3):\n",
        "    tmp = coefs*delta\n",
        "    tmp = (tmp**2/(1+tmp**2))**power\n",
        "    tmp = (torch.sum(tmp) - target)**2\n",
        "    return tmp\n",
        "\n",
        "# here we combine our custom well function with a standard loss\n",
        "class OverboardLoss(nn.Module): # we inherit from nn.Module\n",
        "    def __init__(self, base_loss, weight, delta, target):\n",
        "        super().__init__()\n",
        "        self.base_loss = base_loss\n",
        "        self.weight = weight\n",
        "        self.delta = delta\n",
        "        self.target = target\n",
        "\n",
        "    def forward(self, y_pred, y_obs, params):\n",
        "        part1 = self.base_loss(y_pred, y_obs)\n",
        "        part2 = targeted_well_function(params, self.delta, 0.5, self.target)\n",
        "        return part1 + self.weight*part2\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "18ade59e",
      "metadata": {
        "id": "18ade59e"
      },
      "source": [
        "In the above loss function we drive the polynomial to have __target__ non-zero terms. The more complicated your loss function , harder it often is to minimize it."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "id": "798878e9",
      "metadata": {
        "scrolled": false,
        "id": "798878e9",
        "outputId": "62cf0861-8c2a-4e7f-a15a-a444b39360d2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 loss function 91.503\n",
            "iteration 0100 loss function 12.815\n",
            "iteration 0200 loss function 1.040\n",
            "iteration 0300 loss function 0.749\n",
            "iteration 0400 loss function 0.533\n",
            "iteration 0500 loss function 0.433\n",
            "iteration 0600 loss function 0.340\n",
            "iteration 0700 loss function 0.293\n",
            "iteration 0800 loss function 0.237\n",
            "iteration 0900 loss function 0.232\n",
            "iteration 1000 loss function 0.212\n",
            "iteration 1100 loss function 0.144\n",
            "iteration 1200 loss function 0.134\n",
            "iteration 1300 loss function 0.111\n",
            "iteration 1400 loss function 0.089\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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AgqRNxctPkZ2drerqav9SXl4e7JEAAICNbL3n5WJFR0ersrKy0brKykq5XC517ty5yX2cTqecTmcgxgMAAG1Am7rykpSUpIKCgkbr8vPzlZSUFKSJAABAW2NrvJw5c0YlJSUqKSmR9N+PQpeUlKisrEzSf3/lk5GR4d9+1qxZ+uyzz/TAAw/oo48+0p/+9Ce9/PLLuv/+++0cEwAAGMTWeDl48KCGDRumYcOGSZKysrI0bNgwLV68WJJUUVHhDxlJio+P15tvvqn8/HwlJiZqxYoVev755/mYNAAA8LP1npdx48bJsqxmn2/q23PHjRunQ4cO2TgVAAAwWZu65wUAAOB8iBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUQISL6tWrVLv3r0VFhamUaNGaf/+/c1uu3btWjkcjkZLWFhYIMYEAAAGsD1e1q9fr6ysLC1ZskTFxcVKTExUamqqqqqqmt3H5XKpoqLCvxw/ftzuMQEAgCFsj5cnnnhCM2fO1PTp0zVgwADl5OSoS5cuWrNmTbP7OBwORUdH+5eoqCi7xwQAAIawNV7Onj2roqIipaSkfP+CISFKSUlRYWFhs/udOXNGvXr1UlxcnG655Ra9//77zW5bW1srn8/XaAEAAO2XrfHy1Vdfqb6+/kdXTqKiouT1epvcp1+/flqzZo02bdqkF198UQ0NDUpOTtYXX3zR5PYej0dut9u/xMXFtfp5AACAtqPNfdooKSlJGRkZGjp0qMaOHavXXntNV155pZ577rkmt8/OzlZ1dbV/KS8vD/DEAAAgkDraefBu3bqpQ4cOqqysbLS+srJS0dHRF3SMTp06adiwYTp69GiTzzudTjmdzv95VgAAYAZbr7yEhoZq+PDhKigo8K9raGhQQUGBkpKSLugY9fX1Onz4sGJiYuwaEwAAGMTWKy+SlJWVpWnTpmnEiBEaOXKkVq5cqZqaGk2fPl2SlJGRoe7du8vj8UiSHnnkEY0ePVp9+vTRqVOntHz5ch0/flx333233aMCAAAD2B4vkydP1pdffqnFixfL6/Vq6NCh2rJli/8m3rKyMoWEfH8B6JtvvtHMmTPl9Xp1+eWXa/jw4dqzZ48GDBhg96gAAMAADsuyrGAP0Zp8Pp/cbreqq6vlcrla/fi9F77Z6sf8oc+Xptl6/J/iUjxnAEBgXczP7zb3aSMAAICWEC8AAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAoxAvAADAKMQLAAAwCvECAACMQrwAAACjEC8AAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAoxAvAADAKMQLAAAwCvECAACMQrwAAACjEC8AAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAowQkXlatWqXevXsrLCxMo0aN0v79+1vc/pVXXlFCQoLCwsI0ePBgvfXWW4EYEwAAGMD2eFm/fr2ysrK0ZMkSFRcXKzExUampqaqqqmpy+z179mjKlCmaMWOGDh06pPT0dKWnp+vIkSN2jwoAAAxge7w88cQTmjlzpqZPn64BAwYoJydHXbp00Zo1a5rc/qmnntJNN92k+fPnq3///nr00Ud1zTXX6Nlnn7V7VAAAYABb4+Xs2bMqKipSSkrK9y8YEqKUlBQVFhY2uU9hYWGj7SUpNTW12e1ra2vl8/kaLQAAoP3qaOfBv/rqK9XX1ysqKqrR+qioKH300UdN7uP1epvc3uv1Nrm9x+PRww8/3DoDX4DPl6YF7LV+qPfCN21/jebOLVjnDABAU4z/tFF2draqq6v9S3l5ebBHAgAANrL1yku3bt3UoUMHVVZWNlpfWVmp6OjoJveJjo6+qO2dTqecTmfrDAwAANo8W6+8hIaGavjw4SooKPCva2hoUEFBgZKSkprcJykpqdH2kpSfn9/s9gAA4NJi65UXScrKytK0adM0YsQIjRw5UitXrlRNTY2mT58uScrIyFD37t3l8XgkSXPmzNHYsWO1YsUKpaWlad26dTp48KByc3PtHhUAABjA9niZPHmyvvzySy1evFher1dDhw7Vli1b/DfllpWVKSTk+wtAycnJysvL00MPPaQHH3xQffv21caNGzVo0CC7RwUAAAZwWJZlBXuI1uTz+eR2u1VdXS2XyxXscVpNMD9tBACA3S7m57fxnzYCAACXFuIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTb4uXrr7/W1KlT5XK51LVrV82YMUNnzpxpcZ9x48bJ4XA0WmbNmmXXiAAAwEAd7Trw1KlTVVFRofz8fNXV1Wn69Om65557lJeX1+J+M2fO1COPPOJ/3KVLF7tGBAAABrIlXj788ENt2bJFBw4c0IgRIyRJzzzzjG6++Wb98Y9/VGxsbLP7dunSRdHR0XaMBQAA2gFbfm1UWFiorl27+sNFklJSUhQSEqJ9+/a1uO9LL72kbt26adCgQcrOzta3337b4va1tbXy+XyNFgAA0H7ZcuXF6/UqMjKy8Qt17KiIiAh5vd5m9/vNb36jXr16KTY2Vu+9954WLFig0tJSvfbaa83u4/F49PDDD7fa7AAAoG27qHhZuHChli1b1uI2H3744U8e5p577vH/78GDBysmJkbjx4/Xp59+qquvvrrJfbKzs5WVleV/7PP5FBcX95NnAAAAbdtFxcu8efN05513trjNVVddpejoaFVVVTVa/5///Edff/31Rd3PMmrUKEnS0aNHm40Xp9Mpp9N5wccEAABmu6h4ufLKK3XllVeed7ukpCSdOnVKRUVFGj58uCRp27Ztamho8AfJhSgpKZEkxcTEXMyYAACgHbPlht3+/fvrpptu0syZM7V//369++67mj17tm6//Xb/J41OnDihhIQE7d+/X5L06aef6tFHH1VRUZE+//xzvf7668rIyND111+vIUOG2DEmAAAwkG1fUvfSSy8pISFB48eP180336zrrrtOubm5/ufr6upUWlrq/zRRaGio3nnnHU2YMEEJCQmaN2+efvWrX+mNN96wa0QAAGAg276kLiIiosUvpOvdu7csy/I/jouL086dO+0aBwAAtBP8bSMAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRbPvDjGhdny9NC/YIAAC0CVx5AQAARiFeAACAUYgXAABgFOIFAAAYhXgBAABGIV4AAIBRiBcAAGAU4gUAABiFeAEAAEYhXgAAgFGIFwAAYBTiBQAAGIV4AQAARiFeAACAUYgXAABglI7BHqC1WZYlSfL5fEGeBAAAXKhzP7fP/RxvSbuLl9OnT0uS4uLigjwJAAC4WKdPn5bb7W5xG4d1IYljkIaGBp08eVLh4eFyOBxBncXn8ykuLk7l5eVyuVxBnSVQOGfOub3inDnn9qgtna9lWTp9+rRiY2MVEtLyXS3t7spLSEiIevToEewxGnG5XEH/jyLQOOdLA+d8aeCc27+2cr7nu+JyDjfsAgAAoxAvAADAKMSLjZxOp5YsWSKn0xnsUQKGc740cM6XBs65/TP1fNvdDbsAAKB948oLAAAwCvECAACMQrwAAACjEC8AAMAoxItNVq1apd69eyssLEyjRo3S/v37gz2SrTwej6699lqFh4crMjJS6enpKi0tDfZYAbN06VI5HA7NnTs32KPY6sSJE/rtb3+rK664Qp07d9bgwYN18ODBYI9lm/r6ei1atEjx8fHq3Lmzrr76aj366KMX9LdXTLFr1y5NmjRJsbGxcjgc2rhxY6PnLcvS4sWLFRMTo86dOyslJUWffPJJcIZtJS2dc11dnRYsWKDBgwfrsssuU2xsrDIyMnTy5MngDdwKzvfv/EOzZs2Sw+HQypUrAzbfxSJebLB+/XplZWVpyZIlKi4uVmJiolJTU1VVVRXs0Wyzc+dOZWZmau/evcrPz1ddXZ0mTJigmpqaYI9muwMHDui5557TkCFDgj2Krb755huNGTNGnTp10ttvv60PPvhAK1as0OWXXx7s0WyzbNkyrV69Ws8++6w+/PBDLVu2TI8//rieeeaZYI/WampqapSYmKhVq1Y1+fzjjz+up59+Wjk5Odq3b58uu+wypaam6rvvvgvwpK2npXP+9ttvVVxcrEWLFqm4uFivvfaaSktL9Ytf/CIIk7ae8/07n7Nhwwbt3btXsbGxAZrsJ7LQ6kaOHGllZmb6H9fX11uxsbGWx+MJ4lSBVVVVZUmydu7cGexRbHX69Gmrb9++Vn5+vjV27Fhrzpw5wR7JNgsWLLCuu+66YI8RUGlpadZdd93VaN0vf/lLa+rUqUGayF6SrA0bNvgfNzQ0WNHR0dby5cv9606dOmU5nU7rb3/7WxAmbH3//5ybsn//fkuSdfz48cAMZbPmzvmLL76wunfvbh05csTq1auX9eSTTwZ8tgvFlZdWdvbsWRUVFSklJcW/LiQkRCkpKSosLAziZIFVXV0tSYqIiAjyJPbKzMxUWlpao3/v9ur111/XiBEjdOuttyoyMlLDhg3Tn//852CPZavk5GQVFBTo448/liT961//0u7duzVx4sQgTxYYx44dk9frbfTft9vt1qhRoy659zOHw6GuXbsGexTbNDQ06I477tD8+fM1cODAYI9zXu3uDzMG21dffaX6+npFRUU1Wh8VFaWPPvooSFMFVkNDg+bOnasxY8Zo0KBBwR7HNuvWrVNxcbEOHDgQ7FEC4rPPPtPq1auVlZWlBx98UAcOHNB9992n0NBQTZs2Ldjj2WLhwoXy+XxKSEhQhw4dVF9fr8cee0xTp04N9mgB4fV6JanJ97Nzz7V33333nRYsWKApU6a0iT9caJdly5apY8eOuu+++4I9ygUhXtDqMjMzdeTIEe3evTvYo9imvLxcc+bMUX5+vsLCwoI9TkA0NDRoxIgR+sMf/iBJGjZsmI4cOaKcnJx2Gy8vv/yyXnrpJeXl5WngwIEqKSnR3LlzFRsb227PGd+rq6vTbbfdJsuytHr16mCPY5uioiI99dRTKi4ulsPhCPY4F4RfG7Wybt26qUOHDqqsrGy0vrKyUtHR0UGaKnBmz56tzZs3a/v27erRo0ewx7FNUVGRqqqqdM0116hjx47q2LGjdu7cqaefflodO3ZUfX19sEdsdTExMRowYECjdf3791dZWVmQJrLf/PnztXDhQt1+++0aPHiw7rjjDt1///3yeDzBHi0gzr1nXYrvZ+fC5fjx48rPz2/XV13++c9/qqqqSj179vS/nx0/flzz5s1T7969gz1ek4iXVhYaGqrhw4eroKDAv66hoUEFBQVKSkoK4mT2sixLs2fP1oYNG7Rt2zbFx8cHeyRbjR8/XocPH1ZJSYl/GTFihKZOnaqSkhJ16NAh2CO2ujFjxvzo4+8ff/yxevXqFaSJ7Pftt98qJKTx22SHDh3U0NAQpIkCKz4+XtHR0Y3ez3w+n/bt29eu38/Ohcsnn3yid955R1dccUWwR7LVHXfcoffee6/R+1lsbKzmz5+vrVu3Bnu8JvFrIxtkZWVp2rRpGjFihEaOHKmVK1eqpqZG06dPD/ZotsnMzFReXp42bdqk8PBw/+/D3W63OnfuHOTpWl94ePiP7ue57LLLdMUVV7Tb+3zuv/9+JScn6w9/+INuu+027d+/X7m5ucrNzQ32aLaZNGmSHnvsMfXs2VMDBw7UoUOH9MQTT+iuu+4K9mit5syZMzp69Kj/8bFjx1RSUqKIiAj17NlTc+fO1e9//3v17dtX8fHxWrRokWJjY5Wenh68of9HLZ1zTEyMfv3rX6u4uFibN29WfX29//0sIiJCoaGhwRr7f3K+f+f/H2idOnVSdHS0+vXrF+hRL0ywP+7UXj3zzDNWz549rdDQUGvkyJHW3r17gz2SrSQ1ubzwwgvBHi1g2vtHpS3Lst544w1r0KBBltPptBISEqzc3Nxgj2Qrn89nzZkzx+rZs6cVFhZmXXXVVdbvfvc7q7a2NtijtZrt27c3+f/dadOmWZb1349LL1q0yIqKirKcTqc1fvx4q7S0NLhD/49aOudjx441+362ffv2YI/+k53v3/n/a+sflXZYVjv6qkgAANDucc8LAAAwCvECAACMQrwAAACjEC8AAMAoxAsAADAK8QIAAIxCvAAAAKMQLwAAwCjECwAAMArxAgAAjEK8AAAAoxAvAADAKP8H4g1XNuvytbUAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "\n",
        "funct = MyFunction(torch.ones(K))\n",
        "n_epochs = 1500\n",
        "learning_rate=.01\n",
        "max_norm = 1\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.999)  # Reduce LR every 10 steps\n",
        "criterion = OverboardLoss(nn.MSELoss(),.5, 20, 3)\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs, funct.coefs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%100:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n",
        "\n",
        "\n",
        "x_for_plotting = torch.linspace(-1.1,1.1,1000)\n",
        "with torch.no_grad():\n",
        "    y_for_plotting = funct(x_for_plotting)\n",
        "\n",
        "plt.plot(x_for_plotting.numpy(), y_for_plotting.numpy(), '--', c='black')\n",
        "plt.plot(x_all, y_all, '.')\n",
        "plt.show()\n",
        "plt.bar( np.arange(K), funct.coefs.detach())\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Lets make it even more interesting, we will make a 5'th order polynomial, but only with 3 terms, lets see if we can figure this out!"
      ],
      "metadata": {
        "id": "vAp2z7otaUQ6"
      },
      "id": "vAp2z7otaUQ6"
    },
    {
      "cell_type": "code",
      "source": [
        "SIGMA=.025 # noise levels\n",
        "N_obs = 20 # number of observations\n",
        "\n",
        "# train data\n",
        "x = torch.linspace(-1,1,N_obs)\n",
        "y_obs = 2*x**5 - x**2 + 3 + torch.normal(0, SIGMA, x.shape)\n",
        "\n",
        "# test data\n",
        "x_plot = torch.linspace(-1.1,1.1,1000)\n",
        "y_plot = 2*x_plot**5 - x_plot**2 + 3\n",
        "plt.plot(x.numpy(), y_obs.numpy(), '.')\n",
        "plt.plot(x_plot.numpy(), y_plot.numpy(), '--')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "VO6wRMNUaTEk",
        "outputId": "29a3ab49-9160-43cd-a516-3783c958fb4f"
      },
      "id": "VO6wRMNUaTEk",
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now lets fit this. In order to make this work though, we need to do some trickery: immediate clamping down on 3 non-zero coefficients is very hard, resulting in convergence issues. It is however possible to soften the requirements and ask for 5 non-zero terms with a 'soft' restraint. Once we have this fitted, we can use those coeficients to start anew and clamp down harder.\n",
        "\n",
        "First, lets take it easy"
      ],
      "metadata": {
        "id": "FK1ThfVtbhhj"
      },
      "id": "FK1ThfVtbhhj"
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "funct = MyFunction(torch.ones(K))\n",
        "n_epochs = 500\n",
        "learning_rate=.01\n",
        "max_norm = 1\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.999)  # Reduce LR every 10 steps\n",
        "criterion = OverboardLoss(nn.MSELoss(),.1, 5, 5)\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs, funct.coefs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%100:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n",
        "\n",
        "\n",
        "x_for_plotting = torch.linspace(-1.1,1.1,1000)\n",
        "with torch.no_grad():\n",
        "    y_for_plotting = funct(x_for_plotting)\n",
        "\n",
        "plt.plot(x_for_plotting.numpy(), y_for_plotting.numpy(), '--', c='black')\n",
        "plt.plot(x, y_obs, '.')\n",
        "plt.plot(x_plot, y_plot,'--')\n",
        "plt.show()\n",
        "plt.bar( np.arange(K), funct.coefs.detach())\n",
        "plt.show()\n",
        "\n",
        "my_coefs = funct.coefs.clone()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 932
        },
        "id": "GOgA2VRMbYJ9",
        "outputId": "2e40e4cd-e319-4ccd-8500-7b16739b14fe"
      },
      "id": "GOgA2VRMbYJ9",
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 loss function 18.769\n",
            "iteration 0100 loss function 0.580\n",
            "iteration 0200 loss function 0.114\n",
            "iteration 0300 loss function 0.032\n",
            "iteration 0400 loss function 0.004\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now we have a decent set of coefficients, we can clamp down harder."
      ],
      "metadata": {
        "id": "f1N-61cddV3S"
      },
      "id": "f1N-61cddV3S"
    },
    {
      "cell_type": "code",
      "source": [
        "funct = MyFunction(my_coefs)\n",
        "n_epochs = 5000\n",
        "learning_rate=.001\n",
        "max_norm = 1\n",
        "\n",
        "optimizer = optim.Adam(funct.parameters(), lr=learning_rate)\n",
        "#optimizer = optim.SGD(funct.parameters(), lr=learning_rate)\n",
        "\n",
        "scheduler = optim.lr_scheduler.StepLR(optimizer, step_size=10, gamma=0.999)\n",
        "\n",
        "delta = 100.0\n",
        "weight = 1\n",
        "\n",
        "criterion = OverboardLoss(nn.MSELoss(), weight, delta, 3)\n",
        "\n",
        "\n",
        "# Training loop\n",
        "for ii in range(n_epochs):\n",
        "    optimizer.zero_grad()  # Zero out gradients\n",
        "    y_pred = funct(x)  # Compute function\n",
        "    loss_actual = criterion(y_pred, y_obs, funct.coefs)  # Get the loss\n",
        "    loss_actual.backward()  # Compute gradients\n",
        "    torch.nn.utils.clip_grad_norm_(funct.parameters(), max_norm=max_norm)\n",
        "    optimizer.step()  # Update parameters\n",
        "    scheduler.step()\n",
        "\n",
        "    if not ii%1000:\n",
        "        print(f\"iteration {ii:04} loss function {loss_actual.item():4.3f}\")\n",
        "\n",
        "\n",
        "with torch.no_grad():\n",
        "    y_for_plotting = funct(x_for_plotting)\n",
        "\n",
        "plt.plot(x_for_plotting.numpy(), y_for_plotting.numpy(), '--', c='black')\n",
        "plt.plot(x, y_obs, '.')\n",
        "plt.plot(x_plot, y_plot, '--', lw=1)\n",
        "plt.legend([\"Fitted\",\"Observed\",\"Ground Truth\"])\n",
        "plt.show()\n",
        "\n",
        "plt.bar( np.arange(K), funct.coefs.detach())\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 932
        },
        "id": "xj1ojgk8dIEh",
        "outputId": "0c9aa4e1-1b9f-4325-a772-341f4c9d5075"
      },
      "id": "xj1ojgk8dIEh",
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "iteration 0000 loss function 10.791\n",
            "iteration 1000 loss function 0.013\n",
            "iteration 2000 loss function 0.011\n",
            "iteration 3000 loss function 0.011\n",
            "iteration 4000 loss function 0.007\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0a917bba",
      "metadata": {
        "id": "0a917bba"
      },
      "source": [
        "In the end, fitting a function requires tuning a lot of things\n",
        "\n",
        "- learning rate\n",
        "- regularization terms\n",
        "- specific optimizer\n",
        "- the model you use\n",
        "- the data you have\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "IjJszoZ0rSSI"
      },
      "id": "IjJszoZ0rSSI",
      "execution_count": 96,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.16"
    },
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "include_colab_link": true
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 5
}