{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import torch\n",
    "torch.set_printoptions(edgeitems=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_c = [0.5,  14.0, 15.0, 28.0, 11.0,  8.0,  3.0, -4.0,  6.0, 13.0, 21.0]\n",
    "t_u = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]\n",
    "t_c = torch.tensor(t_c)\n",
    "t_u = torch.tensor(t_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(t_u, w, b):\n",
    "    return w * t_u + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_fn(t_p, t_c):\n",
    "    squared_diffs = (t_p - t_c)**2\n",
    "    return squared_diffs.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([35.7000, 55.9000, 58.2000, 81.9000, 56.3000, 48.9000, 33.9000, 21.8000,\n",
       "        48.4000, 60.4000, 68.4000])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = torch.ones(1)\n",
    "b = torch.zeros(1)\n",
    "\n",
    "t_p = model(t_u, w, b)\n",
    "t_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1763.8846)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss = loss_fn(t_p, t_c)\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = 0.1\n",
    "\n",
    "loss_rate_of_change_w = \\\n",
    "    (loss_fn(model(t_u, w + delta, b), t_c) - \n",
    "     loss_fn(model(t_u, w - delta, b), t_c)) / (2.0 * delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 1e-2\n",
    "\n",
    "w = w - learning_rate * loss_rate_of_change_w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_rate_of_change_b = \\\n",
    "    (loss_fn(model(t_u, w, b + delta), t_c) - \n",
    "     loss_fn(model(t_u, w, b - delta), t_c)) / (2.0 * delta)\n",
    "\n",
    "b = b - learning_rate * loss_rate_of_change_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dloss_fn(t_p, t_c):\n",
    "    dsq_diffs = 2 * (t_p - t_c)\n",
    "    return dsq_diffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dmodel_dw(t_u, w, b):\n",
    "    return t_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dmodel_db(t_u, w, b):\n",
    "    return 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad_fn(t_u, t_c, t_p, w, b):\n",
    "    dloss_dw = dloss_fn(t_p, t_c) * dmodel_dw(t_u, w, b)\n",
    "    dloss_db = dloss_fn(t_p, t_c) * dmodel_db(t_u, w, b)\n",
    "    return torch.stack([dloss_dw.mean(), dloss_db.mean()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def training_loop(n_epochs, learning_rate, params, t_u, t_c):\n",
    "    for epoch in range(1, n_epochs + 1):\n",
    "        w, b = params\n",
    "\n",
    "        t_p = model(t_u, w, b)  # <1>\n",
    "        loss = loss_fn(t_p, t_c)\n",
    "        grad = grad_fn(t_u, t_c, t_p, w, b)  # <2>\n",
    "\n",
    "        params = params - learning_rate * grad\n",
    "\n",
    "        print('Epoch %d, Loss %f' % (epoch, float(loss))) # <3>\n",
    "            \n",
    "    return params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def training_loop(n_epochs, learning_rate, params, t_u, t_c, print_params=True):\n",
    "    for epoch in range(1, n_epochs + 1):\n",
    "        w, b = params\n",
    "\n",
    "        t_p = model(t_u, w, b)  # <1>\n",
    "        loss = loss_fn(t_p, t_c)\n",
    "        grad = grad_fn(t_u, t_c, t_p, w, b)  # <2>\n",
    "\n",
    "        params = params - learning_rate * grad\n",
    "\n",
    "        if epoch in {1, 2, 3, 10, 11, 99, 100, 4000, 5000}:  # <3>\n",
    "            print('Epoch %d, Loss %f' % (epoch, float(loss)))\n",
    "            if print_params:\n",
    "                print('    Params:', params)\n",
    "                print('    Grad:  ', grad)\n",
    "        if epoch in {4, 12, 101}:\n",
    "            print('...')\n",
    "\n",
    "        if not torch.isfinite(loss).all():\n",
    "            break  # <3>\n",
    "            \n",
    "    return params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 1763.884644\n",
      "    Params: tensor([-44.1730,  -0.8260])\n",
      "    Grad:   tensor([4517.2964,   82.6000])\n",
      "Epoch 2, Loss 5802484.500000\n",
      "    Params: tensor([2568.4011,   45.1637])\n",
      "    Grad:   tensor([-261257.4062,   -4598.9707])\n",
      "Epoch 3, Loss 19408031744.000000\n",
      "    Params: tensor([-148527.7344,   -2616.3933])\n",
      "    Grad:   tensor([15109615.0000,   266155.7188])\n",
      "...\n",
      "Epoch 10, Loss 90901075478458130961171361977860096.000000\n",
      "    Params: tensor([3.2144e+17, 5.6621e+15])\n",
      "    Grad:   tensor([-3.2700e+19, -5.7600e+17])\n",
      "Epoch 11, Loss inf\n",
      "    Params: tensor([-1.8590e+19, -3.2746e+17])\n",
      "    Grad:   tensor([1.8912e+21, 3.3313e+19])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([-1.8590e+19, -3.2746e+17])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_loop(\n",
    "    n_epochs = 100, \n",
    "    learning_rate = 1e-2, \n",
    "    params = torch.tensor([1.0, 0.0]), \n",
    "    t_u = t_u, \n",
    "    t_c = t_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 1763.884644\n",
      "    Params: tensor([ 0.5483, -0.0083])\n",
      "    Grad:   tensor([4517.2964,   82.6000])\n",
      "Epoch 2, Loss 323.090546\n",
      "    Params: tensor([ 0.3623, -0.0118])\n",
      "    Grad:   tensor([1859.5493,   35.7843])\n",
      "Epoch 3, Loss 78.929634\n",
      "    Params: tensor([ 0.2858, -0.0135])\n",
      "    Grad:   tensor([765.4666,  16.5122])\n",
      "...\n",
      "Epoch 10, Loss 29.105242\n",
      "    Params: tensor([ 0.2324, -0.0166])\n",
      "    Grad:   tensor([1.4803, 3.0544])\n",
      "Epoch 11, Loss 29.104168\n",
      "    Params: tensor([ 0.2323, -0.0169])\n",
      "    Grad:   tensor([0.5780, 3.0384])\n",
      "...\n",
      "Epoch 99, Loss 29.023582\n",
      "    Params: tensor([ 0.2327, -0.0435])\n",
      "    Grad:   tensor([-0.0533,  3.0226])\n",
      "Epoch 100, Loss 29.022669\n",
      "    Params: tensor([ 0.2327, -0.0438])\n",
      "    Grad:   tensor([-0.0532,  3.0226])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([ 0.2327, -0.0438])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_loop(\n",
    "    n_epochs = 100, \n",
    "    learning_rate = 1e-4, \n",
    "    params = torch.tensor([1.0, 0.0]), \n",
    "    t_u = t_u, \n",
    "    t_c = t_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_un = 0.1 * t_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 80.364342\n",
      "    Params: tensor([1.7761, 0.1064])\n",
      "    Grad:   tensor([-77.6140, -10.6400])\n",
      "Epoch 2, Loss 37.574917\n",
      "    Params: tensor([2.0848, 0.1303])\n",
      "    Grad:   tensor([-30.8623,  -2.3864])\n",
      "Epoch 3, Loss 30.871077\n",
      "    Params: tensor([2.2094, 0.1217])\n",
      "    Grad:   tensor([-12.4631,   0.8587])\n",
      "...\n",
      "Epoch 10, Loss 29.030487\n",
      "    Params: tensor([ 2.3232, -0.0710])\n",
      "    Grad:   tensor([-0.5355,  2.9295])\n",
      "Epoch 11, Loss 28.941875\n",
      "    Params: tensor([ 2.3284, -0.1003])\n",
      "    Grad:   tensor([-0.5240,  2.9264])\n",
      "...\n",
      "Epoch 99, Loss 22.214186\n",
      "    Params: tensor([ 2.7508, -2.4910])\n",
      "    Grad:   tensor([-0.4453,  2.5208])\n",
      "Epoch 100, Loss 22.148710\n",
      "    Params: tensor([ 2.7553, -2.5162])\n",
      "    Grad:   tensor([-0.4445,  2.5165])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([ 2.7553, -2.5162])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_loop(\n",
    "    n_epochs = 100, \n",
    "    learning_rate = 1e-2, \n",
    "    params = torch.tensor([1.0, 0.0]), \n",
    "    t_u = t_un, # <1>\n",
    "    t_c = t_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1, Loss 80.364342\n",
      "Epoch 2, Loss 37.574917\n",
      "Epoch 3, Loss 30.871077\n",
      "...\n",
      "Epoch 10, Loss 29.030487\n",
      "Epoch 11, Loss 28.941875\n",
      "...\n",
      "Epoch 99, Loss 22.214186\n",
      "Epoch 100, Loss 22.148710\n",
      "...\n",
      "Epoch 4000, Loss 2.927680\n",
      "Epoch 5000, Loss 2.927648\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([  5.3671, -17.3012])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = training_loop(\n",
    "    n_epochs = 5000, \n",
    "    learning_rate = 1e-2, \n",
    "    params = torch.tensor([1.0, 0.0]), \n",
    "    t_u = t_un, \n",
    "    t_c = t_c,\n",
    "    print_params = False)\n",
    "\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x201d6207978>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 3600x2400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "t_p = model(t_un, *params)  # <1>\n",
    "\n",
    "fig = plt.figure(dpi=600)\n",
    "plt.xlabel(\"Fahrenheit\")\n",
    "plt.ylabel(\"Celsius\")\n",
    "plt.plot(t_u.numpy(), t_p.detach().numpy()) # <2>\n",
    "plt.plot(t_u.numpy(), t_c.numpy(), 'o')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}