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   "cell_type": "markdown",
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   "source": [
    "# Concise Implementation of Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:59:54.049026Z",
     "start_time": "2019-07-03T21:59:52.500967Z"
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     "classes": [],
     "id": "",
     "n": "2"
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   "outputs": [],
   "source": [
    "import d2l\n",
    "from mxnet import autograd, np, npx, gluon\n",
    "npx.set_np()\n",
    "\n",
    "true_w = np.array([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = d2l.synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Reading Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:59:54.120474Z",
     "start_time": "2019-07-03T21:59:54.051605Z"
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    "attributes": {
     "classes": [],
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    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X =\n",
      "[[ 0.4015098   1.4096868 ]\n",
      " [ 0.65820086 -1.4260322 ]\n",
      " [ 0.00153129 -0.14330608]\n",
      " [-0.843129    0.6070013 ]\n",
      " [ 1.5080738  -0.27229312]\n",
      " [-0.01436996  0.50522786]\n",
      " [-0.2513225  -0.7733599 ]\n",
      " [-0.4892422   0.82852226]\n",
      " [ 0.19469471  0.26424283]\n",
      " [ 0.8269238   1.0562588 ]]y =\n",
      "[ 0.21267602 10.392891    4.7093544   0.45944032  8.140177    2.475876\n",
      "  6.332503    0.4059622   3.69898     2.2603266 ]\n"
     ]
    }
   ],
   "source": [
    "def load_array(data_arrays, batch_size, is_train=True):\n",
    "    dataset = gluon.data.ArrayDataset(*data_arrays)\n",
    "    return gluon.data.DataLoader(dataset, batch_size, shuffle=is_train)\n",
    "    \n",
    "batch_size = 10\n",
    "data_iter = load_array((features, labels), batch_size)\n",
    "for X, y in data_iter:\n",
    "    print('X =\\n%sy =\\n%s' %(X, y))\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Define the Model and initialize Model Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:59:54.129952Z",
     "start_time": "2019-07-03T21:59:54.124685Z"
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     "id": "",
     "n": "5"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from mxnet.gluon import nn\n",
    "from mxnet import init\n",
    "\n",
    "net = nn.Sequential()\n",
    "net.add(nn.Dense(1))\n",
    "net.initialize(init.Normal(sigma=0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Define the loss function and optimization algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:59:54.135619Z",
     "start_time": "2019-07-03T21:59:54.132150Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "8"
    }
   },
   "outputs": [],
   "source": [
    "from mxnet import gluon\n",
    "\n",
    "loss = gluon.loss.L2Loss() \n",
    "trainer = gluon.Trainer(net.collect_params(),\n",
    "                        'sgd', {'learning_rate': 0.03})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T21:59:56.549677Z",
     "start_time": "2019-07-03T21:59:54.137373Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "10"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss: 0.040749\n",
      "epoch 2, loss: 0.000152\n",
      "epoch 3, loss: 0.000051\n",
      "Error in estimating w [[ 0.00024056 -0.00077081]]\n",
      "Error in estimating b [0.00041628]\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(1, 4):\n",
    "    for X, y in data_iter:\n",
    "        with autograd.record():\n",
    "            l = loss(net(X), y)\n",
    "        l.backward()\n",
    "        trainer.step(batch_size)\n",
    "    l = loss(net(features), labels)\n",
    "    print('epoch %d, loss: %f' % (epoch, l.mean()))\n",
    "    \n",
    "w = net[0].weight.data()\n",
    "print('Error in estimating w', true_w.reshape(w.shape) - w)\n",
    "b = net[0].bias.data()\n",
    "print('Error in estimating b', true_b - b)    "
   ]
  }
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