Python/ml/Linear_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression With Multiple Variables in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This algorithms reads housing price data from a file named \"ex1data2.txt\" and predicts the price based on two features size and number of bedrooms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_ones(X):\n",
    "    \"\"\"\n",
    "    adds a column of ones to the matrix\n",
    "    \"\"\"\n",
    "    m = len(X)\n",
    "    X = np.c_[np.ones(m), X]\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(t, X, y):\n",
    "    \"\"\"\n",
    "    computes the squared error function \n",
    "    \"\"\"\n",
    "    m = len(X)\n",
    "\n",
    "    hypo = np.dot(X,t)\n",
    "    J = np.sum(np.power((hypo-y),2)) / (2*m)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scaling(arr):\n",
    "    \"\"\"\n",
    "    implements feature scaling\n",
    "    \"\"\"\n",
    "    arr = arr.astype('float64')\n",
    "    n = len(arr[0])\n",
    "    mu = np.mean(arr, axis=0).reshape(1,n)\n",
    "    sigma = np.std(arr, axis=0).reshape(1,n)\n",
    "    for x in range(n):\n",
    "        arr[:,x]-= mu[0,x]\n",
    "        arr[:,x]/= sigma[0,x]\n",
    "    return (mu,sigma,arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, theta, a, x):\n",
    "    \"\"\"\n",
    "    implements gradient descent over 400 iterations\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    m = len(y)\n",
    "    \n",
    "    j_history = []\n",
    "    for i in range(x):\n",
    "        hypo = np.dot(X, theta) - y\n",
    "        theta -= np.dot(np.transpose(X),hypo) * a / m\n",
    "        j_history.append(cost(theta, X, y))\n",
    "    return (j_history ,theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "65591548106.45744\n",
      "[[334302.06399328]\n",
      " [ 99411.44947359]\n",
      " [  3267.01285407]]\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv('ex1data2.txt', names = ['size', 'bedrooms', 'cost'])\n",
    "\n",
    "inp = df[{'size', 'bedrooms'}].values  # matrix containing features\n",
    "out = df['cost'].values.reshape(len(inp),1) # matrix containing prices\n",
    "mu,sigma,inp = scaling(inp)\n",
    "inp = add_ones(inp)\n",
    "th = np.zeros((len(inp[1]),1))\n",
    "print(cost(th, inp, out))\n",
    "iterations = 400\n",
    "alpha = 0.01\n",
    "j_history, th = gradient_descent(inp, out, th, alpha, iterations)\n",
    "print(th)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7228235.64029964]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# predicting price for a house with 3 bedrooms and 1650 sq feets size\n",
    "a = np.array([3,1650])\n",
    "a = np.divide((a-mu),sigma)\n",
    "a = add_ones(a)\n",
    "np.dot(a,th)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
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       "\n",
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       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
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       "\n",
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       "    fig.ondownload(fig, format);\n",
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       "        fig._resize_canvas(size[0], size[1]);\n",
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       "    };\n",
       "}\n",
       "\n",
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       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
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       "    y1 = Math.floor(y1) + 0.5;\n",
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       "    var min_y = Math.min(y0, y1);\n",
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       "\n",
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       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
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       "    var cursor = msg['cursor'];\n",
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       "        cursor = 'pointer';\n",
       "        break;\n",
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       "        break;\n",
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       "        break;\n",
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       "    }\n",
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       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
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       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
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       "}\n",
       "\n",
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       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1dcfa21d288>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plotting cost w.r.t iterations in gradient descents to make\n",
    "# sure its decreasing\n",
    "plt.plot(j_history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}