Additional Programming Concepts in Python.ipynb

     "text": [
      "[1, 1]\n"
     ]
    }
   ],
   "source": [
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing the values of `a` also changed list `b` for some reason? **WHY!!!!?????!!! WHAT IS GOING ON?!!?**\n",
    "\n",
    "### \"Call by value\" and \"Call by reference\"\n",
    "\n",
    "To understand what is going on here, we have to understand how computer programs store variables and their values. \n",
    "\n",
    "When I create a variable `a` in a python by giving it a value `5`, for example, python creates a space in your computers memory where it puts the value `5` and then makes a name for that variable `a` in the kernel's list of variables that points to that spot in memory. \n",
    "\n",
    "For some types of objects in python, specifically \"immutable\" (\"unchangeable\") object types, when you execute the statement `b = a`, python will create a new spot in your computers memory for variable `b`, copy the value `5` into that memory spot, and then makes variable `b` point to this new spot in the kernel's list of variables. \n",
    "\n",
    "This procedure is called \"call by value\" in programming languages, and is illustrated here: \n",
    "\n",
    "<img src=\"call_by_value.png\"></img>\n",
    "\n",
    "For \"mutable\" objects, python uses a different concept: \"call by reference\". In call by reference, `b = a` instead does the following: it make a new variable `b` in the list of variables, and make it point to the spot in memory where variable `a` is stored, illustrated here:\n",
    "\n",
    "<img src=\"call_by_reference.png\"></img>\n",
    "\n",
    "It is now obvious why changing the values in `a` will also changes the values in `b`: it is because they point to the same data in your computers memory.\n",
    "\n",
    "\"Call by reference\" also holds for when you are passing variables to functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 2]\n"
     ]
    }
   ],
   "source": [
    "def set_first_entry_to_zero(x):\n",
    "    x[0] = 0\n",
    "\n",
    "a = [1,2]\n",
    "set_first_entry_to_zero(a)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that our function changed the value of the variable mylist! This was not possible with integers for example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "def set_to_zero(x):\n",
    "    x = 0\n",
    "\n",
    "a = 1\n",
    "set_to_zero(a)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why use \"call by reference\" at all? I find it confusing!\n",
    "\n",
    "You might ask: why python does this? Well, one reason is that it is that lists, and in particular numpy arrays that we will look at next, can sometime become very big, taking up 100 MB of memory or more. If python used \"call by value\" for such big things all the time, it would use up massive amounts of memory! Every function call or assignment statement would accdientally use up another 100 MB of memory! By using \"call by reference\", it can avoid accidentally filling up your computers memory every time you use the `=` operator. \n",
    "\n",
    "If you really want to have a *copy* of a list (or a numpy array), these objects typically have `copy()` functions built in that return instead a copy of the object, for when you really need one. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [2,1]\n",
    "b = a.copy()\n",
    "print(b)\n",
    "a[0] = 1\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, `b` is unaffected by your changes to `a` because the name `b` points to a new copy of the array in memory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interactive plots with ipywidgets\n",
    "\n",
    "One of the cool things that is easy to do in Jupter notebooks is to make \"interactive\" plots. \n",
    "\n",
    "For example, in the projectile example above, I may want to be able to play with the angle and see how this changes my trajectory. For this, there is a very easy to use and convenient library called `ipywidgets`.\n",
    "\n",
    "The way it works is we make a function that generates our plot that takes the parameter we want to play with as an argument. We then call an `ipywidgets` function called `interact()`, and it will automatically make a \"live update\" plot in your web browser in which you can adjust the parameter an see how the plot changes. \n",
    "\n",
    "Let's look at an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "\n",
    "v0 = 10 # m/s\n",
    "g = 9.8 # m/s^2\n",
    "\n",
    "# We will allow theta to be adjusted and start it at 45 degrees\n",
    "def update_plot(theta=45):\n",
    "    theta *= np.pi/180 # convert to radians\n",
    "    y = -g/(2*v0**2*np.cos(theta)**2)*x**2 + x*np.tan(theta)\n",
    "    plt.plot(x,y)\n",
    "    plt.ylim(-1,6) # Manually set the ylimits\n",
    "    plt.xlabel(\"Distance (m)\")\n",
    "    plt.ylabel(\"Height (m)\")\n",
    "    plt.axhline(0, ls=\":\", c=\"grey\")\n",
    "    plt.show()\n",
    "    \n",
    "# Now we call interact, and give it a tuple specifiying the min, max and step for the theta slider\n",
    "interact(update_plot, theta=(0,89,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a bit slow in updating if you wiggle it too much with the mouse, but if you click on the slider and adjust it using the arrow keys on your keyboard, it works pretty well. \n",
    "\n",
    "If you are fitting a line to your data, this can also be very useful for getting a good initial guess:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_plot2(slope=0.5):\n",
    "    line = t*slope\n",
    "    plt.plot(t,v, '.')\n",
    "    plt.plot(t,line, lw=4)\n",
    "    plt.xlabel(\"Time (s)\")\n",
    "    plt.ylabel(\"Voltage (V)\")\n",
    "    plt.show()\n",
    "\n",
    "interact(update_plot2, slope=(0,10,0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also easy to make two sliders:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_plot3(slope=0.5, offset=0):\n",
    "    line = t*slope+offset\n",
    "    plt.plot(t,v, '.')\n",
    "    plt.plot(t,line, lw=4)\n",
    "    plt.xlabel(\"Time (s)\")\n",
    "    plt.ylabel(\"Voltage (V)\")\n",
    "    plt.show()\n",
    "\n",
    "interact(update_plot3, slope=(0,10,0.1), offset=(-4,3,0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions\n",
    "\n",
    "### Keyword and optional arguments\n",
    "\n",
    "In addition to the \"positional\" arguments we introduced earlier, python also supports another type of argument: the \"keyword\" argument. These are often used for \"optional\" arguments that you don't neccessarily need but may want to give the user the option of using. The syntax is:\n",
    "\n",
    "```\n",
    "def function_name(var1, optional_var2 = default_value)\n",
    "    ...\n",
    "```\n",
    "\n",
    "The \"default_value\" is the value that the optional argument will have if it is not specified by the user. \n",
    "\n",
    "In python-speak, these \"optional\" arguement as called \"keyword\" arguments, and the normal arguments we introduced above are called \"positional\" arguments. In python, in both defining and using functions, keyword arguments must always come after all of the positional arguments. \n",
    "\n",
    "Here, we will show an example where we use an optional parameter to change the way we print the status sentence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of the first input variable is  1\n",
      "The value of the first input variable is  2.5\n",
      "Val is  2.4\n"
     ]
    }
   ],
   "source": [
    "def print_status4(x, long=True):\n",
    "    if long:\n",
    "        print(\"The value of the first input variable is \", x)\n",
    "    else:\n",
    "        print(\"Val is \", x)\n",
    "\n",
    "print_status4(1)\n",
    "print_status4(2.5, long=True)\n",
    "print_status4(2.4, long=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because python assigns the value of keyword argument variables in the function by matching the keyword and not their position in the list, if you have multiple keyword arguments, you can also change the order of them when you use the function. \n",
    "\n",
    "For example, if I define a function:\n",
    "\n",
    "```\n",
    "def myfunction(x, var1=1, var2=4):\n",
    "    ...\n",
    "```\n",
    "\n",
    "then both of these would do the same thing:\n",
    "\n",
    "```\n",
    "myfunction(1,var1=3, var2=54)\n",
    "myfunction(1,var2=54, var2=3)\n",
    "```\n",
    "\n",
    "Finally, one can also use keywords as a way to send values to functions even if the functions are not defined with keyword arguments. This allows you to change to order of variables you send to a function if you  want. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def myfun(x,y):\n",
    "    print(\"x is\", x)\n",
    "    print(\"y is\", y)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is 1\n",
      "y is 2\n"
     ]
    }
   ],
   "source": [
    "myfun(1,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is 2\n",
      "y is 1\n"
     ]
    }
   ],
   "source": [
    "myfun(2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is 1\n",
      "y is 2\n"
     ]
    }
   ],
   "source": [
    "myfun(x=1,y=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x is 1\n",
      "y is 2\n"
     ]
    }
   ],
   "source": [
    "myfun(y=2,x=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Python Error Messages with functions\n",
    "\n",
    "In the first notebook, we learned some of the basics of how to understand python errors.\n",
    "\n",
    "Sometimes, though, if you are using functions from a library, the error messages can get very long, and trickier to understand. \n",
    "\n",
    "Here, we will look at how to dissect an example of a more complicated error you can get from a function in a library and how to figure out where the useful information is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (2,) and (3,)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-11-19f47447b05c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Programs\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   3356\u001b[0m                       mplDeprecation)\n\u001b[0;32m   3357\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3358\u001b[1;33m         \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   3359\u001b[0m     \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   3360\u001b[0m         \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Programs\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1853\u001b[0m                         \u001b[1;34m\"the Matplotlib list!)\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1854\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1855\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1856\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1857\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
      "\u001b[1;32mC:\\Programs\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1525\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1526\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1527\u001b[1;33m         \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1528\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1529\u001b[0m             \u001b[0mlines\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Programs\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_grab_next_args\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    404\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    405\u001b[0m                 \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 406\u001b[1;33m             \u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    407\u001b[0m                 \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    408\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Programs\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m    381\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    382\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 383\u001b[1;33m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    384\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    385\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Programs\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m    240\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    241\u001b[0m             raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[1;32m--> 242\u001b[1;33m                              \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[0;32m    243\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    244\u001b[0m             raise ValueError(\"x and y can be no greater than 2-D, but have \"\n",
      "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (2,) and (3,)"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot([1,2], [1,2,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, that was a really big error message. What do I do with all of this? \n",
    "\n",
    "The most important information is at the very top and at the very bottom (you can just skip the rest for now...). \n",
    "\n",
    "At the top, it shows us the part of our code that triggered the error:\n",
    "\n",
    "<img src=\"big_error_1.png\"></img>\n",
    "\n",
    "The error type is a `ValueError`, which according to the documentation, indicates \"an argument that has the right type but an inappropriate value\". \n",
    "\n",
    "In the middle there is then a whole bunch of stuff we won't easily understand. What is all of this? This is showing us what is happening inside all the functions of the matplotlib library...probably unless you are a bit of an expert, you will not really understand all of this. \n",
    "\n",
    "We can learn more, though, by looking at the last line:\n",
    "\n",
    "<img src=\"big_error_2.png\"></img>\n",
    "\n",
    "What are `x` and `y`? They are the variable names in the library function in matplotlib where we ended up, so probably also maybe not immediately obvious what they are. But we can see more about the problem: it is complaining that two of the variables do not have the same shape. \n",
    "\n",
    "If we look up at the line in our code that triggered the error, we can see that we have supplied two arguments that have a different number of elements: `plt.plot([1,2], [1,2,3])`\n",
    "\n",
    "It would seem that both the first and second variables of the `plot` function should have the same number of elements. Indeed, if we try:\n",
    "\n",
    "`plt.plot([1,2,3], [1,2,3,])`\n",
    "\n",
    "then the error goes away:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot([1,2,3], [1,2,3,])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning objectives list\n",
    "\n",
    "Not crucial since this notebook is optional, but maybe useful to have.\n",
    "\n",
    "**Learning objectives for this notebook:**\n",
    "\n",
    "* Student is able to create and index tuples and lists by hand and using the `range()` operator\n",
    "* Student is able to loop over tuples and lists without indexing\n",
    "* Student is able to extract subsets of lists and tuples using slicing\n",
    "* Student is able to change individual entries of a list using indexing and the assignment operator\n",
    "* Student is able to use built-in functions of lists \n",
    "* Student is able to use indexing to extract substrings from a string\n",
    "* Student is able to use built-in string functions\n",
    "* Student is able to split a string into a list of strings using the `.split()` function\n",
    "* Student is able to search in strings using the `in` operator\n",
    "* Student is able to use formating and the `%` opereator to control how variables are translated into strings\n",
    "* Student is able to predict how variables behave differently for \"mutable\" and \"non-mutable\" objects (call-by-value vs. call-by-reference)\n",
    "* Student is able to use the `ipywidgets` `interact()` function to explore functions using sliders\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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