Lesson6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Computational Methods**\n",
    "## **Interpolation**\n",
    "\n",
    "Written by Niv Keren, nivkeren1@mail.tau.ac.il \n",
    "\n",
    "*Computational Methods* class: 0341-2300\n",
    "\n",
    "2020/Semester I; Tuesdays 14:00-16:00\n",
    "\n",
    "FACULTY OF EXACT SCIENCES | GEOPHYSICS & PLANETARY SCIENCES  \n",
    "Tel Aviv University\n",
    "\n",
    "---\n",
    "## **SciPy**\n",
    "a Python library used for scientific computing and technical computing.  \n",
    "SciPy contains modules for *optimization, linear algebra, integration, interpolation, special functions, FFT,  \n",
    "signal and image processing, ODE solvers and other* tasks common in science and engineering.\n",
    "\n",
    "SciPy builds on the NumPy array object and is part of the NumPy stack which includes tools like Matplotlib,  \n",
    "pandas and SymPy, and an expanding set of scientific computing libraries. [(from wikipedia)](https://en.wikipedia.org/wiki/SciPy)\n",
    "\n",
    "---\n",
    "to refresh your memory about interpolation maybe you'd like to browse this wikipedia entry: [(from wikipedia)](https://en.wikipedia.org/wiki/Interpolation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [15, 6.67]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    "Python's function `interp` receives as input x and y values of functions at certain locations,  \n",
    "and it interpolates them to get the values in other locations that are specified.   \n",
    "Methods of interpolation go from *nearest neighbor*, through *linear interpolation* to *cubic interpolation*.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calulate the sine function at 60 points between\n",
    "0 and 2*pi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.linspace(0, 2 * np.pi, 60);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also sample this function at a much coarser\n",
    "sampling - **only six points** on the same interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x2 = np.linspace(0, 2 * np.pi, 6);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's see the nice plot, of the fine sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1, np.sin(x1), '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see the coarse sampling. The function 'plot'\n",
    "simply connects the points with straight lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2, np.sin(x2), '--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Now let's interpolate.**\n",
    "The function `interp1d()` gets the available points (here, the six points)\n",
    "and then the new x points where the function should be interpolated.  \n",
    "By default the interpolation method is **linear**, i.e., straight lines simply connect\n",
    "the points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f1 = interp1d(x=x2, y=np.sin(x2), kind='linear')\n",
    "z1 = f1(x1)\n",
    "plt.plot(x1, z1, 'C2.')\n",
    "plt.plot(x2, np.sin(x2), 'C1o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Nearest neighbor** - interpolation simply takes the\n",
    "value of the nearest point (along x diretion)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f2 = interp1d(x=x2, y=np.sin(x2), kind='nearest')\n",
    "z2 = f2(x1)\n",
    "plt.plot(x1, z1, 'C2.')\n",
    "plt.plot(x1, z2, 'C3o-')\n",
    "plt.plot(x2, np.sin(x2), 'C1o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Spline interpolation** connects the points with polynomials so that both the function and its\n",
    "derivatives are continuous.  \n",
    "It's very good for very well-behaved, smooth functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f3 = interp1d(x=x2, y=np.sin(x2), kind='cubic')\n",
    "z3 = f3(x1)\n",
    "plt.plot(x1, z1, 'C2.')\n",
    "plt.plot(x1, z3, 'C4.')\n",
    "plt.plot(x2, np.sin(x2), 'C1o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Another example for interpolation**  \n",
    "The human hearing threshold as a function of the frequency.  \n",
    "The arrays *hz.npy* and *sql.hz* (attached) defines the minimum sound pressure level that the human ear is sensitive to.  \n",
    "* Hz - frequencies (in Hertz)\n",
    "* spl - minimal sound pressure level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hz = np.load(\"files/hz.npy\")\n",
    "spl = np.load(\"files/spl.npy\")\n",
    "\n",
    "plt.plot(hz, spl, 'o-')\n",
    "plt.xlabel('[Hz]')\n",
    "plt.ylabel('sound pressure level')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the nature of the x-axis data, it is better to use logarithmic scale only on this axis.  \n",
    "This is obtained by plotting with `semilogx` instead of 'plot'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogx(hz, spl, 'o-')\n",
    "\n",
    "plt.grid(which=\"both\")\n",
    "plt.xlabel('[Hz]')\n",
    "plt.ylabel('sound pressure level')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a good opportunity to introduce also the function **`loglog()`** which plots in logarithmic scale for both x and y.  \n",
    "In this case, since there are negative y values, it will not plot the negative values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(hz, spl, '-o')\n",
    "\n",
    "\n",
    "plt.grid(which=\"both\")\n",
    "plt.xlabel('[Hz]')\n",
    "plt.ylabel('sound pressure level')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to estimate the value of SPL at the\n",
    "frequency 2500 Hz, we can interpolate.  \n",
    "The notation 2.5e3 means 2.5*10^3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spl(2500.0) = -5.5\n"
     ]
    }
   ],
   "source": [
    "spl_linear = interp1d(hz, spl, kind='linear')\n",
    "x = 2.5e3\n",
    "print(f'spl({x}) = {spl_linear(x)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may believe that *spline* will give a better interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spl(2500.0) = -5.868997926788573\n"
     ]
    }
   ],
   "source": [
    "spl_spline = interp1d(hz, spl, kind='cubic')\n",
    "print(f'spl({x}) = {spl_spline(x)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look more closely at the interval between 2000 Hz and 5000 Hz, \n",
    "by interpolating at 100 points between those values.  \n",
    "Let's compare (visually) linear and spline interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x480.24 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hzi = np.linspace(2000,5000, 100) \n",
    "spli = spl_spline(hzi)\n",
    "\n",
    "fig, axs = plt.subplots(1, 2)\n",
    "axs[0].semilogx(hz, spl, 'ro-')\n",
    "axs[0].semilogx(hzi, spli, 'k--')\n",
    "axs[1].plot(hzi, spli, 'k--')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can estimate where the smallest point is.  \n",
    "The accuracy of the value we get depends on how much the interpolation is accurate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8.424551422777906"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(spli)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usually we think of the function 'min' as such that simply gives us the value of 'y' at the minimum.  \n",
    "It only goes over the vector it gets as input and \n",
    "finds the smallest one (no interpolation). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "spl_min = np.min(spli)\n",
    "spl_min_idx = np.argmin(spli)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`idx` is not the x (in this case Hzi) value, but the location in the vector (index)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3333.3333333333335"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hzi[spl_min_idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## **Sorting**\n",
    " \n",
    "Sorting is the action of rearranging the numbers in a vector either in ascending or descending order. \n",
    "\n",
    "To demonstrate sorting we will use the function `np.random.permutation()`. This function gets as input a natural number.   \n",
    "It outputs a vector with all the natural numbers up to the input value, at a random order (no number repeats itself!)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 6, 0, 8, 2, 4, 5, 7, 3, 9])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.permutation(10)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function 'sort' simply sorts the input vector in an ascending order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = np.sort(x)\n",
    "xs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to sort the numbers in descending order we need to flip the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs_rev = xs[: : -1]\n",
    "xs_rev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can sort a multiple dimentions array by a certain axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3, 94,  1, 88, 22],\n",
       "       [82, 29, 18, 54,  2],\n",
       "       [73, 86, 98, 56,  5],\n",
       "       [92, 46, 89, 66,  3],\n",
       "       [ 4,  1, 36, 95,  6]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx = np.random.randint(0, 100, size=(5, 5))\n",
    "xx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  3, 22, 88, 94],\n",
       "       [ 2, 18, 29, 54, 82],\n",
       "       [ 5, 56, 73, 86, 98],\n",
       "       [ 3, 46, 66, 89, 92],\n",
       "       [ 1,  4,  6, 36, 95]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx.sort(axis=1) #sort each line separately\n",
    "xx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also sort a Data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mountain Peak</th>\n",
       "      <th>Mountain Range</th>\n",
       "      <th>Elevation_ft</th>\n",
       "      <th>fourteener</th>\n",
       "      <th>Prominence_ft</th>\n",
       "      <th>Isolation_mi</th>\n",
       "      <th>Lat</th>\n",
       "      <th>Long</th>\n",
       "      <th>Standard Route</th>\n",
       "      <th>Distance_mi</th>\n",
       "      <th>Elevation Gain_ft</th>\n",
       "      <th>Difficulty</th>\n",
       "      <th>Traffic Low</th>\n",
       "      <th>Traffic High</th>\n",
       "      <th>photo</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Mount Elbert</td>\n",
       "      <td>Sawatch Range</td>\n",
       "      <td>14440</td>\n",
       "      <td>Y</td>\n",
       "      <td>9093</td>\n",
       "      <td>670.00</td>\n",
       "      <td>39.1178</td>\n",
       "      <td>-106.4454</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>9.50</td>\n",
       "      <td>4700</td>\n",
       "      <td>Class 1</td>\n",
       "      <td>20000</td>\n",
       "      <td>25000</td>\n",
       "      <td>https://www.14ers.com/photos/mtelbert/peakphot...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Mount Massive</td>\n",
       "      <td>Sawatch Range</td>\n",
       "      <td>14428</td>\n",
       "      <td>Y</td>\n",
       "      <td>1961</td>\n",
       "      <td>5.06</td>\n",
       "      <td>39.1875</td>\n",
       "      <td>-106.4757</td>\n",
       "      <td>East Slopes</td>\n",
       "      <td>14.50</td>\n",
       "      <td>4500</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>7000</td>\n",
       "      <td>10000</td>\n",
       "      <td>https://www.14ers.com/photos/mtmassive/peakpho...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Mount Harvard</td>\n",
       "      <td>Sawatch Range</td>\n",
       "      <td>14421</td>\n",
       "      <td>Y</td>\n",
       "      <td>2360</td>\n",
       "      <td>14.93</td>\n",
       "      <td>38.9244</td>\n",
       "      <td>-106.3207</td>\n",
       "      <td>South Slopes</td>\n",
       "      <td>14.00</td>\n",
       "      <td>4600</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>5000</td>\n",
       "      <td>7000</td>\n",
       "      <td>https://www.14ers.com/photos/harvardgroup/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Blanca Peak</td>\n",
       "      <td>Sangre de Cristo Range</td>\n",
       "      <td>14351</td>\n",
       "      <td>Y</td>\n",
       "      <td>5326</td>\n",
       "      <td>103.40</td>\n",
       "      <td>37.5775</td>\n",
       "      <td>-105.4856</td>\n",
       "      <td>Northwest Ridge</td>\n",
       "      <td>17.00</td>\n",
       "      <td>6500</td>\n",
       "      <td>Hard Class 2</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/blancagroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>La Plata Peak</td>\n",
       "      <td>Sawatch Range</td>\n",
       "      <td>14343</td>\n",
       "      <td>Y</td>\n",
       "      <td>1836</td>\n",
       "      <td>6.28</td>\n",
       "      <td>39.0294</td>\n",
       "      <td>-106.4729</td>\n",
       "      <td>Northwest Ridge</td>\n",
       "      <td>9.25</td>\n",
       "      <td>4500</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>5000</td>\n",
       "      <td>7000</td>\n",
       "      <td>https://www.14ers.com/photos/laplatapeak/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>Uncompahgre Peak</td>\n",
       "      <td>San Juan Mountains</td>\n",
       "      <td>14321</td>\n",
       "      <td>Y</td>\n",
       "      <td>4277</td>\n",
       "      <td>85.10</td>\n",
       "      <td>38.0717</td>\n",
       "      <td>-107.4621</td>\n",
       "      <td>South Ridge</td>\n",
       "      <td>7.50</td>\n",
       "      <td>3000</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>3000</td>\n",
       "      <td>5000</td>\n",
       "      <td>https://www.14ers.com/photos/uncompahgrepeak/p...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>Crestone Peak</td>\n",
       "      <td>Sangre de Cristo Range</td>\n",
       "      <td>14300</td>\n",
       "      <td>Y</td>\n",
       "      <td>4554</td>\n",
       "      <td>27.40</td>\n",
       "      <td>37.9669</td>\n",
       "      <td>-105.5855</td>\n",
       "      <td>South Face</td>\n",
       "      <td>14.00</td>\n",
       "      <td>5700</td>\n",
       "      <td>Class 3</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/crestonegroup/pea...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>Mount Lincoln</td>\n",
       "      <td>Mosquito Range</td>\n",
       "      <td>14293</td>\n",
       "      <td>Y</td>\n",
       "      <td>3862</td>\n",
       "      <td>22.60</td>\n",
       "      <td>39.3515</td>\n",
       "      <td>-106.1116</td>\n",
       "      <td>West Ridge</td>\n",
       "      <td>6.00</td>\n",
       "      <td>2600</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>15000</td>\n",
       "      <td>20000</td>\n",
       "      <td>https://www.14ers.com/photos/lincolngroup/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>Castle Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14279</td>\n",
       "      <td>Y</td>\n",
       "      <td>2365</td>\n",
       "      <td>20.90</td>\n",
       "      <td>39.0097</td>\n",
       "      <td>-106.8614</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>13.50</td>\n",
       "      <td>4600</td>\n",
       "      <td>Hard Class 2</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/castlegroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>Grays Peak</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14278</td>\n",
       "      <td>Y</td>\n",
       "      <td>2770</td>\n",
       "      <td>25.00</td>\n",
       "      <td>39.6339</td>\n",
       "      <td>-105.8176</td>\n",
       "      <td>North Slopes</td>\n",
       "      <td>8.00</td>\n",
       "      <td>3000</td>\n",
       "      <td>Class 1</td>\n",
       "      <td>25000</td>\n",
       "      <td>30000</td>\n",
       "      <td>https://www.14ers.com/photos/graystorreys/peak...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mountain Peak          Mountain Range  Elevation_ft fourteener  \\\n",
       "ID                                                                      \n",
       "1       Mount Elbert           Sawatch Range         14440          Y   \n",
       "2      Mount Massive           Sawatch Range         14428          Y   \n",
       "3      Mount Harvard           Sawatch Range         14421          Y   \n",
       "4        Blanca Peak  Sangre de Cristo Range         14351          Y   \n",
       "5      La Plata Peak           Sawatch Range         14343          Y   \n",
       "6   Uncompahgre Peak      San Juan Mountains         14321          Y   \n",
       "7      Crestone Peak  Sangre de Cristo Range         14300          Y   \n",
       "8      Mount Lincoln          Mosquito Range         14293          Y   \n",
       "9        Castle Peak           Elk Mountains         14279          Y   \n",
       "10        Grays Peak             Front Range         14278          Y   \n",
       "\n",
       "    Prominence_ft  Isolation_mi      Lat      Long    Standard Route  \\\n",
       "ID                                                                     \n",
       "1            9093        670.00  39.1178 -106.4454  Northeast Ridge    \n",
       "2            1961          5.06  39.1875 -106.4757      East Slopes    \n",
       "3            2360         14.93  38.9244 -106.3207     South Slopes    \n",
       "4            5326        103.40  37.5775 -105.4856  Northwest Ridge    \n",
       "5            1836          6.28  39.0294 -106.4729  Northwest Ridge    \n",
       "6            4277         85.10  38.0717 -107.4621      South Ridge    \n",
       "7            4554         27.40  37.9669 -105.5855       South Face    \n",
       "8            3862         22.60  39.3515 -106.1116       West Ridge    \n",
       "9            2365         20.90  39.0097 -106.8614  Northeast Ridge    \n",
       "10           2770         25.00  39.6339 -105.8176     North Slopes    \n",
       "\n",
       "    Distance_mi  Elevation Gain_ft    Difficulty  Traffic Low  Traffic High  \\\n",
       "ID                                                                            \n",
       "1          9.50               4700       Class 1        20000         25000   \n",
       "2         14.50               4500       Class 2         7000         10000   \n",
       "3         14.00               4600       Class 2         5000          7000   \n",
       "4         17.00               6500  Hard Class 2         1000          3000   \n",
       "5          9.25               4500       Class 2         5000          7000   \n",
       "6          7.50               3000       Class 2         3000          5000   \n",
       "7         14.00               5700       Class 3         1000          3000   \n",
       "8          6.00               2600       Class 2        15000         20000   \n",
       "9         13.50               4600  Hard Class 2         1000          3000   \n",
       "10         8.00               3000       Class 1        25000         30000   \n",
       "\n",
       "                                                photo  \n",
       "ID                                                     \n",
       "1   https://www.14ers.com/photos/mtelbert/peakphot...  \n",
       "2   https://www.14ers.com/photos/mtmassive/peakpho...  \n",
       "3   https://www.14ers.com/photos/harvardgroup/peak...  \n",
       "4   https://www.14ers.com/photos/blancagroup/peakp...  \n",
       "5   https://www.14ers.com/photos/laplatapeak/peakp...  \n",
       "6   https://www.14ers.com/photos/uncompahgrepeak/p...  \n",
       "7   https://www.14ers.com/photos/crestonegroup/pea...  \n",
       "8   https://www.14ers.com/photos/lincolngroup/peak...  \n",
       "9   https://www.14ers.com/photos/castlegroup/peakp...  \n",
       "10  https://www.14ers.com/photos/graystorreys/peak...  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "peaks_df = pd.read_csv(\"files/14er.csv\", encoding='ISO-8859-1').set_index(\"ID\")\n",
    "peaks_df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can choose by witch column to sort.  \n",
    "Let sort the peaks bt the busiest peaks from the most to least (decending order)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Mountain Peak</th>\n",
       "      <th>Mountain Range</th>\n",
       "      <th>Elevation_ft</th>\n",
       "      <th>fourteener</th>\n",
       "      <th>Prominence_ft</th>\n",
       "      <th>Isolation_mi</th>\n",
       "      <th>Lat</th>\n",
       "      <th>Long</th>\n",
       "      <th>Standard Route</th>\n",
       "      <th>Distance_mi</th>\n",
       "      <th>Elevation Gain_ft</th>\n",
       "      <th>Difficulty</th>\n",
       "      <th>Traffic Low</th>\n",
       "      <th>Traffic High</th>\n",
       "      <th>photo</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>38</td>\n",
       "      <td>Mount Bierstadt</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14065</td>\n",
       "      <td>Y</td>\n",
       "      <td>720</td>\n",
       "      <td>1.12</td>\n",
       "      <td>39.582600</td>\n",
       "      <td>-105.668800</td>\n",
       "      <td>West Slopes</td>\n",
       "      <td>7.00</td>\n",
       "      <td>2850</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>35000</td>\n",
       "      <td>40000</td>\n",
       "      <td>https://www.14ers.com/photos/evansgroup/peakph...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>Torreys Peak</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14275</td>\n",
       "      <td>Y</td>\n",
       "      <td>560</td>\n",
       "      <td>0.65</td>\n",
       "      <td>39.642800</td>\n",
       "      <td>-105.821200</td>\n",
       "      <td>South Slopes</td>\n",
       "      <td>8.00</td>\n",
       "      <td>3000</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>25000</td>\n",
       "      <td>30000</td>\n",
       "      <td>https://www.14ers.com/photos/graystorreys/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>Grays Peak</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14278</td>\n",
       "      <td>Y</td>\n",
       "      <td>2770</td>\n",
       "      <td>25.00</td>\n",
       "      <td>39.633900</td>\n",
       "      <td>-105.817600</td>\n",
       "      <td>North Slopes</td>\n",
       "      <td>8.00</td>\n",
       "      <td>3000</td>\n",
       "      <td>Class 1</td>\n",
       "      <td>25000</td>\n",
       "      <td>30000</td>\n",
       "      <td>https://www.14ers.com/photos/graystorreys/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Mount Elbert</td>\n",
       "      <td>Sawatch Range</td>\n",
       "      <td>14440</td>\n",
       "      <td>Y</td>\n",
       "      <td>9093</td>\n",
       "      <td>670.00</td>\n",
       "      <td>39.117800</td>\n",
       "      <td>-106.445400</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>9.50</td>\n",
       "      <td>4700</td>\n",
       "      <td>Class 1</td>\n",
       "      <td>20000</td>\n",
       "      <td>25000</td>\n",
       "      <td>https://www.14ers.com/photos/mtelbert/peakphot...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>45</td>\n",
       "      <td>Mount Sherman</td>\n",
       "      <td>Mosquito Range</td>\n",
       "      <td>14043</td>\n",
       "      <td>Y</td>\n",
       "      <td>850</td>\n",
       "      <td>8.06</td>\n",
       "      <td>39.225000</td>\n",
       "      <td>-106.169900</td>\n",
       "      <td>Southwest Ridge</td>\n",
       "      <td>5.25</td>\n",
       "      <td>2100</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>20000</td>\n",
       "      <td>25000</td>\n",
       "      <td>https://www.14ers.com/photos/mtsherman/peakpho...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>Quandary Peak</td>\n",
       "      <td>Mosquito Range</td>\n",
       "      <td>14271</td>\n",
       "      <td>Y</td>\n",
       "      <td>1125</td>\n",
       "      <td>3.16</td>\n",
       "      <td>39.397300</td>\n",
       "      <td>-106.106400</td>\n",
       "      <td>East Ridge</td>\n",
       "      <td>6.75</td>\n",
       "      <td>3450</td>\n",
       "      <td>Class 1</td>\n",
       "      <td>20000</td>\n",
       "      <td>25000</td>\n",
       "      <td>https://www.14ers.com/photos/quandarypeak/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>54</td>\n",
       "      <td>Mt. Cameron</td>\n",
       "      <td>Mosquito Range</td>\n",
       "      <td>14238</td>\n",
       "      <td>N</td>\n",
       "      <td>158</td>\n",
       "      <td>0.48</td>\n",
       "      <td>39.347165</td>\n",
       "      <td>-106.118501</td>\n",
       "      <td>West Ridge</td>\n",
       "      <td>4.75</td>\n",
       "      <td>2250</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>15000</td>\n",
       "      <td>20000</td>\n",
       "      <td>https://www.14ers.com/photos/lincolngroup/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>28</td>\n",
       "      <td>Mount Democrat</td>\n",
       "      <td>Mosquito Range</td>\n",
       "      <td>14155</td>\n",
       "      <td>Y</td>\n",
       "      <td>768</td>\n",
       "      <td>1.27</td>\n",
       "      <td>39.339600</td>\n",
       "      <td>-106.140000</td>\n",
       "      <td>East Slope</td>\n",
       "      <td>4.00</td>\n",
       "      <td>2150</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>15000</td>\n",
       "      <td>20000</td>\n",
       "      <td>https://www.14ers.com/photos/lincolngroup/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>Mount Bross</td>\n",
       "      <td>Mosquito Range</td>\n",
       "      <td>14178</td>\n",
       "      <td>Y</td>\n",
       "      <td>312</td>\n",
       "      <td>0.99</td>\n",
       "      <td>39.335400</td>\n",
       "      <td>-106.107700</td>\n",
       "      <td>West Slopes</td>\n",
       "      <td>3.25</td>\n",
       "      <td>2250</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>15000</td>\n",
       "      <td>20000</td>\n",
       "      <td>https://www.14ers.com/photos/lincolngroup/peak...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>Longs Peak</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14259</td>\n",
       "      <td>Y</td>\n",
       "      <td>2940</td>\n",
       "      <td>43.60</td>\n",
       "      <td>40.255000</td>\n",
       "      <td>-105.615100</td>\n",
       "      <td>Keyhole Route</td>\n",
       "      <td>14.50</td>\n",
       "      <td>5100</td>\n",
       "      <td>Class 3</td>\n",
       "      <td>15000</td>\n",
       "      <td>20000</td>\n",
       "      <td>https://www.14ers.com/photos/longspeak/peakpho...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Mountain Peak  Mountain Range  Elevation_ft fourteener  Prominence_ft  \\\n",
       "ID                                                                            \n",
       "38  Mount Bierstadt     Front Range         14065          Y            720   \n",
       "12     Torreys Peak     Front Range         14275          Y            560   \n",
       "10       Grays Peak     Front Range         14278          Y           2770   \n",
       "1      Mount Elbert   Sawatch Range         14440          Y           9093   \n",
       "45    Mount Sherman  Mosquito Range         14043          Y            850   \n",
       "13    Quandary Peak  Mosquito Range         14271          Y           1125   \n",
       "54      Mt. Cameron  Mosquito Range         14238          N            158   \n",
       "28   Mount Democrat  Mosquito Range         14155          Y            768   \n",
       "22      Mount Bross  Mosquito Range         14178          Y            312   \n",
       "15       Longs Peak     Front Range         14259          Y           2940   \n",
       "\n",
       "    Isolation_mi        Lat        Long    Standard Route  Distance_mi  \\\n",
       "ID                                                                       \n",
       "38          1.12  39.582600 -105.668800      West Slopes          7.00   \n",
       "12          0.65  39.642800 -105.821200     South Slopes          8.00   \n",
       "10         25.00  39.633900 -105.817600     North Slopes          8.00   \n",
       "1         670.00  39.117800 -106.445400  Northeast Ridge          9.50   \n",
       "45          8.06  39.225000 -106.169900  Southwest Ridge          5.25   \n",
       "13          3.16  39.397300 -106.106400       East Ridge          6.75   \n",
       "54          0.48  39.347165 -106.118501       West Ridge          4.75   \n",
       "28          1.27  39.339600 -106.140000       East Slope          4.00   \n",
       "22          0.99  39.335400 -106.107700      West Slopes          3.25   \n",
       "15         43.60  40.255000 -105.615100    Keyhole Route         14.50   \n",
       "\n",
       "    Elevation Gain_ft Difficulty  Traffic Low  Traffic High  \\\n",
       "ID                                                            \n",
       "38               2850    Class 2        35000         40000   \n",
       "12               3000    Class 2        25000         30000   \n",
       "10               3000    Class 1        25000         30000   \n",
       "1                4700    Class 1        20000         25000   \n",
       "45               2100    Class 2        20000         25000   \n",
       "13               3450    Class 1        20000         25000   \n",
       "54               2250    Class 2        15000         20000   \n",
       "28               2150    Class 2        15000         20000   \n",
       "22               2250    Class 2        15000         20000   \n",
       "15               5100    Class 3        15000         20000   \n",
       "\n",
       "                                                photo  \n",
       "ID                                                     \n",
       "38  https://www.14ers.com/photos/evansgroup/peakph...  \n",
       "12  https://www.14ers.com/photos/graystorreys/peak...  \n",
       "10  https://www.14ers.com/photos/graystorreys/peak...  \n",
       "1   https://www.14ers.com/photos/mtelbert/peakphot...  \n",
       "45  https://www.14ers.com/photos/mtsherman/peakpho...  \n",
       "13  https://www.14ers.com/photos/quandarypeak/peak...  \n",
       "54  https://www.14ers.com/photos/lincolngroup/peak...  \n",
       "28  https://www.14ers.com/photos/lincolngroup/peak...  \n",
       "22  https://www.14ers.com/photos/lincolngroup/peak...  \n",
       "15  https://www.14ers.com/photos/longspeak/peakpho...  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "peaks_df.sort_values([\"Traffic High\"], ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also sort by multiple columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID</th>\n",
       "      <th>Mountain Peak</th>\n",
       "      <th>Mountain Range</th>\n",
       "      <th>Elevation_ft</th>\n",
       "      <th>fourteener</th>\n",
       "      <th>Prominence_ft</th>\n",
       "      <th>Isolation_mi</th>\n",
       "      <th>Lat</th>\n",
       "      <th>Long</th>\n",
       "      <th>Standard Route</th>\n",
       "      <th>Distance_mi</th>\n",
       "      <th>Elevation Gain_ft</th>\n",
       "      <th>Difficulty</th>\n",
       "      <th>Traffic Low</th>\n",
       "      <th>Traffic High</th>\n",
       "      <th>photo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>46</td>\n",
       "      <td>47</td>\n",
       "      <td>Pyramid Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14025</td>\n",
       "      <td>Y</td>\n",
       "      <td>1638</td>\n",
       "      <td>2.09</td>\n",
       "      <td>39.071700</td>\n",
       "      <td>-106.950200</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>8.25</td>\n",
       "      <td>4500</td>\n",
       "      <td>Class 4</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/maroongroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>North Maroon Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14014</td>\n",
       "      <td>N</td>\n",
       "      <td>254</td>\n",
       "      <td>0.37</td>\n",
       "      <td>39.076007</td>\n",
       "      <td>-106.987058</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>9.25</td>\n",
       "      <td>4500</td>\n",
       "      <td>Class 4</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/maroongroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>23</td>\n",
       "      <td>24</td>\n",
       "      <td>Maroon Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14163</td>\n",
       "      <td>Y</td>\n",
       "      <td>2336</td>\n",
       "      <td>8.06</td>\n",
       "      <td>39.070800</td>\n",
       "      <td>-106.989000</td>\n",
       "      <td>South ridge</td>\n",
       "      <td>11.50</td>\n",
       "      <td>4800</td>\n",
       "      <td>Class 3</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/maroongroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>Castle Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14279</td>\n",
       "      <td>Y</td>\n",
       "      <td>2365</td>\n",
       "      <td>20.90</td>\n",
       "      <td>39.009700</td>\n",
       "      <td>-106.861400</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>13.50</td>\n",
       "      <td>4600</td>\n",
       "      <td>Hard Class 2</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/castlegroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>Conundrum Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14060</td>\n",
       "      <td>N</td>\n",
       "      <td>280</td>\n",
       "      <td>0.40</td>\n",
       "      <td>39.015682</td>\n",
       "      <td>-106.862749</td>\n",
       "      <td>Via Castle Peak</td>\n",
       "      <td>14.50</td>\n",
       "      <td>4850</td>\n",
       "      <td>Hard Class 2</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/castlegroup/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>Capitol Peak</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14137</td>\n",
       "      <td>Y</td>\n",
       "      <td>1750</td>\n",
       "      <td>7.44</td>\n",
       "      <td>39.150300</td>\n",
       "      <td>-107.082900</td>\n",
       "      <td>Northeast Ridge</td>\n",
       "      <td>17.00</td>\n",
       "      <td>5300</td>\n",
       "      <td>Class 4</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/capitolpeak/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>Snowmass Mountain</td>\n",
       "      <td>Elk Mountains</td>\n",
       "      <td>14099</td>\n",
       "      <td>Y</td>\n",
       "      <td>1152</td>\n",
       "      <td>2.34</td>\n",
       "      <td>39.118800</td>\n",
       "      <td>-107.066500</td>\n",
       "      <td>East Slopes</td>\n",
       "      <td>22.00</td>\n",
       "      <td>5800</td>\n",
       "      <td>Hard Class 3</td>\n",
       "      <td>1000</td>\n",
       "      <td>3000</td>\n",
       "      <td>https://www.14ers.com/photos/snowmassmtn/peakp...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>Mount Evans</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14271</td>\n",
       "      <td>Y</td>\n",
       "      <td>2770</td>\n",
       "      <td>9.79</td>\n",
       "      <td>39.588300</td>\n",
       "      <td>-105.643800</td>\n",
       "      <td>West Ridge via Mount Spalding</td>\n",
       "      <td>5.00</td>\n",
       "      <td>2000</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>15000</td>\n",
       "      <td>20000</td>\n",
       "      <td>https://www.14ers.com/photos/evansgroup/peakph...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>37</td>\n",
       "      <td>38</td>\n",
       "      <td>Mount Bierstadt</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14065</td>\n",
       "      <td>Y</td>\n",
       "      <td>720</td>\n",
       "      <td>1.12</td>\n",
       "      <td>39.582600</td>\n",
       "      <td>-105.668800</td>\n",
       "      <td>West Slopes</td>\n",
       "      <td>7.00</td>\n",
       "      <td>2850</td>\n",
       "      <td>Class 2</td>\n",
       "      <td>35000</td>\n",
       "      <td>40000</td>\n",
       "      <td>https://www.14ers.com/photos/evansgroup/peakph...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>Grays Peak</td>\n",
       "      <td>Front Range</td>\n",
       "      <td>14278</td>\n",
       "      <td>Y</td>\n",
       "      <td>2770</td>\n",
       "      <td>25.00</td>\n",
       "      <td>39.633900</td>\n",
       "      <td>-105.817600</td>\n",
       "      <td>North Slopes</td>\n",
       "      <td>8.00</td>\n",
       "      <td>3000</td>\n",
       "      <td>Class 1</td>\n",
       "      <td>25000</td>\n",
       "      <td>30000</td>\n",
       "      <td>https://www.14ers.com/photos/graystorreys/peak...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    ID      Mountain Peak Mountain Range  Elevation_ft fourteener  \\\n",
       "46  47       Pyramid Peak  Elk Mountains         14025          Y   \n",
       "57  58  North Maroon Peak  Elk Mountains         14014          N   \n",
       "23  24        Maroon Peak  Elk Mountains         14163          Y   \n",
       "8    9        Castle Peak  Elk Mountains         14279          Y   \n",
       "55  56     Conundrum Peak  Elk Mountains         14060          N   \n",
       "28  29       Capitol Peak  Elk Mountains         14137          Y   \n",
       "30  31  Snowmass Mountain  Elk Mountains         14099          Y   \n",
       "13  14        Mount Evans    Front Range         14271          Y   \n",
       "37  38    Mount Bierstadt    Front Range         14065          Y   \n",
       "9   10         Grays Peak    Front Range         14278          Y   \n",
       "\n",
       "    Prominence_ft  Isolation_mi        Lat        Long  \\\n",
       "46           1638          2.09  39.071700 -106.950200   \n",
       "57            254          0.37  39.076007 -106.987058   \n",
       "23           2336          8.06  39.070800 -106.989000   \n",
       "8            2365         20.90  39.009700 -106.861400   \n",
       "55            280          0.40  39.015682 -106.862749   \n",
       "28           1750          7.44  39.150300 -107.082900   \n",
       "30           1152          2.34  39.118800 -107.066500   \n",
       "13           2770          9.79  39.588300 -105.643800   \n",
       "37            720          1.12  39.582600 -105.668800   \n",
       "9            2770         25.00  39.633900 -105.817600   \n",
       "\n",
       "                    Standard Route  Distance_mi  Elevation Gain_ft  \\\n",
       "46                Northeast Ridge          8.25               4500   \n",
       "57                Northeast Ridge          9.25               4500   \n",
       "23                    South ridge         11.50               4800   \n",
       "8                 Northeast Ridge         13.50               4600   \n",
       "55                Via Castle Peak         14.50               4850   \n",
       "28                Northeast Ridge         17.00               5300   \n",
       "30                    East Slopes         22.00               5800   \n",
       "13  West Ridge via Mount Spalding          5.00               2000   \n",
       "37                    West Slopes          7.00               2850   \n",
       "9                    North Slopes          8.00               3000   \n",
       "\n",
       "      Difficulty  Traffic Low  Traffic High  \\\n",
       "46       Class 4         1000          3000   \n",
       "57       Class 4         1000          3000   \n",
       "23       Class 3         1000          3000   \n",
       "8   Hard Class 2         1000          3000   \n",
       "55  Hard Class 2         1000          3000   \n",
       "28       Class 4         1000          3000   \n",
       "30  Hard Class 3         1000          3000   \n",
       "13       Class 2        15000         20000   \n",
       "37       Class 2        35000         40000   \n",
       "9        Class 1        25000         30000   \n",
       "\n",
       "                                                photo  \n",
       "46  https://www.14ers.com/photos/maroongroup/peakp...  \n",
       "57  https://www.14ers.com/photos/maroongroup/peakp...  \n",
       "23  https://www.14ers.com/photos/maroongroup/peakp...  \n",
       "8   https://www.14ers.com/photos/castlegroup/peakp...  \n",
       "55  https://www.14ers.com/photos/castlegroup/peakp...  \n",
       "28  https://www.14ers.com/photos/capitolpeak/peakp...  \n",
       "30  https://www.14ers.com/photos/snowmassmtn/peakp...  \n",
       "13  https://www.14ers.com/photos/evansgroup/peakph...  \n",
       "37  https://www.14ers.com/photos/evansgroup/peakph...  \n",
       "9   https://www.14ers.com/photos/graystorreys/peak...  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "peaks_df.sort_values([\"Mountain Range\", \"Distance_mi\"]).head(10)"
   ]
  }
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