Prosjekt-1-Gruppe-2-Aleks-Vitalijus -Eric.ipynb

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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#   <u><font color=blue>__Course: Modeling & Computational Engineering (MOD510)__</font></u> \n",
    "##  <font color=blue>Professor: __Aksel Hiorth__ | Aksel.Hiorth@uis.no</font>\n",
    "#### <font color=blue> https://github.com/ahiorth/CompEngineering</font>\n",
    "## ![image.png](attachment:image.png)\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font color=green>Project 1 | MOD510</font> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Name: Aleksander Storhaug Strøm\n",
    "- StudentNr: 239655\n",
    "\n",
    "\n",
    "- Name: Vitalijus Gorbunovas \n",
    "- StudentNr: 261262\n",
    "\n",
    "\n",
    "- Name: Eric Severson\n",
    "- StudentNr:261873"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The purpose of this project is to familiarize ourselves with the geneal application of Python to:\n",
    "- Use standard and community-built Python libraries\n",
    "- Writing custom (user-defined) functions\n",
    "- Trying different approaches for data analysis, i.e. timing native function(s) efficieny vs efficiency of imported packages (numpy)\n",
    "- Understand how round off / numerical error can affect the end result and compare that result to the analytical soluction\n",
    "- Unerstand an example of a physical system such as a gravitation effect on an object\n",
    "- Visualize the data using the matplotlib package in order to better understand the correlation of data in a grapical context\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import from standard library:\n",
    "import pathlib\n",
    "import random\n",
    "\n",
    " # Import other stuff:\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    " # Packages needed for the last part? (uncomment to use):\n",
    "import cmocean\n",
    "import rockhound as rh\n",
    "import xarray as xr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Excercise\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "sys.float_info"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* max=1.7976931348623157e+308 \n",
    "* min=2.2250738585072014e-308  \n",
    "* epsilon=2.220446049250313e-16\n",
    "\n",
    "max is the largest finite + number that can be represented as type (float). Min is the smallest - number rep. by a float, and epsilion is substraction of 1.0 and the smallest number greater than 1.0 still of type (float)\n",
    "\n",
    "https://docs.python.org/3/library/sys.html\n",
    "\n",
    "- Describes the maximum AND minimum expontential power min_exp=-1021 and max_exp=1024, a computer-driven system may have to compute the the maximum and minimum value a computed value can have whereas max=1.7976...e+308 and min=2.2250...e-308. \n",
    "- Max_10_exp=308 and min_10_exp=-308 represents the maximum and minimum values these power exponents to the global max and min values can have. \n",
    "- The mant_dig=53 informs how many fractionalbits of the system(in this case 64 bits) which can be utilizied in computing fractional values.\n",
    "\n",
    "- To obtain the epsilon calculation you will have to use only the fractional bits of the system therefore \n",
    " - `Epsilon=print(2**(-52)) =2.220446049250313e-16`\n",
    "- To obtain maximum value you have to utilize the formula =1.F*2**(E-1023). 1023 is derived by in 64bit system by 2**11-1=1023\n",
    "  - `Max=2**1023`\n",
    "  - `bit=2-2**(-52)`\n",
    "  - `y=Max*bit = 1.7976931348623157e+308 `\n",
    "\n",
    "- To obtain minimuim value use similar procedure just towards negative infinte direction. Exponent 1022 is obtain by 2**(F-1023),\n",
    " - hence that F=1\n",
    " - `Min=2**(-1022)`\n",
    " - `print(Min) = 2.2250738585072014e-308`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is a=1 equal to b=1.0?: True.\n"
     ]
    }
   ],
   "source": [
    "a = 1\n",
    "b = a/30\n",
    "b *= 30\n",
    "print('Is a={} equal to b={}?: {}.'.format(a, b, a==b))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`a` is integer, therefore printed without decimal point\n",
    "\n",
    "`b` is float, therefore printed with decimal point\n",
    "\n",
    "`a==b` compares the values of `a` and `b` regardless of data type\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Is a=1 equal to b=1.0?: True.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1\n",
    "b = a/30\n",
    "b *= 30\n",
    "print('Is a={} equal to b={}?: {}.'.format(a, b, a==b))\n",
    "\n",
    "#Correction\n",
    "def isclose(a,b,rel_tol=1e-09,abs_tol=0.0):\n",
    "    return abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)\n",
    "\n",
    "isclose(a,b)\n",
    "\n",
    "# This function utilizes a more precise degree of comparison to determine if A and B are in fact equal,\n",
    "# and thus returns true. This is contingent on the value \"rel_tol\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Since numbers are stored in binary format, it is not possible to represent some decimal value(s) correctly as binary numbers due to a limited precision.\n",
    "\n",
    "When adding `0.1` and `0.2`, the differences in these two numbers' binary representation amounts to being slightly different from `0.3`.\n",
    "\n",
    "In this case, `0.1 + 0.2` is equal to `0.30000000000000004`.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Excercise 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.8 µs ± 795 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "11.1 µs ± 1.67 µs per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "4.43 µs ± 233 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
      "39.9 µs ± 1.03 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random \n",
    "def draw_random_values_using_for_loop(list_of_numbers, N):\n",
    "    drawn = []\n",
    "    for i in range(N):\n",
    "        drawn.append(random.choice(list_of_numbers))\n",
    "    return drawn\n",
    "def draw_random_values_using_list_comprehension(list_of_numbers, N):\n",
    "    return [random.choice(list_of_numbers) for _ in range(N)]\n",
    "N = 10\n",
    "M = 3\n",
    "list_of_numbers = [i+1 for i in range(M)]\n",
    "%timeit draw_random_values_using_for_loop(list_of_numbers, N)\n",
    "%timeit draw_random_values_using_list_comprehension(list_of_numbers, N)\n",
    "%timeit random.choices(list_of_numbers, k=N)\n",
    "%timeit np.random.choice(list_of_numbers, size=N)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A: In the code we choose 10 random values from the non-empty array [1, 2, 3] with 4 different approaches. The efficiency (execution time) of each approach is measured using timeit module.\n",
    "\n",
    "Even the slowest approach with native `random` module outperforms the `numpy.random` implementation at a low iteration interval.\n",
    "\n",
    "When comparing 3 aproaches with the native `random` module, it is obvious that utilizing the `choises` method has advantage over 2 user-defined functions, that use `range` to iterate through random picks `N`. When this functions are transistion over to a higher iteration interval, it becomes clear that `np.random.choice` is the most efficient function to work with high number of iterations (M=3000 & N=10000). However, `random.choices` is excellent in low iteration intervals.\n",
    "\n",
    "- M=3 & N= 10\n",
    " - draw_random_values_using_for_loop= 14.3 µs ± 1.18 µs per loop. \n",
    " - draw_random_values_using_list_comprehension= 13.4 µs ± 290 ns per loo\n",
    " - random.choices(list_of_numbers, k=N)= 6.55 µs ± 65.8 ns per loop  \n",
    " - np.random.choice(list_of_numbers, size=N)= 56.5 µs ± 4.7 µs per loop \n",
    "- M=30 & N=100\n",
    " - draw_random_values_using_for_loop= 133 µs ± 15 µs per loop\n",
    " - draw_random_values_using_list_comprehension= 116 µs ± 1.58 µs per loo\n",
    " - random.choices(list_of_numbers, k=N)= 44.5 µs ± 1.33 µs per loop \n",
    " - np.random.choice(list_of_numbers, size=N)= 64.1 µs ± 5.07 µs per loop\n",
    "- M=300 & N=1000\n",
    " - draw_random_values_using_for_loop= 1.44 ms ± 20.8 µs per loop\n",
    " - draw_random_values_using_list_comprehension= 1.4 ms ± 99.7 µs per loo\n",
    " - random.choices(list_of_numbers, k=N)= 432 µs ± 8.41 µs per loop\n",
    " - np.random.choice(list_of_numbers, size=N)=  159 µs ± 19.6 µs per loop\n",
    "- M=3000 & N=10000\n",
    " - draw_random_values_using_for_loop= 14.8 ms ± 791 µs per loop \n",
    " - draw_random_values_using_list_comprehension= 14.1 ms ± 1.53 ms per lo\n",
    " - random.choices(list_of_numbers, k=N)=  4.41 ms ± 149 µs per loop\n",
    " - np.random.choice(list_of_numbers, size=N)= 880 µs ± 20.2 µs per loop "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "index = np.arange(1000)\n",
    "array_of_zeros = np.zeros(20)\n",
    "array_of_ones = np.ones(20)\n",
    "evenly_spaced_numbers = np.linspace(0, 10, 11)\n",
    "evenly_spaced_numbers2  = np.linspace(0, 10, 11, endpoint=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q: Explain each of the above commands.\n",
    "\n",
    "A:\n",
    "\n",
    "`index = np.arange(1000)` produces an array of `1000` evenly spaced integers, starting at `0` and step equal to `1`, i.e. `[0, 1, ..., 998, 999]`;\n",
    "\n",
    "`array_of_zeros = np.zeros(20)` produces an array of `20` zeros. Default type of produced values is `float`;\n",
    "\n",
    "`array_of_ones = np.ones(20)` produces an array of `20` ones. Default type of produced values is `float`;\n",
    "\n",
    "`evenly_spaced_numbers = np.linspace(0, 10, 11)` produces an array of `11` evenly spaced numbers, starting at `0` and ending at `10`; \n",
    "\n",
    "`evenly_spaced_numbers2 = np.linspace(0, 10, 11, endpoint=False)` produces an array of `11` evenly spaced numbers, starting at `0` and ending at `10`, however `10` (last sample) is not included;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q: How would you go about doing the same things with native Python lists?\n",
    "\n",
    "A: Using `range` function or `while`/`for` loops;\n",
    "\n",
    "The following is an example of custom implementaion of the `np.arange` method.\n",
    "\n",
    "Note: We are not handling default values for `start` and `step`, therefore `start`, `stop` and `step` must be provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def custom_arange_using_while_loop(start, stop, step):\n",
    "    result = []\n",
    "    while start < stop:\n",
    "        result.append(start)\n",
    "        start += step\n",
    "    return result\n",
    "\n",
    "custom_arange_using_while_loop(0, 10, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1]\n",
      "[8]\n"
     ]
    }
   ],
   "source": [
    "example_array = np.array([1, 1, 2, 3, 5, 8, 13, 21, 34])\n",
    "\n",
    "idx_of_ones = np.where(example_array == 1)\n",
    "print(example_array[idx_of_ones])\n",
    "is_equal_to_eight = (example_array == 8)\n",
    "print(example_array[is_equal_to_eight])\n",
    "new_example_array = np.where(example_array == 1, example_array, 0)\n",
    "random_ndim = np.random.randint(100, size=(5,5))\n",
    "nnz = np.count_nonzero(random_ndim)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q: Explain what each line of code does.\n",
    "\n",
    "A: \n",
    "\n",
    "`idx_of_ones = np.where(example_array == 1)` produces an array with indices of matched value, i.e. indices of `1` in the `example_array` array; The resulting array of indices is `[0, 1]`;\n",
    "\n",
    "`print(example_array[idx_of_ones])` prints a portion (a slice?) of `example_array` array, where indices of the `example_array` array match with the values provided in `idx_of_ones` array;\n",
    "\n",
    "`is_equal_to_eight = (example_array == 8)` produces an array of `True` and `False` values, where length of the array is equal to the length of `example_array` array; What value will be in each position in the new array is determined by comparing each value in the `example_array` array with the test value `8`. If values are equal, then we `True` will be the value in the same position of the new array;\n",
    "\n",
    "`print(example_array[is_equal_to_eight])` prints a portion (a slice?) of `example_array` array, where values of the `is_equal_to_eight` array are equal to `True`;\n",
    "\n",
    "`new_example_array = np.where(example_array == 1, example_array, 0)` produces an array with values from the `example_array` array when value equals `1`, otherwise value is set to `0`;\n",
    "\n",
    "`random_mdim = np.random.randint(100, size=(5,5))` produces a 2-dimentional array; The length of the array is equal to `5`, i.e. `random_mdim` has 5 elements; Each element in the array is an array of `5` random integers, raging from `0` to `99`.\n",
    "\n",
    "`nnz = np.count_nonzero(random_mdim)` counts non-zero value in the `random_mdim` array;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4\n",
    "\n",
    "Q: How can we explain what happens in the code below?\n",
    "\n",
    "A: Each value in the `[1, 2, 3, 4, 5]` array is multiplied by `2`; The resulting array is stored in the `result` variable;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2  4  6  8 10]\n"
     ]
    }
   ],
   "source": [
    "vector = np.array([1, 2, 3, 4, 5])\n",
    "result = 2*vector\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 5\n",
    "\n",
    "The text file `riccioli.dat` contains data [1] for experiments in which a clay ball was dropped from a high tower, and subsequently experienced free fall. For each recorded time, the estimated distance traveled has been reported in units of `Roman feet` \\footnote{These are very old measurements....}.\n",
    "\n",
    "- Read the data into a Pandas data frame object (tip: use the function pd.read_csv).\n",
    "- Make a scatter plot in which you distinguish between the different experiments with different markers and/or colors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The panda function imports the datapackage from the current directoary where \n",
    "#this jupyter file is located, and will import riccioli.dat file from the data\n",
    "# foler in the same directoary.\n",
    "df = pd.read_csv(\"data/riccioli.dat\", sep=\"\\t\", skiprows=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Giovanni Riccioli\\'s data on free fall')\n",
    "ax.set_xlabel('Time (seconds)')\n",
    "ax.set_ylabel('Vertical distance travelled (Roman feet)')\n",
    "\n",
    "#To plot the data that corrosponds to each Experiment, there is a need to specify\n",
    "#the specific experiment the data belongs to. Therefore divides data into\n",
    "#Experiment == 1--2--3\n",
    "plt.plot('Time', 'Distance', data=df.loc[df['Experiment'] == 1], \\\n",
    "         marker='^', linewidth=0, \\\n",
    "         label='Experiment #1')\n",
    "plt.plot('Time', 'Distance', data=df.loc[df['Experiment'] == 2], \\\n",
    "         marker='s', linewidth=0, \\\n",
    "         label='Experiment #2')\n",
    "plt.plot('Time', 'Distance', data=df.loc[df['Experiment'] == 3], \\\n",
    "         marker='o', linewidth=0, \\\n",
    "         label='Experiment #3')\n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these 3 different experiments we have experimental `time vs distance` data points, and as we can see they follow a general trend of gravitaional pull effect. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Excercise 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1\n",
    "Write a Python function that returns the analytical solution, equation (2), for any values of t, x0, v0, and g."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-9.620000000000001\n",
      "[   5.095   -9.62   -34.145  -68.48  -112.625]\n"
     ]
    }
   ],
   "source": [
    "def height_above_ground(t, x0=10.0, v0=0.0, g=9.81):\n",
    "    \"\"\"\n",
    "    Calculates the height above ground of an object experiencing\n",
    "    vertical motion in a constant gravitational field.\n",
    "\n",
    "    :param t: Time in seconds. Can be a single number, or an array.\n",
    "    :param x0: Initial height of the object (default: 10.0 m).\n",
    "    :param v0: Velocity at time zero (>0 for downward direction)\n",
    "               (default: 0 m/s).\n",
    "    :param g: Gravitational constant (default: 9.81 m/s^2).\n",
    "    :return: The height above ground at time(s) t (m).\n",
    "    \"\"\"\n",
    "    return  x0 - v0 * t - 1/2 * g * t ** 2\n",
    "\n",
    "# s is a single number\n",
    "s = 2\n",
    "print(height_above_ground(s))\n",
    "\n",
    "# s is a numpy array\n",
    "s = np.array([1, 2, 3, 4, 5])\n",
    "print(height_above_ground(s))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(0,60,0.1)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(t, height_above_ground(t))\n",
    "ax.set_xlabel('Time (s)')\n",
    "ax.set_ylabel('Distance (m)')\n",
    "ax.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- From the s = np.array into the gravitational function we can observe that the the object will reach 10 meters somewhere between 1-2 seconds after exposed to freefall.\n",
    "- The graph is showing the distance moved when an object experiences freefall for 60 seconds, and it is possible to read the theoretical moved distance, when excluding wind resistance, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0,\n",
       "  0.1,\n",
       "  0.2,\n",
       "  0.30000000000000004,\n",
       "  0.4,\n",
       "  0.5,\n",
       "  0.6,\n",
       "  0.7,\n",
       "  0.7999999999999999,\n",
       "  0.8999999999999999,\n",
       "  0.9999999999999999],\n",
       " [10.0,\n",
       "  10.0,\n",
       "  9.9019,\n",
       "  9.705699999999998,\n",
       "  9.411399999999997,\n",
       "  9.018999999999995,\n",
       "  8.528499999999992,\n",
       "  7.93989999999999,\n",
       "  7.253199999999988,\n",
       "  6.468399999999987,\n",
       "  5.5854999999999855])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def height_above_ground_numerical(t_f, h, x0=10.0, v0=0.0, g=9.81):\n",
    "    \"\"\"\n",
    "    :param t_f: Maximum simulation time (seconds).\n",
    "    :param h: Constant time step (seconds).\n",
    "    :param x0: Initial height of the object (default: 10.0 m).\n",
    "    :param v0: Velocity at time zero (>0 for downward direction)\n",
    "               (default: 0 m/s).\n",
    "    :param g: Gravitational constant (default: 9.81 m/s^2).\n",
    "    :return: A tuple of arrays (t, x(t)) containing the numerical\n",
    "             solution at times 0, h, 2*h, 3*h, ..., N*h <= t_f.\n",
    "    \"\"\"\n",
    "    \n",
    "    #t_array = np.arange(0, t_f, h)\n",
    "    #t_array = np.linspace(0, t_f, int(t_f/h+1), endpoint=True)\n",
    "    #t_array = [i for i in range(0, t_f + h, h)]\n",
    "    \n",
    "    t = 0\n",
    "    t_array = []\n",
    "    \n",
    "    \n",
    "    \"\"\"This function will run when t less or eqaul to t_f value, and will continue\n",
    "        to increase t until t_f this icrease by the stepsize.\"\"\"\n",
    "    \n",
    "    while t <= t_f:\n",
    "        t_array.append(t)\n",
    "        t += h\n",
    "    \n",
    "    \n",
    "    \"\"\"Based on starting postition `x0` and the next step `x_current = x_prev -v0 * h`, \n",
    "        and x_next = an empty variable. `x_array = [x_prev, x_current]´ \n",
    "        To start with this array will contain [10,10], but the intial thought is to\n",
    "        use append fucntion input new values onto this list\"\"\"\n",
    "    \n",
    "    x_prev = x0\n",
    "    x_current = x_prev - v0 * h\n",
    "    x_next = None\n",
    "    \n",
    "    x_array = [x_prev, x_current]\n",
    "    \n",
    "    \"\"\"This loop will run aslong t<=t_f. X_next will calculate the next x location\n",
    "         and the new value will be appended to x_array bracket. (x_prev, x_current) = \n",
    "         (x_current, x_next) will make x_current==> x_prev, and x_next==>x_current.\n",
    "         The number of iterations will continue until t<=t_f\"\"\"\n",
    "    \n",
    "    for _ in range(2, len(t_array)):\n",
    "        x_next = 2 * x_current - x_prev - g * h ** 2\n",
    "        x_array.append(x_next)\n",
    "        (x_prev, x_current) = (x_current, x_next)\n",
    "    \n",
    "    return t_array, x_array\n",
    "\n",
    "height_above_ground_numerical(1, .1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3\n",
    "\n",
    "Let x0=10.0, v0=0.0, and g=9.81.\n",
    "\n",
    "1. Apply your previous function to the case tf=1.4.\n",
    "2. For each of the constant step-sizes h=0.1,0.01,0.001, do the following: Compare your numerical solution (scatter plot) to the analytical solution (a solid line). Comment on the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp0_set = height_above_ground_numerical(1.4, .2)\n",
    "exp1_set = height_above_ground_numerical(1.4, .1)\n",
    "exp2_set = height_above_ground_numerical(1.4, .01)\n",
    "exp3_set = height_above_ground_numerical(1.4, .001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title('')\n",
    "ax.set_xlabel('time (h)')\n",
    "ax.set_ylabel('vertical distance (m)')\n",
    "\n",
    "# numerical solutions\n",
    "plt.plot(exp0_set[0], exp0_set[1], \\\n",
    "         marker='^', linewidth=0, \\\n",
    "         label='Experiment #0')\n",
    "plt.plot(exp1_set[0], exp1_set[1], \\\n",
    "         marker='^', linewidth=0, \\\n",
    "         label='Experiment #1')\n",
    "plt.plot(exp2_set[0], exp2_set[1], \\\n",
    "         marker='s', linewidth=0, \\\n",
    "         label='Experiment #2')\n",
    "plt.plot(exp2_set[0], exp2_set[1], \\\n",
    "         marker='o', linewidth=0, \\\n",
    "         label='Experiment #3')\n",
    "\n",
    "\n",
    "# analytical solution\n",
    "x = np.linspace(0, 1.4, int(1.4/0.0001), endpoint=True)\n",
    "y = 10 - 0 * x - 1 / 2 * 9.81 * x ** 2\n",
    "plt.plot(x, y, linewidth=2, color=\"black\", label='Analytical Solution')\n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Compare analytical `(x(t)=x0-vo*t-1/2*gt**2)` to numerical one. We observe that the smaller the step size, the closer appoximation of numerical solution(s) is to the analytical solution.\n",
    "- By observering `Experiment#0` on the graph, we can coclude that the greatest distance between analytical and numerical is at this point.\n",
    "- And the distance minimized when approaching experiments with lower step sizes for example `Experiment#3` contains the smallest difference between the numerical and analytical solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([2.5442610980993174e-16], [2.0816681711721685e-17])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_errors(steps, t_f=0.1):\n",
    "    relative_errors = []\n",
    "    absolute_errors = []\n",
    "    \n",
    "    for step in steps:\n",
    "        t = int(t_f / step) + 1\n",
    "        true_solution = np.linspace(0, t_f, t, endpoint=True)\n",
    "        #print(t)\n",
    "        #print('print solution: ', true_solution, true_solution.sum())\n",
    "        \n",
    "        total = 0\n",
    "        absolute_error = 0\n",
    "        relative_error = 0\n",
    "        \n",
    "        for i in range(t):\n",
    "            absolute_error += abs(total - true_solution[i])\n",
    "            \n",
    "            if true_solution[i] == 0:\n",
    "                relative_error += 0\n",
    "            else:\n",
    "                relative_error += abs((total - true_solution[i]) / true_solution[i])\n",
    "            #print(i, total, true_solution[i], absolute_error)\n",
    "            total += step\n",
    "        \n",
    "        absolute_errors.append(absolute_error)\n",
    "        relative_errors.append(relative_error)\n",
    "        \n",
    "    return relative_errors, absolute_errors\n",
    "\n",
    "step_sizes = [1e-2]\n",
    "get_errors(step_sizes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5e-08, 1e-06, 5e-07, 1e-05, 0.0001, 0.001, 0.01]\n",
      "[1.9467002889312887e-06, 3.1802441420585866e-09, 8.057431488197847e-09, 2.7392819776535498e-11, 6.064017560661328e-13, 3.4382219293860317e-15, 2.0816681711721685e-17]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "step_sizes = [.5e-7, 1e-6, .5e-6, 1e-5, 1e-4, 1e-3, 1e-2]\n",
    "relative_errors, absolute_errors = get_errors(step_sizes)\n",
    "\n",
    "print(step_sizes)\n",
    "print(absolute_errors)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Global and relative error')\n",
    "ax.set_xlabel('Step (t)')\n",
    "ax.set_ylabel('Error')\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")\n",
    "\n",
    "plt.plot(step_sizes, relative_errors, \\\n",
    "         marker='s', linewidth=0, \\\n",
    "         label='Relative Errors')\n",
    "\n",
    "plt.plot(step_sizes, absolute_errors, \\\n",
    "         marker='o', linewidth=0, \\\n",
    "         label='Absolute Errors')\n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With smaller step size, we have a relatively higher accumulated absolute and relative errors, as shown in the graph.\n",
    "\n",
    "With larger step sizes, the errors are smaller, in other words it has a smaller effect on the true solution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat the simulations you did in Part 4, except that now you use x1 from \n",
    "# equation (10) to initialize the model (ignore the last term)\n",
    "\n",
    "# Note: it looks like there is a typo in this task - I think it should be referring to Part 2 (and 3) instead\n",
    "\n",
    "def height_above_ground_numerical_improved(t_f, h, x0=10.0, v0=0.0, g=9.81):\n",
    "    \"\"\"\n",
    "    :param t_f: Maximum simulation time (seconds).\n",
    "    :param h: Constant time step (seconds).\n",
    "    :param x0: Initial height of the object (default: 10.0 m).\n",
    "    :param v0: Velocity at time zero (>0 for downward direction)\n",
    "               (default: 0 m/s).\n",
    "    :param g: Gravitational constant (default: 9.81 m/s^2).\n",
    "    :return: A tuple of arrays (t, x(t)) containing the numerical\n",
    "             solution at times 0, h, 2*h, 3*h, ..., N*h <= t_f.\n",
    "    \"\"\"\n",
    "    t = 0\n",
    "    t_array = []\n",
    "    \n",
    "    while t <= t_f:\n",
    "        t_array.append(t)\n",
    "        t += h\n",
    "    \n",
    "    x_prev = x0\n",
    "    # in previous function we used (x0 - v0 * h) formula to calculate the x1\n",
    "    # in this function have a better approximation of x1\n",
    "    x_current = x_prev - v0 * h - 1 / 2 * g * h ** 2\n",
    "    x_next = None\n",
    "    \n",
    "    x_array = [x_prev, x_current]\n",
    "    \n",
    "    for _ in range(2, len(t_array)):\n",
    "        x_next = 2 * x_current - x_prev - g * h ** 2\n",
    "        x_array.append(x_next)\n",
    "        (x_prev, x_current) = (x_current, x_next)\n",
    "    \n",
    "    return t_array, x_array\n",
    "\n",
    "def get_errors(exp_set, analytical_set):\n",
    "    total = 0\n",
    "    result = []\n",
    "    \n",
    "    for i in range(len(exp_set)):\n",
    "        total += abs(exp_set[i] - analytical_set[i])\n",
    "        result.append(total)\n",
    "        \n",
    "    return result\n",
    "\n",
    "# defining t_f (the time we run the experiment)\n",
    "t_f = 1.4\n",
    "\n",
    "\n",
    "fig, ((ax0, ax1, ax2), (ax3, ax4, ax5)) = plt.subplots(2, 3, figsize=(16, 9))\n",
    "\n",
    "# experiment #0\n",
    "h = 0.2\n",
    "\n",
    "exp0_set = height_above_ground_numerical(t_f, h)\n",
    "exp0_set_improved = height_above_ground_numerical_improved(t_f, h)\n",
    "exp0_analytical_set = 10 - 0 * np.array(exp0_set[0]) - 1 / 2 * 9.81 * np.array(exp0_set[0]) ** 2\n",
    "exp0_analytical_global_errors = get_errors(exp0_set[1], exp0_analytical_set)\n",
    "\n",
    "ax0.set_title('h={}'.format(str(h)))\n",
    "ax0.set_xlabel('time (s)')\n",
    "ax0.set_ylabel('vertical distance (m)')\n",
    "ax0.scatter(exp0_set[0], exp0_set[1], label='initial')\n",
    "ax0.scatter(exp0_set[0], exp0_set_improved[1], label='improved')\n",
    "ax0.plot(exp0_set[0], exp0_analytical_set, label='analytical solution', color=\"black\")\n",
    "ax0.grid(True)\n",
    "ax0.legend()\n",
    "\n",
    "ax3.set_title('global error for initial function, h={}'.format(str(h)))\n",
    "ax3.set_xlabel('time (s)')\n",
    "ax3.set_ylabel('global error (m)')\n",
    "ax3.scatter(exp0_set[0], exp0_analytical_global_errors, label='analytical (initial)')\n",
    "ax3.grid(True)\n",
    "ax3.legend()\n",
    "\n",
    "# experiment #1\n",
    "h = 0.05\n",
    "\n",
    "exp1_set = height_above_ground_numerical(t_f, h)\n",
    "exp1_set_improved = height_above_ground_numerical_improved(t_f, h)\n",
    "exp1_analytical_set = 10 - 0 * np.array(exp1_set[0]) - 1 / 2 * 9.81 * np.array(exp1_set[0]) ** 2\n",
    "exp1_analytical_global_errors = get_errors(exp1_set[1], exp1_analytical_set)\n",
    "\n",
    "ax1.set_title('h={}'.format(str(h)))\n",
    "ax1.set_xlabel('time (s)')\n",
    "ax1.set_ylabel('vertical distance (m)')\n",
    "ax1.scatter(exp1_set[0], exp1_set[1], label='initial')\n",
    "ax1.scatter(exp1_set[0], exp1_set_improved[1], label='improved')\n",
    "ax1.plot(exp1_set[0], exp1_analytical_set, label='analytical solution', color=\"black\")\n",
    "ax1.grid(True)\n",
    "ax1.legend()\n",
    "\n",
    "ax4.set_title('global error for initial function, h={}'.format(str(h)))\n",
    "ax4.set_xlabel('time (s)')\n",
    "ax4.set_ylabel('global error (m)')\n",
    "ax4.scatter(exp1_set[0], exp1_analytical_global_errors, label='analytical (initial)')\n",
    "ax4.grid(True)\n",
    "ax4.legend()\n",
    "\n",
    "# experiment #2\n",
    "h = 0.01\n",
    "\n",
    "exp2_set = height_above_ground_numerical(t_f, h)\n",
    "exp2_set_improved = height_above_ground_numerical_improved(t_f, h)\n",
    "exp2_analytical_set = 10 - 0 * np.array(exp2_set[0]) - 1 / 2 * 9.81 * np.array(exp2_set[0]) ** 2\n",
    "exp2_analytical_global_errors = get_errors(exp2_set[1], exp2_analytical_set)\n",
    "\n",
    "ax2.set_title('h={}'.format(str(h)))\n",
    "ax2.set_xlabel('time (s)')\n",
    "ax2.set_ylabel('vertical distance (m)')\n",
    "ax2.scatter(exp2_set[0], exp2_set[1], label='initial')\n",
    "ax2.scatter(exp2_set[0], exp2_set_improved[1], label='improved')\n",
    "ax2.plot(exp2_set[0], exp2_analytical_set, label='analytical solution', color=\"black\")\n",
    "ax2.grid(True)\n",
    "ax2.legend()\n",
    "\n",
    "ax5.set_title('global error for initial function, h={}'.format(str(h)))\n",
    "ax5.set_xlabel('time (s)')\n",
    "ax5.set_ylabel('global error (m)')\n",
    "ax5.scatter(exp2_set[0], exp2_analytical_global_errors, label='analytical (initial)')\n",
    "ax5.grid(True)\n",
    "ax5.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The improved function gives us a better approximation of the analytical solution. This can be observed in minimized global and relative errors, such as seen above.\n",
    "\n",
    "When using smaller step sizes, the initial function gives us a better approximation of the analytical solution, providing results that are similar to the improved function.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 6 (incomplete)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/riccioli.dat\", sep=\"\\t\", skiprows=8)\n",
    "\n",
    "# converting Roman feet to meters \n",
    "df['Distance'] = 0.296 * df['Distance']\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Giovanni Riccioli\\'s data on free fall')\n",
    "ax.set_xlabel('Time (s)')\n",
    "ax.set_ylabel('Vertical distance travelled (m)')\n",
    "\n",
    "#To plot the data that corrosponds to each Experiment, there is a need to specify\n",
    "#the specific experiment the data belongs to. Therefore divides data into\n",
    "#Experiment == 1--2--3\n",
    "\n",
    "plt.plot('Time', 'Distance', data=df.loc[df['Experiment'] == 1], \\\n",
    "         marker='^', linewidth=0, \\\n",
    "         label='Experiment #1')\n",
    "plt.plot('Time', 'Distance', data=df.loc[df['Experiment'] == 2], \\\n",
    "         marker='s', linewidth=0, \\\n",
    "         label='Experiment #2')\n",
    "plt.plot('Time', 'Distance', data=df.loc[df['Experiment'] == 3], \\\n",
    "         marker='o', linewidth=0, \\\n",
    "         label='Experiment #3')\n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Excercise 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ice volume (km^3): 15000.0\n",
      "ice volume (m^3): 15000000000000.0\n",
      "ice mass (kg): 1.3755e+16\n",
      "ice water mass (kg): 1.3755e+16\n",
      "ice water volume (m^3): 13755000000000.0\n",
      "displaced water volume (m^3): 13354368932038.836\n",
      "net contribution (m^3): 400631067961.16406\n"
     ]
    }
   ],
   "source": [
    "r_ice = 917 # kg/m^3\n",
    "r_iw = 1000 # kg/m^3\n",
    "r_sw = 1030 # kg/m^3\n",
    "\n",
    "v_ice_km = 15 * 1e3 # km^3\n",
    "print('ice volume (km^3):', v_ice_km)\n",
    "\n",
    "v_ice_m = v_ice_km * (1000 ** 3) # m^3\n",
    "print('ice volume (m^3):', v_ice_m)\n",
    "\n",
    "m_ice = r_ice * v_ice_m # kg\n",
    "print('ice mass (kg):', m_ice)\n",
    "\n",
    "m_iw = m_ice # kg\n",
    "print('ice water mass (kg):', m_iw)\n",
    "\n",
    "v_iw = m_iw / r_iw # m^3\n",
    "print('ice water volume (m^3):', v_iw)\n",
    "\n",
    "v_dw = r_iw / r_sw * v_iw\n",
    "print('displaced water volume (m^3):', v_dw)\n",
    "\n",
    "v_net = v_iw - v_dw\n",
    "print('net contribution (m^3):', v_net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "earth radius (km) 6371\n",
      "earth area (km^2) 510064471.90978825\n",
      "water area (km^2) 362145775.0559496\n",
      "water area (m^2) 362145775055949.6\n",
      "water rise (m) 0.0011062701695174234\n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "\n",
    "r_earth_km = 6371\n",
    "print('earth radius (km)', r_earth_km) #Radius of earth\n",
    "\n",
    "s_earth_km = 4 * pi * (r_earth_km ** 2)\n",
    "print('earth area (km^2)', s_earth_km) #Area of the earth\n",
    "\n",
    "s_water_km = s_earth_km * 0.71\n",
    "print('water area (km^2)', s_water_km) #Area of the water contained on earth\n",
    "\n",
    "s_water_m = s_water_km * (1000 ** 2)\n",
    "print('water area (m^2)', s_water_m) #Volume of \n",
    "\n",
    "h_water_m = v_net / s_water_m\n",
    "print('water rise (m)', h_water_m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bedmap = rh.fetch_bedmap2(datasets=[\"thickness\",\"surface\",\"bed\"])\n",
    "plt.figure(figsize=(8, 7))\n",
    "ax = plt.subplot(111)\n",
    "bedmap.surface.plot.pcolormesh(ax=ax,cmap=cmocean.cm.ice,cbar_kwargs=dict(pad=0.01, aspect=30))\n",
    "plt.title(\"Bedmap2 Antarctica\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x28289732b88>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extract cross section using the original coordinates\n",
    "bed1d=bedmap.sel(y=-0.5e6, x=slice(-1.6e6,-1.35e6))\n",
    "\n",
    "# Add a second x-coordinate to make prettier plots\n",
    "# (shift x-axis to start at zero, and convert from m to km)\n",
    "bed1d=bed1d.assign_coords({\"x2\":((bed1d.x+1.6e6)/1e3)})\n",
    "\n",
    "bed1d.surface.plot(x='x2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "surface = bed1d['surface'].values\n",
    "thickness = bed1d['thickness'].values\n",
    "bed = bed1d['bed'].values\n",
    "\n",
    "freeboard = (0 - (surface - thickness) * r_iw / r_ice) + (surface - thickness)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title('cross-section of bedmap2')\n",
    "ax.set_xlabel('distance along track (km)')\n",
    "ax.set_ylabel('height above sea level (m)')\n",
    "\n",
    "x = (bed1d.x + 1.6e6) / 1e3 # x-coord slice\n",
    "\n",
    "plt.plot(x, np.zeros(len(x)), linestyle='--', color='black', linewidth=1, label='surface')\n",
    "plt.plot(x, surface, linewidth=1, label='surface')\n",
    "plt.plot(x, freeboard, color='red', linewidth=1, label='freeboard')\n",
    "plt.plot(x, surface-thickness, color='black', linewidth=1, label='surface-thickness')\n",
    "plt.plot(x, bed, color='black', linewidth=1, label='bed')\n",
    "\n",
    "ax.fill_between(x[0:50], bed[0:50], 0, color='blue') # small hack :)\n",
    "ax.fill_between(x, bed, surface, color='lightblue')\n",
    "ax.fill_between(x, -2000, surface-thickness, color='blue')\n",
    "ax.fill_between(x, -2000, bed, color='black')\n",
    "\n",
    "plt.text(150, 500, 'Only ice above red line\\ncontribute to SLR', color='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The bedrock could have a relation to how the ice is developing, for example at the highest peak of the bedrock, making a narrow passage for waterflow to circulate underneath the ice, and we perhaps observe that the peak of the bedrock is consistent with a increase of the thickness of the ice layers. The ice surface has the steepest slope in this area, but even as the bedrock moves to shallower depth, the ice seems to be increasing in altitude even though ice does has more depth beneath mean sea level."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total SLR volume (m^3): 2.6819354467496132e+16\n",
      "SLR height (m^2): 52.580322575847816\n"
     ]
    }
   ],
   "source": [
    "# Need to import the datasets of the thickness and surface to make the calculations\n",
    "bedmap = rh.fetch_bedmap2(datasets=[\"thickness\",\"surface\"]) \n",
    "\n",
    "bed3d = bedmap.sel()\n",
    "\n",
    "#This function will import values from thickness and surface datasets\n",
    "surface = bed3d['surface'].values\n",
    "thickness = bed3d['thickness'].values\n",
    "\n",
    "#Estimate of freeboard limit\n",
    "freeboard = (0 - (surface - thickness) * r_iw / r_ice) + (surface - thickness) \n",
    "#Estimate of SLR volume in kilometer scale(km^3)\n",
    "slr_volume_km = surface - freeboard\n",
    "#SLR volume converted from kilometer(km^3) scale to meter scale(m^3).\n",
    "slr_volume_m = slr_volume_km * 1e6\n",
    "\n",
    "#Total SLR volume estimated while running np.isnan fucntion which removes non-numerical values, then will only in numerical \n",
    "#values(==True) will be summarized \n",
    "total_slr_volume_m = slr_volume_m[np.isnan(slr_volume_m)==False].sum() # total SRL volume (m^3)\n",
    "print('total SLR volume (m^3):', total_slr_volume_m)\n",
    "\n",
    "#Area of earth surface converted to meter scale(m^2)\n",
    "s_earth_m = s_earth_km * 1e6 # earth surface (m^2)\n",
    "\n",
    "# SRL height in square meters(m^2) if volume was spread evenly over the earth surface\n",
    "spread_slr_height = total_slr_volume_m / s_earth_m \n",
    "print('SLR height (m^2):', spread_slr_height)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The bedmap can be used to correlate the ice thickness in relation to the bedrock, for example at the start of the drastic elevation increase of the ice, it can be observered that the bedrock at a shallower depth and creates a narrow passage for the waterflow/ice. After this point, the ice thickness continues to increase even though bedrock elevation is decreasing. This was not a conclusion for the thickness increase, but to look at these types of data, it is possible to explore the opportunity to make relationships between physical concepts based on the available data presented.\n",
    "\n",
    "\n",
    "- This model lacks a temperature to be able to calculate as an array how the ice will melt corrosponding to an eventual increase in global temperature. In the models current state, the answer is that for Antartica, SLR would be ~52.58 meters but that is if ALL of the ice should suddenly disappear, which would not correspond to the expected reality. A good improvement to the model would be to include how much ice will disappear for each degree of Celsius increase, and make the calculation on how much SLR there will be attributed with respect to global temperature increase.\n",
    "\n",
    "\n",
    "- The data has not been cleaned for numerical round off errors, thus it should be sufficent to say that we assume there are numerical errors within the model, but the size of errors is uncertain with respect to the data we utilized. For example, if the cell size can be reduced from 1000x1000 meters, we coud get a better approximation on the actual SLR results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiences during Project 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Learning output\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Different approaches to use Python as a tool to handle data packages and create estimate(s) from the data itself and create useful functions which can make the neccesary calculations without repeating (copy-pasting) the code.\n",
    "\n",
    "- How to succesfully utilize directories, by importing the necessary files."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The assignment was a quite extensive and there was a need to use a lot of time to work out each question, but was interesting topics throughout the whole assignment. The learning output for doing this amount of work is GREAT. To summarize needed a lot of time but provided good learning.\n",
    "\n",
    "- Some issues when importing the rockhound file (Excercise4 P:3) but learned to problem solve this issue when and install the right GDAL version and rostario version to remove the install error message, and succesfully import the datapackage, through `pip install rockhound` rather than using `conda-forge install rockhound`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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