{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "harmful-woman",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This tutorial will introduce simple implementations of for loops."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "demonstrated-consensus",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "# Here's the simplest for loop.\n",
    "for i in range(10):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "civic-alliance",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note that the loop starts from i = 0 and has 10 iterations.  Therefore,\n",
    "# the output is i = 1, 2, 3, ..., 9.  Also, Python will loop over only the lines\n",
    "# following the 'for' statement that are indented.  Note the difference in the \n",
    "# outputs from the following two blocks of code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "complete-ministry",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i**2 is in the loop:\n",
      "0\n",
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "4\n",
      "3\n",
      "9\n",
      "4\n",
      "16\n",
      "5\n",
      "25\n",
      "6\n",
      "36\n",
      "7\n",
      "49\n",
      "8\n",
      "64\n",
      "9\n",
      "81\n"
     ]
    }
   ],
   "source": [
    "# i**2 is in the loop:\n",
    "print('i**2 is in the loop:')\n",
    "for i in range(10):\n",
    "    print(i)\n",
    "    print(i**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "suburban-desire",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "i**2 is NOT in the loop:\n",
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "81\n"
     ]
    }
   ],
   "source": [
    "# i**2 is NOT in the loop:\n",
    "print('\\ni**2 is NOT in the loop:')\n",
    "for i in range(10):\n",
    "    print(i)\n",
    "print(i**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "great-lender",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Step by two:\n",
      "0\n",
      "2\n",
      "4\n",
      "6\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "# The loop can be made to increment in steps of two as follows:\n",
    "import numpy as np\n",
    "print('\\nStep by two:')\n",
    "for i in np.arange(0, 10, 2):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "encouraging-record",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Often, you may wish to perform calculations within a loop and then store\n",
    "# the results of those calculations in a list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "powerful-needle",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.  1.1 1.2 1.3 1.4 1.5 1.6 1.7\n",
      " 1.8]\n"
     ]
    }
   ],
   "source": [
    "# The first step is to create a list of x values that we will iterate over\n",
    "x = np.arange(0, 1.9, 0.1)\n",
    "print('x:', x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "governmental-fisher",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Next, we will create an empty list that we will use to store the results\n",
    "# of out calculation.\n",
    "results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "urban-induction",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results: [-0.0, 0.019198493654414298, 0.03919043057194907, 0.060070244503352854, 0.08194889882372983, 0.1049575951738314, 0.1292523806498573, 0.15501976986589477, 0.18248332254542876, 0.21191058440110952, 0.24361834453296421, 0.27797032560786367, 0.31535137406103264, 0.3560759822264981, 0.4001223909632299, 0.44643492253916167, 0.49135988237282596, 0.526464135360927, 0.5400000000000005]\n"
     ]
    }
   ],
   "source": [
    "# We can now use our results list within a for loop and append values\n",
    "# to list as the loop iterates.\n",
    "umax = 0.54\n",
    "M = -4.2703\n",
    "D = 1.8\n",
    "for i in x:\n",
    "    results = results + [(umax/M)*np.log(1 + (np.exp(M)-1)*(i/D)*np.exp(1 - i/D))]\n",
    "print('Results:',results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "desperate-hostel",
   "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": [
    "# In fact, we can now easiy plot results vs x.\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(x, results, 'bo')\n",
    "plt.xlabel('x');\n",
    "plt.ylabel('results');\n",
    "plt.axis((0, 1.8, 0, 0.6));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}