Linear_Algebra-project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CompMech04-Linear Algebra Project\n",
    "# Practical Linear Algebra for Finite Element Analysis\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project we will perform a linear-elastic finite element analysis (FEA) on a support structure made of 11 beams that are riveted in 7 locations to create a truss as shown in the image below. \n",
    "\n",
    "![Mesh image of truss](../images/mesh.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The triangular truss shown above can be modeled using a [direct stiffness method [1]](https://en.wikipedia.org/wiki/Direct_stiffness_method), that is detailed in the [extra-FEA_material](./extra-FEA_material.ipynb) notebook. The end result of converting this structure to a FE model. Is that each joint, labeled $n~1-7$, short for _node 1-7_ can move in the x- and y-directions, but causes a force modeled with Hooke's law. Each beam labeled $el~1-11$, short for _element 1-11_, contributes to the stiffness of the structure. We have 14 equations where the sum of the components of forces = 0, represented by the equation\n",
    "\n",
    "$\\mathbf{F-Ku}=\\mathbf{0}$\n",
    "\n",
    "Where, $\\mathbf{F}$ are externally applied forces, $\\mathbf{u}$ are x- and y- displacements of nodes, and $\\mathbf{K}$ is the stiffness matrix given in `fea_arrays.npz` as `K`, shown below\n",
    "\n",
    "_note: the array shown is 1000x(`K`). You can use units of MPa (N/mm^2), N, and mm. The array `K` is in 1/mm_\n",
    "\n",
    "$\\mathbf{K}=EA*$\n",
    "\n",
    "$  \\left[ \\begin{array}{cccccccccccccc}\n",
    " 4.2 & 1.4 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 1.4 & 2.5 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 8.3 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 4.2 & -1.4 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & -1.4 & 2.5 \\\\\n",
    "\\end{array}\\right]~\\frac{1}{m}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "fea_arrays = np.load('./fea_arrays.npz')\n",
    "K=fea_arrays['K']\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project we are solving the problem, $\\mathbf{F}=\\mathbf{Ku}$, where $\\mathbf{F}$ is measured in Newtons, $\\mathbf{K}$ `=E*A*K` is the stiffness in N/mm, `E` is Young's modulus measured in MPa (N/mm^2), and `A` is the cross-sectional area of the beam measured in mm^2. \n",
    "\n",
    "There are three constraints on the motion of the joints:\n",
    "\n",
    "i. node 1 displacement in the x-direction is 0 = `u[0]`\n",
    "\n",
    "ii. node 1 displacement in the y-direction is 0 = `u[1]`\n",
    "\n",
    "iii. node 7 displacement in the y-direction is 0 = `u[13]`\n",
    "\n",
    "We can satisfy these constraints by leaving out the first, second, and last rows and columns from our linear algebra description. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Calculate the condition of `K` and the condition of `K[2:13,2:13]`. \n",
    "\n",
    "a. What error would you expect when you solve for `u` in `K*u = F`? \n",
    "\n",
    "b. Why is the condition of `K` so large?\n",
    "\n",
    "c. What error would you expect when you solve for `u[2:13]` in `K[2:13,2:13]*u=F[2:13]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Condition number of K =  1.4577532625238035e+17\n",
      "Condition number of K[2:13,2:13] =  52.23542514351006\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\n\\n(A) I would expect some roundoff error due to the use of finite precision numers. Some \\nerror will also arise from the matrix inversion algorithm used by python.\\n\\n(B) The condition number of K is very large due to the high number and value of elements in K. \\nConsequently, the norm, defined as the square root of the sum of the squares of the elements, \\nwill be a very large number, causing the condition number to be large as well.\\n\\n(C) \\n\\n'"
      ]
     },
     "execution_count": 315,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "fea_arrays = np.load('./fea_arrays.npz')\n",
    "\n",
    "K=fea_arrays['K']\n",
    "K_aug = K[2:13,2:13]\n",
    "\n",
    "cond_K = np.linalg.cond(K)\n",
    "cond_K_aug = np.linalg.cond(K_aug)\n",
    "\n",
    "print(\"Condition number of K = \", cond_K)\n",
    "print(\"Condition number of K[2:13,2:13] = \", cond_K_aug)\n",
    "\n",
    "'''\n",
    "\n",
    "(A) I would expect some roundoff error due to the use of finite precision numers. Some \n",
    "error will also arise from the matrix inversion algorithm used by python.\n",
    "\n",
    "(B) The condition number of K is very large due to the high number and value of elements in K. \n",
    "Consequently, the norm, defined as the square root of the sum of the squares of the elements, \n",
    "will be a very large number, causing the condition number to be large as well.\n",
    "\n",
    "(C) Here I would expect error because only a subset of the stiffness and force matrices is be used\n",
    "\n",
    "'''\n",
    "#fea_arrays.files\n",
    "\n",
    "#nodes = fea_arrays['nodes']\n",
    "#elements = fea_arrays['elems']\n",
    "#print(nodes)\n",
    "#print(elements)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Apply a 100-N downward force to the central top node (n 4)\n",
    "\n",
    "a. Create the LU matrix for K[2:13,2:13]\n",
    "\n",
    "b. Use cross-sectional area of $0.1~mm^2$ and steel and almuminum moduli, $E=200~GPa~and~E=70~GPa,$ respectively. Solve the forward and backward substitution methods for \n",
    "\n",
    "* $\\mathbf{Ly}=\\mathbf{F}\\frac{1}{EA}$\n",
    "\n",
    "* $\\mathbf{Uu}=\\mathbf{y}$\n",
    "\n",
    "_your array `F` is zeros, except for `F[5]=-100`, to create a -100 N load at node 4._\n",
    "\n",
    "c. Plug in the values for $\\mathbf{u}$ into the full equation, $\\mathbf{Ku}=\\mathbf{F}$, to solve for the reaction forces\n",
    "\n",
    "d. Create a plot of the undeformed and deformed structure with the displacements and forces plotted as vectors (via `quiver`). Your result for aluminum should match the following result from [extra-FEA_material](./extra-FEA_material.ipynb). _note: The scale factor is applied to displacements $\\mathbf{u}$, not forces._\n",
    "\n",
    "![Deformed structure with loads applied](../images/deformed_truss.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L=\n",
      " [[ 1.          0.          0.          0.          0.          0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [ 0.          1.          0.          0.          0.          0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [-0.16666667  0.28867513  1.          0.          0.          0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [ 0.28867513 -0.5         0.12371791  1.          0.          0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [-0.66666667  0.         -0.17857143 -0.09622504  1.          0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.         -0.18557687 -0.72222222 -0.08247861  1.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.         -0.42857143  0.12830006 -0.23809524  0.33425542\n",
      "   1.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.24743583 -0.78947368\n",
      "   0.18426072  1.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.         -0.57142857 -0.09116057\n",
      "  -0.24822695 -0.21650635  1.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "  -0.23339692 -0.875      -0.32768529  1.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "  -0.53900709  0.24056261 -0.59459459  0.28867513  1.        ]]\n",
      "U=\n",
      " [[ 0.005       0.         -0.00083333  0.00144338 -0.00333333  0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.005       0.00144338 -0.0025      0.          0.\n",
      "   0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.00777778  0.00096225 -0.00138889 -0.00144338\n",
      "  -0.00333333  0.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.00321429 -0.00030929 -0.00232143\n",
      "   0.00041239  0.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.00583333 -0.00048113\n",
      "  -0.00138889  0.00144338 -0.00333333  0.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.          0.00301587\n",
      "   0.00100807 -0.00238095 -0.00027493  0.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "   0.00618421  0.00113951 -0.00153509 -0.00144338 -0.00333333]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "   0.          0.00255319 -0.00055278 -0.00223404  0.0006142 ]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "   0.          0.          0.00256944 -0.00084197 -0.00152778]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "   0.          0.          0.          0.00243243  0.00070218]\n",
      " [ 0.          0.          0.          0.          0.          0.\n",
      "   0.          0.          0.          0.          0.00111111]]\n",
      "\n",
      "\n",
      "\n",
      "Steel reactions =  [-3.03576608e-18  2.50000000e-03  0.00000000e+00  4.33680869e-19\n",
      "  8.67361738e-19 -1.08420217e-18 -4.14613386e-19 -5.00000000e-03\n",
      " -8.67361738e-19 -1.08420217e-18  0.00000000e+00  0.00000000e+00\n",
      "  0.00000000e+00  2.50000000e-03]\n",
      "\n",
      "\n",
      "Aluminum reactions =  [-8.67361738e-18  7.14285714e-03  3.46944695e-18 -8.67361738e-19\n",
      "  3.46944695e-18  6.07153217e-18 -1.98659719e-18 -1.42857143e-02\n",
      "  0.00000000e+00 -1.43114687e-17  1.73472348e-18 -1.73472348e-18\n",
      "  0.00000000e+00  7.14285714e-03]\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": [
    "import numpy as np\n",
    "#from pretty_print import array_print as AP #a defined printing command for matrices\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import lu\n",
    "fea_arrays = np.load('./fea_arrays.npz')\n",
    "\n",
    "K=fea_arrays['K']\n",
    "K_aug = K[2:13,2:13]\n",
    "\n",
    "\n",
    "\n",
    "P,L,U =lu(K_aug)\n",
    "print('L=\\n',L)\n",
    "print('U=\\n',U)\n",
    "\n",
    "print(\"\")\n",
    "\n",
    "F=np.zeros(2*len(nodes)-3)\n",
    "F[5]=-100\n",
    "Es = 200 * 1000 #GPa\n",
    "Eal =70 * 1000 #GPa\n",
    "A = 0.1 #mm^2\n",
    "bs = (1/(Es*A))*F\n",
    "bal = (1/(Eal*A))*F\n",
    "\n",
    "def solveLU(L,U,b):\n",
    "    '''solveLU: solve for x when LUx = b\n",
    "    x = solveLU(L,U,b): solves for x given the lower and upper \n",
    "    triangular matrix storage\n",
    "    uses forward substitution for \n",
    "    1. Ly = b\n",
    "    then backward substitution for\n",
    "    2. Ux = y\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    b = output vector\n",
    "    \n",
    "    returns:\n",
    "    ---------\n",
    "    x = solution of LUx=b '''\n",
    "    n=len(b)\n",
    "    x=np.zeros(n)\n",
    "    y=np.zeros(n)\n",
    "        \n",
    "    # forward substitution\n",
    "    for k in range(0,n):\n",
    "        y[k] = b[k] - L[k,0:k]@y[0:k]\n",
    "    # backward substitution\n",
    "    for k in range(n-1,-1,-1):\n",
    "        x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
    "    return x\n",
    "\n",
    "ufs = solveLU(L,U,bs)\n",
    "ufal = solveLU(L,U,bal)\n",
    "\n",
    "# form full displacement vectors us (steel) and ual (Al)\n",
    "us=np.zeros(2*len(nodes))\n",
    "ual = np.zeros(2*len(nodes))\n",
    "us[2:13]=ufs\n",
    "ual[2:13]=ufal\n",
    "\n",
    "#Reactions\n",
    "reactions_st = K@us\n",
    "reactions_al = K@ual\n",
    "print('\\n')\n",
    "print(\"Steel reactions = \", reactions_st)\n",
    "print('\\n')\n",
    "print(\"Aluminum reactions = \", reactions_al)\n",
    "\n",
    "\n",
    "scale = 5\n",
    "plt.figure()\n",
    "\n",
    "nodes = fea_arrays['nodes']\n",
    "elements = fea_arrays['elems']\n",
    "\n",
    "\n",
    "# Plot Steel structure. FIrst compute the displaced nodes #Define Force Vector\n",
    "F = np.zeros((len(nodes),2))\n",
    "displaced_nodes = np.zeros((len(nodes),3))\n",
    "\n",
    "for i in range(0,len(nodes)):\n",
    "    displaced_nodes[i,1] = nodes[i,1] + us[2*i]\n",
    "    displaced_nodes[i,2] = nodes[i,2] + scale*us[2*i+1]\n",
    "    F[i,0] = reactions_st[2*i]\n",
    "    F[i,1] = reactions_st[2*i+1]\n",
    "\n",
    "for i in range(0,len(elements)):\n",
    "    node1 = elements[i,1]\n",
    "    node2 = elements[i,2]\n",
    "#    print(node1,node2,i,len(nodes))\n",
    "    plt.plot([nodes[node1-1,1],nodes[node2-1,1]],[nodes[node1-1,2],nodes[node2-1,2]],'s-',label='orignal')\n",
    "    plt.plot([displaced_nodes[node1-1,1],displaced_nodes[node2-1,1]],[displaced_nodes[node1-1,2],displaced_nodes[node2-1,2]],'s-',label='displaced')\n",
    "    plt.plot([displaced_nodes[node1-1,1],displaced_nodes[node2-1,1]],[displaced_nodes[node1-1,2],displaced_nodes[node2-1,2]],'s-',label='displaced')\n",
    "    plt.quiver(displaced_nodes[node1-1,1],displaced_nodes[node1-1,2],F[node1-1,0],F[node1-1,1],color=(1,0,0,1),label='applied forces')\n",
    "    \n",
    "#    plt.plot(us[i],us[i+1],'o-',label='deformed')\n",
    "\n",
    "plt.axis([-100,1000,-100,400])\n",
    "#plt.legend(loc='center left', bbox_to_anchor=(1,0.5));\n",
    "plt.title('original and deformed steel structure\\nscale = {}x'.format(scale));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Determine cross-sectional area\n",
    "\n",
    "a. Using aluminum, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
    "\n",
    "b. Using steel, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
    "\n",
    "c. What are the weights of the aluminum and steel trusses with the chosed cross-sectional areas?\n",
    "\n",
    "d. The current price (2020/03) of [aluminum](https://tradingeconomics.com/commodity/aluminum) is 1545 dollars/Tonne and [steel](https://tradingeconomics.com/commodity/steel) is 476 dollars/Tonne [2]. Which material is cheaper to  create the truss?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The minimum cross-sectional area for Al that produces a maximum displacement of 0.2mm is  3.093 mm^2\n",
      "The minimum cross-sectional area for Steel that produces a maximum displacement of 0.2mm is  1.083 mm^2\n",
      "\n",
      "\n",
      "Mass of steel truss with chosen cross section =  28.5912 g\n",
      "Mass of Al truss with chosen cross section =  27.456561 g\n",
      "\n",
      "\n",
      "Price of steel truss = $ 0.015001803601250021 \n",
      "Price of Al truss = $ 0.04676045872120902\n",
      "It is cheaper to create the steel truss\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "#from pretty_print import array_print as AP #a defined printing command for matrices\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.linalg import lu\n",
    "\n",
    "K=fea_arrays['K']\n",
    "K_aug = K[2:13,2:13]\n",
    "\n",
    "P,L,U =lu(K_aug)\n",
    "\n",
    "F=np.zeros(2*len(nodes)-3)\n",
    "F[5]=-100\n",
    "Es = 200 * 1000 #GPa\n",
    "Eal =70 * 1000 #GPa\n",
    "A = 0.1 #mm^2\n",
    "bs = (1/(Es*A))*F\n",
    "bal = (1/(Eal*A))*F\n",
    "\n",
    "def solveLU(L,U,b):\n",
    "    '''solveLU: solve for x when LUx = b\n",
    "    x = solveLU(L,U,b): solves for x given the lower and upper \n",
    "    triangular matrix storage\n",
    "    uses forward substitution for \n",
    "    1. Ly = b\n",
    "    then backward substitution for\n",
    "    2. Ux = y\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    b = output vector\n",
    "    \n",
    "    returns:\n",
    "    ---------\n",
    "    x = solution of LUx=b '''\n",
    "    n=len(b)\n",
    "    x=np.zeros(n)\n",
    "    y=np.zeros(n)\n",
    "        \n",
    "    # forward substitution\n",
    "    for k in range(0,n):\n",
    "        y[k] = b[k] - L[k,0:k]@y[0:k]\n",
    "    # backward substitution\n",
    "    for k in range(n-1,-1,-1):\n",
    "        x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
    "    return x\n",
    "\n",
    "ufal = solveLU(L,U,bal)\n",
    "ufs = solveLU(L,U,bs)\n",
    "\n",
    "delta = 0.001\n",
    "i = 1\n",
    "while np.max(ufal) >= 0.2 :\n",
    "    Aal = 0.1 + i*delta #mm^2\n",
    "    bal = (1/(Eal*Aal))*F\n",
    "    ufal = solveLU(L,U,bal)\n",
    "    i=i+1\n",
    "    \n",
    "print('The minimum cross-sectional area for Al that produces a maximum displacement of 0.2mm is ', Aal, \"mm^2\")\n",
    "\n",
    "delta = 0.001\n",
    "i = 1\n",
    "while np.max(ufs) >= 0.2 :\n",
    "    As = 0.1 + i*delta #mm^2\n",
    "    bs = (1/(Es*As))*F\n",
    "    ufs = solveLU(L,U,bs)\n",
    "    i=i+1\n",
    "    \n",
    "print('The minimum cross-sectional area for Steel that produces a maximum displacement of 0.2mm is ', As, \"mm^2\")\n",
    "\n",
    "length = 0\n",
    "for i in range(0,len(elements)):\n",
    "    node1 = elements[i,1]\n",
    "    node2 = elements[i,2]\n",
    "    length = length + ((nodes[node2-1,1]-nodes[node1-1,1])**2 + (nodes[node2-1,2]-nodes[node1-1,2])**2)**0.5\n",
    "    \n",
    "mass_s = As*length * 0.008 #area*length*density \n",
    "mass_al = Aal*length * 0.00269 #area*length*density \n",
    "print('\\n')\n",
    "print(\"Mass of steel truss with chosen cross section = \", mass_s, \"g\")\n",
    "print(\"Mass of Al truss with chosen cross section = \", mass_al, \"g\")\n",
    "print('\\n')\n",
    "\n",
    "price_s = (mass_s/907185)*476\n",
    "price_al = (mass_al/907185)*1545\n",
    "\n",
    "print(\"Price of steel truss = $\", price_s, '\\n' \"Price of Al truss = $\", price_al)\n",
    "print(\"It is cheaper to create the steel truss\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Future Predictions using past data\n",
    "\n",
    "The data from the price of aluminum and steel are in the data files `../data/al_prices.csv` and `../data/steel_price.csv`. If you're going to produce these supports for 5 years, how would you use the price history of steel and aluminum to compare how much manufacturing will cost?\n",
    "\n",
    "a. Separate the aluminum and steel data points into training and testing data (70-30%-split)\n",
    "\n",
    "b. Fit the training data to polynomial functions of order n. _Choose the highest order._\n",
    "\n",
    "c. Plot the error between your model and the training data and the error between your model and you testing data as a function of the polynomial function order, n. [Create the training-testing curves](../notebooks/03_Linear-regression-algebra.ipynb)\n",
    "\n",
    "d. Choose a polynomial function to predict the price of aluminum and steel in the year 2025. \n",
    "\n",
    "e. Based upon your price model would you change your answer in __3.b__?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Price of Steel and Al in 2025 will be $ -1706.236328125 , and $ 1850985.1484375 respectively.\n",
      "The high degree of the polynomials (93) makes the polynomial perform poorly as predictors\n",
      "I would not change my answer to 3d, steel is still cheaper\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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O3DBqF5wVl+dxa4S+a9SKGUYTxISWYRiGkTU0K0UMwzAMo3ljQisK4twnZNxHkIhMFZGXE6dsGohIob820dbqxMozRkTiWtTPtusQj7pcozhlzRaR+9NRr3QgIieJ86m2VUSmppCvWEQ+S5zSEJFnJeC3T0SWhxYkR8uT8vPTmPdERHqIyDdekShlTGgZqfAWzrTTF4kSpsglJOfaogoRGSv1963WJIhzLiNoOLczcfHroB7ELd/ojrtnLQ5xzhPfFWf66msR+ZMEDMqKSIE4018rRWSjT1MiznBxorKPxC04vjPFaqX8/DQU4nz+FQfDvDmwx3EGq1PGhJaRNKq6SZ0PnrDpn/qWWxbDIkCDIEn6YmtoVHVtE1LG2AW3AP0FVV1dF+sXmUZE8kQkmqmldJX/M9zavcdwWp4jcWuogr1hxa0pOxnn2uUYnJb2K5LYC/llOPuEKWkLN/bzU0fuB0aLSOeUc6ZqYbepbLhFfx/j7Imtwvmg2j4QPwa3mvxQ3OLEctyCuAND5RyBW4i40f8egWt4o+Mcuxi3ZulU3GLMjTjDvHuE0p2BW+RciVtQORHIDcRPBV4O1GMrsHuUMtbjXFz09HU7Gec+pdwf/7RQnl1wBmBLcdYwZuOt2vv4Ql/O0biFoxU4Ezl9/faGL/tdolti383vC25F/BJfxlKcqn5++D4kuJdV1yG4j1t0uQK30PTvQJdAmRrain1crr8/y/x9WQicGzqe4kwHTcdZ834icG1PA17x57OM2lb6e+O0+yLW9p8F9qrrNUpwLrOB+wNl5+Es8q/GWSH4L3BqlHP7NW5x+Hrcs/HbJJ6ng3EGYitwZq6m4/3QxahjYYxy8nEGnMt8OXfjXIN8Fkp3Cm7R+EbcQvnbgHaB+ALcguVIOXeFywm0k4t8Gduotlp+EdU+yj7FLTMJPnsJ20mUc5tGyG8YzvWJErDkHyVff5+mf5w0O+Ke/x+Hwpfj7Hj+Cbe84GucB4ScOM9PK9/G1uDa6KO4hclbAmmKce+w4/11+h7nO23P0PEPxNlx3ODLm4n3xODjd8MJ8m+obt9XBtpvuN30DORdQciLRDJbowufum44qwGDcS+bI/2F/2sgfoxvxP/y6fr4i78k0nhxFh++x63s3g+3sv9DkhNaEcdqB/ltDs6ycUQj8xjfCK/BWXz/Be7hC5rnDze2RcC40LH+Ddzn//f0dVuKE1x74V5iW3C29MC9JOfgXgiH4SwFPOaP3dmnKfTlzAN+4s/9bX/u//LXc19/fnMCdYnki7yQW+EE8SBft+NwFg/Gh+5DXYRWGc7O3/5U+/f6q48v8Oe9CmcCaGeqX1ZT/Xn8HGcy6xc44X1WoHzFmTW6CGdQeZ/Atf0CGIUTThNxbWhg4LgrcELtQL+9hnv4W9flGiU4l9nUFFo3+3pH/MRd6+t3ZOjcvsbZudsTJ5wVOCLO9d8Z92EwHddeDvPX8N+BOh7kyznOp28do6w/4tabHY975m7xZQeFzRhcezwNt/7vcH+8vwXS3OHP4zh/Lyb5NhEWWt/hrEoc4OseEUYrcAJlD9zH2UpqP3tx20mUc3sSKAmFRVzNnBEjz3Y4g72fE98Z5fG457hNKHy5v1ZX4yzw/8KnOzN0LsHn5zKckDnN57kMJ/DCQut7nB+3A3GCdR7weiDNfr6c8f5e9sN94C2O1BPn9+xlf/174j6+R/q4TriPgluobttBYfs4AQe2Sb/7U83QVDffQCup9hczxjemHwbSRPz29Pb7E33jDn6BHUtyQkup+YW9jw/7qd//N7X9bV2C+xqJvOCiNbYVgXPo7cs8yO/39PuXBfLk+oZ1rt8/ktq+qvJxL8rf+/1Cn6YokOYkH3ZC6Joq1S/RSL7d4lyb3wCfBvbHUDehtYaaPbargS8D+2NxrjOC5eyBe4n3CYX/Hu9d2O8rzk19ME3k2k4Ihb8FTPP/z8L1QDsH4nfy9/T0elyjWufiw2fjhRbOsV8lAb9vPvxp4NXQud0RSrMImBSnPhNwL9XWgbBI7+Dw0PWJ6f8I52hwI7U9/M6lprBZTm0/bRGfXDv4cioJCRDcAuyw0Cqlplfstv4eHRXKezrVXomTaidRzu8sXA/3ONzHyO44U1MKXBNKexPuuVTciNBescr16S8Fvo4SvpzaXsz/AcyI8/ysjtKOH6W20NqCH73wYaf469ImUO6joXLy/fUt8vsfEPCdFaX+n8WKx/Wu34t3XaJtWTunJSIjRORfIvKFOL85j+DcD+wcSKbU9OsSzZfRu+otwnuS9dm0Rr37B6iyIfeNLxPcMFs0fzxtiO79FVwj6YpzpwDua/kDdTYVgwR9f23BfZFGzqkv8K2q/jeQphLX+wpbjq+3zxsROVtE5vgJ5w24L+IesdKnwMe+3hGCvspiMRDX05wrNf1EXUttv2Cx/CCFfVm9Sc17+l+tdg2Dqn6Ns9UY0yp/mq7RXrj2Ha1NhY8dz89bNPrifJdVGT5V1Q9wPZtkvQ2Aa9f51PakXfVMiUgX3LnfFrpHs3ySvag+12T8jH2szqN28FwKgKdC5U8BtvfHT6WdBHkQJ4wilv4/Bkp83NZQ2ptxHnqPwI3uPC0i28UpO55/tKTvp4h0wI0gJXPtvlDVoDuZ1bjrEnneDwKGh67Rt7h3WOQ63Y4zPj1HRG4SZ1w6WRL65otGVppx8taFn8A9/Ffius8H4wx6BifVt6kzFhpB/W88n03h/ZSqlqAsiRHuAlXXisiTwNlehfV03BdRmER+vKKVH+1c6+XzRkROwnnevRr38vwO12O7IVr6FIl2jokm2SP1/DG1fSeFzz2hHyRPonsaSRP1nmbgGkVrU+GwuviGi9XuU3ke4rZvT6Qel+CGVsN8jhthSPbY4fsYKf8k3DBWmLWk1k6qI1z34HciMg43b/wtbnjzD4S8LPgPm2+AT7290W9xw873xCg+nn+0VO5nMvcgXrkEym6FmxudHCXvtwCq+pCI/AM3THoEMEtEnlbVZJYMdaIOPtiytad1GM4N9VhVneN7OXVZF7MQ594g6JcnWU+iXcT5kgFARPbBTaZGHCQupLZ7kcOpnqyMxRTg/3Au6dvhepCpsBDnqbVKxVZE8nGuNRamWFYiDgfmqeptqvq+OqOtPdN8jFhE86cU8bfUXVU/C22xXLeECfuyOoSa97RvUONJRHbCDQ3HurbJXKNo5xLmM9yQWbQ2Vd/7uhA4JKhFKSL9ge1TLPsz3LmE/Z79OPLH90xX4Ybow/foM3Wac5FyDgmVk4yfsYW4L/heMcrfSj3biapuU6dBuRGnjLWe2lbowwiuFxqL/+C8e3dPeIbx61aGm5ety7ULMxfnIX1JlOtUpa2oql+q6kOqejpuCHWU7/FB/Lbdzx8jJbKyp4UbjukiImfhvtYOw2lMpcrduHmke0XkFly3Otkv4HLgIRH5Da5B/hnnPiCyyG8S8KyIXI3TuDkA12u6VeM4WlTVN0TkE9zk5XRNXbX4VdzQ13QRuQA3xPM7XJf+7hTLSsQnwFkicjzwEW4+cESajxGLZcDOInIITjusXFU/E5EHgftE5Le4IZF2uInmLqp6UxLlniUii3AP02jcw3+pj5uOm/d4TESuxN33W3DDKrEcSiZzjaKdS40egKqWi8gdwAQRWYMbMjoJN4H/syTOKx534no+U8VZbe+I09Z7Q1X/nWwhqvq9iNwDTBSRyLDpWbhJ/P8Fkl4HPCAipbjhtc04xZ9hqnquL2dKoJzFOC3afUnwZa6qG/w53Oi131/Cvef6AQNU9aq6thMR2QEnpF7DvYhPxPWgz1O/NEFECn0938KNAO2OcyeyDTf/GIv5uHnnIcR3spoMtwLjfTt+F6cU9nNSH0W60eefJs7X3BrcB1cR8CdVXSrObuYLuHvdBte2V1HtrmQZcKgXxuXAWnXe2bfDXe9kjIfXJNVJsKay4SaPv8YND7yAWzOheJVKoigA4HpjSkBdF6e4sAD3FfsRTptOSU7lfTRuorQSJyzC6qJn4L7SN+FebDcQQ+U9lO8SX4dDQuE9iTIZTmiyk9oq768TXeV9t0DYYcHr58Miiit7RcuHU8GeghtyiWifXYgfSYl1H6Kcb43rEO26+GsdLDfPH28tNdXEc3D+whb56/6NP/+TAnlr3d/AtT0NpwARUcUOLyfojWtvEZX354iv8p7MNYp1LrOpm8p7+NxeBqYmuAdBlfdSAirv8dpelHIK/PmW+e1eoqu8F+GERbm/LvPxikKBcu71caU4IXo7sCDR8+PjzqJapX4dbk73/EB8wnYSpcwdcHOc3/nrNIeAMpNPM8iX8y3uvbACpyq/X7zr5vOOA/4ZClsOjA2F3Q/MjvP8tPLX/BuqVd6vBdaH32GhcqO9A/rhlpus8+f8mb8vnXz8X3AfFRX+nJ/H+UeL5B+I69lWUPP9fCawKNE1ibaZwdw64Fd4j1bVvTJU/h9wX539MlG+URsR6Yn7KhyssV3QG42IiLwKrFPVExq7LplAnAfsxTjNx/+kuewHcevEDkxnuXWsSyucEthEVY01QhGTbB0ebJaIc7TYD6c12Jgelw2jURGRfsAPcb2x1rge8BG4NVfNElUtFWfztE42+SKIyK645Sqv4bQa/w+n1HVhvSuZHrrhev4pCywwodXU+DtueOEx4OFGrothNCYKnI9bZNwKN4w3XFVnxc2V5ajqP9NQzFbcfOcE3DzTZ7ih0fvSUHa9Uefc9Na65rfhQcMwDCNryFaVd8MwDKMFYkLLMAzDyBpa7JxW586dtWfPno1dDcMwjKzi/fff/0ZVuzTW8Vus0OrZsydz56a8GNswDKNFIyIrGvP4NjxoGIZhZA0mtAzDMIyswYSWYRiGkTWY0DIMwzCyBhNahmEYRtZgQsswmjEl81Zz3LVPMKd7P/7vuicpmbc6cSbDaMK0WJV3w2julMxbzTUzF3DtrIc4aNVCTn7hQa5p1R6AogHdGrl2hlE3GsT2oIhsCAUVAHep6kU+/kicX5buOB81Y1R1hY8TnA+hX/m8DwBXqa+4dynxEM7Q7ErgQlV9mQQMHDhQbZ2W0ZypzMsnf0ttf6OVua3J31zZCDUymgMi8r6qDmys4zfI8KCqto9swE44h2BPAHjX5TNx3nU74TzGBk3Wn4NzGNcf5/r5WODcQPwMYB7O1f11wJMi0mirtQ2jqTD43Psp2XcIFbnOy3tFbj5P71fIYec+0Mg1M4y60xhzWifiXG9H3HiPABaq6hOquhHnUbO/iPTx8WfgXNR/rqqrcSbtxwCIyD44nzvjVLVCVZ/CeSFulk7iDCMV8nbrxob8tuRv2cTGnDzyt2xiQ+sCWu+2a2NXzTDqTGMIrTOAh7V6XLIvzoslAKr6PbDEh9eK9/+DcUtVdX2MeMNosVw5tDddK8qYNmAYw0+/lWkDhrFTRRlXDu3d2FUzjDrToEJLRLoDQ4C/BoLbA2WhpGXAdjHiy4D2fq4rUd7w8c8RkbkiMnfNmjV1OwnDyBKKBnSjfMbjTDn5chZ17cWUky+nfMbjpoRhZDUNrT14OvCGqi4LhG0AOoTSdQDWx4jvAGxQVfUKHvHy1kBV7wXuBaeIUaczMIwsomhANxNSRrOioYcHT6dmLwtgIU7JAgARaQfs6cNrxfv/wbheIrJdjHjDMAyjGdFgQktEfgx0w2sNBnga2F9EThCRNsDvgQ9VdZGPfxi4TES6iciuwOXAVABVXQzMB8aJSBsRGY7TMHwq4ydkGIZhNDgNOTx4BjAzpDSBqq4RkROAO4FpuHVapwSSTAF64bQCAe73YRFOwQmxdbh1Wieqqk1YGYZhNEMaZHFxU8QWFxuGYaROi1hcbBiGYRjpwISWYRiGkTWY0DIMwzCyBhNahmEYRtZgQsswDMPIGkxoGYZhGFmDCS3DMAwjazChZRiGYWQNJrQMwzCMrMGElmEYhpE1mNAyDMMwsgYTWoZhGEbWYELLMAzDyBpMaBmGYRhZgwktwzAMI2swoWUYhmFkDSa0DMMwjKzBhJZhGIaRNZjQMgzDMLIGE1qGYRhG1mBCyzAMw8gaGlRoicgpIvKxiHwvIktEZLAPP1JEFolIuYi8JiI9AnlERG4SkW/99gcRkTpJ+jsAACAASURBVEB8T5+n3Jfx04Y8J8MwDKPhaDChJSI/A24CzgS2Aw4HlopIZ2Am8DugEzAXeCyQ9RygCOgP/AA4Fjg3ED8DmAfsCFwHPCkiXTJ6MoZhGEaj0JA9rfHA9ar6jqpuU9XVqroaGAEsVNUnVHUjUAz0F5E+Pt8ZwK2q+rlPfyswBkBE9gF+CIxT1QpVfQpYAJzQgOdlGFlNybzVHDr5Vfa4+nkOnfwqJfNWN3aVDCMmDSK0RCQHGAh0EZHPRORzEblTRAqAvsAHkbSq+j2wxIcTjvf/g3FLVXV9jHjDMOJQMm8118xcwOrSChRYXVrBNTMXmOAymiwN1dPaCcgDTgQGAwcAA4CxQHugLJS+DDeESJT4MqC9n9dKlLcGInKOiMwVkblr1qyp+9kYRjPh5hc/oWLz1hphFZu3cvOLnzRSjQwjPg0ltCr8759V9UtV/Qa4DTga2AB0CKXvAER6T+H4DsAGVdUk8tZAVe9V1YGqOrBLF5v2MowvSitSCjeMxqZBhJaqrgM+BzRK9EKckgUAItIO2NOH14r3/4NxvURkuxjxhmHEYdeOBSmFG0Zj05CKGA8BF4lIVxHZAbgUeA54GthfRE4QkTbA74EPVXWRz/cwcJmIdBORXYHLgakAqroYmA+ME5E2IjIcp2H4VAOel2FkLVcO7U1BXk6NsIK8HK4c2ruRamQY8cltwGNNADoDi4GNwOPADaq6UUROAO4EpgFzgFMC+aYAvXBagQD3+7AIp+CE2DpgJXCiqtqEldGiKZm3mptf/IQvSivYtWMBVw7tTdGAbrXSRcKSSWsYTQFxU0Mtj4EDB+rcuXMbuxqGkXYiGoFBBYuCvBwmjehnwsioNyLyvqoObKzjmxknw2hmmEag0ZwxoWUYzQzTCDSaMya0DKOZEUvzT8EsXhhZjwktw2hmRNMIjGAWL4xsxxQxDKMZEtEeXB1jSHCHtnm0bZ1rGoNGypgihmEYMH8+dOwIH36YluKKBnTjzat/gsSIX1e+ucre4KbPV7PL8Ufx0ysftR6Y0eQxoWUYTYHRo6GsDE49Na3FJmPZ4uI3Z3DQqoWc8fLDNnRoNHmSGh4Ukf44O4H9gY5AKc6a+ixVnZ/RGmYIGx40mgQSqy8EpGHoPtqarQiLbhlOm62ba4VX5rYmf3NlvY9tNE+a9PCg9yj8Ds4s0t7A+0CJ/90b53BxjnkLNow6Mm8e9OhRM6xnT1559J9p8XFVNKAbk0b0o1vHAgTo1rGAjgV5AAw+7wFK9h1CRW4+ABW5+Ty9XyGHnftAfc7IMDJKIjNOFwO/UdW3YyUQkUOAq4CX01kxw2gRHHAAtGtXI6isVWsu/GgrFZs3AdUaf0CdlCWKBnSrkS/S+1rTvhMb8tuSv2UTG3PyyN+yiQ2tC2i92671OCHDyCxxe1qqenw8geXTvK2qRemtlmG0INatg7594bHHoG9fNq35NqMWLSK9r44FeXQuL2XagGEMP/1Wpg0Yxk4VZWYs12jSpKzyLiKdcM4Xq1DVlemsVENgc1pGU2WPq5+P6sNHgGWTj0nrsZI1rGsYERp7TitpK+8i8jPgAaAb1NCkVSD6SkbDMFJm144FUddXZcLHVXjo0DCaOqmovN8N/AGnPZgX2FpnoF6G0WIxH1eGEZtU/GntCPxFW6oJDcNoIIp2bsVhLxRz5lFX8NHWgrQM240tWcCMOavYqkqOCCMH7c7Eon5prLVhNAypCK2HgNOBv2aoLoZhAEyYQOf57/HsoFfhrruqgus6/zS2ZAHT3qmedt6qWrVvgsvINpJWxBCR2cAhwBLgq2Ccqv4k7TXLMKaIYTQ5Cgpg48ZawZW5rel9+UwEaihoJOvYcc9rXmBrlOc8R4Qlk46uZ6WNlkbWKGIAf/ObYRiZYOlSuOIKKCmB8nK2tGnDC3sdwoQhvwSopVEYUYNPJLSiCaxY4aZNaDR1khZaqmrL5A0jk+yyC3To4HpbbdrQqrKSstw2rGm/Q8wsyTh2zBGJ2dMKEjb5VN9FzRF+dttsPv3f91X7e3dtx0uXFda5PKNlk8iM08jA/9NjbZmvpmG0EL7+Gs47D955h2kHDKNLeWnc5MmowY8ctHtS4Te/+EnaFzWHBRbAp//7np/dNrvOZRotm0Q9rTHADP//7BhpFHg4XRUyjBbNzJlVf6ecfHlMf1iQvBp8RNkikfZgrF5bMr25WIQFVqJww0hEXKGlqkMD/wfX50BekeNgYIsPWq2qvX3ckcBfgO7AHGCMqq7wcQJMBn7l8z0AXBVRvReRnjjNxkHASuBCVTU7iEbWc+XQ3rUstEeUMbqlON80sahfQk3BhlzUbBh1JRVFjHRwoareHwwQkc7ATJxQehaYADyGE3AA5wBFOLcoCrwELAXu8fEzgLdxrlOOxlme31tV12T2VAwjs0QEUkMpRkQTkrao2WhqpGLGaVfgdmAI0DkYp6r1MeM0Alioqk/44xQD34hIH1VdBJwB3Kqqn/v4W3FDlfeIyD7AD4Gfq2oF8JSIXAqcQLVQM4ysJZqF9kMnv5oRIZYJIbl313ZRhwL37touSmrDSEwqPa17gE3AMcArwE+AccDzKZQxSUQmA58A16nqbKAvzqEkAKr6vYgs8eGLwvH+f1//vy+wVFXXx4g3jLTT0Grho+57m8UffMadz/yBG467qkqbMF3afUHqaosw1jV56bJC0x400koqtgcPxc01zQVUVd8HzgQuTTL/VUAvnMHde4FnRWRPnMX4slDaMmA7/z8cXwa093NdifLWQETOEZG5IjJ3zRobPTRSJ6IWvrq0AqVacGTKRf2o+97mzSVrufjNGRy0aiEXvzm9RnxYu69waiEAxbOLo/5mgkTX5KXLClk++ZiqzQSWUR9SEVpbcT0tgDIR6QKsB3ZLJrOqzlHV9apaqap/Bd7EzUFtADqEknfwZRMlvgOwwStiJMobrsO9qjpQVQd26dIlmWobRg0yoRYejwfOH8Lym47ltPmzuL5QOW3+LJbfdCyLbhlelSao3ff6itcBGP/6+Ki/SfPllzBkCHz1VcKkDX1NjJZNKkLrPWCY//8SMB14AvhPHY+tOGWohTglCwBEpB2wpw8nHO//B+N6ich2MeINI61kQi08QmS+ao+rn+fQya9SMm81g897gJJ9h1CRm8/4QqjIzefp/QoZfN6DVfnSod1Xqyc2YQK88QZcf33CvJm8JoYRJhWhdRqudwRwsf//GXBqoowi0lFEhopIGxHJFZFRwOHAi8DTwP4icoKItAF+D3zolTDArQG7TES6eWWQy4GpAKq6GJgPjPNlDwd+ADyVwnkZRtLEEhCHl6+Gjh3hww/rVG54iG3hhvu5ZuYC1rTvxIb8tuRvcYMc+Vs2saF1QdW8VkFeDmXtrkPGCzLeWbiI9yvjJepQYVVPrKAARODuu2HbNvcr4sJjEOuamKq8kQmSEloikgPcjB92U9VyVS1W1ctVNZnB/DxgIrAG+Aa4CChS1U+8avoJwA3AOtx6q1MCeafgVOEXAB/hFD+mBOJPAQb6vJOBE03d3cgUsXxd3fH8rVBWBqcm/IaLys0vfsIyubJqvyxvBhWbt/Jd3iOcVjSLnGJnhimnWDm9aBaluY/QrWMBk0b046OL3kbHKTrOpYn3q+OU4sLi2BVZutSdQ9u2FBcCbdvCqFGwbFnMLOb/y2hIktIeVNWtInI0bl4rZbwQOShO/MtAnxhxCvzWb9HilwOFdamXYaRKRLPu2pkfUr55G8tuOraGG28WLgQRFPj7fz5PWhPvi9IKKgs+qhW+LYYThu3a5PFFaUXVvFFdNP6KZxfXmOuK9MjG7XogxRs3Mr4Qiv+10dlD3HnnmOU09Hoyo2WTyvDgHbhhuPqsyTKMrGfuirWUb94GwLAxd7CqQ9cqC+wKrOzQlWFj/pxQqzCi6QfVQ2krCo5lRcGxVf/L8mYwbsi4qt7S08d9Tp8ts8jZcHJUTb0hPYYAMG7IuKi/QYoLi2v10HScUryku7N/CO43CWWMogHdePPqn7Bs8jG8efVPTGAZGSMVf1rLcJqCm4GvCXhKUNVeGaldBjF/WkZdCfun+uf957P3t6uq9hfvuDtDf3U34MwtvXl1dHdzMl4Y0mNIlcZfmD5bZtXwlyXjhR/nvxLV1FK84ySDjBcnsEK9rwjjhoyLP6xotBiyyZ/WrxInMYzmT9jNR4fKDXyyY3fuOGwkF78xg46V1SsuEmnQzR4zu+p/RCh9UVrB8oJjqwTW2JIFvPzKB5y1sgsf7P4FRHFVUl9NvUhPrLiwuEo4RQSZYTQlEgotEblLVX+tqq80RIUMI9s4+IJq36gv9KlpVzqsQVc4tbBGzyoyjxQZ1ov0lopnj6sSWNPeWcmEN6Yzav43PHLAdH439IJadQgfp2Teah584i2um3Y9E08bx1knHhJ3yM56UUa2kExPazTw60xXxDCygVH3vR0zrpXUVJyIpkEX7lkFezLBOa6IEBl74oFM3Lq5Kvy0+bM4bf4sNubk0eeKp6MeJ6I+f+2shzho1UJOfuFBrmnVHkhNYSPaPJhhNDapKGIYRoujZN5qzrj4Xr5r047TLrmPN5esjZn21EHd6daxAIEqdfRUhERQoEUILi6G2ouLc0SqrE9ElDGG/agXH08cxmnzZ9EKZ0Xj44nDGPaj1KaeU+19ZdJUlGFESKanlS8icZfFq+rv01Qfw2gyRHosJdMnsl1lOWMfmVClYBGNp95fnZKgigwJxmPtdjtWLS7emJNXtbj4m/Y7UJCXU2U+KWg898Zz7+faVx9g6KfvULClkorcfP6xzyHceMRZvJdUzerG+NfH2zCjkXGSEVoCRPfX7bCZWqNZcvwPd6MosN/721Usv+lYFNjjqudqpY/0eJIVWtF6VmFGDtqdzjNLmTZgGDMOOIqR8/9B1+/X0bZ1Dt9vim7vL2+3blEFXevddk2qXobRlElGaG1U1TMzXhPDaGIcPeYO7p05kd2++1+Vx+BVHbpyzojfRU3/VeurkdLJaa3DxKJ+jGUKM+asYqsq44dewMhBu1P+zsqo6b8oreCPvziAtlPLagi6nctL62WhIpbrkZgLlE1F3sgQyfa0DKPF8V3vvlTkubmkyHBCRV4+i3baI2r6ypyPMmJvb2JRPyYW9asR9tqiNVHXa+3asYCiAd0omfE4U7yQmXLy5fWyUBEZJo02FGkq8kZDk4wixr8zXgvDaIJcObQ321d+zyc7dueC46/ikx27s33lhoR5GqpuYXt/fb5eyqzi/2PYL+9k7oq1abNQYa5HjKZE3J6WiHRV1aMTFSIiO6nq1+mrlmE0PkUDulHyrw+59LH5QO01WABr217Leq227D78md3gGadkkcycVX3qBk6gRHpcf3r2ZrarLOf2Z/7A0K6uNxjuodWFZF2PmIq80RDENeMkIguB14G/AXNUdVsgrhXwI+B04HBV3T/DdU0rZsbJSJaw2aYIOSIsmVT9TddYw2MqEnUMXwFJ0kxbPA6d/GraTEcVzy62ua4sp7HNOCUaHhwA/Be4F1gvIgtE5C0RWYBzU3IPzmXIDzNbTcNoPEYOiq48Gyu8oYlntDcdpNP1SMoelA0jRNzhQVXdBNwJ3CkiuwP9gI4431UfJulLyzCymsgQW0SDL0eEkYN2rzX0lsy6q0zw6c57RlUY+XTn9NixNtcjRlMiaYO5qroKWJUwoWE0Q94ovYglk2bHTZPJOax4jBy0Ox3urG20N509waIB3WIKqUR2Dk0t3kgnqVh5N4xmT6z1SLHchzQFBvboxKEXTWOrN3z4Qp/B5LQSbu3RKePHTsbOoanFG+nEhJZheOKtR2rK3PziJ1UCK8LWbZqSdY66MuxHvSjasqlqP2LQt3Jya9hcmdFjGy0TM5hrGJ7weqSvWl/NotxhTo0d10uQ8VLDGntTIFmV9Eww+Nz7oxr0PezcB6KmN7V4o74kFFoi8nxDVMQwGpvwS37nTZPpUfEcPSucncGIO/r6zl2NLVnAwRdNY073fgy6aBpjS+rXm4tlhSMT1jnCpGrn0OawjPqSzPBg7RWVhtEM2bVjQUzTSMvTNNIVdOp40KqFXPjGdH7XznkirutC4CuH9q4xrAl1V0lPRHjO74g+XehakV47h4YRj7iLiwFE5DtV7dBA9WkwbHGxESY8pwXu5T9pRD9u/2BUWrQDN+a2pk3AqWNVeE4ebQJzQ6kSS4EkncS6Picc2I3XFq2Je+yUPSnbIuQmS2MvLk6mp9VGRB6Ol0BVT0/2gCKyN25B8pOqOtqHHQn8BegOzAHGqOoKHyfAZOBXvogHgKvUS1sR6Qk8BAwCVgIXqurLydbHMCLc/sEoJo14JOrLv2jA7LQcY/B5D3BdBnxdxVNJTxexbBC+tmhNTMsYo+57u8px5oQXk/ekbL65jFgkI7QUWJLGY/4Fqp9PEekMzMQJpWeBCcBjwME+yTlAEdDf1+UlYCnOGgfADOBt4Gi/PSkie6vqmjTW2WgBvL7idWaPyezLv9qpYyXbEPK3VLKhdQFrt8u8enp9SVXhIyKwFt0yvEbv0jQMjfqQjNCqVNW02F4RkVOAUuAtYC8fPAJYqKpP+DTFwDci0kdVFwFnALeq6uc+/lbgbOAeEdkHZ0Lq56paATwlIpcCJ1At1AyjyXBwrx3oXF7K4h27s8+3q1i8Y3e6lJdycK8dGrtqcSmZt5pWIlFtMMZS+Ij0sJLtXdoiZCMZGsyfloh0AK4HjgTOCkT1BT6I7Kjq9yKyxIcvCsf7/30DeZeq6voY8YYRl56392RF2Yqq/ciLMlNW2h/8dSH5gbmrPt+upM+3Kzni14VwdtPsdUTmsqIJrGQUPta075SUhqEtQjaSIZl1WtPSdKwJwAPeHFSQ9kBZKKwM2C5GfBnQ3s91JcpbAxE5R0TmisjcNWts9NCAFWUrqlTZIX1q7bFIdV1TUyDaXBY4K/eTRvRLaji1c3kp0wYMY/jptzJtwDB2qihLScOweHZxKlU2mjHJ9LRmiMjh8RKo6r/ixYvIAcBPcVbjw2wAwtqJHXBW5KPFdwA2qKqKSKK84Xrei7NYz8CBA+0zzmhwUl3X1BSINWe1TTWuwDp0z05VQ4TnDb+uKnzCUb/m5pMOcP7KYmg9hhchm2KGESEZoTUb+B+wiehDhYrT+otHIdATWOk6SLQHckRkP9zc0xmRhCLSDtgTWOiDFuKUMN71+/1Dcb1EZLvAEGF/YHoS52W0UGLNnfTYvkfGj33l0N60nZpd65rirV+LxyNnH1JDexCcIHvk7EOA+GazTEAZsUhmnVYJTp18JvCwqs5J+SAibanZI7oCJ8TO9/ufAb8EngfGA0NU9WCf9zzgElxPLaI9+GdVvcfHvwO8AYwFhuHU3xNqD9o6LQMaZ+4kk2uqUl0PlWyZsdav1afsRM4lwx8XEUwxo3Fp8uu0VLVIRDoBI4E7RGR7nCfjh6PMT8Uqoxwoj+z7Yb2NEcEiIifg/HZNw63TOiWQfQrQC7e2C+B+HxbhFGAqzsfXSuBEU3c3mjKZWlOVjMX1upApf1qJVOijKWbIeDGB1cJJ2NOqlcGpmV8EnIfrEb2ViYplGutpGdC8LC9U5uXX0EysCs9tTX4TXA+VqKcVJCi0TKuwcWnyPa0IXlvv57j5p5/gekVLM1Qvw6gTY0sWJPQwHKS5CCxwmonXZsDaRqaIZTNxy9at9Ly62k53q+2fAKrnHm39VssmodASkX7A6cAvgP8CDwNn+cW8htFkiBijjbBVtWq/rsZos4ls00yMNuy4ZetWvl5fs7e4rewkftp1DC9dVmg9LSOpdVofAMfiVMUfB9oAI0Xkl5EtkxU0WhhffglDhsBXX6Wcdcac6FOsscKbG1cO7V1lcb2u66Eam7DAivDp/75v4JoYTZVkhgf/hdPaOzJGvAIPpq1GRstmwgR44w24/nq4666Uskaz2BAObwhr6I1F0YBulMx4nCn+/KacfHmTPr9oKu+JiOVEsnBqYcYWhBtNi2SE1tFe+88wMkdBAWzcWL1/991ua9MGKpIbic6JYRsvx60NjLsuqKm+2FOlIay9p4tYljbiEWsO6/UVr6ehRkY2kMzw4AoR+aeIXCoieyVObhh1YOlSOPVUaNvW7bdtC6NGwbJlSRcxctDuccNjuda4+cVP6lZno17EUnkP02XDWp554to6DRkbzY9khNauwE3A7sCzIvKpiPxJRH4uIq0zWz2jxbDLLtChg+tttWnjfjt0gJ13TrqIiUX9GH1w96qeVY4Iow/uXqWEkaprDSOzxLKosdOGtTw2/Wq6bFgHwO/mPckPln/khowDFE51ihlBrUIZLxROLcxovY3GpS7rtPYAjsH5rvoRzs3IC8DTqvp12muYIWydVhNkxAgnvM45B+691yllzJyZtuJjrQvKEWGbarOb42rqxLK08fwn0+n11CMgAlujDB9GGTI2rcKGI2vWaUVQ1WU46xV3ikgbnILG0cAWnLUKw6gbQQH1l7+klDWZRcJH9OlSQyU+QmQerDnOcTVlwirvi24dEXVxdBVt28Lw4XDLLQ1UQ6Mpksri4i5AhapuEJEc3NqtLcAjqvp8/NyGEZ2xJQt4+ZUP+NPfb+Li46/iZ0f2j7umKqz9d0SfLnz47iKezR/P+y/tH9fW3muLElv3isxxmdBqGGoojlyyHK64AkpKoLzcCalu3eCzzyA/P+6Q8ZAeQ6KWH24vPXcs4J2l65JefG40PZKZ04rwHLC3/38Dzujt5cCt6a6U0TKILAa+4I3pHLRqIRe+MZ1p76xkbMmCqOkjw0mrSytQXM9o2jsrOWnWQwDO1t7MBZTMWx01f7y5qz5fL+XD20+mz9fLklK9NjJAtHnNLVvg/PPhnXfgvPNiKmNEU3eP1l7eXLK2qmcdWXweq70ZTZOk57REZB3Qyfux+hz4Mc7X1UJV3SWDdcwINqfV+GzMbU2brZtrh+fk0SbKMFF4Tmr0u8dxw5BttdJd969WTHyl9lxIrDktgBfvP599vl3F4h13Z+iv7q7hQsNoQNI4rxnvfgfJEWHJpKPrdIyWSDbNaW0FWnuDuWWqulJEWuF8YxlGygw+7wGuS8FWXrin9OJ+U3n6MZe/7dhKyidW55/o0wSHhzq2zSOvlbB5W/WH2rKbjq3hJK73t6tYftOxKMDZNrHf4NRjXjNMsL2U5j5Cxy2joqaLtSjdaJqkMjz4D5wZp7uBR33YfkD0sRjDSMDa7XaMaitv7XadoqYPq0ivad+pKj9Qy9ZeeHhoXflmEOhYkIcAP2hVzoKd9mR1+85EXlsKrOzQlWFj/pyZkzYajGB7KcubETNdZImEkR2kIrTOwjlpfAC40Yd1BorTXCejhTBy0O50Li+tYSuvS3lpzEXCVw7tTUFeTo2wSP49S4+qZWsv2mLizVuVdvm5LJt8DM+Uvsb+Xy+l7Wb3RR4RXBV5+SzaaY/0nqzR4ITbS2nuI1HTxWpvRtMkqeFBry34IjBUVasc86jq7AzVy2gBTCzqx1imVLkSGT/0grjaXNGsgr9x0xReW7SGraUVTDm55jqrWIoXr4w9Cq5xc2mtgB0qnTHWTa1yWLpDNzpWrufQPaP39ozsYX7ZfSzKHV/1livLm0FZ3gw6bjmV7TefatqDWUoqihgrgN6qujFh4izAFDGaP7Em4n/QqpxnVpRUqVZXts7nhb3cXNia9juYEkYzomTeah584i2ezT8ZgKeP+9yWM9STbFLEGA/cIyLjgM+pHk1BVWurcBlGAxHL8WMsJ4O/HPFjuPfVKtXq/E2bGD5kX4bfOboRz8JINyXzVvOrkqv4Nr96WHD4M7vBM+ZAMptJpacVEUzBDAKoquZEydKksZ5W8yDs+DFCxOZgRHtwdWlFlRX4bh0LeOKfN7Prvr0yZjLKaHwq8/KrlHSKC2F8IWgxVOa2Jn9zZY20zdllTbpp7J5WKooYe/itV2CL7BtGo5DI8WPRgG5VE/JBc01HHnoJJb+6Fvr3d6rVJrCaHYPPvZ+SfYdQkZtP8WwX9vR+hRx27gM10kVbhFy1SH3+fOjYET78sMHrb0QnaaGlqitibZmsoGHEIxnHj+aSpGWSt1u3Gksqfj+bGksiIsRtH6NHQ1mZc5tjNAlS6WkhIseJyK0i8lcReTiyJZl3moh8KSLfichiEflVIO5IEVkkIuUi8pqI9AjEiYjcJCLf+u0PItULK0Skp89T7sv4aSrnZGQ3sdbYBMPNJUnzZWzJAo755Z1816Ydw355Zw2TTFcO7U3XijKmDRjGL08cx/nvdaL7+jVVSyIibP58dQ1XKOAWnb95zZGwcKELWLjQWZ23NV2NTtJCyytgTPF5TgK+BYYCpUkWMQnoqaodgOOAiSJyoIh0BmYCvwM6AXOBxwL5zgGKgP7AD4BjgXMD8TOAecCOwHXAk964r9ECSOT4EWL7bYoVbmQHkfnM2575A9tVlnP7M3+oYUuwaEA3ymc8zpSTL2fYJ2/StXwdu/9w31pzVVfPfYIX9vyIi9+cXhU2bMwdfNlxp5oH7NkTPvgg06dlJCBVlfdjVPUjESlV1Y4i8iNgrKoel9JBRXoDs4FLgI7AGFX9sY9rB3wDDFDVRSLyFjBVVe/18WcBZ6vqwd6k1AKgs6qu9/H/xlmevydeHUwRo+mSjJuRILG0ByPE8ts0aUQ/m2zPEiKq69dNu56Jp43jrBMP4fgf7ka0fo8CEnmvFRQ4LdEwbdq4Xx8nxU5JA5ztywHXPMOc6RfTYemn1Xn69oWPPkrTGWUv2aSI0VFVI3dsk4jkqeq7QHSfAFEQkbtEpBxYBHyJcx7ZF6j6fFHV74ElPpxwvP8fjFsaEVhR4o0mSsm81Rx37RPM6d6P/7vuyRqW2ce/Pj6lsiYW9WPJpKNZPvkYlkw6utZi0aIB3Zg0oh/dOhYgQLeOBSawsojIuSPs4wAAHpFJREFUR8dJsx7ioFULq6z5DxtzB6s6dI1vgmvpUjcf1bat22/bFkaNgmXLasVtzMvn6f0KOemq6Uwa0Y8OFRucoHrsMfe7dm2Dnnd9iPd8ZTuprNNaIiJ9VXUh8BFwvrf8vi5BvipU9dcichFwCFAIVOIM7oYdHZUB2/n/7f1+MK69n9cKx0Xio76NROQc3HAj3bt3T7baRpqJvISuDb6EWjm7y5kSJDX8NhlZxbAf9aIoYPX/tPmzOG3+LDbm5LGyo/OtFTTB9enOAYXmaO5OvE+u4tnFjN9nOvzWJS24rhKYzbghQygacCJ88UV1OSefnNmTTCON8Xw1KKqa1IbzTny4/z8I+Az4ChiRbBmh8u4BLgb+BNwVilsAnOD/lwE/CsQdCKz3/4cD/w3l/TPw50THP/DAA9VoHDbmtlaFGtuQMSjFtbdxr41r7OoajcxBFzysT+87RMtz81VBy3PzdeZ+hTrwgr/pl+130I937K7nH3+Vfrxjd/2y/Q563dMf1ixg+HDVX/9adf589zt8eK04iqkdlwzz5qluv73qBx/U/0TTxMacvFrPl4JW5OTpjye9ok//5/N6lQ/M1Tq889O1Jd3TUtUXAv/nAHvVVVB6coE9gYXAGZFAP6cVCcf/9gfe9fv9Q3G9RGQ7rR4i7A9Uz6gaTY7B597PtSGXJK/3rGTgmr/x3p2jkfGCjjN3EYYjrLoetOZ/599er5rPfHHfw6PbEozn7iQSN/6uurlCCarEN5H5rmf3HcwJH73KVmlFrm6r4fJnjV+DBtnb64ortEQkqYXDqro0QTldgZ/gvB9XAD8FRgKnAm8BN4vICTgr8r8HPlTVRT77w8BlIvICbhTgclxvClVdLCLzgXEiMhYYhtMwPCGZehuNQ/AlNPaIVlz/mhv6Ca+fMQxwquttpzrV9RkHHMXI+f9g5/LSKqsV6TB4O27IuNQyhFXfIyrx4Po1jYFXOjnR7+Z663pttlSyoXUBa9rvAFSvQctWoZVIEeMz4FP/G2v7NGbuahQ4H2ezcB1wC3Cpqv5dVdfghMwNPm4QcEog7xTgWdyQ4Uc4wTYlEH8KMNDnnQyc6Ms0miCj7nub1aUVdC4v5YRT9uSGIdvIKXYP+VuVRyLjhSE9ktbtMVoAQdX1RV17MeXkyymf8XhaX7op2yGcNw969KgZlkmV+C+/hCFD4KuvYqfxiiVbvGbkFmnFq70O5In9j6RLec2VSdm8RjFuT0tVU1p8HKecNcTRMlTVl4E+MeIUN1X62xjxy3FKHUYTZ9R9b/PmEqeBdd7w63zoseyz+QUW5x1tQ4JGTBpakSbRMgoOOADatauZqV07+MEPMmPHcMIEeOMNuP56uOuu6Gm80knupk1sbZ1Pq82bWN2hK78bekGtpNm8RjEtQskwkiEisEpzH2FFwbGsKDgWgMV5RwNufZZhNCYl81bT9/f/YNo7K6tMga1oPabGouUq1q2rpRIf145h6DiHTn6VPa5+nkMnvxpbJb2gwA073n03bNvmfkVceDS+/hrOO4+cd+fQ6vzzOXIHreU4tSAvp5ZVkGwi7uJiv1A34eevqh6ezko1BLa4uOHpefXztcJWFBxLj4rnGHPUe+YqwohLpi2xR1uEDtVtNEeEJZOOjltGLB9u3ToW8ObVP4l5nJiL3b/8Eq64osr3G23bwvDhcMstsPPOSZ9XOq9bYy8uTqQ9eH+D1MJo8ZjAMuIRftGvzoAWXDTDuUFiGWcOkoydy3gGemudS5x1ZsnS3NYoJprT+mtDVcRo/hy6Z6eqIcII228eaa7tjYSk9KKvI0HB8nn+mWxtVa3PFRnK7nl7D5ZfujxmGbt2LIja0wrOIaVswNkP+dXw/daCSdXK+5ki8qqIfOJ/z8xUxYwsIhnNJuCRsw+pJaCO6XGRubY3EtIQlvqDgmW3yofoUfEcD5cMA+DhkmHsUfEctw95M24ZEd9tQcJzSCkbcJ45060hM99vQApmnETkOuB04FZgBdAD+K2I7KqqN2SofkYTJKxZNX3+XxkUR7MpaADXBJRRF5LpwdSXK4f2rhqCXHTLcNps3QzA6UXVpqMqb20NIa/HQSK9vnhzSMHjRMh25YiGJBUr78uAQg04ffR+r/6lqj1i52yamCJG3Qi6tw8+2DVo0wYqql8wZuHCqC8NZak/orSw6fPVXOettux7YSUf31ltVeK9O0en7TiZUirJJE1dESNIO2obtv0WyF6FfyNlgu7tB5/3QNWDXbClsqZmU4g9r3kh9poXw0hAMj2YdB2naEA3Dp38apXVlkV/zqP11k1RvR7X9zhG6qQitP4BPCIiVwMrccODNwAvZqJiRtMkqEG1pn2nGjbh2oQtaAdcjCxtcwzgFC+mvTMKwASXkRIN+aKPZzoqTOHUQmaPmd0g9UqVVH3TZQOpKGJcCKzH+avaAMwHvgcuykC9jCZK2L195/JSpg0Yxgmn3+Y0nLwyRnFhMTpO6bXRrc3qUfEcPSqeo+MWJ7CCPTbDaGqkYjrq9RWvp/XY6fSFlapvumwgFSvv3wGni8gYoDPwjaq3yGi0GEYO2r1qTguqzTGNPrg7FF1YK32stS3JrHkxjMakMYbwkvWFlc1zYvUlFUWM/YDBQCdgLfBvVf1vBuuWUUwRo+7EsssWbShiz2te4NucaVU9rAjJWBcwjKZK4dTCqD2sIT2GxB0qTCRsKvPyyQ84vKwKz21NvtdaTKSUEh6ajzBuyLi0DBU2tiJGwuFBcTyIs7J+LXAccB3woYg85D0IGy2IgT06sfP2bRBg5+3bMLCHW3sV7UEZOWj3WgIrEm4Y2crsMbPRcVqlFRv5n0hgJbJLOPjc+ynZdwgVufkAVOTm8/R+hRx27gNVaeIttIZq6zLhujWXua1k5rTOwVlRP1hVe6jqIaraHTgE1/M6N4P1M5oYsR68U2ZcFjX9xKJ+jD64e9VcWI4Iow/ubkoYRosjkbCB+A4vIzTEQuumTDJzWqcBF6vqe8FAVX1PRC4FrgHuyUTljKZH+MErzX2EFbkzWLTY7ct4J5yCQxETi/qZkDKaLcn6f0tG2CSjtbh9QR6lFbXXR25p/zgy/tiq/ciz2Nw0CJMRWvsBsdRjXgf+lr7qGE2daA9ej4rnqmyz2SJio6WRrLp7MlY9igZ0o2TG40zx815TTr68xrxXybzVfL9pS60y8loJtx9zI0UDnLnY5rygPxmhlaOq66NFqOp6ETGfXC2I4INXmvsIZXkzKMubURUv4yVtE76G0ZxI1nxTPK3Fm1/8hM1bawuj9m1yW4z2YDJCK09EjgBiKVykskDZyHKCD17HLaMoy5tBny2zWJQ7jHHLulM8eU5KbhMMo6WQDqsesYYYS8trDheOGzKu7hVt4iQjcP4HPJgg3mghFA3oxqOLbuWxxX+sCluU6yxhs3JlfHfghtHCqe/ar2QNBzfnkY6EQ3uq2lNV94i3NURFjabDoyNvq6nuWwzjZkPxayR2B24YRlIUzy6utZ+M65Pmzv+3d+/RVZVnHse/D/dAQEQuVaxAWCNYSylYbat1oOoqoowGUQdE0TVOgXG6ZtaoWKgoodIplDq92BtUrBco9VKgrciwlheslVLLKgpmjJ2Ri0DRoWoyQEIg8Mwfe5/DzslJcpKca/L7rLUXOfvd7867XwJP9t7v+7x6HyVtd9NNlL3WM/i6Z0+YPh127cptm0QKXOK8x4UvL6R0zGC+ed0oBvctwoDBfYvSnuk+32UlaJlZdzNbYWZ7zOyQmW0zs4mR8svNrMLMqs3spXDJk1iZmdkSM/sg3L4VndBsZkPDOtXhOa7IxjUVopbkNFu3bT+XLH6RYXPXc8niF5Mfe+AAC3adA126tGk5cBFJXemYwbw69zJ2Lb6aV+de1qECFmTvTqsLsBcYB5wG3Ac8FQac/sCacF8/YCvwZKTuTKAUGA18CphE/QnNq4FtwBkEmTqeMbMBGb2afJdkJeHYpOAbojnNEmbjJx7b1Mx9AB54gLIn9sErrwTJcrdsqZc0t7G2iEhyZZvKsIUWn2MV+zrxc+Kjw1TMX7eD4fOeY+jc9Qyf9xzz1+1IZ9OzJuXcg2n/xmbbgYUEweY2d7843N8L+Cswxt0rzGwz8Ki7Lw/Lbwe+7O6fM7NzCdJL9Y8NyzezV4BV7t7khOd2nXvwjjtg2TKYNSs+KCKVnGYxlyx+MenL3sF9i3h17mXB+6qjRxt+34TFHxtri4g0L3GuVVvmXkUXb41qTXaavM89mAlmNgg4FygHzidY7gQAdz8CvBPuJ7E8/DpatjNhHlm0vGMpKgoGQfz4x3DyZL1BEankNItpdub+zp1w003B+ytI/h6ribaISHY1thRQIS4RlPWgZWZdgVXAY+5eARQDVQmHVQG9w68Ty6uA4vC9VnN1E7/3TDPbamZbDx5MXIS5cK3btp9b/2U5h04am8+9iLoePYKCSDBJJadZTOLw2Qb7zzwzeG/V1HusVAKbiDQqca5VW+ZetaclgrIatMLsGU8AxwgWlYRgQck+CYf2IVhwMll5H+CwB881m6tbj7svd/fPuPtnBgxoH6+94uvv/HwRxcdqOG9POZ1qaznRrXu9YDJnwggG1gQ5zSbPeJCVYyYyqKYq6VDZjw95tvlhte+/3/h7LEgtsIlIoxLnWrVl7lXi4q3N7c9nWctmEd4ZrQAGAVe5e2wKdzlwa+S4XsDwcH+sfDTwWvh5dEJZiZn1jjwiHA38PFPXkW+uHXs2pZHPp9ceAcCP1Qbvkw4cAJrPaQZBAHzk6c38pvt3uKzmIj7s04/K6uPJZ+6vWXPq6x/+MHnjYoFt5kxYvjzeFhHJrsTFW6P7C467Z2UjyAS/BShO2D+A4JHeFKAHsATYEimfDbwFDAbOIghUsyPlW4Bvh3UnA5XAgObac8EFF3h7cOVt3/d3+wz0k+AOfhJ8T5+BPuG2h1p0nrV/2ucj52/wxz890SnDH//0RB85f4Ov/dO+DLVcRLLp3rXbvWTueh/y1We9ZO56v3ft9ladB9jqWYobybas3GmF865mAbXAe5FpVrPcfZWZTQF+AKwE/gBMjVRfBpQQjBIEeDjcFzMVeBT4CHgXuN7dC/eF1YEDMHUqPPlkSo/S/m/E+dR0DQZXxJ5O96+upOtZkboJ50y2eurWu8+h4m9PMiO8bZtRugHYwNa7O1H6Qv01gESk8LSXJYKy8k7L3fe4u7l7D3cvjmyrwvLn3X2kuxe5+3h33x2p6+5+j7v3C7d7wmgfK98d1ily9xHu/nw2riljHngAfve7IIdfCuZMGMFptUd4+4xz+Odrv0pl92KK6o7xvf/+ddJzJs7BKj/8MPPW7GDjeY+y9slxVC8KAmD1ou6seWo8G897LAMXKSLSOkrjlC9aOUS8dMxgfv/b7Qyreo8f/WoJp9cexoCSp58I6iecs3Ts2Wz75jXx+lVdV1Nz/AQf9j4jProQaHJ0oYhIriho5YsWDhGPpllauvFtXlz/+4b1r7sOJk+ut2/tJ8Zz6eyGSftPuMdHFw6vvLLJ0YUiIrmitbDyRQuGiMce8cUWk9tfWcOdrxxj5LFODIvWHzQoGJ4R2ee9e7Oj3xJqO78ZP19s1eFHFvwbe/dM4kRlDctuLIoHrEsWv9jq9X9ERNJJQSufpDhEfOnGt+utfgpQc/wEe97azbBk9SP7PvfWTmo7v8mQmmeBIGCNrNuQNFN0suA4b00wHkaBS0RyIWe5B3OtkHMPDpu7nmR/awbsWnx10jplm8rikxNtoXFx9xf4S2UNu4smsfaafUmDULM5CEWkw+mQuQelbZpNs5TEwpcX1ssWvbn2cnYXTWLckHGN3jU1m4NQRCTL9HiwAM2ZMKLeY7uYA1U1zF+3g0WloxrMxQLiGaJTzRad6tLeIiLZoqCVp5JNAI7dEcX+nLdmOzXHT8brnHRYueVddh08zMZ9P6TuxEmqilazO1x5JHaXlapkwbGjLe0tIvlFjwezoKWLr6WyCGPpmMEcq0t+t7R+z0N80GkVfeumM6Tm2figi4u7v4Av8FPZoptZoFFLe4tIvtGdVoYlLr52wj3+ubGUKo2NDly68e16ASNxWYH3us3lY8cWU9V1ddLzxt5FxbNFRzJlzP/SP7H6D3s54U5nM6Z99uMsKg0ClIKUiOQL3WllWGsWX0t1AETisgK1nd+Mz7mCYDj7nqJJVHZZxWnHp516F5Uk+8aiyZ+ifGmQeDAWWAt1OW4Rab8UtDKsNYuvpTo6MLqsQGWXVUnrnHZ8Gn3rpnOmzTj1Lioh+0ZsFePETBmFuKqpiLRvCloZFH0HlaipxdfmTBjR+CKMkfdQi0pH4f0XsKdoUtJHghd3f4HT66Y3fBcVyb5xolv3eJ7Bg8Wn16tfiKuaikj7pndaGRIbTNGYphZfiwWXpKMH77iDss6/pezrX4cf/Yg9d5+aIB0bym4LjQXjFlA2vokJwO+/z84pN3Nn389y3db1DDzyUYNDCnFVUxFp35QRI0MayyYBcPPnzmn5ujZFRUEOQcDKwMvC/T16QE3wfWJBK5r9orVtbHU7RaRdU0aMdqqxwRRG46MGE63btp9rvvY0Y2f34qppS1l33jiOhgs+JssCP27IOICUAlZTbQQFLBHJTwpaGdKaVEtRsceLN2z4GdvOrKZ7zfeY/PcvU3RvMFPY7qnG/mYVZRU/idfZdNumtLRxcN8iBSwRyUsKWhnyxZEDSHwjlGo2ibJNZUy8qIS3Fk3kltc3ALD2F/+Dl8HxsuCsj//qava/fGXKd1XJNDngQ0QkD+mdVgs0lVop8bjE9EcGTE/xkZstNIqPjeBwt7cblBUfG8nhbhUMqXmWoq6d25yhItVrEhGB3L/T0ujBFLVkbalkGS0ceKniYMrf7+CSnfQITxEdeHG08zt8bO40IHmWjJZSxgsRKSQKWilqLrXS/HU74mmQIJjs27duer3j91fWMHzecw1SJUHwSHDhywvjxxbddxyA+zYFn+usE/9b3I9rZ3yHvnWn5lNpmRAR6Uiy9k7LzL5iZlvNrNbMHk0ou9zMKsys2sxeMrMhkTIzsyVm9kG4fcvs1AQiMxsa1qkOz3FFJtrfVGqlWH7B6GTcxvL/xY5JTJVUNr4MX+DxJUMu7v4CT6ybSNkm49Ld0MmdF4Zf2GACsJYJEZGOJJsDMf4CLALq5Qoys/7AGuA+oB+wFXgycshMoBQYDXwKmATMipSvBrYBZwD3As+Y2YB0N76p0YBtSXfUWN05E0YwsKaKlWMm0su+z8oxExlQXVnvGA2aEJGOJmtBy93XuPs64IOEouuAcnd/2t2PAmXAaDMbGZbfCjzo7vvcfT/wIHAbgJmdC4wFFrh7jbv/EtgBTEl3+5saaRd9JBhLUgunEtaeKH6q0fMmS5W0YNwCSscMpnr1Uyy78S7eGljC/V+6g9mT740fo2VCRKQjyod3WucDb8Q+uPsRM3sn3F+RWB5+fX6k7k53P9RIedo0lVrprqfe4IQ7feumx99j7SmaRMnR9bzzzasA4u+yEiVLlRQbxq5BEiIi9eXDPK1ioCphXxXQu5HyKqA4fK/VXN16zGxm+F5t68GDqY/ka05jeQSj+1M5RkREmpYPd1qHgT4J+/oAhxop7wMcdnc3s+bq1uPuy4HlEMzTakkjmxryHhsBGF1E8dJBs+vNyUp2THT0oIiINC8fglY5wXsrAMysFzA83B8rHw28Fn4enVBWYma9I48IRwM/T3cjmxvyvqh0FItKR7Fu234eeXoz9/777/i7vc9w+/Wfjz/iix0jIiKtk7WgZWZdwu/XGehsZj2AOmAtsNTMpgDrgfuB7e5eEVZ9HLjTzJ4jmKN7F/AQgLv/2cxeBxaY2XxgIsEIw7QPxEhlNeHY3djXNvyMC/eWc+NzjzCvUzHQcAJydF6X7rpERFKTzTut+cCCyOebgYXuXhYGrB8AK4E/AFMjxy0DSghGBQI8HO6LmQo8CnwEvAtc7+7pe2EVOqtvUdJlPKJD4SdeVEJp3bH451te38Atr2+gdnE3OF4b3x+b1xUTm7MFqWeAFxHpiLI55L3M3S1hKwvLnnf3ke5e5O7j3X13pJ67+z3u3i/c7vFIwkR33x3WKXL3Ee7+fCban2zIO8CR2rr4CsWXznqYdeeNo6ZLsHxIbBn7L8xaUa9OY3OztLy9iEjT8uGdVkGIPd5b+JtyPqo+Ht9fWXM8PiCj69mDOdy9J93rjnG0c9f4Mvbdzj6r3rkaW8Zey9uLiDQtH4a8F4zSMYPp2a1hnI8NyIhmsZg840FWjpnIoJqqBlkrGlvGXsvbi4g0TUGrhZoakBHNYlExsIRlN95F9eqnGgzC0JwtEZHW0ePBFmpuQEYqWSw0Z0tEpHUUtFpozoQRDRZ4bE3iWs3ZEhFpOQWtFmoqB6GIiGSWglYrKJGtiEhuaCCGiIgUDAUtEREpGApaIiJSMBS0RESkYChoiYhIwTDvoPnuzOwgsKeV1fsDf01jc9or9VNq1E+pU1+lJpP9NMTdB2To3M3qsEGrLcxsq7t/JtftyHfqp9Son1KnvkpNe+4nPR4UEZGCoaAlIiIFQ0GrdZbnugEFQv2UGvVT6tRXqWm3/aR3WiIiUjB0pyUiIgVDQUtERApGhw5aZtbdzFaY2R4zO2Rm28xsYqT8cjOrMLNqM3vJzIZEyr4Y7qsys92NnP9fzWyXmR0xs7fM7NwsXFbaZaqfzOwcMzucsLmZ3ZXFy0ubTP48mdmnzeyVsHyfmd2fpctKuwz308Vm9lp43u1m9oUsXVZGtLGv5pjZm2G9XWY2J+HcQ8M61eE5rsjmtbWau3fYDegFlAFDCQL4JOBQ+Lk/UAXcAPQAlgJbInUvAm4BZgK7k5z7H4HtwCcAA4YD/XJ9zfnWTwnfZxhwAhia62vOt34C/gv4BtA5/Fk6AFyT62vOp34C+hFMqL0h7KebgY+A03N9zTnqq3uAsQRLUI0gSKYwNVL+e+A/gCJgClAJDMj1NTfbJ7luQL5tYaCZEv6j2Jzww1MDjEw4/ook/3g6AXuBy3N9PfncT0nOuQB4KdfXlo/9BFQDn4h8fhqYl+vry6d+Cv9DL0/Y92fg9lxfXy77KlL+feCh8OtzgVqgd6T8FWB2rq+vua1DPx5MZGaDCP4yy4HzgTdiZe5+BHgn3N+cs8Ptk2a2N7w1X2hm7aK/09hPiWYAj6Wjjfkgzf30XWCGmXU1sxHA54Hn09vi3EhjP1m4Je77ZHpamnut7SszM+DSsB7hMTvd/VDksDeS1c037eI/0XQws67AKuAxd68AigluvaOqgN4pnO7s8M8vAaOALwLTgNvT09rcSXM/Rc97KTAIeCYd7cy1DPTTs8D1BL9JVwAr3P2PaWpuzqS5nzYDZ5nZtDC430rwKLVnOtucK23sqzKC/+9/Fn5Oy7/bXFDQAsI7oCeAY8BXwt2HgT4Jh/YheJ7cnJrwz2+5e6W77waWAVe1vbW5k4F+iroV+KW7H25TI/NAuvvJzPoB/wl8neDdxceBCWZ2R7ranAvp7id3/wC4FrgTeB+4kuBudF+ampwzbekrM/sKwVOMq929tiV181GHD1rhbfMKgt/yp7j78bCoHBgdOa4XwW9t5Q1O0tDbBD9c7Wbmdob6KVaniOBlcsE/GsxQP5UAJ9z9cXevc/d9wC8o4F+CMvXz5O4vu/uF7t6PYMDGCOC1dLY929rSV2b2D8Bcgvfr0eBdDpSYWfTOajQt+HebM7l+qZbrDfgJsAUoTtg/gOB2eQrBb7dLqD8yp1O4fyLBqJweQLdI+eMEj3R6EzwurKCAXwhnqp/CY24KyyzX15mP/UTwG3Bl2E+dgI8RjPz6Rq6vN5/6KSwfA3QN++y7wKu5vtYc9tV04D3gvEbOuwX4dlh3Mho9mP8bMITgbugowe1ybJsell8RBpsaYBORodjA+LBudNsUKe9D8NvwIYKRhPcX6n/Kmeyn8JiNwAO5vs587ifgMuCP4X9S7wE/BXrm+przsJ9Wh31UBTwJDMz19eawr3YBxxPq/SRSPjSsU0PwdOiKXF9vKptyD4qISMHo8O+0RESkcChoiYhIwVDQEhGRgqGgJSIiBUNBS0RECoaCloiIFAwFLRERKRgKWiIiUjAUtEREpGAoaInkkJkNN7MPzWxs+PksM/urmY3PcdNE8pLSOInkmJl9mWA5jQuAtcAOd787t60SyU8KWiJ5wMx+DQwjSI56oZ9a90hEIvR4UCQ//JRgWfiHFLBEGqc7LZEcM7Ni4A3gJYJ1oka5+4e5bZVIflLQEskxM1sB9Hb3G81sOdDX3W/MdbtE8pEeD4rkkJldC1wJzA533QmMNbPpuWuVSP7SnZaIiBQM3WmJiEjBUNASEZGCoaAlIiIFQ0FLREQKhoKWiIgUDAUtEREpGApaIiJSMBS0RESkYChoiYhIwfh/3HPNlGbB0sQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "#from pretty_print import array_print as AP # a defined printing command for matrices\n",
    "from numpy.polynomial.polynomial import polyval\n",
    "\n",
    "#Import rcParams to set font styles\n",
    "from matplotlib import rcParams\n",
    "\n",
    "%matplotlib inline\n",
    "#Set font style and size \n",
    "rcParams['font.family'] = 'sans'\n",
    "rcParams['font.size'] =12\n",
    "rcParams['lines.linewidth'] = 3\n",
    "\n",
    "fsname = '../data/steel_price.csv'\n",
    "st = pd.read_csv(fsname,skiprows=0)\n",
    "xs = st['Year'].values\n",
    "ys = st['dollars/MT'].values\n",
    "\n",
    "falname = '../data/al_price.csv'\n",
    "al = pd.read_csv(falname,skiprows=0)\n",
    "xal = al['Year'].values\n",
    "yal = al['dollars/MT'].values\n",
    "\n",
    "# randomize testing/training indices\n",
    "np.random.seed(103)\n",
    "i_rands=np.random.randint(0,len(xs),size=len(xs))\n",
    "i_randal=np.random.randint(0,len(xal),size=len(xal))\n",
    "\n",
    "# choose 70% of data as training data\n",
    "train_per=0.7\n",
    "xs_train=xs[i_rands[:int(len(xs)*train_per)]]\n",
    "ys_train=ys[i_rands[:int(len(xs)*train_per)]]\n",
    "\n",
    "# choose the 30% of data as testing\n",
    "xs_test=xs[i_rands[int(len(xs)*train_per):]]\n",
    "ys_test=ys[i_rands[int(len(xs)*train_per):]]\n",
    "\n",
    "# choose 70% of data as training data\n",
    "xal_train=xal[i_randal[:int(len(xal)*train_per)]]\n",
    "yal_train=yal[i_randal[:int(len(xal)*train_per)]]\n",
    "\n",
    "# choose the 30% of data as testing\n",
    "xal_test=xal[i_randal[int(len(xal)*train_per):]]\n",
    "yal_test=yal[i_randal[int(len(xal)*train_per):]]\n",
    "\n",
    "plt.figure(1)\n",
    "\n",
    "coeff_s = np.polynomial.polynomial.polyfit(xs_train, ys_train, 93)\n",
    "\n",
    "plt.plot(xs_train,ys_train,'o')\n",
    "plt.plot(xs_test,ys_test,'r*')\n",
    "plt.plot(xs_test,polyval(xs_test, coeff_s),'g+')\n",
    "\n",
    "#Error for STeel\n",
    "for i in range(0,len(xs_test)):\n",
    "    plt.figure(2)\n",
    "    plt.plot(xs_train[i],ys_train[i] - polyval(xs_train[i],coeff_s),'r*')\n",
    "    plt.figure(3)\n",
    "    plt.plot(xs_test[i],ys_test[i] - polyval(xs_test[i],coeff_s),'g+')\n",
    "\n",
    "plt.figure(1)\n",
    "plt.title('Training (Blue) and Testing (Red) Data for STEEL \\n and polynomial interpolation of degree 93 (highest)')\n",
    "\n",
    "plt.xlabel('x ')\n",
    "plt.ylabel('Dollars/MT (Train)');\n",
    "\n",
    "plt.figure(2)\n",
    "plt.title('Error in predicted vs measured values for STEEL (TRAIN)')\n",
    "plt.xlabel('x ')\n",
    "plt.ylabel('y error (Train)');\n",
    "\n",
    "plt.figure(3)\n",
    "plt.title('Error in predicted vs measured values for STEEL (TEST)')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y error (Test)');\n",
    "\n",
    "# Aluminum\n",
    "coeff_al = np.polynomial.polynomial.polyfit(xal_train, yal_train, 93)\n",
    "plt.figure(4)\n",
    "\n",
    "plt.plot(xal_train,yal_train,'o')\n",
    "plt.plot(xal_test,yal_test,'r*')\n",
    "plt.plot(xal_test,polyval(xal_test, coeff_al),'g+')\n",
    "\n",
    "#Error for STeel\n",
    "for i in range(0,len(xal_test)):\n",
    "    plt.figure(5)\n",
    "    plt.plot(xal_train[i],yal_train[i] - polyval(xal_train[i],coeff_al),'r*')\n",
    "    plt.figure(6)\n",
    "    plt.plot(xal_test[i],yal_test[i] - polyval(xal_test[i],coeff_al),'g+')\n",
    "\n",
    "plt.figure(4)\n",
    "plt.title('Training (Blue) and Testing (Red) Data for Aluminum \\n and polynomial interpolation of degree 93 (highest)')\n",
    "plt.xlabel('x ')\n",
    "plt.ylabel('Dollars/MT (Train)');\n",
    "\n",
    "plt.figure(5)\n",
    "plt.title('Error in predicted vs measured values for ALUMINUM (TRAIN)')\n",
    "plt.xlabel('x ')\n",
    "plt.ylabel('y error (Train)');\n",
    "\n",
    "plt.figure(6)\n",
    "plt.title('Error in predicted vs measured values for ALUMINUM (TEST)')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y error (Test)');\n",
    "\n",
    "#Prediction\n",
    "predicted_s = polyval(2025, coeff_s)\n",
    "predicted_al = polyval(2025, coeff_al)\n",
    "\n",
    "print(\"Price of Steel and Al in 2025 will be $\", predicted_s, \", and $\", predicted_al, \"respectively.\")\n",
    "print(\"The high degree of the polynomials (93) makes the polynomial perform poorly as predictors\")\n",
    "print(\"I would not change my answer to 3d, steel is still cheaper\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "1. <https://en.wikipedia.org/wiki/Direct_stiffness_method>\n",
    "\n",
    "2. Aluminum and steel price history on <https://tradingeconomics.com>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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