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": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00416667,  0.00144338, -0.00083333, -0.00144338, -0.00333333,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.00144338,  0.0025    , -0.00144338, -0.0025    ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.00083333, -0.00144338,  0.005     ,  0.        , -0.00083333,\n",
       "         0.00144338, -0.00333333,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.00144338, -0.0025    ,  0.        ,  0.005     ,  0.00144338,\n",
       "        -0.0025    ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.00333333,  0.        , -0.00083333,  0.00144338,  0.00833333,\n",
       "         0.        , -0.00083333, -0.00144338, -0.00333333,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.00144338, -0.0025    ,  0.        ,\n",
       "         0.005     , -0.00144338, -0.0025    ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        , -0.00333333,  0.        , -0.00083333,\n",
       "        -0.00144338,  0.00833333,  0.        , -0.00083333,  0.00144338,\n",
       "        -0.00333333,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        , -0.00144338,\n",
       "        -0.0025    ,  0.        ,  0.005     ,  0.00144338, -0.0025    ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        , -0.00333333,\n",
       "         0.        , -0.00083333,  0.00144338,  0.00833333,  0.        ,\n",
       "        -0.00083333, -0.00144338, -0.00333333,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.00144338, -0.0025    ,  0.        ,  0.005     ,\n",
       "        -0.00144338, -0.0025    ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        , -0.00333333,  0.        , -0.00083333, -0.00144338,\n",
       "         0.005     ,  0.        , -0.00083333,  0.00144338],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        , -0.00144338, -0.0025    ,\n",
       "         0.        ,  0.005     ,  0.00144338, -0.0025    ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        , -0.00333333,  0.        ,\n",
       "        -0.00083333,  0.00144338,  0.00416667, -0.00144338],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.00144338, -0.0025    , -0.00144338,  0.0025    ]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "fea_arrays = np.load('./fea_arrays.npz')\n",
    "K=fea_arrays['K']\n",
    "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": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1a. 1.457753e+17\n",
      "Expected error = 10\n"
     ]
    }
   ],
   "source": [
    "print('1a. {:e}'.format(np.linalg.cond(K)))\n",
    "print('Expected error =', 10**(17-16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1b. The condition K is so large because the constant matrix is ill-conditioned. This is due to the boundary conditions not being set in K which have linearly dependent elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1c. 5.223543e+01\n",
      "Expected error = 1e-15\n"
     ]
    }
   ],
   "source": [
    "print('1c. {:e}'.format(np.linalg.cond(K[2:13,2:13])))\n",
    "print('Expected error =', 10**(1-16))"
   ]
  },
  {
   "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": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "rcParams['font.family'] = 'sans'\n",
    "rcParams['font.size'] = 16\n",
    "rcParams['lines.linewidth'] = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LUNaive(A):\n",
    "    '''LUNaive: naive LU decomposition\n",
    "    L,U = LUNaive(A): LU decomposition without pivoting.\n",
    "    solution method requires floating point numbers, \n",
    "    as such the dtype is changed to float\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    A = coefficient matrix\n",
    "    returns:\n",
    "    ---------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    '''\n",
    "    [m,n] = np.shape(A)\n",
    "    if m!=n: error('Matrix A must be square')\n",
    "    nb = n+1\n",
    "    # Gauss Elimination\n",
    "    U = A.astype(float)\n",
    "    L = np.eye(n)\n",
    "\n",
    "    for k in range(0,n-1):\n",
    "        for i in range(k+1,n):\n",
    "            if U[k,k] != 0.0:\n",
    "                factor = U[i,k]/U[k,k]\n",
    "                L[i,k]=factor\n",
    "                U[i,:] = U[i,:] - factor*U[k,:]\n",
    "    return L,U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "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",
      "\n",
      "U =\n",
      " [[ 5.00000000e-03  0.00000000e+00 -8.33333333e-04  1.44337567e-03\n",
      "  -3.33333333e-03  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
      " [ 0.00000000e+00  5.00000000e-03  1.44337567e-03 -2.50000000e-03\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
      " [ 0.00000000e+00  0.00000000e+00  7.77777778e-03  9.62250449e-04\n",
      "  -1.38888889e-03 -1.44337567e-03 -3.33333333e-03  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
      " [-2.16840434e-19  0.00000000e+00  0.00000000e+00  3.21428571e-03\n",
      "  -3.09294787e-04 -2.32142857e-03  4.12393049e-04  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
      " [-2.08654805e-20  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   5.83333333e-03 -4.81125224e-04 -1.38888889e-03  1.44337567e-03\n",
      "  -3.33333333e-03  0.00000000e+00  0.00000000e+00]\n",
      " [-1.58327936e-19  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  3.01587302e-03  1.00807190e-03 -2.38095238e-03\n",
      "  -2.74928700e-04  0.00000000e+00  0.00000000e+00]\n",
      " [ 7.57746398e-20  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  6.18421053e-03  1.13950711e-03\n",
      "  -1.53508772e-03 -1.44337567e-03 -3.33333333e-03]\n",
      " [-1.33795162e-19  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  2.55319149e-03\n",
      "  -5.52782173e-04 -2.23404255e-03  6.14202414e-04]\n",
      " [-3.65145909e-20  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   2.56944444e-03 -8.41969143e-04 -1.52777778e-03]\n",
      " [-1.11350493e-19  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  2.43243243e-03  7.02182760e-04]\n",
      " [ 8.34619222e-20  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "   0.00000000e+00  0.00000000e+00 -4.33680869e-19  0.00000000e+00\n",
      "   0.00000000e+00 -1.08420217e-19  1.11111111e-03]]\n"
     ]
    }
   ],
   "source": [
    "L,U = LUNaive(K[2:13,2:13])\n",
    "print('L =\\n',L)\n",
    "print('\\nU =\\n',U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "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, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aluminum Forward and Backward Substitution Method\n",
      "-----------------\n",
      " y =\n",
      " [ 0.          0.          0.          0.          0.         -0.01428571\n",
      "  0.00477508 -0.01215805 -0.00274929 -0.01042471  0.00687322] \n",
      "\n",
      "u =\n",
      " [  5.56730617  -6.07142857   1.23717915 -11.42857143   3.09294787\n",
      " -15.35714286   4.94871659 -11.42857143   0.61858957  -6.07142857\n",
      "   6.18589574]\n",
      "\n",
      "Steel Forward and Backward Substitution Method\n",
      "-----------------\n",
      " y =\n",
      " [ 0.          0.          0.          0.          0.         -0.005\n",
      "  0.00167128 -0.00425532 -0.00096225 -0.00364865  0.00240563] \n",
      "\n",
      "u =\n",
      " [ 1.94855716 -2.125       0.4330127  -4.          1.08253175 -5.375\n",
      "  1.73205081 -4.          0.21650635 -2.125       2.16506351]\n"
     ]
    }
   ],
   "source": [
    "L,U = LUNaive(K[2:13,2:13])\n",
    "F_tot = np.array([0,0,0,0,0,0,0,-100,0,0,0,0,0,0])\n",
    "F = F_tot[2:13]\n",
    "A = 0.1\n",
    "F_Al = F/(70e3*A)\n",
    "F_St = F/(200e3*A)\n",
    "u_Al, y_Al = solveLU(L,U,F_Al)\n",
    "u_St, y_St = solveLU(L,U,F_St)\n",
    "print('Aluminum Forward and Backward Substitution Method\\n-----------------\\n','y =\\n',y_Al,'\\n\\nu =\\n',u_Al)\n",
    "print('\\nSteel Forward and Backward Substitution Method\\n-----------------\\n','y =\\n',y_St,'\\n\\nu =\\n',u_St)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reaction forces using Steel modulus\n",
      "-----------------\n",
      "F =\n",
      " [ 0.00000000e+00 -1.77635684e-15 -1.42108547e-14  3.55271368e-15\n",
      "  5.32907052e-15 -1.00000000e+02 -5.68434189e-14  1.42108547e-14\n",
      " -1.77635684e-15  0.00000000e+00  1.42108547e-14]\n",
      "\n",
      "Reaction forces using Aluminum modulus\n",
      "-----------------\n",
      "F =\n",
      " [-1.42108547e-14 -2.84217094e-14  0.00000000e+00  4.97379915e-14\n",
      "  2.48689958e-14 -1.00000000e+02  1.42108547e-14 -4.26325641e-14\n",
      "  1.06581410e-14  0.00000000e+00  0.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "F_St_sol = 200e3*A*K[2:13,2:13]@u_St\n",
    "F_Al_sol = 70e3*A*K[2:13,2:13]@u_Al\n",
    "print('Reaction forces using Steel modulus\\n-----------------\\nF =\\n',F_St_sol)\n",
    "print('\\nReaction forces using Aluminum modulus\\n-----------------\\nF =\\n',F_Al_sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "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": [
    "l=300 # mm\n",
    "nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
    "nodes[:,1:3]*=l\n",
    "elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\n",
    "ix = 2*np.block([[np.arange(0,5)],[np.arange(1,6)],[np.arange(2,7)],[np.arange(0,5)]])\n",
    "iy = ix+1\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "u_Al_tot = np.zeros(14)\n",
    "u_St_tot = np.zeros(14)\n",
    "u_Al_tot[2:13] = u_Al\n",
    "u_St_tot[2:13] = u_St\n",
    "F_tot[1] = 50\n",
    "F_tot[13] = 50\n",
    "s = 5\n",
    "\n",
    "plt.plot(r[ix],r[iy],'-',color='k')\n",
    "plt.plot(r[ix] + u_Al_tot[ix]*s,r[iy] + u_Al_tot[iy]*s,'-',color='g')\n",
    "plt.plot(r[ix],r[iy],'o',color='b')\n",
    "plt.plot(r[ix] + u_Al_tot[ix]*s,r[iy] + u_Al_tot[iy]*s,'o',color='r')\n",
    "\n",
    "plt.quiver(r[ix],r[iy],F_tot[ix],F_tot[iy],color=(1,0,0,1),label='applied forces')\n",
    "plt.quiver(r[ix],r[iy],u_Al_tot[ix],u_Al_tot[iy],color=(0,0,1,1),label='displacements')\n",
    "    \n",
    "\n",
    "plt.title('Aluminum Truss Structure Deformation scale = {:.1f}x\\n'.format(s))\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.axis(l*np.array([-0.5,3.5,-1,1.5]))\n",
    "plt.legend(bbox_to_anchor=(1,0.5));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "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": [
    "s = 10\n",
    "plt.plot(r[ix],r[iy],'-',color='k')\n",
    "plt.plot(r[ix] + u_St_tot[ix]*s,r[iy] + u_St_tot[iy]*s,'-',color='g')\n",
    "plt.plot(r[ix],r[iy],'o',color='b')\n",
    "plt.plot(r[ix] + u_St_tot[ix]*s,r[iy] + u_St_tot[iy]*s,'o',color='r')\n",
    "\n",
    "plt.quiver(r[ix],r[iy],F_tot[ix],F_tot[iy],color=(1,0,0,1),label='applied forces')\n",
    "plt.quiver(r[ix],r[iy],u_St_tot[ix],u_St_tot[iy],color=(0,0,1,1),label='displacements')\n",
    "    \n",
    "plt.title('Steel Truss Structure Deformation scale = {:.1f}x\\n'.format(s))\n",
    "\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.axis(l*np.array([-0.5,3.5,-1,1.5]))\n",
    "plt.legend(bbox_to_anchor=(1,0.5));"
   ]
  },
  {
   "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": 317,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3a. Minimum cross-sectional area for aluminum = 7.679 mm^2\n",
      "3b. Minimum cross-sectional area for steel = 2.687 mm^2\n"
     ]
    }
   ],
   "source": [
    "y_St = np.min(u_St_tot[iy[0]]) # max y deflection in steel truss\n",
    "y_Al = np.min(u_Al_tot[iy[0]]) # max y deflection in aluminum truss\n",
    "A_St = .1*np.abs(y_St)/.2\n",
    "A_Al = .1*np.abs(y_Al)/.2\n",
    "print('3a. Minimum cross-sectional area for aluminum =', A_Al.round(3),'mm^2')\n",
    "print('3b. Minimum cross-sectional area for steel =', A_St.round(3),'mm^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3c. Weight of Aluminum truss = 0.674 Newtons\n",
      "Weight of Steel truss = 0.696 Newtons\n"
     ]
    }
   ],
   "source": [
    "density_Al = 0.00271 # density of aluminum g/mm^3\n",
    "density_St = 0.008 # density of steel g/mm^3\n",
    "bars = 11\n",
    "weight_Al = density_Al*l*A_Al*bars*9.81/1000 # weight of aluminum truss in Newtons\n",
    "weight_St = density_St*l*A_St*bars*9.81/1000 # weight of steel truss in Newtons\n",
    "print('3c. Weight of Aluminum truss =',weight_Al.round(3),'Newtons')\n",
    "print('Weight of Steel truss =', weight_St.round(3),'Newtons')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost of truss using aluminum = $ 10206617.18\n",
      "Cost of truss using steel = $ 3248994.94\n"
     ]
    }
   ],
   "source": [
    "Al_cost = 1545*weight_Al*9806.65 # cost of aluminum truss \n",
    "St_cost = 476*weight_St*9806.65 #cost of steel truss\n",
    "print('Cost of truss using aluminum = $',Al_cost.round(2))\n",
    "print('Cost of truss using steel = $',St_cost.round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3d. Based on the results above, steel is the cheaper material"
   ]
  },
  {
   "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": 407,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import random\n",
    "\n",
    "aluminum_prices = pd.read_csv('../data/al_price.csv')\n",
    "steel_prices = pd.read_csv('../data/steel_price.csv')\n",
    "al_year = aluminum_prices.values[:,0]\n",
    "al_year = (al_year-al_year.min())/(al_year.max()-al_year.min()) #normalizing data\n",
    "st_year = steel_prices.values[:,0]\n",
    "st_year = (st_year-st_year.min())/(st_year.max()-st_year.min()) #normalizing data\n",
    "al_price = aluminum_prices.values[:,1]\n",
    "st_price = steel_prices.values[:,1]\n",
    "\n",
    "\n",
    "i_rand_al = random.sample(range(0,len(al_price)),len(al_price))\n",
    "itrain = i_rand_al[:int(0.7*len(al_price))]\n",
    "itest = i_rand_al[int(0.7*len(al_price)):]\n",
    "al_year_train = al_year[np.sort(itrain)]\n",
    "al_train = al_price[np.sort(itrain)]\n",
    "al_year_test = al_year[np.sort(itest)]\n",
    "al_test = al_price[np.sort(itest)]\n",
    "\n",
    "\n",
    "i_rand_st = random.sample(range(0,len(st_price)),len(st_price))\n",
    "itrain = i_rand_st[:int(0.7*len(st_price))]\n",
    "itest = i_rand_st[int(0.7*len(st_price)):]\n",
    "st_year_train = st_year[np.sort(itrain)]\n",
    "st_train = st_price[np.sort(itrain)]\n",
    "st_year_test = st_year[np.sort(itest)]\n",
    "st_test = st_price[np.sort(itest)]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "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": [
    "Z_train_al=np.block([[al_year_train**0]]).T\n",
    "Z_test_al=np.block([[al_year_test**0]]).T\n",
    "#np.append(Z,np.array([d**2]),axis=0)\n",
    "max_N= 11\n",
    "SSE_train=np.zeros(max_N)\n",
    "SSE_test=np.zeros(max_N)\n",
    "for i in range(1,max_N):\n",
    "    Z_train_al=np.hstack((Z_train_al,al_year_train.reshape(-1,1)**i))\n",
    "    Z_test_al=np.hstack((Z_test_al,al_year_test.reshape(-1,1)**i))\n",
    "    A_al = np.linalg.solve(Z_train_al.T@Z_train_al,Z_train_al.T@al_train)\n",
    "    St=np.std(al_train)\n",
    "    Sr=np.std(al_train-Z_train_al@A_al)\n",
    "    r2=1-Sr/St\n",
    "    SSE_train[i]=np.sum((al_train-Z_train_al@A_al)**2)/len(al_train)\n",
    "    SSE_test[i]=np.sum((al_test-Z_test_al@A_al)**2)/len(al_test)\n",
    "\n",
    "plt.plot(np.arange(1,max_N), SSE_train[1:], label = 'Training Error')\n",
    "plt.plot(np.arange(1,max_N), SSE_test[1:], label = 'Testing Error')\n",
    "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "plt.title('Aluminum Testing-training Error vs Order of Polynomial Fit\\n')\n",
    "plt.xlabel('Order of Polynomial Fit')\n",
    "plt.ylabel('Testing-training Error');\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "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": [
    "Z_train_st=np.block([[st_year_train**0]]).T\n",
    "Z_test_st=np.block([[st_year_test**0]]).T\n",
    "#np.append(Z,np.array([d**2]),axis=0)\n",
    "max_N= 11\n",
    "SSE_train=np.zeros(max_N)\n",
    "SSE_test=np.zeros(max_N)\n",
    "for i in range(1,max_N):\n",
    "    Z_train_st=np.hstack((Z_train_st,st_year_train.reshape(-1,1)**i))\n",
    "    Z_test_st=np.hstack((Z_test_st,st_year_test.reshape(-1,1)**i))\n",
    "    A_st = np.linalg.solve(Z_train_st.T@Z_train_st,Z_train_st.T@st_train)\n",
    "    St=np.std(st_train)\n",
    "    Sr=np.std(st_train-Z_train_st@A_st)\n",
    "    r2=1-Sr/St\n",
    "    SSE_train[i]=np.sum((st_train-Z_train_st@A_st)**2)/len(st_train)\n",
    "    SSE_test[i]=np.sum((st_test-Z_test_st@A_st)**2)/len(st_test)\n",
    "\n",
    "plt.plot(np.arange(1,max_N), SSE_train[1:], label = 'Training Error')\n",
    "plt.plot(np.arange(1,max_N), SSE_test[1:], label = 'Testing Error')\n",
    "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
    "plt.title('Steel Testing-training Error vs Order of Polynomial Fit\\n')\n",
    "plt.xlabel('Order of Polynomial Fit')\n",
    "plt.ylabel('Testing-training Error');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "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": [
    "plt.plot(al_year,al_price,'s', label = 'stress data')\n",
    "plt.plot(al_year_train,Z_train_al@A_al, label = 'best fit')\n",
    "plt.title('Price of Aluminum\\n')\n",
    "plt.xlabel('Time (years)')\n",
    "plt.ylabel('Price (dollars)')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vF97y9AbvOeCK3xEOwUo9Vn2XnwUVYwheiglVLRIqaBS7hOTOgo3fOkHkl09h99qi01ZvxJt7j2e+9wQWeNPYSt3g1w6iRDdIVwI07uRs3W90SjRr58LKj9j5wwfUk/25SWvIYS5I+JYLEr6FZ1+HLldB5yFwTNPiv38pCfZvFY8lnFiyoGJMCKFuGlGtVjuwA9Z85gSRNXMg64+i0zbpCu0GQrsB0LgTI0Z8Evn7lbakKpB2DqSdwynzB9JVfqF/wiIGuBZynGt7Xrq9G+GLR2HuY9CmH3S92vlsCaVXPWZKhwUVY2LJ64VtS2H1LKdEsimTIhvAk6pB677OzbZtf6jRMGrZKIuG3zrVU8k80J5Md3tGcwXHy0YuSZjHnxK/phYHnETqdb6L1bOgWn2n5NLtb1Creannz0SHBRVTaUSyNG5pqsUf9HQtpU/CEhh3OxzcXmTa37z1+dzblczkbky459aoDDgszvow0RC4Wu1myD4CKz+CH16DdfPyDh3cAd88A98+6wTSU66Hln3Cbnsp6t+7qBkGAgXWcHuQ5ayRY+0rFlRMJeL/n73gQlmlyYWXk2QtvV1L6JOwhE7yKy7x3dYKdJTyqJCpaczxdGG2twtrtCkg4IYJ5XAEe1iSUqHjn51t9zpY/Dr8+F9nlD84pZdVnzhb3TbQ7TrofAWkHhP0sqW5FHK00ldEFlRMuVWWg+laDP847Osm4qaDbKCbaxVMe5MfUudSiyBtI1XqQOszod1Aur7hZR/Vi5XHcEti/gE17n5Z12kJZ46E3sOdQZULJsHaL/KO71oDnw6H2Q/DSZc6pZeGJwS8lA22jA0LKqZMRfM/ekkayItTFVZU+qocoatrNd1cq0iXVXRxraGqHHUOroBaBU8QFzRNdxqk2/SDJp2dXlPAvjeKX4Iq+P2FUxoLtLwxlM6NN6J/+4REaD/I2XauhoUvweI34Kiv91j2QVj0qrMdd4ZTejn+/HwN++V5nq9wqt3iNTiGHVREJAU4DTgVaAJUAXYCq4AvVTVIf0djHPHyHz3Yf8aQN+M/tsHG+c5YjI3z+SnlJxLFG/yc6g19QeQsaNUXqtYpRq7LTmn8exT7375eWzhnDJx5Pyx9yym9bP857/iGb5ytRmM4+a/OVqNR1PIdC+F8//EaHEMGFRFpA9wODAGOAbzAPuAwUAdIBVREFgHPA6+paoj/YcaUF0or2UK6axWnuFbB+Puc+a78JAaYBmWT1mOhN42LBl8MzU+D+u1LPLivYLCL11+qpSalOqRfCycPdQZ/LpgIKz7MGwT6xxanS/KXY+H4wXSTE1moaRQ1yX9FqB4rq1JmJIIGFRF5DrgeWAw8BHwJLFFVt1+ahjill0HAU8A9IvJXVf0+wPX+DPwFSAcaABuB6cBoVf3DL90JwMO+6x4DrAdeAcYXeO9UX7orcWoZFgP3qOqXEX0LxvhpLtvo5fqJHq5ldHOtpK74tYfsKZzeq8JKbc5CbzsyvWlketPY4ht8eFG3yHpaRVItF6+/VEudCLQ4w9n2/w6LJjvbgW3Oca8blk/n7ZTprPA25zXP2bzvOYPDpOa7TDglp2j0ICtrsf67CFVSaQZ0V9XFRSVQ1W3ADGCGiPwDuBHoBBQKKsBdOIHkXmAT0AXIAPqKyOmq6hWRJsBcYDNOCWkncBYwFicQ3eN3vZdxgtndwFrgFmCmiJwWLM/G5HN4L6z/yplS5Nc5fJmyPmjyoySRctwpPPdrPTK9afzgbct+qkX8tuHWm0d6k4jmssZxr2YT6Hsv9LwLVn7oVI1tnJ97+HjXRh5zvcyIxDf50HMa0z09WKTtQl42ko4ZJr+gQUVVL4zkYqp6FHg2SJLzVXWH3+t5IrIbmAL0AeYA5wH1gDNU9Rdfujki0hq4Gl9QEZFOwBXAtar6qm/fPGA5TqlqcCR5N+VPsefr8npg86LcIMKmzKDzaO3R6mR603JLIsu0Jb8MvZAnQ7S9hMpHadWbV5qA4i8xGU682Nm2LoWFL3F40ZtUwekwUVMOOXOOJc5mEw1gzhJaSQPWapMiL1kpv8coKNPeXwUCSo6FvsecCX9y/ifuL5BuL+SbM3swkA1M87u+W0SmAsNFJMUX5EwcKW4giEb998UPT+aso7P5U8JXNJIA9Vg5kqpBy548uLwh33pPYI02KTRdeyixGmAYSsF8leUSx2U2jXujjnD+eKr0G+X0GFs4Kd+8ac3YDl8+wZwUWOxtxfueHnzoOY1dBB/3UpbiZaBucUTS++sCoI5fqeA4YCpwIjAT+KuqHihGHnr7Hlf4Ht8GHgSeE5G7gV041V9XAaP8zjsBWKeqh8hvOU5gauN7buJIcasTit1zKOsgLH0bfnyddz0LAv7Fe1VwNe3sjBVpfSY0OwUSk5lShgMkY6Usq3fKvCqpSi047WbofhP89h38NM1Z4+XIvtwknV1r6exay/2J/2GhtmemJ53PvOls0vplm9cCQn1XZTl4N1KRlFRG4tzwczyF0+YyEeeGn4HTZhI2EWmKU1X1uapmgtNGIyKn4bTT5Py8UCBDVZ/wO70OAZtN2e13vKj3vQG4AaB5c5tTKF5E9VfzwV1O76AFEwOuNbJTazLb05WvvB35xnsCP97wl4jfoiS/vNMf+Szi9yvO+1QEJS6lulxw3OnONnCMM6/YT9PIXvkpSTj9fhJEOVVWcKprBQ/yH9Z6G/GN90RY4YUWPZ0AVUZK+nlj/XcRSVBpDfwEICJVgHOBq1X1bRFZAYwggqAiItVxAocbGOq3vz5Oj7CDwJ9xSipnAiNF5KiqjslJSuAOGCEXx1bViTjBkPT09OIuqGpKKNwG5YiqAY7+Ad+Mh/kT8q3jAZCtCcz2duUdTy/mejvhLkHtb0lHpZe0aiNeq9eKqzidC3KWJQh2XqF/m6RU6DAYOgwm6dBu+HkG33/wb7rJqrypc4BWrq20cm2FaZ/jUeEnbc1X3hP52tORjVU78N3950b8GSP5XJHsLyjWnQsi+V+VijM2BeB037mzfK9X4QyIDIuvK/AHQCugt6pu8jv8T6AFcJyq5pRE5opIAvCwiLysqjtxSiSBihm1fY/Bl8IzMRfVOmOPG358Db4Y7UxE6K9Wc+g+jO4zarObmmFfMtx67Xir+y6PS9AW9zss7rIEgDMANX0ot3zaDDmwnX4Ji+jvyuRU1wqqSN55CaJ0kTV0ca3h1sT3OeROgVdOhmYnOzMjNEuHmk2drs4moqCyHugBzAMuABapak7lZAOcAZEhiUgS8C5wCtBPVZcWSNIRWOMXUHIsAJJw2kp24rSXXCQiVQu0q3QAsoA1YX4uU95t+QneH+asOOiv4YnQ4w7ocCEkJLJ7RmT10LGagDKnFFLc94z1L9XyJu/7GuI8uI/Cb98z4eVJ9HAto6Osy1eKqSpHncXTNn6bd5HqjZzg0qQzNO7iPFarV3YfIo5EElReBJ4UkYuAzsAwv2OnAT8HPMuPiLiA13Ea3gep6ncBkm0FTheR2gUCS3ff42bf4wc4DfeX4HRJRkQSgcuAWdbzKz4VdwxFoF/fCXi4s+onMOkd8Gbn7t+idRibfSnvbeiBbnDh9CMJfm1TduJxHE3gPF3OWJylCk53LaeHaxk9XEtp7grQifXAVmf6/pUf5e2r2Ywv/mjCoqzjWKYtWOZtxU5fD7PijoEJp7ov1sIOKqo6XkR24ASQZ1X1Nb/DNYBXw7jMBJwg8ChwUERO9Tu2yVcN9m+cnwyzRGQsTptKH5z2mvdU9TdffhaLyDTgGV/pZx1OoGtJ7k8OE2+KezMp9B9w16/w3o2waWHursOazHPuC3nZcw5HCD5NfEVpkyiPU43EW0CB4HnaSw0+8Z7KJ17ndtWAPXRxreHFvgqbF3Fw/UKqcaTwifs30ZdN9E1akLtri9ZhmbclSw+3hF+8zrLLEcxTFiyf8fI3HVZQEZFknBv2bFV9o+BxVb0xzPc7x/d4n2/zNwqnh9d3ItITeAAYD9TEqXp7CBhX4JyhOAHqEZxpWpYAA1X1hzDzY8qBQr++lr8H79/izFTr86O3DXdmD2OdNi7j3BVPOO0e4aSJlwk6K5Pt1Gamtxuc7dzEOw7/kDaymU6uX+ko6+joWsfxsoFUyS50bmPZTeOE3ZydsAjeeMfZWb2RU13WNB1a9qJhNRfbDhaePrG8jF0R1fA6P4nIYWBARZtXKz09XTMzM2OdjUojnHaCIn9lq8Kch+GrvN8WbhJ4Ovti/u05Hw8JYecj0l91waodYlkqCPZ9xssv14JiMcYi1L9RcfNU1I0+AQ9tZDMdXes40RdoOsiGfB0AipRcA1r2cqbyTxsIVWrnHirR/58oEpFFqpoe6FgkbSorcHprVaigYuJPwP8QXg98fKczcWCOOq24YMt1LNcWscmTibpAgTAaQai0fuEXdV0PCazS5qzyNOcd3/juBDy0ki10lLV0dK1jaMt9sPWnQl3fyfoDVn3sbK5EaNkbOv3F6QpdgjyVlUiCygPAeF+EKthjy5jS48l2enct9Rt72+ZsuPgllo/6Jnb5MiYCHhJYrc1Yrc2Y7u3F0L8Ncn4s7VoDv//om9R0Luz3G2HhdcOvs53tf3UYkXgar7oHstU3C3Y8iiSo3ANUB34UkfXAFvIPPlRV7R3oRGNyRFwv7D4Kbw91frXlOOkyuOB5Z3XAYuYhUuWxQTxexeM4mrJur8j9rK4EqJ/mbJ0ud6p4d61x1olZ8SH87tc8fHg3NyZ+zDUJs5jsGcjz7vPZX8ylp0tTJP8rPYTRbdiYYHJuwMGqNHKOVeEIr1Z5hlP1p9xj70h/7l5wProgeDdhiG6bQrw2iMfjDTqYcINzWXc7LusxSf7LOAeeGiQNSKMJO7ko4Wv+kjiHZrITgFTJ5qbED/lLwmwmuC9gimcAR4mff+9IuhT3KcV8GJNPVY4wJflxuuWufgCcfit3zelOGDPxVBrlrZQUbnCOdbAuqUgGsAbrKvU79ZjguZAXPIPp41rM7YnvcpLLWXn0GDnEvUlv8tfEmdyfPZTZ3pOjkfUSK9Op703lFOmvzkTcPJ80nm4uv4DSdyT0ugvmfBLWNeL1l3pBVq0WuVCls5KW3KJRFRbt0o4XF3O8XfkiqzPnuhZwV+I0WrqclS6byG5eTh7Hf91n8bD7Ko6SHNNFxiIOKiJSG2gLBdbmBCpad2MTHZH9B1UeSXyFPglL8nYNGA2n3RLyzFh1oc25gURzYsmi9lsQKv3SWbjXj0XXaMXFx95TmZmVzmUJc3m01oe5c91dmTibk1xruTn7NjZpg5iV9sJeeUhEUkXkDWAHMB/4IsBmTIncmvAelyfOzX093n1RWAElHpTFf+J4bdsxZctNIq97+sEtC/jI0z13/0mudXyQPJKu8kuQs0tXJMvZ3Y8zXco1OJXafweuA74GfsVZBtiYYjvPNZ87k97Jff2OpxdPu/8cwxzlKS/VaabsxPpvol71ZKhah79n38oD2deQpc7g3zpygDeSH6Wn66cQVygdkVR/XYwzVcpU4D/A977pUF4VkbeBgcD/op9FUxm0lU2MSZqY+/pLT0dGZF9Hver55/AKVZ9eWtVDsZqxuKIJt7daeejVFujvqSz/NvLeX3jNM4Bl3pZMTH6KerKfVMnmpaRx3PqQi2cfuKfM8gSRBZXmwHJV9YhINlDN79grOBNK3hbNzJnKoQaHeDHpKaqJb2LpOq3odf1HrA6w2l6owGDVQ/Et3MBeEduHwukRVrBdMJIg9YO24+KsDF5PHk0z2UmKZPOYZxzsvgTqtCpeposhkqCyC3JH2vwGdAK+8r2uB1SJYr5MBRK8N40yLukFZ5U94JCmUPWy18t0+dZYKg+/yKOtInc2iPa/Z6QTj27QRlyedT9Tkx+mmex0fqhNvwGGflrswcKRiuRdvgO64FRxvYuzCmMNnOWA/w+nbcWYQoJVE1yTMIv+CYty99+TfT0fPr0OZyWD+LzRRPPGEelnqwhBqCKXJqP9txrO9TJHnp2vRLNJ63NT1u28l/wgSeJxlof4ciz0HRHVvBUlkqAyhrzlex/BWYHxISABJ+AMK+I8YwJqJ79xb2LeSgqvuAfyoff0fGni8UYTyyAXbwHWxKdl2uuMH/wAACAASURBVIqn3X/mn0nTnB1fjoU2Z8Gxp5T6e0cyoj4TyPQ9/wO4WERSgBRV3V9K+TMVVApZjE+aQIpvzYnl3uN43P2XGOfKmNgq2IZSkpL6vz3n0zthCd1dK0E9bJg0hHOzHuNggJaKaNYIRNKluBBVPWoBxRTHA1Xe4XjXRgCOaBK3Zd9CFkklvm5R1UDlqXrIVGyR/C2GW1IPdE0vLh5Ouo39WhWA41zbeTDxtULpInmfcAQtqYjI1ZFcrMASw8YAhRtmT5EVvJWSt5Z36qDHWDO9SZHnRzJi3aqHTLwrje7pwf7ub713Gc8mTwDg0sR5zPF24VNv6VWDhar+mhzBtRSwoGIK8Q8oKWTxWNJLeQfbnA3droPpoef0isf2FRO5itDZoDz5wHsGZ3l+5IKEbwF4LOklfjzahm3UKZX3CxVUWpbKu5pyq6TdQf+R+B6tXVsA+EOrUOP88SBSbtbfjpWK1A23vOU32kprWv9g170/eygnu36hmeykthzgyaR/c3X2cLRkLSABBQ0qqroh6u9oyrWSdAc9XjZwY0Jetdfj7r/w6DFNARuxHkpF7oZb2ZT10sYA+6nG/2UN483kR3CJ0jNhGUO9M3nFc07U8xH9MGVMAC68PJ40yek3DyzwpvGG58wY58qY+BbNKsHv9Xj+7Tk/9/U9iVNJk41Rf59QDfXrCL6GjD9V1dYlz5KpiIYmfEon11oAjmoiI7KvK5WitzHlWWku31CvejI3D38ZXu4HW5aQItnMPPY1uP4LSCq0kkmxhWpTmUf4QcWYgNKqHeR297u5r591/4lftWnQ7r/WkGtMdO08kAWJyfCnl+DFXuA+DMedTrRv8aHaVP4a1XczldLME+fAksPOi3pp3H3TBO5OLDpAVPaGXGNKVf12cN7TUKU2pA2M+uVtOWETkXBLETk9UbrKL0xPeTN3/827L+P5IAHF/9xI81WRg5GV3iqO0vq3jKgHZefSm70ioqAiIh2BB4HeQG1gNzAXeFhVl0Y9dybuhHvj3nkgCxdeHkqanLvvf55ufHKkfVjnRqqi94KqyAGzsimtf8uc68a692TYQUVEuuG0sRwGPgC2Ao2A84FBItJLVRcFuYSpZC5L+IITXesBZyqWR7KvjG2GjDGlLpKSymPAMuAs34SSAPimv//cd7x/dLNn4lWowXjVOMydiW/n7n/efQGbqV+WWTSmUop1VWkkQeVU4Cr/gALOjMUiMgaYEtWcmbgWajDejYkfUl+cuUY3a11e9JxXZnkzpjKLdVVpJAMFQvU7s67HxrFvM9cn5M3lNTb7Mo5iDcrGVAaRlFS+B+4Vkc8LVH9VA+7BWajLVEAR98b64lGqiJN+qbcFM/wW3gqnCF6cecCsF5Qx8SGSoHIvTk+vDSLyEbAFp6F+EM769H2inTkTHyK5wXeQ9Xh/fAOXOK9Hu4dQt3pqREXyWBffjTHFF8nKjwtE5FTgAWAAUAenS/EcrEux8bk7cRoucWpCP/d0Yb73BKjg3X2NMXkiGqeiqj8Bfy6lvJhyrqv8Qt+EJQB4VRhjywMbU+nYiHpTIv4T4H19/6O5z2d4T2e1NotFlowxMRRqluJXIriWqurfSpgfU16t/5oeCcsBcKuL8e4/xThDxphYCFVSOZP8XYVrAccAbmAXUNd3jX3AntLIoIm9kIOpVGFOXilluqcn67VxWWXPGBNHRDW84SUi0gN4E/g/4F1V9YhIAk4by5PAZar6banltJSkp6drZmZmrLNR7vh3M+7hWsp/kx8DIFsT6Js1jk3aIOj5FX0CSGMqMhFZpKrpgY5F0qbyFPCYqr6Vs0NVPcA0EakHPAOcUqKcmnIjr+Si+aZjecvTh68fG5r7uqjJ7Sr6BJDGVFaRBJWOwJoijq0GTgx1ARH5M/AXIB1oAGwEpgOjC07/4uu+nIEzPUwSsBZ4VFWn+qVJBR4GrsSpmlsM3KOqX0bwuUwJ9HEtpqvL+bM4qok8576QIVG4bqi5xYwx8SmSoLIVuBSYFeDY5cC2MK5xF04guRfYBHTBCRx9ReR0VfUCiMgg4D3gDeAKIAvoABRc8/JlnMGXd+MEnVuAmSJymqoujuCzmTAUvtErdya+k/vqDc9ZbKFuVN4r1Nxixpj4FElQeQZ4WkQaA2/jBJGGOIFmAHB7GNc4X1V3+L2eJyK7cSaj7APM8c16/CrwvKr6X/Nz/wuJSCecgHOtqr7q2zcPWA48BAyO4LOZMBS8ofd3ZXKSax3gTG3/vNu+cmMqu0hG1I8XkQM4i3Sd43foN+B6VQ3Z/bhAQMmx0PfY1Pd4CVAfGBficoOBbGCa3/XdIjIVGC4iKap6NFSeTPEIXu7wK6W85unPDmrHMEfGmHgQySzFqOrLwHG+7VTfY4twAkoQvX2PK3yPPXCmf+koIktFxC0iv4nIg77eZjlOANap6qEC11sOJANtSpAnE8K5rgUc7/oNgIOawotuZ2r7ghM7FjXRo00AaUzFFPGIenX6IP/m20pERJriVFV9rqo5/XqbAFVx2lMeBhYB/YD7cRrj7/Clq0PgsTG7/Y4X9b43ADcANG/evGQfohJy4eX2xHdzX0/xDGDR41cETGuN6sZULkFLKiJyUaQXFJHGvp5bodJVB2bgDKQc6nfIhdMg/5CqjlPVuao6EpgE3CIix+RcgsBruEio91bViaqarqrp9evbaoSRGuz6lrauzQD8oVWY6B4U4ozIWQnHmPIpVEllgohkAC8Ab6nq7qISikhP4CpgCE5posj1VXxdgT8AWgG9VXWT3+FdvsfPCpw2C7gJp9rrW5wSSaBiRk7FfpF5NcVTr3oyew4c5ja/UsornnPYS41C41FK2vXXSjjGlE+hgkobnG7ADwH/EpEVwBJgB3AU5wbeCmfcyTHAl8DZwUbWi0gS8C7OQMl+AabMX+57LFgKySmBeP3SXSQiVQu0q3TA6YJc1JgaU0yZI8+GH/4DH/h6j6cew8t7zwmY1rr+GlM5Ba3+UtVDqvoQTs+sK4FM4GTgWpzSyPlAAjAeOEFV+4YIKC7gdeAs4AJVDVSaed/3OLDA/gHAEWCZ7/UHOIMiL/G7fiJwGTDLen6VAncWfPlE3uvT/8F+qsUuP8aYuBNWQ72q5nTdnRYqbQgTcILAo8DBAm0vm1R1k6ouE5HJwEO+IPQDTkP9dTiLgR3w5WmxiEwDnvGVftYBw4CWEJVB3aWm3I4WX/xf2LvReV6lDnS/CT6xyQuMMXnKej2VnLqS+3ybv1E4o+sBbgQ2A//AGWC5HrhTVccXOGcoToB6BKdn2BJgoKr+EO2MR1O5HC2efQS+fDLvdY/bIaVG7PJjjIlLZRpUVLVFmOmygJG+LVi6w8Cdvs2Uph+mwH6nxxfVGkC362ObH2NMXIpo8KOpfNIf+Yz2w6ez/ZPRuftG7R1A+hPfANb11xiTny0nbILaeSCL6xI+p4HsBWCr1uYNz1kc9VXVxXUbkDGmzFlJxQRVlSMMS/wg9/Vz7gs5ipVCjDGBWVCJgfJUZfTXhJnUFWepm01aj7c8fWKbIWNMXIuo+ktEBGdsSi+c9ekzVHWDiPQGVqvq76WQxwqn3FQZHdnHDYkf5b78l/siskiKYYaMMfEu7KAiIrWBT4DuwH6gBvAvYANwPc60KLeWQh5NrHz3ArXkIAAbvA1419MzxhkyxsS7SKq/xgLHAmcA9cg/cePnOKPkTUVxeA/Mn5D7crz7T7j9foPEY1WdMSb2Iqn+ugC4S1XnF1jXBJwlgo+NXrYqtnIxov6bZ+Hofud53bY8dctonnIV/Gc3xpj8IimpVMcZ5R5IKmFMOW8ccT+ifu9G+O75vNd9hoMFFGNMGCIJKquA/kUc6w0UnG3YlFefZ4D7iPO8cWc44U8xzY4xpvyIpPprAs76KvtwVmUEqCUiQ4G/41tJ0ZRMzrokMasK+20BLMtbL4WBj4HLep4bY8ITdlBR1Uki0hpn4seHfLs/w1nf5AlVfb0U8ldpxaQqzOuFT0fkve5wIRx3etnnwxhTbkU0TkVVh4vIC8DZQAOcVRo/U9W1pZE5U8aWvQObM53nCclw9qjY5scYU+5EPPeXqm4AXiqFvFQa9aonx0+jfI6sQ05bSo7TboHaLWKVG2NMORXJ4MehwHGqmhHgWAawTlWnRC9rFZd/W0nBtd1j5tt/+U1tXx962GoCxpjIRVJSuQ14uYhj24HbAQsqEUh/5LNYZ8Gx/3f45pm812feD6k1gXIypsYYEzciCSptgOVFHFsBtC55diqXUFVgLYZ/XDY379kPQfYh53nDjpzySUO2vx28BBV31XfGmLgQSV9RN870LIHUj0JeTAClfvPe/AMseTPv9cDRbD/oKd33NMZUWJGUVBYANwFvBTh2E7AwKjkyJRJRdZUqzLw373XaIGjZC4iTdh5jTLkTSVB5FPhcRL7H6f21GWgKXAd0xelmbGIsoilgfn4fNs53nruSoP/DpZgzY0xlEMngx3ki8mfgGeBFv0PrgYtVdW50s1YxFVWSKHPZR+CzB/Jed78R6lqzmDGmZCId/DgDmCEiaTiLdO1U1V9KJWcVVFwEFHAmjNy70XlepQ70ujui023qe2NMIBEPfgRQ1VXRzogJrKibd4lKPLt+hXlP5L3uey9UqZXvPa0bsTGmOIIGFRG5GvhYVXf5ngelqq9FLWeV0PrHB4WdttgBxeuB924C92HndYMT4OSh+ZJY4DDGFFeokspk4FScOb4mh0irgAWVEig4uj7aJYMWwz/mloT3uTtpgbPDlQgXvQAJxSqwGmNMIaHuJi2BLX7PTRmKdvtLD9dS7kx8O29H7+HQuFNU38MYU7kFDSq+ySMRkSSgM/CTqq4ri4yZ6GrCTp5N+hcJogB8721P9x63xzhXxpiKJqwR9aqajTPosUWp5qYSaSFbGOz6hv6uhdRnT6m+VwpZvJD8DHXkAADbtBZ/z7oVEpJK9X2NMZVPJJXpa3HWUDElkFbtIH89+gaXJczF5Ss1APzsPY4pnv685+lBFqFv9uFOn59CFs8l/YtOLmfJm2xN4JasW9lBrXzpbOJIY0w0RBJUngDuE5E5qrqjtDJUYbmzYP5zTPeMoVrikUKHO7g2MMY1idsT3+WJ7Mt433sGGqQgGc70+VU4wsSkp+iZsCx332j3FWRq+0JpIxqJb4wxRYgkqJwJ1AHWich3OA346ndcVfWaaGauwlCF6dfDz+9TzW/3Um8LDlKFrvILyeJM4thYdvN08gtc7f2M8UnXhnX5QKWWGhzileQn6ObKG5v6b/f5vOoZmHuOMcZEWyRBpQeQDezAmea+4JweWugM4/hhijPPls8v3qY84r6SL71Oz6vqHOIvCXO4r9bncHA7AF1ca5jsuRemL4F+GVCzCRDeoMe67OPV5Cc4yeXXp+LMkdzU8y5uEonqRzPGGH+RzP1lXYqL48g+mJU3x9ZUdx/uc/8NDwm5+w5QlUme87jv1ifgq6dg/nPg8QWOn6bBig+h+01w0mVBA0oCHga7vuX+pP/kNsoDMOAxOO3mqH80Y4wpKJLlhOsBB1S1cIOAKdrCl+DoPud57ZY8uOWv+QJKPik1oN+D0PVq+Ox+J5iAs4DW10/B108xM7kZH3tO5RPvKWzQRrjw0lK2MijhOy5JmEcjyetJ5lVhhPs6xlhAMcaUkVDTtCQA9+MsFVwD8IjIh8DfVHVvGeSvfMs6xO7Zz1DH9/Lu7WdzlDDaMuq0hMv+C+u+gk9HwLaluYfSXJtIc73DnbwT9BKbtS4jsq/jS28npgVoyC/YqyvYfF/GGBOuUCWVm4AHgLk4i3C1Ai4C9gNDiz7NAPDjf6jDfgA2aT3e8/QoMmnAm3fLnnDjPFj5ESybDr/MzJuzqwg79BimefrwgnswB6lSZLqdB7JKfVoYY0zlEyqoXA9MUtUbc3aIyI3AcyJyo6paf9OiqDpVXz4T3YNwB/i6Q04i6UqADhc4W9ZBbsl4nEEJ39HdtYKaHEJQNml9VmpzBl5xG/XbDeTvCUn83Xd6Ud2NA7HuwxXD/v372b59O9nZ2bHOiilnkpKSaNCgATVr1iz2NUIFlVbAXQX2TQNeAI4DVhf7nSu6rT/BTqc770FN4R1P75JfM7ka31ftxccHTvXbqYCvR9cUgFlW4qjE9u/fz7Zt22jatClVqlRBrLefCZOqcvjwYTZv3gxQ7MASKqhUB1/9TZ4/fI81ivWOlcW6r3Kffu49mUOkRuWyhQc9Fr5pWImj8tq+fTtNmzalatWqsc6KKWdEhKpVq9K0aVN+//33YgeVcOb+aioirXI2nNJLof2+Y6Ey/WcReVdENojIYRFZJSKPiUiRAUpEXhQRFZH/BjiWKiJjRWSL73rzRaRXGJ+p9P32fe7TBd7CI9iNKQ3Z2dlUqVJ0W5oxoVSpUqVEVafhdCkuqpvR+wH2FdFXNtddwEbgXmAT0AXIAPqKyOmq6vVPLCKnA0MoXFrK8TIwCLgbZ26yW4CZInKaqi4OkZfSo5ovqCzytotZVsKdI8xUHFblZUqipH8/oYJKtHt4nV9g3rB5IrIbpzWgDzAn54Bvuv2JwKPAjRQgIp2AK4BrVfVV3755wHLgIWBwlPMevr0b4cA253lyDXYntISDnkLJittdN5KlhMOZI6zgta09xhhTXKHWU5kSzTcrYiLKhb7HpgX2341T8hlHgKCCEzSycToO5FzfLSJTgeEikqKqR0ue62L4bUHe82bpLLh6YFQvX5olDyvVGGNKIh7Wkc3pFrUiZ4eItAZGAoNUNauI4tgJwDpVPVRg/3IgGWjje172/Kq+OLZ7WKdEc+p5G7BoKovFixfz/vvvc+utt1KnTp3QJ8QxEeHBBx8kIyMjovMmT56M1+vl2mvDm4C2tMU0qIhIU5yqqs9VNdPv0L+B6ar6RZDT60DA1a12+x0v6n1vAG4AaN68eUR5DseKhbM53vf8qs/gq5lOtVOwABGtqeeDjXux9hVT0SxevJhRo0Zx5ZVXlvugUlyTJ0/G7XZbUBGR6sAMwI1f242IXAl0A0J1mRICz4wcspVJVSfitNeQnp4e3dmVjx6gra4HcebeWuxtk3so1jf0SNtXjKlIPB4PqkpiYjxU0FRcYS0nHG0ikgp8gNM9eYCqbvLtrw48BYwBjohILRGp5ctnku91zrKIuwlcGqntd7zs/f4DieJ0YlulzfgDGy9gyqf0Rz6jxfCPC23pj3xWZnn45ZdfuOiii2jQoAGpqak0b96cSy65BLfbzeTJkxk61Pk92rZtW0QEEWH9+vWAU51033338fjjj9OyZUuSk5NZutSZR2/nzp0MGzaMpk2bkpKSQvv27Zk4cWK+9966dSvXXHMNTZo0ISUlhcaNG3PeeeexfbuzPIXb7eb++++ndevWpKamUq9ePXr06MHXX38d9DN5PB5GjhxJ48aNqVq1Kn369GH58sI19WvWrOGqq66iZcuWVKlShVatWjFs2DD27MmroOnTpw/z5s3jm2++yf38ffr0AWDHjh3ceOONtGvXjqpVq3LsscdyxRVX5A5uLC1lHrJ9QeFd4BSgn6ou9TtcD6gPjPZt/o4FLsWZe+x9nPaSi0SkaoF2lQ5AFrCmdD5BCH7tKT9625bKW0Rj8kebQNKEEg+rgZ533nnUqlWLF154gXr16rF582Y++eQTvF4vgwYNYuTIkTzyyCO8/fbbNGvWDIDGjRvnnj958mRatWrFk08+SbVq1WjSpAn79+/njDPO4PDhw2RkZNCyZUtmzpzJsGHDOHr0KP/4xz8AuOqqq9iwYQNjx47l2GOPZdu2bcyePZtDh5zbzZgxY3j66ad59NFH6dy5M/v37yczM5Pdu4P/ns3IyGD06NHceeed9O/fn8zMTAYPLtxZ9ffff6dZs2Y888wz1K5dm7Vr1zJ69GjOPfdc5s+fD8Dzzz/PlVdeicfj4cUXXwTyRsLv3r2b1NRUHnvsMerXr8/vv//OuHHjOOOMM1i5ciWpqdEZkF1QmQYVEXEBrwNn4TTCf1cgyVagb4BTpwJLcboX56yN+wEwCrgE3wQlIpIIXAbMioeeX9EanxJo4seQc4aFYN2GTbzbuXMnq1evZsaMGfluuldccQUA9evXp3VrZ63Azp0706ZNm0LXUFVmzZqVb0Doww8/zIYNG1i6dClt2zo//Pr168fevXsZNWoUw4YNIzExkfnz5zN69GiGDBmSe+4ll1yS+3z+/Pn079+f2267LXff+eefH/Qz7dmzh6effpobbriBJ598EoD+/fuTkJDA8OHD86Xt1asXvXrljeU+/fTTadOmDT179uTHH3+kS5cudOjQgZo1a+J2uzn11FPznZ+Wlsb48eNzX3s8Hs444wyaN2/O//73Py666KKgeS2usq7+moATBJ4EDorIqX5bM1U9oqpzC27AEWCb7/VOAN/gxmnAMyJynYichRN8WgIPlvHncni9+YOKhl9SiaSEEOu2GWPKQt26dWnVqhXDhw9n0qRJrF4d+VSDAwcOLDTDwKeffkr37t1p2bIlbrc7dxswYAC7du3i559/BqBbt26MHTuW8ePHs3TpUlTzN79269aNTz75hPvuu4+vv/6arKzQ/y+XLl3KwYMHufTSS/Ptv/zyywulzcrKYvTo0bRv354qVaqQlJREz549AVi1alVYn/+FF16gU6dOVK9encTExNyOSeGeXxxlHVTO8T3eB8wvsF1XjOsNBV4FHgE+xqkiG6iqP5Q8q8WwazUccZaZ2aU1WK+NCiUpqj46c+TZrH98kFU/GeMjInz22Wekp6czYsQI2rVrR6tWrXjhhRfCvoZ/VViO7du38+WXX5KUlJRvyymF7Nq1C4Bp06YxePBgnnjiCU466SSaNm3KQw89hNfrtJnee++9jBo1ig8++ICePXtSt25dhg4dys6dO4vMz5YtWwBo2LBhvv0FXwOMGDGCjIwMrrzySj7++GMWLFjA9OnTAThyJPRaif/617+4+eab6devH9OnT2fBggV89913YZ9fXGVa/aWqLaJ5nqoeBu70bbHnV0r5wduO4kz2aKUQY/K0atWK1157DVVlyZIlPPfcc9x88820aNGCc845J+T5gca41a1blwYNGuSrGvKXlpYGQIMGDZgwYQITJkxg1apVTJkyhQcffJD69eszbNgwkpKSuOeee7jnnnvYunUrH330EXfeeSeHDh1i2rRpAa+dE+S2bdvGCSeckLt/27ZthdJOnTqVq6++mpEjR+buO3DgQKF0RZk6dSpnnXUW48aNy923bt26sM8vrpj0/qqw8s33VTqN9DnKsgeOqZyKKjXHojQtInTu3JmnnnoKgGXLnKbVlJQUAA4fDr54nb+BAweycuVKmjdvTnp6eqGtRo3C89umpaUxevRoateunfve/ho1asR1111Hv379Ah7PcdJJJ1GtWjXeeuutfPunTp1aKO2hQ4dISkrKt+/VV18tlC4lJSXg5w/3/GizDtvRVAqN9EWxEo0pbbHuzPHTTz9x2223cdlll9GmTRs8Hg+TJ08mMTGRM888E4AOHToAMGHCBK655hqSkpI46aSTSE4uOvDdcccdTJs2jZ49e3LHHXeQlpbGwYMHWblyJV999RUzZsxg37599OvXjyFDhtC+fXuSkpKYMWMGe/bsoX///gBccMEFdOrUia5du1K7dm1+/PFHPv30U268MdCsUo5atWpxxx138Oijj1KjRg369+/PwoULefnllwulHThwIFOmTKFjx460adOG6dOn8+233xZK16FDB55//nmmTZtG69atqVGjBmlpaQwcOJAxY8YwevRoTjnlFObMmcM77wRfhjwaLKhEy6HdsNPX+OVK5CcNuRKAMSaIRo0a0bx5c5566ik2bdpEamoqHTt25KOPPuLkk08GoFOnTmRkZDBx4kQmTZqE1+tl3bp1tGjRosjrHnPMMXz77bc89NBDjBkzhs2bN1OrVi3S0tK4+OKLAUhNTaVr165MmjSJDRs24HK5SEtL4/XXX+eCCy4AnN5Zb7/9NhMmTODQoUM0b96cf/7zn9x3331BP1dGRgaqyksvvcRzzz1H9+7d+fDDD/NVh4HTJqKqudc799xzefPNNznllFPypbvnnntYtWoV1113HQcOHKB3797MnTuXBx54gL179/L0009z5MgRevfuzcyZM2nVqnTvTVKwR0Nlk56erpmZmaEThvLLLHjD192wSVdarC24YGaeYN2BIxnpXtJuxabiWbFiBccff3zohMYEEervSEQWqWp6oGPWphItW3/Ke96sW7Hro633lzGmPLPqr2jZ6deHvn5aseujc86LZM0UY4yJF1ZSiZZdfkGlXskb6UMFFCvRGGPikZVUoiD94VnMcf9MTV+X+G4vbmAH+4u1Fko4rC3FGBOvrKQSBdkH91BTnH7iBzWFHdQCrNuvMabysaASBU0lb1qGzVqPMJZ0McaYCsmCShT4B5XftV4Mc2KMMbFlbSoRCtQr65qEXbnPf9e6+Y61GP5xsdeZt/VOjDHljQWVCAW60TcpVP0V+pxQYj1FhjHGFIdVf0VBU8krqQQKKsYYU1lYUImC/G0qdYOkNMZEIiMjAxHB7XaXyfutX7+ejIwM1q5dG1Z6r9fL7bffTuPGjXG5XFx44YWsX78eEWHy5Mm56SZPnswrr7xSSrmOL1b9FQX+1V+/YyUVY8qr9evXM2rUKHr06BHWxIvvvPMO48ePZ9y4cZx22mnUrVuXxo0bM3/+/NyljsEJKm63m2uvvbY0sx8XLKiUUDLZNBRntUePClu1doxzZIwpKytWrADg9ttvx+XKq/gpuF58ZWLVXxEq2PuqoezOfb6N2rgDxGnrsWVMyaxYsYK+fftStWpVGjduzAMPPJC7rG+OnTt3MmzYMJo2bUpKSgrt27dn4sSJ+dJs3bqVa665hiZNmpCSkkLjQ1b/FQAAEKxJREFUxo0577zz2L59O3PnzqVv374AnH322YgIIsLcuXMD5qlFixZkZGQAkJCQkFvlVbD6q0+fPsybN49vvvkm95p9+vSJ5tcTV6ykEqGcXlk5U9Q3CzJGxaZTMSY6LrzwQq699lpGjBjBzJkzefjhh3G5XLk39f3793PGGWdw+PBhMjIyaNmyJTNnzmTYsGEcPXqUf/zjHwBcddVVbNiwgbFjx3Lssceybds2Zs+ezaFDh+jatSsTJkzglltu4dlnn6Vbt25A3kJgBb333ns8++yzTJ48mfnz5wPQunVrDh48mC/d888/z5VXXonH4+HFF18EoGbNmqXxNcUFCyrFlDOOpAlFj1ExJi5kHBPrHOTJ2Fes066//nqGDx8OQP/+/dm/fz/jxo3j9ttvp1atWowfP54NGzawdOlS2rZ1lvLu168fe/fuZdSoUQwbNozExETmz5/P6NGjGTJkSO61L7nkktznOQHk+OOPD1mF1aVLF5o2bQrkr+4qGFQ6dOhAzZo1cbvdlaJazKq/iilz5Nmsf3wQbVL35O7zL6lYlZcx0XPppZfme3355Zdz4MCB3PXgP/30U7p3707Lli1xu92524ABA9i1axc///wzAN26dWPs2LGMHz+epUuXUtkXKSwNVlIpoWGdU+AH5/lNg3tz0ylW5WVMtDVs2DDg682bNwOwfft21qxZQ1JSUsDzd+1yahSmTZvGqFGjeOKJJ3K7At90002MHDkyX0O7KT4LKiW197e858ccG7t8GFOUYlY5xZNt27bl6+K7bds2gNzqp7p169KgQQPGjx8f8Py0tDQAGjRowIQJE5gwYQKrVq1iypQpPPjgg9SvX59hw4aV8qeoHCw0l9S+TXnPj2kWu3wYU4G99dZb+V5PnTqV6tWrc+KJJwIwcOBAVq5cSfPmzUlPTy+01ahRo9A109LSGD16NLVr186tRktJSQHg8OHDUc1/SkpK1K8Zr6ykUhKqFlSMKQOTJk3C6/XSrVs3Zs6cyUsvvURGRga1ajlrF91xxx1MmzaNnj17cscdd5CWlsbBgwdZuXIlX331FTNmzGDfvn3069ePIUOG0L59e5KSkpgxYwZ79uyhf//+ALRr147ExEReeeUV6tSpQ0pKCmlpaQGDUiQ6dOjA8//f3r2HSVXXcRx/f4AF1rhtJVZ4waRoKR97CJMsXe1iF0sq7WaWVph2McsuaooaWkalPamZlzS7YKKVafUURkpqaEWSGiFkKuaigQkisgritz9+v8HZs7PMOud3OMPu9/U855nZ35kz8/3uzJzv/M7td/75zJkzh912242RI0du7j31N15U8lj/CDwVf30MGwWtY8qNx7l+6pprruGYY47h9NNPZ/To0Zx88snMmDFj8/zRo0ezYMECZs6cyaxZs+js7GTMmDFMnDiRgw8+GIDhw4czefJkLr74YpYvX86gQYOYOHEis2fPZtq0aUDYjHbeeecxa9YsOjo62LRpEzfccEPu80qOP/54li5dyvTp01m3bh0dHR29nv+yrdNAP/phypQptnDhwsYWXrEILtov3B87CT55S7K4nGvEkiVLaG9vLzsMt42r9zmS9Dczm1Jrnu9TycM3fTnnXDdeVPLwouKcc914UcmjW1Hxw4mdc86LSh5r7n/mvhcV55zzopKLb/5yzrluvKjk4UXFNaGBfkSnyyfv58eLSqM2PgGPrwz3NRhGvrDceJwDWlpaBsyZ264YXV1dvV5DrS/85MdGaRB84IrQW3liDQz2f6Ur39ixY+ns7GTcuHG0trYiqeyQ3DbCzOjq6qKzs7PHBTyfDV8TNmrIUJj41rKjcK6byuBPK1asYOPGjSVH47Y1LS0t7LDDDrkGEfOi4lw/M2rUqH49sqBrbr5PxTnnXDJeVJxzziXjRcU551wyXlScc84l40XFOedcMl5UnHPOJTPgB+mStApY3uDizwceThjOtsBz7v8GWr7gOT9bu5jZ9rVmDPiikoekhb2NftZfec7930DLFzznlHzzl3POuWS8qDjnnEvGi0o+F5UdQAk85/5voOULnnMyvk/FOedcMt5Tcc45l4wXFeecc8l4UcmQtJOkn0l6VNJaSb+QtHMflx0u6ZuSHpTUJekWSfsWHXNejeYsaYqkiyTdJWm9pPslzZa069aIO48873PmeU6UZJJuLiLOlPLmLKld0lWSHo6f76WSji0y5rxyfp93lvTD+LleL2mZpDMkPafouBslaUdJ58Z1z/r42Rzfx2WTrL+8qFSRtB1wPfAy4HDgQ8BLgBv6+EG6BDgSOAV4O/AgMFfSK4uJOL+cOb8feDlwDvBW4ARgMrBQ0k6FBZ1Tgve58jwvBk4CVhYRZ0p5c5Y0BfgzMAyYDrwNOAsYXFTMeeXJOc6fB+wLzAAOBL4PfB64tMCw85oAvBdYDdz0LJdNs/4yM5/iBBwLbAImVLXtCjwFHFdn2T0AAz5S1TYEWApcW3ZuBeW8fY22XYCngZll51ZEzpnnmQtcCMwHbi47rwLf50HAYuDqsvPYijkfEL/PB2Tavx6X367s/Hp7r6ruT485jO/DcsnWX95T6e4g4FYzu7vSYGb3An8CpvVh2Y3AnKplnwKuAN4saVj6cJNoOGczW1WjbTmwChiXOM6U8rzPAEg6lNArO7GQCNPLk/N+wCTg7MKiK0aenIfG27WZ9jWEIqtUQaZkZk83uGiy9ZcXle5eDvyjRvtiwpeq3rL3mtn6GssOJXRLm1GenHuQ1A6MBZbkjKtIuXKW1AZ8G/iSmT2SOLai5Mn5dfF2uKRbJW2UtFLSOZJak0aZVp6c5wH/AmZJmiRphKTXE3o/F5jZ42lDLV2y9ZcXle6eS9gWmfUI0JZj2cr8ZpQn524kDQEuIPRULskfWmHy5vxNYBlwWcKYipYn5xfF2znAdcCbgG8QNq9cnirAAjScs5k9QSimlU1/jwF/AH4NfDptmE0h2fprSJJw+pdaZ4P2paurHMuWLVXc5wF7AweaWa0PaDNpKGdJ+wAfBiZb3PC8DWn0fa78+PyJmZ0S78+XNBj4uqRJZvbPJBGm1+j7PJxQRMcSdvDfD7yasBP7KeATCWNsBsnWX15UultN7YrcRu0qXu0RoNahim1V85tRnpw3k3Qm8HHgcDO7LlFsRcmT84WEXtgDksbEtiHA4Ph3l5k9mSzSdPLk/L94+/tM+3WEHdevBJqxqOTJ+WOEfUkTzOzfse1GSY8CF0m6wMxuTxZp+ZKtv3zzV3eLCdsWsyZR/0uzGNg1HsaYXXYDcHfPRZpCnpwBkHQS4XDiY83sxwljK0qenNuBowkrpcr0WmBqvN+sv2Dzfrah5y/Zyq/YRncOFy1PzrsDq6sKSsVf4m17ztiaTbL1lxeV7q4FpsbzDwCIJw69Ns6rt2wL8J6qZYcA7wOua9Jfr5AvZyR9BjgDOMnMzi0oxtTy5Lx/jel2wg7h/YGfpQ83iTw5/xZ4EnhLpv3N8XZhmhCTy5PzQ0CbpOwO6r3ibWeiGJtFuvVX2cdVN9MEPIdQke8kHHJ4EGGFcQ8woupxuxC2q56SWf4Kwq/V6cAbCCuYJwjb30vPL3XOhJMfnyasdKZmpkll51bU+1zj+ebT/Oep5P1snxrbvwa8kdAz7QIuKzu3InIGxhMOJ15GOHFyf+CLsW0hVeeDNNsEHBKn7xF6l5+If3fUeY+TrL9K/wc020TYrvjz+OF5DPglmZOH4gfOgNMy7a2EY/kfim/Gn4H9ys6pqJwJRz9ZL9P8svMq6n2u8VxNX1Ty5kzY1HVcXElvIAzBPRNoKTuvAnOeBFwJ/IdQQJcB3wLays6rTs5b/E4Wvf7yS98755xLxvepOOecS8aLinPOuWS8qDjnnEvGi4pzzrlkvKg455xLxouKc865ZLyouH4lDp9ab7ovPvayyv1mEYeC/VXZcTRKUmscjvY99R/t+iM/T8X1K5KmZpquJpxFfVpV25NmtkjSbsAoM1u0teLbkhjPEmBvM2vWS5/UJelzwKeAdjPbWHY8buvyouL6tdgTudnMDis7lnoknQtMNbM9y44lK17mXhZGA6z32DbCWdkfMrMrCw/ONRXf/OUGrOzmL0nj4+axoyWdKekhSY9J+omk7SRNkDRX0jpJd0s6vMZz7iHpWkmrJXVJ+lMcg6VeLMOAw6ga9ErSCyRtkHRsjcefJml9XIFX2t4dR2ZcL2mNpKsk7ZxZ7v2Srpe0KuaxqJc8TNJXJZ0g6V7CpVl2jyMgnivpfklPSvqvpHmSXlZZ1sJYOnMJ15ByA4wXFed6OpEw2uHhhEGZ3kcY0fJq4DfAu4A7gB9I2nxpdUmTgQWEMTyOBA4mjEUyT9Kr6rzmVGAMcFOlwcweIlyr6qjqB8Zew8eAK+MKHElHE65x9U/CxQOPAl4B/FHSyKrFX0y4UOAHgXcCvwK+H5fPOgI4EPhCvF1BGEb5vcBXCCNAHg38PcZe7UagIw525QaSsi9+5pNPRU7AfYQRC2vNuwy4r+rv8YQL7V2fedwvYvthVW1thCu9nlrV9gfCPpGhVW2DY9sv68R5POGKz0Mz7fvF196nqu2g2DY1/j0CeBS4NLPseEIP47O9vOYgwgBjFwO3Z+YZoYi0Ztr/AZzdh//7G+Jz7F32Z8CnrTt5T8W5nn6b+fuueDu30mChh7AS2AnCUU9AB3AV8LSkIXE8CgHzgH3rvOaLgLVmtqG60czmE3of1b2Vo4A7zOzW+PdrgFHA7Mrrxtd+IMa++bUlvUTSTyV1AhvjNB2YWCOm35lZV6btr8ARkr4saUrsNdWyqiovN4B4UXGup+xQsxu20F7ZvPNcQq9kBs+srCvTpwkDPm3p+zacMBBWLd8DDpH0PEm7EAbLuqBq/th4O6/Ga+8OPA9A0gjCkMB7EMZD2QfYE7gUGFbjdR+s0XYMYUjljxIKzEpJ364xYmClGLX2kpPrp3yMeufSWEPYfPVd4Ee1HmBmWxp29388Mx541o+AMwn7ONoIK+zZmWWJ8xfT02Px9jWEAZr2MbObKzNjr6ZmyD0azNYR9jmdGAvcIYRx6jcQNuFVVMaGf7iX53b9lBcV5xIws8cl3UToBdxWp4DUchfQImlHM3sg89xrJc0mbPYaAVxuZmurHrKAUDgmmNkPt/Aald7E5nNH4tFj055lrJW4lgNnSfog4aCAarvG26WNPLfbdnlRcS6d4whHPc2VdAlh89HzgcnAYDM7YQvL3hhvX03YF5J1Ps/sV6ne9FUpOl8Evitpe8I+oUeBcYT9PPPN7HJC8VkbH3cqYbjdkwm9idF9SVDSLYTxzO8E1sXn3wPIFrO9gE4zu6cvz+v6Dy8qziViZrdJ2pMwnvs5hBX1KuA2MoWgxrL3SfoL8A7C0WbZ+XdIWkbYmX9bjfkXSvoPYRz1Q4EWoJNQrP4eH7NK0ruAswiHFa8AvkPYVHVqH9O8kXBI8QmE9cc9wOfM7JzM4w4kjHnuBhg/o965JiHpCMJK/oVmtj4z76WETWRHmtklJYTXZ5L2IvSK2s1sWdnxuK3Li4pzTSIennsn4XyTb8W2HYEJhJMNJxD2m2QP820qkq4GVpvZR8uOxW19fkixc03CzDYRDtWt7qVMB64HdgAO3QYKynBgEXBS2bG4cnhPxTnnXDLeU3HOOZeMFxXnnHPJeFFxzjmXjBcV55xzyXhRcc45l8z/AT06SlvQzSHjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(st_year,st_price,'s', label = 'stress data')\n",
    "plt.plot(st_year_train,Z_train_st@A_st, label = 'best fit')\n",
    "plt.title('Price of Steel\\n')\n",
    "plt.xlabel('Time (years)')\n",
    "plt.ylabel('Price (dollars)')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aluminum price in 2025 is $ 2311.9942877590656\n",
      "Steel price in 2025 is $ 269.689721591305\n"
     ]
    }
   ],
   "source": [
    "year = np.linspace(2016,2025,len(al_year))\n",
    "year_norm = (year-year.min())/(year.max()-year.min())\n",
    "\n",
    "i_rand_al = random.sample(range(0,len(al_price)),len(al_price))\n",
    "i_rand_st = random.sample(range(0,len(st_price)),len(st_price))\n",
    "itrain_al = i_rand_al[:int(0.7*len(al_price))]\n",
    "itrain_st = i_rand_al[:int(0.7*len(st_price))]\n",
    "year_train_al = year_norm[np.sort(itrain_al)]\n",
    "year_train_st = year_norm[np.sort(itrain_st)]\n",
    "\n",
    "Z_train_al=np.block([[year_train_al**0]]).T\n",
    "Z_train_st=np.block([[year_train_st**0]]).T\n",
    "\n",
    "for i in range(1,max_N):\n",
    "    Z_train_st=np.hstack((Z_train_st,year_train_st.reshape(-1,1)**i))\n",
    "    Z_train_al=np.hstack((Z_train_al,year_train_al.reshape(-1,1)**i))\n",
    "Al_price_2025 = Z_train_al@A_al\n",
    "St_price_2025 = Z_train_st@A_st\n",
    "\n",
    "print('Aluminum price in 2025 is $',Al_price_2025[-1])\n",
    "print('Steel price in 2025 is $', St_price_2025[-1])\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4e. Based on the price module I would not change my answer in 3d."
   ]
  },
  {
   "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"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}