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": 205,
   "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": 205,
     "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"
   ]
  },
  {
   "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": 217,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.457753e+17\n",
      "The expected rounding error in the solution for K is 10\n"
     ]
    }
   ],
   "source": [
    "#Problem 1a\n",
    "\n",
    "#for full K array\n",
    "K_full=K\n",
    "\n",
    "#condition of full K array\n",
    "print('{:e}'.format(np.linalg.cond(K_full)))\n",
    "\n",
    "#expected error\n",
    "print('The expected rounding error in the solution for K is', 10**(17-16))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem 1b\n",
    "#The matrix condition is the product of the matrix and its inverse. A problem with a low condition number is said to \n",
    "#be well-conditioned while a problem with a high condition number is said to be ill-conditioned. In non-mathematical \n",
    "#terms, an ill-conditioned problem is one where for a small change in the inputs there is a large change in the \n",
    "#answer or dependent variable. This means that the correct answer to the equation becomes hard to find.\n",
    "#Therefore the condition of K is large because of the size of the matrix compared to K[2:13] resulting in a harder \n",
    "#solution to find. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.223543e+01\n",
      "The expected rounding error in the solution for K is 1e-15\n"
     ]
    }
   ],
   "source": [
    "#Problem 1c\n",
    "\n",
    "#for partial K array (K[2:13,2:13])\n",
    "K_partial=K[2:13,2:13]\n",
    "\n",
    "#condition of partial K array\n",
    "print('{:e}'.format(np.linalg.cond(K_partial)))\n",
    "\n",
    "#expected error\n",
    "print('The expected rounding error in the solution for K is', 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": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L= [[ 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= [[ 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": [
    "#Problem 2a\n",
    "\n",
    "#Function to solve for L & U\n",
    "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\n",
    "\n",
    "#Solving and printing L & U\n",
    "L=((LUNaive(K[2:13,2:13]))[0])\n",
    "U=((LUNaive(K[2:13,2:13]))[1])\n",
    "print('L=',L)\n",
    "print('U=',U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem 2b\n",
    "\n",
    "#Function to solve for x when LUx=b\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01948557, -0.02125   ,  0.00433013, -0.04      ,  0.01082532,\n",
       "       -0.05375   ,  0.01732051, -0.04      ,  0.00216506, -0.02125   ,\n",
       "        0.02165064])"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Problem 2b for steel\n",
    "#Force array\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])\n",
    "#E for steel\n",
    "E_st=200e3\n",
    "#Area\n",
    "a=0.1\n",
    "#Variable for 1/EA\n",
    "o_1=1/E_st*a\n",
    "#Variable for F(1/EA)\n",
    "b=F*o_1\n",
    "#Solve\n",
    "u_s=solveLU(L,U,b)\n",
    "u_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.05567306, -0.06071429,  0.01237179, -0.11428571,  0.03092948,\n",
       "       -0.15357143,  0.04948717, -0.11428571,  0.0061859 , -0.06071429,\n",
       "        0.06185896])"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Problem 2b for aluminum\n",
    "#Force array\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])\n",
    "#E for aluminum\n",
    "E_al=70e3\n",
    "#Area\n",
    "a=0.1\n",
    "#Variable for 1/EA\n",
    "o_2=1/E_al*a\n",
    "#Variable for F(1/EA)\n",
    "b=F*o_2\n",
    "#Solve\n",
    "u_a=solveLU(L,U,b)\n",
    "u_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steel reaction forces: [-2.22044605e-16  5.00000000e-01  0.00000000e+00  8.32667268e-17\n",
      " -2.22044605e-16 -3.88578059e-16  1.04280369e-16 -1.00000000e+00\n",
      "  0.00000000e+00 -3.88578059e-16  5.55111512e-17  0.00000000e+00\n",
      " -4.44089210e-16  5.00000000e-01]\n",
      "Aluminum reaction forces: [-3.33066907e-16  5.00000000e-01 -2.22044605e-16  1.11022302e-16\n",
      "  0.00000000e+00 -8.32667268e-17  3.26595333e-16 -1.00000000e+00\n",
      "  4.44089210e-16 -3.88578059e-16  5.55111512e-17  0.00000000e+00\n",
      "  0.00000000e+00  5.00000000e-01]\n"
     ]
    }
   ],
   "source": [
    "#Problem 2c\n",
    "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",
    "\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "s = 5\n",
    "u_st = np.zeros(2*len(nodes))\n",
    "u_st[2:13] = u_s\n",
    "u_al = np.zeros(2*len(nodes))\n",
    "u_al[2:13] = u_a\n",
    "F_st = E_st*a*K@u_st\n",
    "F_al = E_al*a*K@u_al\n",
    "print('Steel reaction forces:',F_st)\n",
    "print('Aluminum reaction forces:',F_al)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Problem 2d\n",
    "plt.figure(figsize = (15,10))\n",
    "plt.plot(r[ix],r[iy],'-',color='k')\n",
    "plt.plot(r[ix]+u_al[ix]*s,r[iy]+u_al[iy]*s,color='r')\n",
    "#plt.plot(r[ix]+u_st[ix]*s,r[iy]+u_st[iy]*s,'-',color='y')\n",
    "plt.quiver(r[ix],r[iy],u_al[ix],u_al[iy],color='g',label='displacements')\n",
    "plt.quiver(r[ix],r[iy],F_al[ix],F_al[iy],color='b',label='forces')\n",
    "#plt.quiver(r[ix],r[iy],u_st[ix],u_st[iy],color='b')\n",
    "\n",
    "plt.title('Our truss structure\\neach element is 2 nodes and length L\\ntriangle markers are constraints')\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.legend(bbox_to_anchor=(1,0.5))\n",
    "plt.axis(l*np.array([-0.5,3.5,-1,1.5]));"
   ]
  },
  {
   "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": 271,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem 3: same code as above, guess and check area for deflection<0.2mm\n",
    "#Force array\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])\n",
    "#E for steel\n",
    "E_st=200e3\n",
    "#Area\n",
    "a=0.031\n",
    "#Variable for 1/EA\n",
    "o_1=1/E_st*a\n",
    "#Variable for F(1/EA)\n",
    "b=F*o_1\n",
    "#Solve\n",
    "u_s=solveLU(L,U,b)\n",
    "u_s\n",
    "\n",
    "#Problem 2b for aluminum\n",
    "#Force array\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])\n",
    "#E for aluminum\n",
    "E_al=70e3\n",
    "\n",
    "#Variable for 1/EA\n",
    "o_2=1/E_al*a\n",
    "#Variable for F(1/EA)\n",
    "b=F*o_2\n",
    "#Solve\n",
    "u_a=solveLU(L,U,b)\n",
    "u_a\n",
    "\n",
    "#Problem 2c\n",
    "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",
    "\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "s = 5\n",
    "u_st = np.zeros(2*len(nodes))\n",
    "u_st[2:13] = u_s\n",
    "u_al = np.zeros(2*len(nodes))\n",
    "u_al[2:13] = u_a\n",
    "F_st = E_st*a*K@u_st\n",
    "F_al = E_al*a*K@u_al"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.19878750000000003\n"
     ]
    }
   ],
   "source": [
    "#Problem 3b\n",
    "d_tot_1=np.sum(u_st[iy])\n",
    "print(d_tot_1)\n",
    "#Therefore minimum cross sectional area to keep total y deflections < 0.2 for steel is a=0.031mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem 3: same code as above, guess and check area for deflection<0.2mm\n",
    "#Force array\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])\n",
    "#E for steel\n",
    "E_st=200e3\n",
    "#Area\n",
    "a=0.010\n",
    "#Variable for 1/EA\n",
    "o_1=1/E_st*a\n",
    "#Variable for F(1/EA)\n",
    "b=F*o_1\n",
    "#Solve\n",
    "u_s=solveLU(L,U,b)\n",
    "u_s\n",
    "\n",
    "#Problem 2b for aluminum\n",
    "#Force array\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])\n",
    "#E for aluminum\n",
    "E_al=70e3\n",
    "\n",
    "#Variable for 1/EA\n",
    "o_2=1/E_al*a\n",
    "#Variable for F(1/EA)\n",
    "b=F*o_2\n",
    "#Solve\n",
    "u_a=solveLU(L,U,b)\n",
    "u_a\n",
    "\n",
    "#Problem 2c\n",
    "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",
    "\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "s = 5\n",
    "u_st = np.zeros(2*len(nodes))\n",
    "u_st[2:13] = u_s\n",
    "u_al = np.zeros(2*len(nodes))\n",
    "u_al[2:13] = u_a\n",
    "F_st = E_st*a*K@u_st\n",
    "F_al = E_al*a*K@u_al"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.18321428571428566\n"
     ]
    }
   ],
   "source": [
    "#Problem 3a\n",
    "d_tot_2=np.sum(u_al[iy])\n",
    "print(d_tot_2)\n",
    "#Therefore minimum cross sectional area to keep total y deflections < 0.2 for aluminum is a=0.010mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weight of Aluminum Truss= 0.00813 grams\n",
      "Weight of Steel Truss= 0.006422700000000001 grams\n"
     ]
    }
   ],
   "source": [
    "#Problem 3c\n",
    "\n",
    "#Aluminum\n",
    "vol_al=0.01*l\n",
    "#density of aluminum (g/mm**3)\n",
    "den_al=0.00271\n",
    "weight_al=vol_al*den_al\n",
    "print('Weight of Aluminum Truss=',weight_al,'grams')\n",
    "\n",
    "#Steel\n",
    "vol_st=0.0079*l\n",
    "#density of steel (g/mm**3)\n",
    "den_st=0.00271\n",
    "weight_st=vol_st*den_st\n",
    "print('Weight of Steel Truss=',weight_st,'grams')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weight of Aluminum Truss= 8.129999999999999e-09 tons\n",
      "Weight of Steel Truss= 6.4227e-09 tons\n",
      "Price of Aluminum Truss= 1.2560849999999999e-05 dollars\n",
      "Price of Steel Truss= 3.0572052e-06 dollars\n"
     ]
    }
   ],
   "source": [
    "#Problem 3d\n",
    "\n",
    "#Conversion 1gram=1e-6 tons\n",
    "print('Weight of Aluminum Truss=',weight_al*1e-6,'tons')\n",
    "print('Weight of Steel Truss=',weight_st*1e-6,'tons')\n",
    "\n",
    "#Prices\n",
    "print('Price of Aluminum Truss=',weight_al*1e-6*1545,'dollars')\n",
    "print('Price of Steel Truss=',weight_st*1e-6*476,'dollars')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Therefore the cheaper of the two options would be 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": 196,
   "metadata": {},
   "outputs": [
    {
     "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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7UwFby0SoSWXbcTDyJ6hTYRh39K9QSkFETAyQiIiIfMGWrmB1awEw6LLmlwrA27gYP6hfhTM1jThaVmtebEREROQzJl3BKi4NiEtvfikAekVH4SS0Obu2czA9ERFRl8KkK5hVnwRiUptf9recaF7mzPRERERdC5OuYDbvL8DQK5pfVmf9sHmZLV1ERERdC5OuYJeW07x4TsP+5uXCYxWw25UZEREREVEHMOkKdoakK+r0LiTHhgMAqupt+P5UtVlRERERkY+YdAW71GGAaB+TlO7D6PSI5qIdx9jFSERE1FUw6Qp24dFA0kBtWdkxsXdpc9H2IxxMT0RE1FUw6eoKrCOaF0eGH25e3sGZ6YmIiLoMJl1dgWFcV7/G75uXdx4vh63JbkZERERE5CMmXV1BWm7zYvTpb5EeHwkAqGu0Y29JlVlRERERkQ+YdHUFhpYunChEXkZc88sCztdFRETUJTDp6grirEBMirbcWI2Lk1patwo4Mz0REVGXwKSrqzC0do2OONK8zKSLiIioa2DS1VUYkq7spgPNy7tPVKDe1mRGREREROQDJl1dhWEwfeSpXeiXFA0AaGxS2F1UaVZURERE5CUmXV2FYa4unNiBnIz45pcFnK+LiIgo6DHp6iqSBgKh2lQRqDyOC1JbbnZdcIRXMBIREQU7Jl1dRUiodh9G3ZioY83LHExPREQU/Jh0dSVpLV2MA5oOQERb3ltSiZoGm0lBERERkTeYdHUlhsH0Ead2YkBKLADAroCdxyvMioqIiIi8wKSrK3GZmT430zCYnl2MREREQY1JV1diHd6yfGoPRqZFNr/k7YCIiIiCG5OuriQiDuidrS3bbRgTe7K5aAdbuoiIiIIak66uxtDFOLDpe4RatNH035+qRnlto1lRERERUTuYdHU1hsH0Yad2YZA1rvn1Tk6SSkREFLSYdHU1ToPpdyDvnJbB9NvZxUhERBS0mHR1NWkutwPq05J07TjGwfRERETBiklXV9MrA4jqrS3XV2B0fMv8XNuPsKWLiIgoWDHp6mpEnLoYB9gPIjxU+xiPnalFaVW9WZERERFRG5h0dUXWlqQrtKQQw9J7Nb8u4GB6IiKioMSkqytyGUxvnJme83UREREFJyZdXZEx6SregdzMhOaXnJmeiIgoODHp6oqSBwEh4drymcM4L6WliPdgJCIiCk5Murqi0HAgZXDzy2zbAUSHhwAASirrcaK8zqzIiIiIyAMmXV2VYWb6kJJCjDDM18UuRiIiouDDpMtHIhIpIutE5FsR+UZEPhCR/gEPxGkwfaHTYHp2MRIREQUfJl0d84xSaqhS6jwA6wH8MeAROCVdBcgxJl2cNoKIiCjo9IikS0QyReRJEflcRGpERIlIloe654jIGyJSLiIVIrJWRPo6ypVSdUqpDwybfAEg8C1d1uEtyyd3Iy89uvllwdEzUEoFPCQiIiLyrEckXQAGArgGQBmA//NUSUSiAWwEMATATwH8N4BzAWwSkRgPm90C4C2/RuuNqN5AvJ4LNjWgnzqKXpGhAIAzNY04WlYb8JCIiIjIs56SdH2qlLIqpWYAWNNGvRuhtVrNVkqtU0q9BWAmgH4AfulaWUSWABgEYEknxNw+QxejFO90mq9rOwfTExERBZUekXQppexeVp0J4Aul1D7DtgcAbAYwy1hRRH4HYA6A6UqpGn/F6pO0ES3LJ3Y4jevizPRERETBpUckXT4YDqDQzfqdAIY5XojIbwD8GMClSimPTUoi8gsR2SoiW0+ePOn3YF0H0+cZki62dBEREQUXJl3OEqGN+3J1GkBvQBuUD+BRAAnQxnp9IyJb3e1MKfWcUmqMUmpMSkqKuypnx2XaiJyMlqSr8FgF7HYOpiciIgoWoWYHEITcZSrSXKjUUeNrUyX0AyJ6AfUVQO1p9LGcRnJsOE5VNaCq3obvT1VjYGqs2VESERER2NLlqgxaa5er3nDfAmYuEcDaMq5LXFq7dhxjFyMREVGwYNLlbCe0cV2uhgHYFeBYvOPUxbjD+QrGIxxMT0REFCyYdDn7J4Bxxtv66JOoXqSXBR9j0lW8w+l2QDs4Mz0REVHQ6DFJl4jMFZG5AEbrq6br6yYaqj0P4CCAt0RklojMhDbx6REAzwY0YG+5tHQZp43YebwctiZvZ8sgIiKiztSTBtK7Tor6tP78CYBJAKCUqhaRKQAeA/AqtAHzGwD8WilVFaA4fZMyBJAQQDUBp79Hangj0uMjUVReh7pGO/aWVGFoei+zoyQiIurxekzSpZTy6opDpdRhaJOedg1hkUDKYKBEH3JWvAu5mfEoKq8DoN2HkUkXERGR+XpM92K35jJJqnEwfQFnpiciIgoKTLq6A6vz7YCMg+mZdBEREQUHJl3dgetgesNcXbtPVKDe1mRCUERERGTEpKs7MCZdJbuQEGFBv6RoAEBjk8LuokqTAiMiIiIHJl3dQUwyENdHW7bVAaf3O7V2FXC+LiIiItMx6epkInKFiDxXXt7JiU+a87iuPONg+iO8HRAREZHZmHR1MqXUeqXUL+Lj49uvfDZcrmDM4cz0REREQaXHzNPV7TklXYUYMSEeIoBSwHfFlahpsCE6nB83EXU/27ZtmxYaGrpUKZUGNiaQOewicsJms90zatSoDzxV4l/h7iItt2X5xA7ERoRiQEos9pVUwa6AXccrMCYr0bz4iIg6wbZt26ZFRESszsrKaoiKiiqzWCzK7Jio57Hb7VJbWxt/8ODB1du2bbvZU+LF/wi6i97ZQFiMtlxdAlQWO83XtZ3zdRFRNxQaGro0KyurISYmppYJF5nFYrGomJiY2qysrIbQ0NClHusFMijqRBYLYB3e8rp4B3INVzDuOMrB9ETU/Sil0qKiourMjoMIAKKiour0bm63mHR1Jy6TpOaew9sBEVG3Z2ELFwUL/bvoMbdi0tWduEwbMSy9F0It2n2+vz9VjYq6RpMCIyIiIiZd3YnLYPrIsBAMssY1rypkaxcREZFpmHR1J6nDANE/0tJ9QEON882vOV8XEVFQe/XVVxPy8/OtnbHvOXPmZGVkZOS0X7O1jIyMnDlz5mT5OaQex6cpI0QkHkCdUqq+k+KhsxEeDSQNBE59Byg7UPItcjNT8LevjgAACjiYnogoqK1bty7hs88+65Wfn1/s733fe++9RWfOnOnQfl9//fV9CQkJdn/H1NN4nXSJSCiAUgBXAljfaRHR2bGO0JIuADhRgNzMq5qLOJieiKhtf/7iUOITG/ZmnKysD0+Ji2j4n6nnHrtuXL/TZsflTm1trURFRXl9EcHw4cM73GBy0UUX1XZ0WzPY7XY0NDRIZGRkq/NTX18vYWFhymLpeGefr+fewesjKqVsAIoBNPl6EAoglysYB1njEB6qfcxHy2pRWsVGSiIid/78xaHE+97e1a+ksj5cASiprA+/7+1d/f78xaGAzCw9Z86crLVr1yaVlJSEichoERnt6A58++2340Rk9CuvvJIwb968fr17985LTU3NA4DCwsKI2bNnZ2dkZORERkaOyszMzLn22mv7njx5MsR1/8buxT179oSLyOhHHnkk+de//nWflJSU3Li4uPOmTJkycP/+/WHGbV27F5944okkERm9YcOGmJkzZ2bHxsaOTE1Nzb3hhhvOqampEeO2u3btCp84ceLAqKiokYmJiXk33nhj5ooVK5JFZPSePXvC2zsvr7zySkJeXt6QqKiokXFxcedNnz69/969e522y8jIyJk1a1b2448/npSdnT08PDx81Ouvvx7veI8PPfRQyoIFCzJTU1Nzo6KiRpWWloYAwKZNm6IvvPDCQdHR0SOjoqJGjh8/ftCmTZuiXc+b1WrN/eijj2JGjhw5JDIyctTChQsz24vbHV9npP8zgJ8DeLcjB6MAMA6mLy5EeKgFQ9N7Ybt+0+sdx8oxaXCqScEREXW+rMXvjPbXvuptdstd6wqz71pXmN2R7Q8+9KOvva177733FpWWloYWFBTErFmzZh8AREZGOnXpLVq0qO/kyZPLn3/++QO1tbUWADhy5EhYRkZGw9y5c48kJSXZ9u7dG7Fy5cr0Sy+9NPqbb77Z3d5xH3/88fRRo0ZVPfXUUweLi4vD7r777sx58+b1/+qrr/a0t+38+fOzr7zyytPz58/ft3nz5tiVK1f26d27d9Njjz12HADq6upk2rRpg+rr6y3Lly8/bLVabS+88ELyO++809ubc/Lwww+n3H777X3nzp1bescddxRVVFRYli1b1mfSpEmDCwsLd/bu3bv5/Hz++edxu3btil68eHFRWlpa48CBAxscZStXrkzPzc2tXrVq1aGmpiaJioqyf/nll1HTp08fMmDAgNqnnnrqoIioFStWpE+fPn3Ipk2bvh0/fnxz615VVVXI9ddf3/+mm24qzsvLOxYdHd2hrlZfk66DAH4iIl8BeAtAEQCn5jWl1IsdCYT8xOUejLDbkZcZ35x0FRxl0kVEFIyGDx9en5SUZAsLC1NTp06tdlcnLy+v+u9///sh47rp06dXTZ8+vcrx+pJLLqkaPHhw/WWXXTZ48+bNUe11Dfbp06dh/fr1BxyvT548GXrfffdlHjx4MCwrK6vNuYauuuqq044Ea/bs2ZVbt26NefPNNxMd61avXp109OjRiI0bN347efLkGgC4+uqry4cOHTqsqKiozfNRXl5uue+++zLmzp1bumbNmoOO9RMmTKgeMWLEiCeffDL57rvvLnGsr6ysDNm6deuuvn372hzrHC1pycnJjR9++OF+Y5fi0qVL08PCwuyffPLJd8nJyU0AMHPmzIrs7OzcpUuX9vnwww/3O+rW1NRYnn322SPXXXfdWQ2O9rVD8ykAGQBGA7gXwPMA/mh4PH82wZAfxFmBmBRtubEaKDuAHMPM9BzXRUTUdc2aNavVH/26ujpZvHhxWnZ29vDIyMhR4eHhoy+77LLBALBz587I9vY5bdo0p33m5eXVAsD+/fvb7fqbOXOm07bDhg2rLSoqat7uyy+/jE1PT29wJFwAYLFYcMUVV5S1t++NGzfGVlVVhVx33XWljY2NcDz69+/fkJ2dXffZZ5/FGevn5eVVGxMuoxkzZpxxHcO1ZcuWuClTppQ7Ei4ASExMtF9yySVntmzZ4rTvkJAQNW/evLO+Gs3Xlq4ONa/2ZCJyBYArBg4cGLiDpuUA+zdqyyd2IO+cqc1FvIKRiLo7X7r0jBxjuupt9ua/zhGhFvsfLh92KFgG02dkZLRqebrlllsyXn755dTbbrut6OKLL66Kj49vOnToUPhPf/rTAXV1de02riQmJjqN1Y6IiFAA4Oi+bEtKSkqrbRsaGprHdBUXF4clJia2SoSsVmu7s3WfOHEiFABmz549yF15fHy807FTU1M97jM9Pb1VWUVFRWhaWlqr9VartbGiosJpPFxiYqItNNTXlKk1n/aglDrUfi0yUkqtB7B+zJgxNwbsoC5J14ChsxAdHoKahiaUVNbjRHkd0uLb/eeHiKhHcSRWwXz1ooi0umLurbfeSrzqqqtKH3744eb+uvXr14e41jOD1Wpt3LdvX6s/OMXFxWHu6hulpKTYAOCJJ5446Gh9M3JNukTEtUqbZb169bK5i6O4uDgsPj7eKVFsa9++6FDaJiIjAEwEkAhtGolPlVKFfomIzp7V+QrGEItgRJ94bDmo/d4oOHoGafEe78dJRNRjXTeu32kzk6yIiAhVX1/v09Cfuro6S2hoqFMy9uKLLyb5N7KOGTt2bNUbb7yRtGnTpmhHF6Pdbsf69evbHUg/ZcqUqpiYGPu+ffsibrnlltJOiK1y06ZN8WVlZRbHgPyysjLLhg0bEsaOHVvp7+MBvk+OGgrgZQA/BmBM+5SI/BXADUopTilhNpdpIwAgJ9OYdJXjh8OZdBERBZuhQ4fWvvbaa8nLly9PGTduXHVUVJS64IIL2hwIP3HixPK1a9cmPfTQQ7WDBg2qf+ONNxK+/vrr2EDF3Jabb765dNWqVWnz5s0beNdddx1LTU21vfDCC8mO7ru25spKTEy0L1269MiSJUv6nTx5MnTGjBkVCQkJTUeOHAn79NNP4yZOnFi5YMGCDifI+fn5RRMnTkyYMGHC4N/+9rdFImTcIIMAACAASURBVIJHH300ra6uzpKfn3+8o/tti68D6ZcCuAbA3dDGd0Xpz3cD+C/9mcyWNBAI1VtzK48D1aW8HRARURdw6623nrr88stPP/DAAxmTJk0aeuWVV7Y7IPi55547MnXq1PIHH3ww44YbbuhfVVUV8uqrr34fiHjbExkZqd5///29Q4YMqVm0aFG/BQsWZGVkZDTMnz//JNB6PJmrRYsWnfrLX/6yb//+/ZELFizInjt37rnLli3rY7PZ5Pzzz69pa9v2jB07tvbdd9/dExcX17Rw4cLsBQsWZMfExNjfe++93cbpIvxJlPJ+QlUROQDgRaXUfW7K7gbwM6UUB9u7MWbMGLV169bAHfC5ycDxbdry9W/hQK/zMXnFxwCAhOgw/OcPl/qtj5qIqLOIyNdKqTGeyrdv334wLy/vVCBjorM3efLkgfv27Ys8cuRItxuatH379uS8vLwsd2W+junqA+BzD2X/BnCnj/ujzpI2oiXpOrEDWdkTERcZiso6G87UNOJoWS3OSYxuex9ERERnKT8/3xobG9s0ePDg+oqKCsuaNWsSP/744/jly5cfNju2QPM16ToO4CIAH7kpu1Avp2BgnJn+xA6ICHIz47F5nzYWcfvRM0y6iIio00VERNiffvppa1FRUbjdbpesrKy6lStXHrrtttt6XAulr0nXXwDcKSJ2fbkIQBqAedBauZb7NzzqMNeZ6QHkZiY0J107jpbj8tw+ZkRGREQ9yJIlS04uWbLkpNlxBANfk658AP0B3KMvOwiA1/T1FAysw1uWT+0BGuuQZxhMv52TpBIREQWUr5Oj2qDde/EBABOgzdN1GsAnSqldnRAfdVREHNA7Gyg7ANhtwMndyMkc3FxceKwCdruCxcLB9ERERIHgddIlIuHQug//qpT6CsDOTouK/CMtR0u6AKC4EH3Oy0NybDhOVTWgqt6G709VY2BqUEzlQkRE1O15PU+XUqoBwC+hzc1FXYGbwfTGm1/vOMYuRiIiokDxdXLU/wDIabcWBYe0ES3L+sz0uZkJzau2H+EkqURERIHia9L1WwC/E5HLhTNrBj/XKxiVcpqZfgdnpiciIgoYX69eXAMgHsBbAGwiUgLAOKW9Ukr181dwdJZ6ZQBRvYHaMqC+HDhzGDmZ1ubincfLYWuyIzTE19ybiIiIfOXrX9sNAP4B4E8A/gptktQNhsdGv0ZHZ0ek1c2vU+MikR6v3ZexrtGOvSVVJgVHRESuXn311YT8/Hxr+zU7Zs+ePeG/+c1v+uzatSvctSwjIyNnzpw5WZ11bPJ9yogbOikO6izWHODAp9ryiR3A0MuRmxmPovI6AEDB0TMYmt7LxACJiMhh3bp1CZ999lmv/Pz84s7Y/969eyMee+yx9AkTJlQOGzaswVj2+uuv70tISLB3xnFJ43VLl4iEi8g2EflhZwbU3YjIFSLyXHm5SeOnXFq6AOfB9AVHOa6LiMjJmSNheG7SYJQf9XUITpd20UUX1Q4fPrze7Di8ZbfbUVdX53Z8eX19vdjtZ5c/1tbW+n3suq9TRmQDsPk7iO5MKbVeKfWL+Pj49it3BmPSVexIulpiYdJFRORi473pOP5NLDbcE9B7pc2ZMydr7dq1SSUlJWEiMlpERmdkZDT/Ei8qKgq99tpr+6ampuaGh4ePys7OHr5ixYpk4z4OHz4cetVVV2U56qSkpOROnjx54LFjx0LffvvtuCuuuGIQAFx55ZWDHMd4++2344DW3YtPPPFEkoiM3rBhQ8zMmTOzY2NjR6ampubecMMN59TU1DglJLt27QqfOHHiwKioqJGJiYl5N954Y+aKFSuSRWT0nj17WnVlunrllVcS8vLyhkRFRY2Mi4s7b/r06f337t3rtF1GRkbOrFmzsh9//PGk7Ozs4eHh4aNef/31+D179oSLyOiHHnooZcGCBZmpqam5UVFRo0pLS0MAYNOmTdEXXnjhoOjo6JFRUVEjx48fP2jTpk1ONx+eM2dOltVqzf3oo49iRo4cOSQyMnLUwoULM73+8Lzkaxb/LwA/BMdudR3Jg4CQcKCpAThzGKg94zRX1+4TFai3NSEiNMTEIImI/Cg/frRf9lPwegoKXk85u1jKv/a26r333ltUWloaWlBQELNmzZp9ABAZGWkHgNOnT1vGjx8/pL6+Xm6//fbjAwYMqH/vvffib7/99n719fWWO++8swQA5s2bl338+PGIe+6552hWVlZDUVFR2EcffRRXVVVlufDCC6uXLVt2eMmSJX3vv//+I+PGjasGgJEjR9a2Fdf8+fOzr7zyytPz58/ft3nz5tiVK1f26d27d9Njjz12HADq6upk2rRpg+rr6y3Lly8/bLVabS+88ELyO++809ub9/3www+n3H777X3nzp1bescddxRVVFRYli1b1mfSpEmDCwsLd/bu3bu5yerzzz+P27VrV/TixYuL0tLSGgcOHNjcRbpy5cr03Nzc6lWrVh1qamqSqKgo+5dffhk1ffr0IQMGDKh96qmnDoqIWrFiRfr06dOHbNq06dvx48c3v/eqqqqQ66+/vv9NN91UnJeXdyw6OtrvXa2+Jl1PAviziIQCWAfthtfGqxehlPreT7GRP4SGAymDm7sWUVyIhKyL0S8pGodKa9DYpLC7qBJ55yS0vR8iIupUw4cPr09KSrKFhYWpqVOnVhvLli1bZi0qKgrfunXrzpycnHoAmD17dmV5eXnIihUr0n//+9+XhIWF4Ztvvom94447jv3qV7867dh2/vz5ZY7lESNG1OnHqnU9hidXXXXVaUeCNXv27MqtW7fGvPnmm4mOdatXr046evRoxMaNG7+dPHlyDQBcffXV5UOHDh1WVFTU5r7Ly8st9913X8bcuXNL16xZc9CxfsKECdUjRowY8eSTTybffffdJY71lZWVIVu3bt3Vt2/f5l43R0tacnJy44cffrjfYmnpxFu6dGl6WFiY/ZNPPvkuOTm5CQBmzpxZkZ2dnbt06dI+H3744X5H3ZqaGsuzzz575Lrrruu0mcN9vXrxEwDnAPiNvvwdgL0uDwo2TjPTFwKAU2tXAefrIiIKahs2bIjPzc2tHjJkSH1jYyMcj2nTplWcOXMmdNu2bVEAkJOTU7169eq0++67L3XLli1RZzuuCQBmzpzplIQMGzastqioqLnr78svv4xNT09vcCRcAGCxWHDFFVeUoR0bN26MraqqCrnuuutKje+rf//+DdnZ2XWfffZZnLF+Xl5etTHhMpoxY8YZY8IFAFu2bImbMmVKuSPhAoDExET7JZdccmbLli1O+w4JCVHz5s3r1Fu1+NrS9bNOiYI6l5vB9HmZCXi7QPsPpODIGWAcp1cjom7Chy69Vv40ewBiUxtx/s9P4qs/pqCqJAzXr9vf/oadq7S0NPTw4cMR4eHhbrtOS0pKQgFg7dq13y9evLjPk08+mXb33Xefk5KS0nj99defXL58eVFISMeGkaSkpDQZX0dERKiGhobmMV3FxcVhiYmJrRIhq9Xa2N6+T5w4EQoAs2fPHuSuPD4+3unYqampHveZnp7eqqyioiI0LS2t1Xqr1dpYUVHhdEISExNtoaGde+2Er1NGvOKpTERCoE2cSsHGarwdUAEAIIcz0xMRtWZMsM654LCJkThJSEiwJSUl2R5//HG3MeXk5NQBQEZGhu3VV189DODw9u3bI55//vnkRx99tE9KSort9ttvP9kZsVmt1sZ9+/ZFuq4vLi4Oa2/blJQUGwA88cQTB/Py8lqNLXNNutq6GY67sl69etncxVFcXBwWHx/vlCgG4kY77SZdInIawCVKqW36a4E2I/2vXcZvjQHwbwAckR1sjPdgPLkbaGrEiIx4iABKAd8VV6KmwYbo8B51dTQRUdCJiIhQ9fX1rYb+TJ06teLFF19MHTBgQENGRoZXswjk5eXVr169+tirr76aUlhYGAW0DMyvqanx261Ixo4dW/XGG28kbdq0KdrRxWi327F+/fp2B9JPmTKlKiYmxr5v376IW265pdRfMRliq9y0aVN8WVmZxTEgv6yszLJhw4aEsWPHVvr7eO3x5q9sgks9C4DLAeR3RkDUCaJ6A/F9gfLD2lWMp75DrHU4BqTEYl9JFewK2HW8AmOyEs2OlIioRxs6dGjta6+9lrx8+fKUcePGVUdFRakLLrig9s477yxet25d74suumjIwoULi4cOHVpXVVVl+fbbbyM3b94cu2HDhv2lpaUhEydOHHTNNdeUDhs2rC4sLEy9+eabCRUVFSHTpk2rALSB9CEhIeqll15KTk5OtkVGRqqcnJw64xWCvrr55ptLV61alTZv3ryBd91117HU1FTbCy+8kOzovnMdZ2WUmJhoX7p06ZElS5b0O3nyZOiMGTMqEhISmo4cORL26aefxk2cOLFywYIFpz3uoB35+flFEydOTJgwYcLg3/72t0UigkcffTStrq7Okp+ff7yj++0oNm30FGk5WtIFaOO6rMORmxmPffptgLYfLWfSRURksltvvfXUli1bYh544IGMysrKkD59+jQcO3ZsR1JSUtOXX365e/HixX1WrVqVVlJSEhYXF9eUnZ1dN2vWrDIAiI6Otufm5tb86U9/Sjl+/Hi4xWJBVlZW3TPPPHPAcUVeWlpa07Jlyw6vWrUqfcaMGUOampqwfv367y6//PIOt/pERkaq999/f+/ChQvPWbRoUb+oqKim2bNnnz7//POrH3zwwYzExMSmtrZftGjRqb59+zauXLnSumDBgiSbzSapqakNY8eOrTr//PNr2tq2PWPHjq19991399x1110ZCxcuzFZK4bzzzqt+7733dhuniwgUUUq1XUHEDmCcUmqL/joEQCOAMY4uR339WAD/Vkqxe9GNMWPGqK1bt5oXwKYHgU+Wa8vjbwamPYCXNx9A/vpdAIDZ5/XB4/NGmhcfEZEbIvK1UmqMp/Lt27cfzMvLOxXImMg7kydPHrhv377II0eOFJodSyBt3749OS8vL8tdGVu6egqnKxi1wfS55/B2QEREdPby8/OtsbGxTYMHD66vqKiwrFmzJvHjjz+OX758edBcjBAMvE26MkSkv74cYlhnnM/C79Plkx85JV2FgFIYlt4LoRaBza7w/alqVNQ1oldkuxebEBEROYmIiLA//fTT1qKionC73S5ZWVl1K1euPHTbbbexFdLA26TrDTfr1rm8FrjMTk9BJKEfENELqK8Aak8DFccRGZ+BQdY47CqqAAAUHi3HhQOT29kRERGRsyVLlpxcsmRJp0xJ0Z14k3RxQtTuQESbr+vwv7XXJ3YA8RnIzYxvTroKjjHpIiIi6iztJl1tTYjak4nIHQB+CuBcAFcppVxb/oJPWk5L0lW8Axh8GXIzE/C3r44AAAqOdurdD4iIOoPdbreLxWJhTwuZzm63CwCP02/4bXK0HmgDgBkAPjU7EK+5uR1QrmFmeg6mJ6KuRkRO1NbWtpoNncgMtbW1kSJywlO5aUmXiMwQkU9FpEpEKkRkq4hM6aRjZYrIkyLyuYjUiIgSkaw26p8jIm+ISLke21oR6Wuso5T6Uill+v24fGKcmV5PugZZ4xAeqn0NjpbVorSq3ozIiIg6xGaz3XPw4MHw6urqKL2VgSjg7Ha7VFdXRx08eDDcZrPd46meKVNGiMgvAazWH/dBS/7OAxDdSYccCOAaAF8D+D8AP2wjtmgAGwHUQ+s+VADuB7BJRHKVUtWdFGPnSxkKSAigmoDT3wP1lQiPiMPQ9F7YfkTrWtxxrByTBqeaHCgRkXdGjRr1wbZt227ev3//UqVUGtiDQ+awi8gJm812z6hRoz7wVCngSZfewvQ4gEVKqccNRR6D1LdLA9BfKfVvN2VRACYppd7zsPmnSimrXvfnaCPpAnAjgP4ABiul9unbFADYC+CXAFa2FWdQC4sEUgYDJdqEqCjeBfQdi7zM+Oakq+Aoky4i6lr0P3Jt/g0hCgZm/EcwH9ogs//1cbvbAHwoIj8wrtQTrrcBvCQise42VEr5ck+pmQC+cCRc+vYHAGwGMMvHmIOPm0lSczI4rouIiKizmZF0XQxgN4B5IrJfRGwisk9EbmpnuzsBvAvgXRG5CGhOuNYDyAPwQ6VUlR/iGw7A3S0LdgIY5uvOROQKEXmuvDxIkhlr63FdeU4z0/MKRiIios5gRtLVB9o0C48AeAhaV9+/AKwWkVs9baSUsgH4CbQm5PdEZCqAf0IbCzZVKVXgp/gSAZS5WX8aQG/HCxG5S0SOAhgP4I8iclTvAnWNe71S6hfx8fGuReZwcwXjgJRYRIdrNxooqaxHcUWdGZERERF1a2YkXRYAcQB+qZR6Xim1USn1KwDvA1giIh6vPtETr3kAPtIfowFcqpTa7ucY3c334hSXUup+pVSmUipCKZWsL3u8TDRoGJOukl1Akw0hFsGIPi1JoWN8FxEREfmPGUlXqf78L5f1HwKwAkhvZ/tQALHQxoWFwf9XPJZBa+1y1RvuW8C6lphkIK6PtmyrA05rs17kGObr2nEsSLpCiYiIuhEzkq6dHtY7WpI8DnoXkUho93wcBWActNau90RkvJ/jG+5m/TAAu/x4HPO4ma/LOEnqdg6mJyIi8jszkq439edpLuunATjqqYtORCIArAVwPoBLlFJfQZt7awOA90VknJ/i+yeAcSLS33DsLAAX6WVdn9uZ6VsG0+84egZK8Y4aRERE/mTG5KjvAtgE4FkRSQbwPYC50AbUt3Vz7QcAjIWWcH0DAEqpRhG5BsDrANaLSLanKxhFZK6+OFp/ni4iJwGcVEp9Yqj6PICbAbwlIndBG991H4AjAJ71+d0GIzdJV1ZSNOIiQ1FZZ0NZTSOOltXinMTOmquWiIio5wl40qWUUiIyG8AyAPdAGyu1G8C1Sqm/trHpAwBeUUrtcNmfI/E6v50pI9a4vH5af/4EwCTD/qr12xE9BuBVaN2eGwD82k9TUpjP2jrpEhHkZsZj8z5tyF3B0XImXURERH5kym2AlFIVAG7SH95uUwYPA9mVUo0AWs1U71LH63tyKaUOA5jjbf0uJzEbCIsBGquB6hKgshiIsyI3M8GQdJ3Bj3Lbu6aBiIiIvMV7VPVElhDAarhWoFgf18WZ6YmIiDoNk66eyt1gesPM9IXHymG3czA9ERGRvzDp6qncTBvRJz4SSTHhAIDKehsOlFabERkREVG3xKSrp0rLbVl2GUzvwPswEhER+Q+Trp4qdRgg+sdfug9oqAEA5GQab37NcV1ERET+wqSrpwqPBpIGasvKDpR8CwDIy+RgeiIios7ApKsnsxrHdRUAcL4H487j5bA1ebwrExEREfmASVdPZryCsbgQAJAaF4n0+EgAQF2jHXtLusd8sERERGZj0tWTuRlMDwA5GRxMT0RE5G9Munoyp2kjCgG71pWYdw4H0xMREfkbk66eLNYKxKRoy43VQNkBAK4tXUy6iIiI/IFJV08m4n5mesNg+t0nKlBvawp0ZERERN0Ok66ezk3SlRAdjr6J0QCAxiaF3UWVZkRGRETUrTDp6umsrZMuwLm1q+AYuxiJiIjOFpOuns5NSxcA5Blnpj/CKxiJiIjOFpOuni5pIBCqzcuFyuNAdSkA50lSd7Cli4iI6Kwx6epkInKFiDxXXh6kiUtIqHYfRodirbVrREY8RLRV3xVXoqbBZkJwRERE3QeTrk6mlFqvlPpFfHx8+5XN4jRfl5Z0xUaEYkBKLADAroBdxyvMiIyIiKjbYNJFLjPTFzYvGgfTb+d8XURERGeFSRd5HEyfa5gkdQdvB0RERHRWmHQRYB3esnxqD9BYBwDI5e2AiIiI/IZJFwERcUDvbG3ZbgNO7gYADEvvhVCLNpr++1PVqKhrNCtCIiKiLo9JF2mMXYzF2riuyLAQDLLGNa8uZGsXERFRhzHpIo3TYHrOTE9ERORvTLpI42baCADINc5Mz8H0REREHcakizROVzAWAkoBcGnpYvciERFRh4WaHQAFiV4ZQFRvoLYMqC8HzhwGevfDIGscQgRoUsDRslqMW7YBiy8bgtkjMwIe4rr/HMMjH+zB8TO16JMQhUXTBjMOk+MIhhgYB+Mg6ipE6S0a1LnGjBmjtm7danYYbXvlCuDAp9ryf/0FGHo51v3nGG57/RsYvyZhIYK5ozMxqm9vp83Fcd8gNzyVtLGJU9nWQ6fx+ldH0djUEkhYiOCa8zMxpl+i5534mcc4xmRitIc4fP0R86b614dO442vW8cxd7TnONrSxsfQZgxr3MRwdTsx+HI6vPn9tO1wmdtzcfXoTIzJSoQIIJDm75OINL9fY5nA8Z0zvhbD+pb6cFP+732leOGzA2hosjfHER5iwfyLszB+QDKUUtp7V4CCglLad0Pp71N71irYm8uUUx3AZb3L9lDa57L2P8danY9Z52UgLzO++TjN2wBtHkPfbet1ynO5ArCnqBwbdp+Ezd4SR1RYCJZdleNT4iUiXyulxni9AVEQY9IVIF0i6Xr/DuCLp7TliYuByUtw0UMbcexMrblxEVG3kZEQhc2Lp3hdn0kXdScc00Ut3EwbcZwJFxH5EX+nUE/GMV3UwmkwfQEAoE9ClNuWrqiwEMzISQegdSl41LGiVt1KH+wsRm1jk9s4pg23trEn/2orjstGpHnczufuu3Y2eG/HCY9xTM/xHIdbHWzsfq+wjRjaOBcAfDoh0k7ld3cUtfndaOn6cu5Sa93NZ+zK0yo4XsOwraeuuK0Hy1Bvs8NVRKgFF2Rr3a3G7sjW3Zdat6bF2OXZRnem8TX0ehYB3tlRhJqG1ucjOjwEV47McNOl2nJ+3XW3OsqNx3Eq1z8fxzroMb24+QAq62yt4uiTENVqHVFPwaSLWiQPAixhgL1RG0hfewaLpg3GkrU7nP6odWRcxtla959jjMNgwrnmxzFhkPkxAMAPzk0OijiC5btx0UD35+PBKwMbR3ZyjNs4Fk0bHLAYiIINky5qERoOpA5pmaeruBCzR14MAKZfgeQ4HuMInjiCIQbGwTiIuhIOpA+QLjGQHgDWLQS++Yu2fNlyYNwCc+Mhoh6NA+mpO+FAenLmNK5rh+d6RERE5BMmXeTMarwdUIF5cRAREXUzTLrImfEejCd3A02N5sVCRETUjTDpImdRvYH4vtpyUwNw6jtz4yEiIuommHRRaxzXRURE5HdMuqg1Yxcjky4iIiK/YNLVQSJyh4jsERG7iMw2Ox6/YksXERGR3zHp6rgNAGYA+NTsQPzONeniXG5ERERnzfSkS0TeFxElIvd34jEyReRJEflcRGr042W1Uf8cEXlDRMpFpEJE1opIX2MdpdSXSqn9nRWzqRL6ARG9tOXa00DFcXPjISIi6gZMTbpE5McA8gJwqIEArgFQBuD/2okpGsBGAEMA/BTAfwM4F8AmEYnp5DiDg4jLfF3sYiQiIjpbpiVdIpIA4DEAv/GyfpqIXOihLEpEprex+adKKatSagaANe0c6kYA/QHMVkqtU0q9BWAmgH4AfulNrN2CsYuxmEkXERHR2TKzpethADuVUq95Wf82AB+KyA+MK0UkCsDbAF4SkVh3Gyql7D7ENRPAF0qpfYbtDwDYDGCWD/vp2jiYnoiIyK9MSbpE5GIA1wNY6MNmdwJ4F8C7InKRvp8oAOuhdVH+UClV5YfwhgModLN+J4Bhvu5MRK4QkefKy8vPOrCA4rQRREREfhXwpEtEwgA8C2CFUmqPt9sppWwAfgLgAwDvichUAP8EcB6AqUopf90oMBHa2C9XpwH0drwQkbtE5CiA8QD+KCJHRSTNTdzrlVK/iI+P91N4AZIyFJAQbfn0AaC+0tx4iIiIujgzWrpuBxAF4AFfN9QTr3kAPtIfowFcqpTa7tcIAXdzJIhLLPcrpTKVUhFKqWR9+YSf4zBPWCSQMlh/oYDiXaaGQ0RE1NUFNOnSp124E8AfAESISII+oB6G1yHt7CYUQCwAO4AwANF+DrMMWmuXq95w3wLWfTmN6/JXQyIREVHPFOiWrv4AIgH8GVoC43gAwO/05Rz3mwIiEglgHYBRAMZBa+16T0TG+zHGndDGdbkaBqBnNfdw2ggiIiK/CXTS9Q2AyW4egJaITQawz92GIhIBYC2A8wFcopT6CtrcWxsAvC8i4/wU4z8BjBOR/oZjZwG4SC/rOZymjXB3bQERERF5KzSQB1NKnQHwset6EQGAQ0qpVmUGDwAYCy3h+kbfX6OIXAPgdQDrRSTb0xWMIjJXXxytP08XkZMATiqlPjFUfR7AzQDeEpG7oI3vug/AEWgXAPQcTknXTqDJBoQE9CtDRETUbXSlv6APAHhFKeXUz2VIvM5vZ8oI10lRn9afPwEwybC/ahGZAm3i1lehDaDfAODXfpqSouuISQbi0oHKIsBWB5zebxhcT0RERL4IiqRLKSVe1DGO/3ItawTw77M9hqHuYQBzvK3fraXlaEkXoI3rYtJFRETUIabf8JqCHGemJyIi8gsmXdQ2Jl1ERER+waSL2mZl0kVEROQPTLqobYnZQFiMtlxdApzg1BFE5IPKE8BL04HKYrMjITJdUAykpyBmCQGsw4GjW7TX7/wOmPYAYLFo92a0hBieLS2vjcuuZY7XEqLtxxeVJ4A3fgbMfRmIs/r97TKOLhoD4/Acx5wXgZgUQNnbeKh2yt3Ugbtt3Kz7fDVw6HNg04PAzFXmnQ+iICBKubvNIPnbmDFj1NatW80Ow3f3pwK2+s49RqvkTU/GxDWxswA1ZUBDJRARB0Qn6zswfIebv8+qVVHLOuXjOjf7r6/QptEIjQQienXgTfuJUxxxJsVQqcUQEuESg5vfLa1+33hTx1M9l9eNtYC9AQgJ1+Jwl+C7/kMglvbXO+0jBBBpe/2RL4GTu4HkQUDmBYBqAuxNLs92/dnmZp1r3ba2b6uOre3PzSyhEcBdJV5XF5GvlVJj7eaeaQAACoNJREFUOjEiooBhSxe17dYC4O//3dLS1RlUE9DU5Ns29ZXaw2y2Ou1htmCIo6keqOnkBN2rOBqAmlKzowBOfac9SBMaCQy9AvjhA2ZHQmQaJl3Utrg0wDpMT7oEgAKik4BeGVrXgeO/auOy2//Y7S3PxjIiCgwJNbTOGR/iZp27ck/12tj+9AGg6oS2bKvXWoXN7HIlMhmTLmpf9SlgzP8DxvwM2PoSUFUMzPuLf/btqUtFqdbrProHKPwHEBIGNDUCI+YCk5do+xHj3Lfiss5Q1tF1xv3/Kx8o+JvWjdXUAOTNAy65p6NnoOP+tdQljh8DlwY4jn/dDWx3jeHelnJxNyexyzq3ddxt1sa+PrgD+OavznFcstRNoq+c/xFod73Ld9HpHw0367f/DTj8uZbc2JuArIuAvJ+4dJvr3ZGW0NbrWnWx6/XaHB/p2J9h+b3FwH/+1PKzMvpnwOUrvTvP/vS3a4FYq/PvDqIejEkXtc+YYPn7F7fFAsCi/XFoj60OGDPf+Rd40gD/xuONhsrWcZjx37u7OGJTAxtDvbsYUgIbAwDUlbv5TNICH8feD1vHMfLawMdRc0pLtMxOdjrzdwdRF8SB9AHSZQfSExGZiAPpqTvhPF1EREREAcCki4iIiCgAmHQRERERBQCTLiIiIqIAYNJFREREFABMuoiIiIgCgFNGBIiInARwyOw4zlIygFNmBxFEeD5a8Fw44/lwdjbno59SyoTJ34j8j0kXeU1EtnK+nBY8Hy14LpzxfDjj+SDSsHuRiIiIKACYdBEREREFAJMu8sVzZgcQZHg+WvBcOOP5cMbzQQSO6SIiIiIKCLZ0EREREQUAky4iIiKiAGDSRR6JyFwR+YeIHBKRWhHZIyLLRCTO7NiCgYi8LyJKRO43OxaziMgMEflURKpEpEJEtorIFLPjMoOIXCQiH4pIiX4utonIfLPj6mwikikiT4rI5yJSo/9MZLmp11tE/igip0SkWkQ+EpGcwEdMZB4mXdSW3wFoAnAHgMsAPAPgVwD+JSI9+rsjIj8GkGd2HGYSkV8CeAvA1wCuBHA1gDUAos2MywwikgvgIwBhAG4EMAfAVwBeEJFfmRlbAAwEcA2AMgD/566CiAiAf0L7PXILtPMTBmCTiGQGKE4i03EgPXkkIilKqZMu664H8AqAqUqpjeZEZi4RSQCwG8BtAP4K4AGl1F3mRhVYekvGtwCWKKUeNzca84nIg9D+SUlUSlUZ1n8BQCmlxpsWXCcTEYtSyq4v/xzA8wCylVIHDXVmAVgHYIpSapO+Lh7AAQB/Vkr9T8ADJzJBj26toLa5Jly6r/TnjEDGEmQeBrBTKfWa2YGYaD4AO4D/NTuQIBEOoBFArcv6M+jmv2cdCVc7ZgI47ki49O3KAawHMKuzYiMKNt36lwF1ion687emRmESEbkYwPUAFpodi8kuhtbaN09E9ouITUT2ichNZgdmkpf15ydEpI+IJIjIjQCmAnjMvLCCxnAAhW7W7wTQV0RiAxwPkSlCzQ6Aug4RyQBwL4CPlFJbzY4n0EQkDMCzAFYopfaYHY/J+uiPR6CN+dsPbUzXahEJVUqtMjO4QFNKFYrIJABvoiUhb8T/b+/eQqyq4jiOf39pORZddKKQqEzooSLoAmkPphZpSWmREEGhRYQIPRSZTZJYNl66WVGhvUQxZQ/ZTeiiaVqQlQVFBSGVl2wy1LFIaTTr38Pao8ftOdOAuPecOb8PHLaz1jr7/B0c/bvWf60NUyPi1dIC6z0GAxurtHdk10HArir9Zn2Kky7rkex/om8B+4BbSw6nLDOAgUBr2YH0AkcBxwNTIuL1rG1VVuvVIunpaKCCUUlnA0tJMzdTScuME4FFkjoj4uUy4+sFBFT786CiAzErk5Mu+1+Smkg7j4YBoyJiS8khFU7SGcBM4HZggKQBFd0DsuL6PyPin1ICLN4O4GxgRa59OWmH2hCgveigSjSXNLN1TUT8nbWtlNQMPCVpSQ9rn/qqDtJsV96g7LqzwFjMSuOaLutWtqS2FLgEGB8R35QcUlmGAU1AG+kfiK4XpF1rO4FGOnPouxrtXTMXjZZgnA98XZFwdfkcaAZOKT6kXuU7Ul1X3rnA5sodn2Z9mZMuqyk7i+tlUjHwxIj4tOSQyvQVMKbKC1IiNgb4oZzQSvFGdh2Xax8HbImIrQXHU7atwAWSjsm1Dwc6OVC71KjeBk6T1LURB0knANdmfWYNwcuL1p1nScXRrcBuSSMq+rY00jJjRPwOrM63pzMf2RQRh/T1ce8AHwKLJZ0M/ARMAsbSmDV/z5AOhl0m6TlSTdcE4CZgYUTsLTO4I03SpOyXF2fXqyVtA7ZFxBpSYrUWaJM0nTQz3EKaGX2k6HjNyuLDUa0mSRuBM2t0PxgRs4uLpneSFDTg4aiwf6ZiHinZGkQ6QmJ+RLxSamAlkXQ1abPFeaSl6B+B54HFfb3WL/s5qGZNRIzOxgwGHgOuI31/1gJ3R8TXhQRp1gs46TIzMzMrgGu6zMzMzArgpMvMzMysAE66zMzMzArgpMvMzMysAE66zMzMzArgpMvMzMysAE66zOqQpLGS3pW0Q1KnpPWSFkga9P/v7va+s7s5c8nMzA6Dky6zOiPpfuB90uNlbic9emcRMAVYJ+n08qIzM7Na/BggszoiaQzwMPBkRNxV0bVG0hvAl8BLHHguZP79/UiHIu8rINajgX3hE5jNzADPdJnVm3tJD09uyXdExAZgPjBa0nBIj2eR1CrpPkkbgL3A+VnfhZI+zpYnf5H0AOlZeAeR1F9Si6TvJe2R1C7pcUlNFWOGZp81TdIjktqBPcBJR+B7YGZWlzzTZVYnJPUHRgFvRURnjWFvAwuAy4HPsrYppAdS3wPsBtqzh1SvArYCk0kJ0nTgjCr3bAOuze77CXAOMAcYCtyQGzsTWAfcAfQjLYGamRlOuszqSTMwENjYzZiuvsq6LgFjI+Kv/Q1SK3AcMC4iNmdtK4BNlTeTNBK4EZgcES9lzR9I6gDaJF0QEV9VvOU34HovKZqZHcrLi2b145Clvx56rzLhylwKfNqVcAFExG5gWW7cVaQlyaXZMmP/bMZtedZ/WW78m064zMyq80yXWf3YDvxFWtarpavv54q2X6uMGwJ8W6X9t9zXpwDHALtqfF5z7utqn2VmZjjpMqsbEbFP0kfAlZKaatR1TciuqyrfWmXcr8CpVdrzbTtIdVkja4TVng+zxjgzs4bn5UWz+vIoaXZpbr5D0lnADOCjiPgs35+zFhhReaaXpONIBfOV3gOagBMj4osqr3zSZWZmNXimy6yORMRKSbOAhyQNJZ3JtRO4CLgP+AO4pQe3WghMA5ZLms2B3YsH1X5FxGpJS4DXJD0BfA78S1rGHA/MiIj1h/0bMzNrAE66zOpMRMyRtA64C3gBOBbYTErA5kVERw/usV3SFcBTwIukZcRFpL8TZuWG3wzcCdxGOhJiD2mX5PscWgNmZmY1yBuNzMzMzI4813SZmZmZFcBJl5mZmVkBnHSZmZmZFcBJl5mZmVkBnHSZmZmZFcBJl5mZmVkBnHSZmZmZFcBJl5mZmVkB/gMT1T8rysCvAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Problem 4 \n",
    "\n",
    "#load data\n",
    "al = np.loadtxt('../data/al_price.csv',skiprows=1,delimiter=',')\n",
    "steel=np.loadtxt('../data/steel_price.csv',skiprows=1,delimiter=',')\n",
    "\n",
    "#assign variables \n",
    "t_al = al[:,0] # year data\n",
    "p_al = al[:,1] # value data\n",
    "\n",
    "#assign variables \n",
    "t_st= steel[:,0] # year data\n",
    "p_st= steel[:,1] # value data\n",
    "\n",
    "#Problem 4a: 70% testing 30% training###################################################################\n",
    "\n",
    "# randomize testing/training indices\n",
    "np.random.seed(103)\n",
    "i_rand=np.random.randint(0,len(t_al),size=len(t_al))\n",
    "\n",
    "# choose the first half of data as training\n",
    "train_per=0.7\n",
    "t_al_train=t_al[i_rand[:int(len(t_al)*train_per)]]\n",
    "p_al_train=p_al[i_rand[:int(len(t_al)*train_per)]]\n",
    "\n",
    "# choose the second half of data as testing\n",
    "t_al_test=t_al[i_rand[int(len(t_al)*train_per):]]\n",
    "p_al_test=p_al[i_rand[int(len(t_al)*train_per):]]\n",
    "\n",
    "# randomize testing/training indices\n",
    "np.random.seed(103)\n",
    "i_rand=np.random.randint(0,len(t_st),size=len(t_st))\n",
    "\n",
    "# choose the first half of data as training\n",
    "train_per=0.7\n",
    "t_st_train=t_st[i_rand[:int(len(t_st)*train_per)]]\n",
    "p_st_train=p_st[i_rand[:int(len(t_st)*train_per)]]\n",
    "\n",
    "# choose the second half of data as testing\n",
    "t_st_test=t_st[i_rand[int(len(t_st)*train_per):]]\n",
    "p_st_test=p_st[i_rand[int(len(t_st)*train_per):]]\n",
    "\n",
    "#Problem 4b (aluminum): fitting data##########################################################################\n",
    "t_ext = np.linspace(min(t_st),2025)\n",
    "Z_al_train=np.block([[t_al_train**0]]).T\n",
    "Z_al_test=np.block([[t_al_test**0]]).T\n",
    "Z_al_ext=np.block([[t_ext**0]]).T\n",
    "max_N=11\n",
    "SSE_train=np.zeros(max_N)\n",
    "SSE_test=np.zeros(max_N)\n",
    "plt.figure()\n",
    "plt.plot(t_al,p_al,'b-',label='original data')\n",
    "for i in range(1,max_N):\n",
    "    Z_al_train=np.hstack((Z_al_train,t_al_train.reshape(-1,1)**i))\n",
    "    Z_al_test=np.hstack((Z_al_test,t_al_test.reshape(-1,1)**i))\n",
    "    Z_al_ext=np.hstack((Z_al_ext,t_ext.reshape(-1,1)**i))\n",
    "    a_al = np.linalg.solve(Z_al_train.T@Z_al_train,Z_al_train.T@p_al_train)\n",
    "    SSE_train[i]=np.sum((p_al_train-Z_al_train@a_al)**2)/len(p_al_train)\n",
    "    SSE_test[i]=np.sum((p_al_test-Z_al_test@a_al)**2)/len(p_al_test)\n",
    "    if i == 10:        \n",
    "        plt.plot(t_ext,Z_al_ext@a_al,'o',label='order {:d}'.format(i))\n",
    "        #plt.plot(t_4,Z_al_train@t_4)\n",
    "        plt.title('Aluminum Price over time')\n",
    "        plt.xlabel('Time (years)')\n",
    "        plt.ylabel('Price (Dollars/tonne)')\n",
    "        plt.legend(loc='best')\n",
    "\n",
    "#Problem 4c (aluminum): plotting error##########################################################################    \n",
    "plt.figure()\n",
    "plt.xlabel('Order')\n",
    "plt.ylabel('Error')\n",
    "plt.semilogy(np.arange(1,max_N),SSE_train[1:],'o-',label='training error')\n",
    "plt.semilogy(np.arange(1,max_N),SSE_test[1:],'*-',label='testing error');\n",
    "plt.title('Error in Aluminum Price vs. Order')\n",
    "plt.legend(loc = 'center left', bbox_to_anchor = (1, 0.5));\n",
    "\n",
    "#Problem 4b (steel): fitting data##########################################################################\n",
    "Z_st_train=np.block([[t_st_train**0]]).T\n",
    "Z_st_test=np.block([[t_st_test**0]]).T\n",
    "Z_st_ext=np.block([[t_ext**0]]).T\n",
    "max_N=11\n",
    "SSE_train=np.zeros(max_N)\n",
    "SSE_test=np.zeros(max_N)\n",
    "plt.figure()\n",
    "plt.plot(t_st,p_st,'b-',label='original data')\n",
    "for i in range(1,max_N):\n",
    "    Z_st_train=np.hstack((Z_st_train,t_st_train.reshape(-1,1)**i))\n",
    "    Z_st_test=np.hstack((Z_st_test,t_st_test.reshape(-1,1)**i))\n",
    "    Z_st_ext=np.hstack((Z_st_ext,t_ext.reshape(-1,1)**i))\n",
    "    a_st = np.linalg.solve(Z_st_train.T@Z_st_train,Z_st_train.T@p_st_train)\n",
    "    SSE_train[i]=np.sum((p_st_train-Z_st_train@a_st)**2)/len(p_st_train)\n",
    "    SSE_test[i]=np.sum((p_st_test-Z_st_test@a_st)**2)/len(p_st_test)\n",
    "    if i == 10:\n",
    "        plt.plot(t_ext,Z_st_ext@a_st,'o',label='order {:d}'.format(i))\n",
    "        #plt.plot(t_4,Z_al_train@t_4)\n",
    "        plt.title('Steel Price over time')\n",
    "        plt.xlabel('Time (years)')\n",
    "        plt.ylabel('Price (Dollars/tonne)')\n",
    "        plt.legend(loc='best')\n",
    "    if t_ext[i] == 2025:\n",
    "        print(Z_st_ext@a_st)\n",
    "        \n",
    "#Problem 4c (steel): plotting error##########################################################################       \n",
    "plt.figure()\n",
    "plt.xlabel('Order')\n",
    "plt.ylabel('Error')\n",
    "plt.semilogy(np.arange(1,max_N),SSE_train[1:],'o-',label='training error')\n",
    "plt.semilogy(np.arange(1,max_N),SSE_test[1:],'*-',label='testing error');\n",
    "plt.title('Error in Steel Price vs. Order')\n",
    "plt.legend(loc = 'center left', bbox_to_anchor = (1, 0.5));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Problem 4d: price prediction\n",
    "\n",
    "#Based on the above graphs, I chose to use a polynomial function with order 10 to predict the prices for steel and \n",
    "#aluminum. This is because all of the polynomial functions after order 1 have the lowest error for both metals. Based \n",
    "#on the above graphs, the price for aluminum and steel in 2025 will be approximately #-30000 and $90 respectively.\n",
    "\n",
    "#Problem 4e: price model\n",
    "#Based on the data I would change my answer in number 3 based on the fact that its value is predicted to drop\n",
    "#significantly when compared to steel in the near future. "
   ]
  },
  {
   "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>"
   ]
  }
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