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": 1,
   "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": 1,
     "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": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The condition of K is 17 and the condition of K[2:13,2:13] is 0.\n"
     ]
    }
   ],
   "source": [
    "K[2:13,2:13]\n",
    "np.linalg.cond(K)\n",
    "print('The condition of K is 17 and the condition of K[2:13,2:13] is 0.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I would expect the error in u to be 10 when solving for u in K*u = F.\n"
     ]
    }
   ],
   "source": [
    "#1a\n",
    "cond_K = 17\n",
    "err = 10**(cond_K - 16)\n",
    "print('I would expect the error in u to be', err,'when solving for u in K*u = F.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The condition of K is so large because K is large and has multiple possible solutions with more room for error.\n"
     ]
    }
   ],
   "source": [
    "#1b\n",
    "print('The condition of K is so large because K is large and has multiple possible solutions with more room for error.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I would expect the error in u[2:13,2:13] to be 1e-14 when solving for u in K[2:13,2:13]*u = F[2:13,2:13].\n"
     ]
    }
   ],
   "source": [
    "#1c\n",
    "np.linalg.cond(K[2:13,2:13])\n",
    "cond_K2 = 2\n",
    "err2 = 10**(cond_K2 - 16)\n",
    "print('I would expect the error in u[2:13,2:13] to be', err2,'when solving for u in K[2:13,2:13]*u = F[2:13,2:13].')"
   ]
  },
  {
   "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": 6,
   "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": [
    "#2a\n",
    "\n",
    "K = K[2:13,2:13]\n",
    "def LUNaive(A):\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",
    "L,U = LUNaive(K)\n",
    "print('L =',L)\n",
    "print('u =',U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#2b\n",
    "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\n",
    "\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",
    "A = 0.1 #mm\n",
    "E_s = 200*1000 #1000 N/m^2\n",
    "E_a = 70*1000 #1000 N/m^2\n",
    "F = np.zeros(len(K))\n",
    "F[5] = -100\n",
    "def solveLU(L,U,b):\n",
    "    n=len(b)\n",
    "    x=np.zeros(n)\n",
    "    y=np.zeros(n)     \n",
    "    # forward substitution\n",
    "    for k in range(0,n):\n",
    "        y[k] = b[k] - L[k,0:k]@y[0:k]\n",
    "    # backward substitution\n",
    "    for k in range(n-1,-1,-1):\n",
    "        x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
    "    return x\n",
    "u_s = solveLU(L,U,F/(E_s*A))\n",
    "u_a = solveLU(L,U,F/(E_a*A))\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#2c\n",
    "K = fea_arrays['K']\n",
    "\n",
    "#Steel\n",
    "F_s = K@u_st\n",
    "#Aluminum\n",
    "F_a = K@u_al"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#2d\n",
    "\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "s = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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"
    },
    {
     "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": [
    "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.quiver(r[ix],r[iy],u_al[ix],u_al[iy],color='g',label='displacements')\n",
    "plt.quiver(r[ix],r[iy],F_a[ix],F_a[iy],color='b',label='forces')\n",
    "\n",
    "plt.title('Forces and Displacements for Aluminum Truss')\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]));\n",
    "\n",
    "plt.figure(figsize = (15,10))\n",
    "plt.plot(r[ix],r[iy],'-',color='k')\n",
    "plt.plot(r[ix]+u_st[ix]*s,r[iy]+u_st[iy]*s,color='r')\n",
    "plt.quiver(r[ix],r[iy],u_st[ix],u_st[iy],color='g',label='displacements')\n",
    "plt.quiver(r[ix],r[iy],F_s[ix],F_s[iy],color='b',label='forces')\n",
    "\n",
    "\n",
    "plt.title('Forces and Displacements for Steel Truss')\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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The minimum surface area for aluminum to deflect less than 0.2 mm is 7.693975903614457 mm.\n"
     ]
    }
   ],
   "source": [
    "#3a\n",
    "A = np.linspace(0.1,10,250)\n",
    "for i in range(len(A)):\n",
    "    A_ref = A[i]\n",
    "    F_a = F/(E_a*A_ref)\n",
    "    u_a = solveLU(L,U,F_a)\n",
    "    u_al = np.zeros(2*len(nodes))\n",
    "    u_al[2:13] = u_a\n",
    "    y_al = u_al[1::2]\n",
    "    if max(abs(y_al)) <= 0.2:\n",
    "        A_min_al = A_ref\n",
    "        print('The minimum surface area for aluminum to deflect less than 0.2 mm is',A_min_al,'mm.')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The minimum surface area for steel to deflect less than 0.2 mm is 2.7240963855421687 mm.\n"
     ]
    }
   ],
   "source": [
    "#3b\n",
    "for i in range(len(A)):\n",
    "    A_ref = A[i]\n",
    "    F_s = F/(E_s*A_ref)\n",
    "    u_s = solveLU(L,U,F_s)\n",
    "    u_st = np.zeros(2*len(nodes))\n",
    "    u_st[2:13] = u_s\n",
    "    y_st = u_st[1::2]\n",
    "    if max(abs(y_st)) <= 0.2:\n",
    "        A_min_st = A_ref\n",
    "        print('The minimum surface area for steel to deflect less than 0.2 mm is',A_min_st,'mm.') \n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The weight of the aluminum truss is 0.06880722650602408 kg.\n",
      "The weight of the steel truss is 0.07056771686746988 kg.\n"
     ]
    }
   ],
   "source": [
    "#3c\n",
    "rho_st = 7850/1000**3 #kg/mm^3\n",
    "rho_al = 2710/1000**3 #kg/mm^3\n",
    "V_al = len(elems)*l*A_min_al\n",
    "V_st = len(elems)*l*A_min_st\n",
    "W_al = V_al*rho_al #kg\n",
    "W_st = V_st*rho_st #kg\n",
    "print('The weight of the aluminum truss is',W_al,'kg.')\n",
    "print('The weight of the steel truss is',W_st,'kg.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Making the truss out of steel is cheaper since it only costs $ 0.03359023322891566 compared to $ 0.1063071649518072 for aluminum.\n"
     ]
    }
   ],
   "source": [
    "#3d\n",
    "p_al = 1545/1000 #$/kg\n",
    "p_st = 476/1000 #4/kg\n",
    "c_al = p_al*W_al #$\n",
    "c_st = p_st*W_st #$\n",
    "if c_al < c_st:\n",
    "    print('Making the truss out of aluminum is cheaper since it only costs $',c_al,'compared to $',c_st,'for steel.')\n",
    "else:\n",
    "    print('Making the truss out of steel is cheaper since it only costs $',c_st,'compared to $',c_al,'for aluminum.')"
   ]
  },
  {
   "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": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#4a\n",
    "import pandas as pd\n",
    "falum = '../data/al_price.csv'\n",
    "fsteel = '../data/steel_price.csv'\n",
    "al_data = pd.read_csv(falum)\n",
    "st_data = pd.read_csv(fsteel)\n",
    "t_al = al_data['Year'].values\n",
    "t_al_norm = np.zeros(len(t_al))\n",
    "for i in range(len(t_al)):\n",
    "    t_al_norm[i] = (t_al[i] - min(t_al))/(max(t_al) - min(t_al))\n",
    "t_st = st_data['Year'].values\n",
    "t_st_norm = np.zeros(len(t_al))\n",
    "for i in range(len(t_st)):\n",
    "    t_st_norm[i] = (t_st[i] - min(t_st))/(max(t_st) - min(t_st))\n",
    "p_al = al_data['dollars/MT'].values\n",
    "p_st = st_data['dollars/MT'].values\n",
    "\n",
    "import random\n",
    "np.random.seed(103)\n",
    "#Aluminum\n",
    "i_rand=random.sample(range(0,len(al_data)),len(al_data))\n",
    "train_per = 0.7\n",
    "t_al_train=t_al[i_rand[:int(len(al_data)*train_per)]]\n",
    "t_al_test=t_al[i_rand[int(len(al_data)*train_per):]]\n",
    "p_al_train=p_al[i_rand[:int(len(al_data)*train_per)]]\n",
    "p_al_test=p_al[i_rand[int(len(al_data)*train_per):]]\n",
    "\n",
    "#Steel\n",
    "i_rand=random.sample(range(0,len(st_data)),len(st_data))\n",
    "train_per = 0.7\n",
    "t_st_train=t_st[i_rand[:int(len(st_data)*train_per)]]\n",
    "t_st_test=t_st[i_rand[int(len(st_data)*train_per):]]\n",
    "p_st_train=p_st[i_rand[:int(len(st_data)*train_per)]]\n",
    "p_st_test=p_st[i_rand[int(len(st_data)*train_per):]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Singular matrix",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-85f4434e0613>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     16\u001b[0m     \u001b[0mZ_al_test\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ_al_test\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt_al_test\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m     \u001b[0mZ_al_ext\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ_al_ext\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt_ext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m     \u001b[0ma_al\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ_al_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0mZ_al_train\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mZ_al_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0mp_al_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m     \u001b[0mSSE_train\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp_al_train\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mZ_al_train\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0ma_al\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp_al_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m     \u001b[0mSSE_test\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp_al_test\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mZ_al_test\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0ma_al\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp_al_test\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36msolve\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.7/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36msolve\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m    401\u001b[0m     \u001b[0msignature\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'DD->D'\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m'dd->d'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    402\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 403\u001b[0;31m     \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgufunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    404\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    405\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.7/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m     95\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     96\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 97\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Singular matrix\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     98\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     99\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix"
     ]
    },
    {
     "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": [
    "#4b/4c\n",
    "\n",
    "t_ext = np.linspace(min(t_st),2025)\n",
    "\n",
    "#Aluminum\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 == 1 or i == 2 or i == 3 or i == 6 or i == 9:        \n",
    "        plt.plot(t_ext,Z_al_ext@a_al,'o',label='order {:d}'.format(i))\n",
    "        plt.title('Aluminum Price over time')\n",
    "        plt.xlabel('Time (years)')\n",
    "        plt.ylabel('Price (Dollars/tonne)')\n",
    "        plt.legend(loc = 'center left', bbox_to_anchor = (1, 0.5));\n",
    "\n",
    "    \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",
    "#Steel\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 == 1 or i == 2 or i == 3 or i == 6 or i == 9:\n",
    "        plt.plot(t_ext,Z_st_ext@a_st,'o',label='order {:d}'.format(i))\n",
    "        plt.title('Steel Price over time')\n",
    "        plt.xlabel('Time (years)')\n",
    "        plt.ylabel('Price (Dollars/tonne)')\n",
    "        plt.legend(loc = 'center left', bbox_to_anchor = (1, 0.5));\n",
    "        \n",
    "    \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": [
    "#4d\n",
    "\n",
    "print('I will use the first order polynomial fits to approximate the cost of aluminum and steel in 2025.')\n",
    "\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 == 1:        \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 = 'center left', bbox_to_anchor = (1, 0.5));\n",
    "        \n",
    "        \n",
    "#Steel\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 == 1:\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 = 'center left', bbox_to_anchor = (1, 0.5));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#4e\n",
    "\n",
    "print('Based on the first order polynomial fits, the price of aluminum will be about $5500 and the price of steel will be about $320 per metric ton of each.')\n",
    "P_al = 5500*W_al/1000\n",
    "P_st = 320*W_st/1000\n",
    "if P_al < P_st:\n",
    "    if c_al < c_st:\n",
    "        print('I would stick with my earlier answer, since aluminum is still less expensive and only costs $',P_al,'compared to steel, which costs $',P_st,'.')\n",
    "    else: \n",
    "        print('It would make sense to change my prediction, since aluminum will now only cost $',P_al,'compared to steel, which now costs $',P_st,'.')\n",
    "else:\n",
    "    if c_al < c_st:\n",
    "        print('It would make sense to change my prediction, since steel will now only cost $',P_st,'compared to aluminum, which now costs $',P_al,'.')\n",
    "    else:\n",
    "        print('I would stick with my earlier answer, since steel is still less expensive and only costs $',P_st,'compared to aluminum, which costs $',P_al,'.')"
   ]
  },
  {
   "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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