{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Loading numpy and math library\n",
"import numpy as np\n",
"# math library has radians method\n",
"import math\n",
"\n",
"\n",
"# This method returns matrix A and vector b\n",
"# using Load1 and Load2\n",
"def system_form_problem_12_15(Load1, Load2):\n",
" # Initial Matrix A 10x10 with all 0\n",
" A = [[0 for x in range(10)] for y in range(10)]\n",
" # Initial vector b\n",
" b = [0] * 10\n",
"\n",
" # Horizontal forces at node 0\n",
" A[0][0] = 1.0\n",
" A[0][4] = np.cos(math.radians(45))\n",
" A[0][6] = -np.cos(math.radians(45))\n",
" # Vertical forces at node 0\n",
" A[1][4] = -np.sin(math.radians(45))\n",
" A[1][6] = -np.sin(math.radians(45))\n",
" b[1] = Load1\n",
"\n",
" # Horizontal forces at node 1\n",
" A[2][0] = -1.0\n",
" A[2][3] = -np.cos(math.radians(60))\n",
" A[2][1] = np.cos(math.radians(30))\n",
" # Vertical forces at node 1\n",
" A[3][1] = -np.sin(math.radians(30))\n",
" A[3][3] = -np.sin(math.radians(60))\n",
" b[3] = Load2\n",
"\n",
" # Horizontal forces at node 2\n",
" A[4][2] = -1.0\n",
" A[4][1] = -np.cos(math.radians(30))\n",
" # Vertical forces at node 2\n",
" A[5][7] = 1.0\n",
" A[5][1] = np.sin(math.radians(30))\n",
"\n",
" # Horizontal forces at node 3\n",
" A[6][5] = -1.0\n",
" A[6][2] = 1\n",
" A[6][3] = np.cos(math.radians(60))\n",
" A[6][4] = -np.cos(math.radians(45))\n",
"\n",
" # Vertical forces at node 3\n",
" A[7][3] = np.sin(math.radians(60))\n",
" A[7][4] = np.sin(math.radians(45))\n",
"\n",
" # Horizontal forces at node 3\n",
" A[8][8] = 1.0\n",
" A[8][5] = 1.0\n",
" A[8][6] = np.cos(math.radians(45))\n",
"\n",
" # Vertical forces at node 4\n",
" A[9][9] = 1.0\n",
" A[9][6] = np.sin(math.radians(45))\n",
"\n",
" A = np.array(A)\n",
" b = np.array(b)\n",
" return A, b\n",
"\n",
"\n",
"def main():\n",
" A, b = system_form_problem_12_15(Load1=LOAD1, Load2=LOAD2)\n",
" np.set_printoptions(precision=3, suppress=True)\n",
" print(A)\n",
" print(b)\n",
" # Solve for f\n",
" f = np.linalg.solve(A, np.transpose(b))\n",
" print(f)\n",
"\n",
"\n",
"LOAD1 = 400.0\n",
"LOAD2 = 200.0\n",
"main()"
]
},

Simple Linear Regression (35%) In this programming assignment, you...