ML_course/assignment 2/iml_assignment2b_solved.ipynb

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  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "import numpy as np"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Create a 10x50 matrix with random numbers using numpy"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 50)\n"
     ]
    }
   ],
   "source": [
    "x = np.random.rand(10,50)\n",
    "# Print the shape of the matrix\n",
    "print(x.shape)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.23987495 0.91661312 0.86479877 0.97246676 0.2996044  0.19370428\n",
      " 0.38302033 0.45876654 0.23953333 0.88275397 0.39823726 0.68814433\n",
      " 0.69320487 0.87894669 0.12043348 0.56381261 0.41057224 0.44619567\n",
      " 0.83936425 0.11512131 0.10305665 0.30666838 0.10695437 0.77828681\n",
      " 0.26825193 0.88529244 0.13623807 0.85569497 0.56312584 0.83247308\n",
      " 0.4950099  0.66125172 0.45603826 0.41389193 0.04471278 0.74099649\n",
      " 0.82862858 0.73879875 0.10928491 0.47473116 0.1124304  0.02034965\n",
      " 0.3651702  0.24298615 0.02315607 0.63034624 0.86772443 0.45138212\n",
      " 0.68984731 0.45618784]\n"
     ]
    }
   ],
   "source": [
    "# Ask from the user for a row number and print the row given\n",
    "row = int(input(\"Enter a row number: \"))\n",
    "print(x[row])\n",
    "# Do the same for a column\n",
    "col = int(input(\"Enter a column number: \"))\n",
    "print(x[:,col])"
   ],
   "metadata": {
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   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Create the following arrays and calculate their dot product\n",
    "| 5 | 1 | 3 |\n",
    "| 1 | 2 | 1 |\n",
    "| 1 | 2 | 1 |\n",
    "\n",
    "| 1 | 2 | 3 |"
   ],
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    "collapsed": false
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  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5 1 3]\n",
      " [1 2 1]\n",
      " [1 2 1]]\n",
      "[1 2 3]\n",
      "[16  8  8]\n"
     ]
    }
   ],
   "source": [
    "tmp_array = np.array([[5,1,3],[1,2,1],[1,2,1]])\n",
    "tmp_array2 = np.array([1,2,3])\n",
    "print(tmp_array)\n",
    "print(tmp_array2)\n",
    "# print dot product of tmp_array and tmp_array2\n",
    "print(np.dot(tmp_array,tmp_array2))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Given the following matrices calculate their (matrix) multiplication\n",
    "A = | 1 | 0 |\n",
    "| 0 | 1 |\n",
    "\n",
    "B = | 4 | 1 |\n",
    "| 2 | 2 |\n",
    "\n",
    "c = | 1 | 2 |"
   ],
   "metadata": {
    "collapsed": false
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  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 1]\n",
      " [2 2]]\n",
      "[1 2]\n"
     ]
    }
   ],
   "source": [
    "# A*B\n",
    "A = np.array([[1,0],[0,1]])\n",
    "B = np.array([[4,1],[2,2]])\n",
    "print(np.dot(A,B))\n",
    "# A*c\n",
    "c = np.array([1,2])\n",
    "print(np.dot(A,c.T))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Find the third power of this matrix\n",
    "\n",
    "| 0 | 1 |\n",
    "| -1 | 0 |"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "tmp_array = np.array([[0,1],[-1,0]])\n",
    "print(np.linalg.matrix_power(tmp_array,3))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Find the determinant of this matrix\n",
    "\n",
    "| 1 | 2 |\n",
    "| 3 | 4 |"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.0000000000000004\n"
     ]
    }
   ],
   "source": [
    "tmp_array = np.array([[1,2],[3,4]])\n",
    "print(np.linalg.det(tmp_array))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Use the functions ‘eye’ and ‘ones’ from numpy to create 4x4 matrices. Find their ranks."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]]\n",
      "4\n",
      "[[1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]]\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "tmp_array = np.eye(4)\n",
    "print(tmp_array)\n",
    "print(np.linalg.matrix_rank(tmp_array))\n",
    "tmp_array = np.ones((4,4))\n",
    "print(tmp_array)\n",
    "print(np.linalg.matrix_rank(tmp_array))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Find the inverse of this matrix\n",
    "\n",
    "| 2 | 2 | 1 |\n",
    "| 1 | 3 | 1 |\n",
    "| 1 | 2 | 2 |"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.8 -0.4 -0.2]\n",
      " [-0.2  0.6 -0.2]\n",
      " [-0.2 -0.4  0.8]]\n"
     ]
    }
   ],
   "source": [
    "tmp_array = np.array([[2,2,1],[1,3,1],[1,2,2]])\n",
    "print(np.linalg.inv(tmp_array))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Find the pseudo inverse of this matrix\n",
    "\n",
    "| 2 | 8 |\n",
    "| 1 | 4 |"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.02352941 0.01176471]\n",
      " [0.09411765 0.04705882]]\n"
     ]
    }
   ],
   "source": [
    "tmp_array = np.array([[2,8],[1,4]])\n",
    "print(np.linalg.pinv(tmp_array))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Find the eigenvalues and eigenvectors of this matrix\n",
    "\n",
    "| 1 | -1 |\n",
    "| 1 | 1 |"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.+1.j 1.-1.j]\n",
      "[[0.70710678+0.j         0.70710678-0.j        ]\n",
      " [0.        -0.70710678j 0.        +0.70710678j]]\n"
     ]
    }
   ],
   "source": [
    "tmp_array = np.array([[1,-1],[1,1]])\n",
    "eigenvalues, eigenvectors = np.linalg.eig(tmp_array)\n",
    "print(eigenvalues)\n",
    "print(eigenvectors)\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [],
   "metadata": {
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