00. np_array.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3,)\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "# column vector\n",
    "c = np.array([1,2,3])\n",
    "print(c.shape)\n",
    "\n",
    "# obtaining a particular entry\n",
    "print (c[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 3)\n"
     ]
    }
   ],
   "source": [
    "# row vector\n",
    "r = np.array([ [1,2,3] ])\n",
    "print (r.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "# obtaining a particular entry\n",
    "print (r[0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.]\n",
      " [ 0.  0.]]\n",
      "[[ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[[7 7]\n",
      " [7 7]]\n",
      "[[ 0.93589863  0.19331487]\n",
      " [ 0.14309097  0.43003853]]\n"
     ]
    }
   ],
   "source": [
    "# creating a matrix with all zeros\n",
    "a = np.zeros((2,2))\n",
    "print (a)\n",
    "# creating a matrix with all ones\n",
    "b = np.ones((2,2))\n",
    "print (b)\n",
    "             \n",
    "# creating a matrix filled with the same constant\n",
    "c = np.full((2,2), 7)\n",
    "print (c)\n",
    "             \n",
    "# creating a matrix with random values\n",
    "d = np.random.random((2,2))\n",
    "print (d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]\n",
      " [5 6]]\n"
     ]
    }
   ],
   "source": [
    "# creating a matrix\n",
    "A=np.array([[1,2],[3,4],[5,6]])\n",
    "print (A)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11, 12, 13, 14],\n",
       "       [15, 16, 17, 18]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# creating another matrix\n",
    "B=np.array([[11,12,13,14],[15,16,17,18]])\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3, 5],\n",
       "       [2, 4, 6]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transpose a matrix\n",
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 41,  44,  47,  50],\n",
       "       [ 93, 100, 107, 114],\n",
       "       [145, 156, 167, 178]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# matrix-matrix multiplication\n",
    "np.dot(A,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (2,4) and (3,2) not aligned: 4 (dim 1) != 3 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                    Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-30-1c2410a4aca9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# matrix-matrix multiplication\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;31m# size should match!\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mB\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: shapes (2,4) and (3,2) not aligned: 4 (dim 1) != 3 (dim 0)"
     ]
    }
   ],
   "source": [
    "# matrix-matrix multiplication \n",
    "# size should match!\n",
    "np.dot(B,A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# coefficient matrix A and a vector b\n",
    "A=np.array([[60, 5.5, 1],[65, 5.0, 0],[55, 6.0, 1]])\n",
    "b=np.array([66, 70, 78])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# identity matrix \n",
    "eye3 = np.eye(3)\n",
    "eye3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.08695652,  0.00869565, -0.08695652],\n",
       "       [-1.13043478,  0.08695652,  1.13043478],\n",
       "       [ 2.        , -1.        , -1.        ]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# computing an inverse\n",
    "from numpy.linalg import inv\n",
    "A_inv = inv(A)\n",
    "A_inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  5.21739130e+00,   4.78260870e-02,  -8.69565217e-02],\n",
       "       [ -7.34782609e+01,   4.34782609e-01,   0.00000000e+00],\n",
       "       [  1.10000000e+02,  -6.00000000e+00,  -1.00000000e+00]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# wrong matrix multiplication\n",
    "A*A_inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# correct matrix multiplication\n",
    "A.dot(A_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.43478261,  19.65217391, -16.        ])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solution of a linear system\n",
    "x=A_inv.dot(b)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.43478261,  19.65217391, -16.        ])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# a better way to solve the same linear system\n",
    "from numpy.linalg import solve\n",
    "x = solve(A,b)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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