numpy_basics.ipynb

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([1, 1])"
      ]
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     "metadata": {},
     "execution_count": 48
    }
   ],
   "source": [
    "#Vector Addition Using Numpy\n",
    "a = np.array([1,0])\n",
    "b = np.array([0,1])\n",
    "c = a + b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ 1, -1])"
      ]
     },
     "metadata": {},
     "execution_count": 49
    }
   ],
   "source": [
    "#Vector Subtraction Using Numpy\n",
    "a = np.array([1,0])\n",
    "b = np.array([0,1])\n",
    "c = a - b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([2, 0])"
      ]
     },
     "metadata": {},
     "execution_count": 50
    }
   ],
   "source": [
    "#Scalar Multiplication\n",
    "a = np.array([1,0])\n",
    "b = np.array([0,1])\n",
    "c = 2*a\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "metadata": {},
     "execution_count": 51
    }
   ],
   "source": [
    "#Dot Product Using Numpy\n",
    "a = np.array([1,2])\n",
    "b = np.array([3,4])\n",
    "c = np.dot(a,b)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([105, 100, 101, 102, 104, 101, 105])"
      ]
     },
     "metadata": {},
     "execution_count": 52
    }
   ],
   "source": [
    "#Adding a Constant to Numpy Array\n",
    "a = np.array([6,1,2,3,5,2,6])\n",
    "b = a + 99\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ 8, 12,  8,  5, 10, 12, 30])"
      ]
     },
     "metadata": {},
     "execution_count": 53
    }
   ],
   "source": [
    "#Cross Product OR Simple Multiplication\n",
    "a = np.array([1,3,4,5,2,4,5])\n",
    "b = np.array([8,4,2,1,5,3,6])\n",
    "c = a*b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.75"
      ]
     },
     "metadata": {},
     "execution_count": 54
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   ],
   "source": [
    "#UNIVERSAL FUNCTIONS\n",
    "#Mean of All Elements\n",
    "a = np.array([8,-1,1,-1])\n",
    "b = a.mean()\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": [
       "8"
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     "execution_count": 55
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   ],
   "source": [
    "#Maximum Value in the Array\n",
    "a = np.array([8,-1,1,-1])\n",
    "b = a.max()\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#Array Mapping\n",
    "x = np.array([0, np.pi])\n",
    "y = np.sin(x)\n",
    "%matplotlib inline\n",
    "print(x)\n",
    "print(y)\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])"
      ]
     },
     "metadata": {},
     "execution_count": 57
    }
   ],
   "source": [
    "#Use of Linespace Function #array = np.linspace(start, end, num=intervals)\n",
    "a = np.linspace(-2,2,num=9)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x5db448d460>]"
      ]
     },
     "metadata": {},
     "execution_count": 58
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "#Plotting Mathematical Functions\n",
    "x = np.linspace(0, 2*np.pi, 100)\n",
    "y = np.sin(x)\n",
    "%matplotlib inline\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TWO DIMENSIONAL (2D) NUMPY\n",
    "\n",
    "# 2D NUMPY is very similar to 1D. All the rules of Matrices and Linear Algebra apply, so in order to excel in 2D NUMPY, it is important to go through those concepts and ideas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[1 2 3]\n [1 4 3]\n [4 3 1]]\n[[7 2 3]\n [3 4 4]\n [9 2 1]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2,3],[1,4,3],[4,3,1]])\n",
    "b = np.array([[7,2,3],[3,4,4],[9,2,1]])\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "metadata": {},
     "execution_count": 61
    }
   ],
   "source": [
    "a.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "metadata": {},
     "execution_count": 62
    }
   ],
   "source": [
    "b.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "metadata": {},
     "execution_count": 63
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "metadata": {},
     "execution_count": 64
    }
   ],
   "source": [
    "b.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 8,  4,  6],\n",
       "       [ 4,  8,  7],\n",
       "       [13,  5,  2]])"
      ]
     },
     "metadata": {},
     "execution_count": 65
    }
   ],
   "source": [
    "# Matrices Addition\n",
    "\n",
    "c = a + b\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[-6,  0,  0],\n",
       "       [-2,  0, -1],\n",
       "       [-5,  1,  0]])"
      ]
     },
     "metadata": {},
     "execution_count": 66
    }
   ],
   "source": [
    "# Matrices Subtraction\n",
    "\n",
    "d = a - b\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Matrices Multiplication\n",
    "\n",
    "e = a*b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 7,  4,  9],\n",
       "       [ 3, 16, 12],\n",
       "       [36,  6,  1]])"
      ]
     },
     "metadata": {},
     "execution_count": 68
    }
   ],
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[40, 16, 14],\n",
       "       [46, 24, 22],\n",
       "       [46, 22, 25]])"
      ]
     },
     "metadata": {},
     "execution_count": 69
    }
   ],
   "source": [
    "# OR\n",
    "\n",
    "e = a.dot(b)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The dot product and the multiplication outcome are different, as in arrays 'e' and 'd'. Why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 2, -9, 20],\n",
       "       [ 0,  8, 20],\n",
       "       [12,  0, 30]])"
      ]
     },
     "metadata": {},
     "execution_count": 71
    }
   ],
   "source": [
    "# Checking once again\n",
    "\n",
    "a = np.array([[2,3,4],[3,4,5],[4,5,6]])\n",
    "b = np.array([[1,-3,5],[0,2,4],[3,0,5]])\n",
    "c = a*b\n",
    "c\n",
    "\n",
    "# 'c' is not the regular output we get in Math/Linear Algebra (LA), which means that multiplying 'a' and 'b' does not give the standard matrix-multiplication output!\n",
    "\n",
    "# This is the cross product of these two vectors! Numpy perceives np.array() as a vector by default, so it is natural that we talk in vector terms only. By default, the cross product exists only in the case of vectors - not matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[14,  0, 42],\n",
       "       [18, -1, 56],\n",
       "       [22, -2, 70]])"
      ]
     },
     "metadata": {},
     "execution_count": 72
    }
   ],
   "source": [
    "# This gives the simple matrix-multiplication output just like we do in Math/LA. In vector terms, this is the dot product.\n",
    "\n",
    "d = a.dot(b)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "#CONCLUDING REMARKS\n",
    "\n",
    "# 1. In 1D, NUMPY will give the regular output of '*' in the form of cross product.\n",
    "\n",
    "# 2. In 2D, the output of '*' will be the same i.e. cross product/vector product.\n",
    "\n",
    "# 3. In 1D, the output of 'a.dot(b)' will be the dot product, which is always a scalar quantity.\n",
    "\n",
    "# 4. In 2D however, the output is going to be a simple matrix-multiplication resulting in a vector/matrix output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Some Additional Practice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8],\n",
       "       [ 9, 10, 11, 12]])"
      ]
     },
     "metadata": {},
     "execution_count": 75
    }
   ],
   "source": [
    "# Consider the following list a, convert it to Numpy Array.\n",
    "\n",
    "a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]\n",
    "A = np.array(a)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "metadata": {},
     "execution_count": 76
    }
   ],
   "source": [
    "# Calculate the numpy array size.\n",
    "\n",
    "A.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "metadata": {},
     "execution_count": 77
    }
   ],
   "source": [
    "# Access the element on the first row and first and second columns.\n",
    "\n",
    "#A[0,0:2] #this can also be used\n",
    "\n",
    "A[0][0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 0,  1],\n",
       "       [ 1,  0],\n",
       "       [ 1,  1],\n",
       "       [-1,  0]])"
      ]
     },
     "metadata": {},
     "execution_count": 78
    }
   ],
   "source": [
    "B = np.array([[0, 1], [1, 0], [1, 1], [-1, 0]])\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 1,  4],\n",
       "       [ 5, 12],\n",
       "       [ 9, 20]])"
      ]
     },
     "metadata": {},
     "execution_count": 79
    }
   ],
   "source": [
    "#Order of Matrix A is 3x4, while that of B is 4x2, so that the resulting array will have an order of 3x2.\n",
    "C = A.dot(B)\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 1,  4],\n",
       "       [ 5, 12],\n",
       "       [ 9, 20]])"
      ]
     },
     "metadata": {},
     "execution_count": 80
    }
   ],
   "source": [
    "# The above may be done as follows:\n",
    "\n",
    "C = np.dot(A,B)\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8],\n",
       "       [ 9, 10, 11, 12]])"
      ]
     },
     "metadata": {},
     "execution_count": 81
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[ 1,  5,  9],\n",
       "       [ 2,  6, 10],\n",
       "       [ 3,  7, 11],\n",
       "       [ 4,  8, 12]])"
      ]
     },
     "metadata": {},
     "execution_count": 82
    }
   ],
   "source": [
    "#Transposing a Matrix\n",
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(3, 4)"
      ]
     },
     "metadata": {},
     "execution_count": 83
    }
   ],
   "source": [
    "A.shape #Returns the order of the array ... Rows'by'Columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [1, 1]])"
      ]
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "X=np.array([[1,0],[0,1]])\n",
    "Y=np.array([[0,1],[1,0]])\n",
    "Z=X+Y\n",
    "Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[1, 0, 1],\n",
       "       [2, 2, 2]])"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "X=np.array([[1,0,1],[2,2,2]]) \n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([0, 1])"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "out=X[0,1:3]   #This means 1st row and 2nd + 3rd column.\n",
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([[2, 2],\n",
       "       [2, 2]])"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "X=np.array([[1,0],[0,1]])\n",
    "Y=np.array([[2,2],[2,2]])\n",
    "Z=np.dot(X,Y)\n",
    "Z"
   ]
  }
 ]
}