1-2. basic numpy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading package(s)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "print (\"Loading package(s)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, world\n",
      "Integer: 3, 03, 003, 0003, 00003\n",
      "Float: 123, 123.5, 123.46, 123.46, 123.46\n",
      "String: [Hello, world], [Hello, world], [        Hello, world]\n"
     ]
    }
   ],
   "source": [
    "print (\"Hello, world\")\n",
    "\n",
    "# THERE ARE THREE POPULAR TYPES\n",
    "# 1. INTEGER\n",
    "x = 3;\n",
    "print (\"Integer: %01d, %02d, %03d, %04d, %05d\" \n",
    "       % (x, x, x, x, x))\n",
    "# 2. FLOAT\n",
    "x = 123.456;\n",
    "print (\"Float: %.0f, %.1f, %.2f, %1.2f, %2.2f\" \n",
    "       % (x, x, x, x, x))\n",
    "# 3. STRING\n",
    "x = \"Hello, world\"\n",
    "print (\"String: [%s], [%3s], [%20s]\" \n",
    "       % (x, x, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have seen ANN\n",
      "We have seen MLP\n"
     ]
    }
   ],
   "source": [
    "dlmethods = [\"ANN\", \"MLP\", \"CNN\", \"RNN\", \"DAE\"]\n",
    "\n",
    "for alg in dlmethods:\n",
    "    if alg in [\"ANN\", \"MLP\"]:\n",
    "        print (\"We have seen %s\" % (alg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ANN is a feed-forward network.\n",
      "MLP is a feed-forward network.\n",
      "CNN is a feed-forward network.\n",
      "RNN is a recurrent network.\n",
      "DAE is an unsupervised method.\n"
     ]
    }
   ],
   "source": [
    "dlmethods = [\"ANN\", \"MLP\", \"CNN\", \"RNN\", \"DAE\"];\n",
    "for alg in dlmethods:\n",
    "    if alg in [\"ANN\", \"MLP\", \"CNN\"]:\n",
    "        print (\"%s is a feed-forward network.\" % (alg))\n",
    "    elif alg in [\"RNN\"]:\n",
    "        print (\"%s is a recurrent network.\" % (alg))\n",
    "    else:\n",
    "        print (\"%s is an unsupervised method.\" % (alg))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0 + 20.0 = 30.0\n"
     ]
    }
   ],
   "source": [
    "# Function definition looks like this\n",
    "def sum(a, b):\n",
    "    return a+b\n",
    "X = 10.\n",
    "Y = 20.\n",
    "# Usage \n",
    "print (\"%.1f + %.1f = %.1f\" % (X, Y, sum(X, Y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deep learning is very HARD.\n",
      "Deep learning is very very very HARD.\n",
      "Deep learning is very very very very very very very very very very HARD.\n",
      "\n",
      "==================================================\n",
      "               It is used in this way\n",
      "==================================================\n",
      "\n",
      "Index: [00/12] Char: H\n",
      "Index: [01/12] Char: e\n",
      "Index: [02/12] Char: l\n",
      "Index: [03/12] Char: l\n",
      "Index: [04/12] Char: o\n",
      "Index: [05/12] Char: ,\n",
      "Index: [06/12] Char:  \n",
      "Index: [07/12] Char: w\n",
      "Index: [08/12] Char: o\n",
      "Index: [09/12] Char: r\n",
      "Index: [10/12] Char: l\n",
      "Index: [11/12] Char: d\n"
     ]
    }
   ],
   "source": [
    "head = \"Deep learning\" \n",
    "body = \"very \"\n",
    "tail = \"HARD.\"\n",
    "print (head + \" is \" + body + tail)\n",
    "\n",
    "# Repeat words\n",
    "print (head + \" is \" + body*3 + tail)\n",
    "print (head + \" is \" + body*10 + tail)\n",
    "\n",
    "# It is used in this way\n",
    "print (\"\\n\" + \"=\"*50)\n",
    "print (\" \"*15 + \"It is used in this way\")\n",
    "print (\"=\"*50 + \"\\n\")\n",
    "\n",
    "# Indexing characters in the string\n",
    "x = \"Hello, world\" \n",
    "for i in range(len(x)):\n",
    "    print (\"Index: [%02d/%02d] Char: %s\" \n",
    "           % (i, len(x), x[i])) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "(-2)th char is l\n",
      "String from 0 to 8 is [Hello, w]\n",
      "String from 4 to END is [o, world]\n",
      "[20160607Cloudy] -> [2016] + [0607] + [Cloudy] \n"
     ]
    }
   ],
   "source": [
    "# More indexing \n",
    "print (\"\")\n",
    "idx = -2\n",
    "print (\"(%d)th char is %s\" % (idx, x[idx]))\n",
    "idxfr = 0\n",
    "idxto = 8\n",
    "print (\"String from %d to %d is [%s]\" \n",
    "       % (idxfr, idxto, x[idxfr:idxto]))\n",
    "idxfr = 4\n",
    "print (\"String from %d to END is [%s]\" \n",
    "       % (idxfr, x[idxfr:]))\n",
    "x = \"20160607Cloudy\"\n",
    "year = x[:4]\n",
    "day = x[4:8]\n",
    "weather = x[8:]\n",
    "print (\"[%s] -> [%s] + [%s] + [%s] \" \n",
    "       % (x, year, day, weather))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[]\n",
      "['a']\n",
      "['a', 123]\n",
      "['a', 123, ['a', 'b']]\n",
      "Length of x is 3 \n",
      "[00/03] a\n",
      "[01/03] 123\n",
      "[02/03] ['a', 'b']\n"
     ]
    }
   ],
   "source": [
    "a = []\n",
    "b = [1, 2, 3]\n",
    "c = [\"Hello\", \",\", \"world\"]\n",
    "d = [1, 2, 3, \"x\", \"y\", \"z\"]\n",
    "x = []\n",
    "print (x)\n",
    "x.append('a')\n",
    "print (x)\n",
    "x.append(123)\n",
    "print (x)\n",
    "x.append([\"a\", \"b\"])\n",
    "print (x)\n",
    "print (\"Length of x is %d \" \n",
    "       % (len(x)))\n",
    "for i in range(len(x)):\n",
    "    print (\"[%02d/%02d] %s\" \n",
    "           % (i, len(x), x[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "Hello\n"
     ]
    }
   ],
   "source": [
    "z = []\n",
    "z.append(1)\n",
    "z.append(2)\n",
    "z.append(3)\n",
    "z.append('Hello')\n",
    "for i in range(len(z)):\n",
    "    print (z[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'job': 'Software Engineer', 'name': 'Antonio', 'age': 43}\n"
     ]
    }
   ],
   "source": [
    "dic = dict()\n",
    "dic[\"name\"] = \"Antonio\"\n",
    "dic[\"age\"] = 43\n",
    "dic[\"job\"] = \"Software Engineer\"\n",
    "\n",
    "print (dic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, Fred\n",
      "HELLO, FRED!\n"
     ]
    }
   ],
   "source": [
    "class Greeter:\n",
    "\n",
    "    # Constructor\n",
    "    def __init__(self, name):\n",
    "        self.name = name  # Create an instance variable\n",
    "\n",
    "    # Instance method\n",
    "    def greet(self, loud=False):\n",
    "        if loud:\n",
    "            print ('HELLO, %s!' \n",
    "                   % self.name.upper())\n",
    "        else:\n",
    "            print ('Hello, %s' \n",
    "                   % self.name)\n",
    "\n",
    "g = Greeter('Fred')  # Construct an instance of the Greeter class\n",
    "g.greet()            # Call an instance method; prints \"Hello, Fred\"\n",
    "g.greet(loud=True)   # Call an instance method; prints \"HELLO, FRED!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def print_np(x):\n",
    "    print (\"Type is %s\" % (type(x)))\n",
    "    print (\"Shape is %s\" % (x.shape,))\n",
    "    print (\"Values are: \\n%s\" % (x))\n",
    "    print"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[1 2 3]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[5 2 3]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2, 3]) # rank 1 array\n",
    "print_np(x)\n",
    "\n",
    "x[0] = 5\n",
    "print_np(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 3)\n",
      "Values are: \n",
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "y = np.array([[1,2,3], [4,5,6]]) \n",
    "print_np(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3, 2)\n",
      "Values are: \n",
      "[[ 0.  0.]\n",
      " [ 0.  0.]\n",
      " [ 0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((3, 2))  \n",
    "print_np(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (1, 2)\n",
      "Values are: \n",
      "[[ 1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "b = np.ones((1, 2))   \n",
    "print_np(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 2)\n",
      "Values are: \n",
      "[[ 1.  0.]\n",
      " [ 0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "c = np.eye(2, 2)   \n",
    "print_np(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 2)\n",
      "Values are: \n",
      "[[ 0.1946807   0.15497216]\n",
      " [ 0.58723898  0.16583897]]\n"
     ]
    }
   ],
   "source": [
    "d = np.random.random((2, 2))    \n",
    "print_np(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (1, 10)\n",
      "Values are: \n",
      "[[-0.88089409  1.77647708 -0.59681193 -2.09430761 -0.00245805 -1.28253932\n",
      "  -1.25116176 -0.37738168  0.27690442  0.82254266]]\n"
     ]
    }
   ],
   "source": [
    "e = np.random.randn(1, 10)    \n",
    "print_np(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3, 4)\n",
      "Values are: \n",
      "[[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 2)\n",
      "Values are: \n",
      "[[2 3]\n",
      " [6 7]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Create the following rank 2 array with shape (3, 4)\n",
    "# [[ 1  2  3  4]\n",
    "#  [ 5  6  7  8]\n",
    "#  [ 9 10 11 12]]\n",
    "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "print_np(a)\n",
    "\n",
    "print\n",
    "# Use slicing to pull out the subarray consisting \n",
    "# of the first 2 rows\n",
    "# and columns 1 and 2; b is the following array \n",
    "# of shape (2, 2):\n",
    "# [[2 3]\n",
    "#  [6 7]]\n",
    "b = a[:2, 1:3]\n",
    "print_np(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3, 4)\n",
      "Values are: \n",
      "[[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4,)\n",
      "Values are: \n",
      "[5 6 7 8]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (1, 4)\n",
      "Values are: \n",
      "[[5 6 7 8]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (1, 4)\n",
      "Values are: \n",
      "[[5 6 7 8]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "print_np(a)\n",
    "\n",
    "row_r1 = a[1, :]    # Rank 1 view of the second row of a  \n",
    "row_r2 = a[1:2, :]  # Rank 2 view of the second row of a\n",
    "row_r3 = a[[1], :]  # Rank 2 view of the second row of a\n",
    "\n",
    "print_np(row_r1)\n",
    "print_np(row_r2)\n",
    "print_np(row_r3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3, 2)\n",
      "Values are: \n",
      "[[1 2]\n",
      " [3 4]\n",
      " [5 6]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[1 4 5]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[1 4 5]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2], [3, 4], [5, 6]])\n",
    "print_np(a)\n",
    "\n",
    "# An example of integer array indexing.\n",
    "# The returned array will have shape (3,) and \n",
    "b = a[[0, 1, 2], [0, 1, 0]]\n",
    "print_np(b)\n",
    "\n",
    "# The above example of integer array indexing \n",
    "# is equivalent to this:\n",
    "c = np.array([a[0, 0], a[1, 1], a[2, 0]])\n",
    "print_np(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2,)\n",
      "Values are: \n",
      "[1 2]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2,)\n",
      "Values are: \n",
      "[ 1.  2.]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2,)\n",
      "Values are: \n",
      "[1 2]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2])  # Let numpy choose the datatype\n",
    "y = np.array([1.0, 2.0])  # Let numpy choose the datatype\n",
    "z = np.array([1, 2], dtype=np.int64)  # particular datatype\n",
    "\n",
    "print_np(x)\n",
    "print_np(y)\n",
    "print_np(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  6.   8.]\n",
      " [ 10.  12.]]\n",
      "[[  6.   8.]\n",
      " [ 10.  12.]]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]], dtype=np.float64)\n",
    "y = np.array([[5,6],[7,8]], dtype=np.float64)\n",
    "\n",
    "# Elementwise sum; both produce the array\n",
    "print (x + y)\n",
    "print (np.add(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4. -4.]\n",
      " [-4. -4.]]\n",
      "[[-4. -4.]\n",
      " [-4. -4.]]\n"
     ]
    }
   ],
   "source": [
    "#  Elementwise difference; both produce the array\n",
    "print (x - y)\n",
    "print (np.subtract(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  5.  12.]\n",
      " [ 21.  32.]]\n",
      "[[  5.  12.]\n",
      " [ 21.  32.]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise product; both produce the array\n",
    "print (x * y)\n",
    "print (np.multiply(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.2         0.33333333]\n",
      " [ 0.42857143  0.5       ]]\n",
      "[[ 0.2         0.33333333]\n",
      " [ 0.42857143  0.5       ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise division; both produce the array\n",
    "# [[ 0.2         0.33333333]\n",
    "#  [ 0.42857143  0.5       ]]\n",
    "print (x / y)\n",
    "print (np.divide(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          1.41421356]\n",
      " [ 1.73205081  2.        ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise square root; produces the array\n",
    "# [[ 1.          1.41421356]\n",
    "#  [ 1.73205081  2.        ]]\n",
    "print (np.sqrt(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 2)\n",
      "Values are: \n",
      "[[1 2]\n",
      " [3 4]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 2)\n",
      "Values are: \n",
      "[[5 6]\n",
      " [7 8]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2,)\n",
      "Values are: \n",
      "[ 9 10]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2,)\n",
      "Values are: \n",
      "[11 12]\n",
      "219\n",
      "219\n",
      "[29 67]\n",
      "[29 67]\n",
      "[[19 22]\n",
      " [43 50]]\n",
      "[[19 22]\n",
      " [43 50]]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "y = np.array([[5,6],[7,8]])\n",
    "v = np.array([9,10])\n",
    "w = np.array([11, 12])\n",
    "\n",
    "print_np(x)\n",
    "print_np(y)\n",
    "print_np(v)\n",
    "print_np(w)\n",
    "\n",
    "# Inner product of vectors; both produce 219\n",
    "print (v.dot(w))\n",
    "print (np.dot(v, w)) # <= v * w'\n",
    "# Matrix / vector product; both produce the rank 1 array [29 67]\n",
    "print (x.dot(v))\n",
    "print (np.dot(x, v)) # <= x * v'\n",
    "# Matrix / matrix product; both produce the rank 2 array\n",
    "# [[19 22]\n",
    "#  [43 50]]\n",
    "print (x.dot(y))\n",
    "print (np.dot(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 2)\n",
      "Values are: \n",
      "[[1 2]\n",
      " [3 4]]\n",
      "[[1 2]\n",
      " [3 4]]\n",
      "[[1 3]\n",
      " [2 4]]\n",
      "10\n",
      "[4 6]\n",
      "[3 7]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "x = np.array([[1,2],[3,4]])\n",
    "print_np(x)\n",
    "print\n",
    "print (x)\n",
    "print (x.T)\n",
    "print (np.sum(x))  # Compute sum of all elements\n",
    "print (np.sum(x, axis=0))  # Compute sum of each column\n",
    "print (np.sum(x, axis=1))  # Compute sum of each row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n",
      "[[1 3]\n",
      " [2 4]]\n"
     ]
    }
   ],
   "source": [
    "print (x)\n",
    "print (x.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "v = np.array([1,2,3])\n",
    "print (v)\n",
    "print (v.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]]\n",
      "[[1]\n",
      " [2]\n",
      " [3]]\n"
     ]
    }
   ],
   "source": [
    "v = np.array([[1,2,3]])\n",
    "print (v)\n",
    "print (v.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4, 3)\n",
      "Values are: \n",
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[1 0 1]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4, 3)\n",
      "Values are: \n",
      "[[0 0 0]\n",
      " [0 0 0]\n",
      " [0 0 0]\n",
      " [0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "# We will add the vector v to each row of the matrix x,\n",
    "# storing the result in the matrix y\n",
    "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "v = np.array([1, 0, 1])\n",
    "y = np.empty_like(x)    # Create an empty matrix \n",
    "                        # with the same shape as x\n",
    "\n",
    "print_np(x)\n",
    "print_np(v)\n",
    "print_np(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4, 3)\n",
      "Values are: \n",
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "# Add the vector v to each row of the matrix x \n",
    "# with an explicit loop\n",
    "for i in range(4):\n",
    "    y[i, :] = x[i, :] + v\n",
    "print_np(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4, 3)\n",
      "Values are: \n",
      "[[1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]]\n"
     ]
    }
   ],
   "source": [
    "vv = np.tile(v, (4, 1))  # Stack 4 copies of v on top of each other\n",
    "print_np(vv)             # Prints \"[[1 0 1]\n",
    "                         #          [1 0 1]\n",
    "                         #          [1 0 1]\n",
    "                         #          [1 0 1]]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4, 3)\n",
      "Values are: \n",
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[1 0 1]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (4, 3)\n",
      "Values are: \n",
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# We will add the vector v to each row of the matrix x,\n",
    "# storing the result in the matrix y\n",
    "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "v = np.array([1, 0, 1])\n",
    "y = x + v  # Add v to each row of x using BROADCASTING\n",
    "print_np(x)\n",
    "print_np(v)\n",
    "print_np(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 3)\n",
      "Values are: \n",
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (3,)\n",
      "Values are: \n",
      "[1 0 1]\n",
      "[[2 2 4]\n",
      " [5 5 7]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each row of a matrix\n",
    "x = np.array([[1,2,3], [4,5,6]])\n",
    "\n",
    "print_np(x)\n",
    "print_np(v)\n",
    "print (x + v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2, 3)\n",
      "Values are: \n",
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "Type is <class 'numpy.ndarray'>\n",
      "Shape is (2,)\n",
      "Values are: \n",
      "[11 12]\n",
      "[[12 13 14]\n",
      " [16 17 18]]\n",
      "[[12 13 14]\n",
      " [16 17 18]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each column of a matrix\n",
    "print_np(x)\n",
    "print_np(w)\n",
    "print ((x.T + w).T)\n",
    "\n",
    "# Another solution is to reshape w \n",
    "# to be a row vector of shape (2, 1);\n",
    "print\n",
    "print (x + np.reshape(w, (2, 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f01d9140668>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Qw4vxc+CBcPTR0X0CS/b54Qd4/XXIyQmdRNKtalVbNxPV16NYFBT5+dbI6tRT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\nwv4fpbvLm1mJOvcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f01db43ec88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the x and y coordinates for points on a sine curve\n",
    "x = np.arange(0, 3 * np.pi, 0.1)\n",
    "y = np.sin(x)\n",
    "\n",
    "# Plot the points using matplotlib\n",
    "lt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xJo/zzeZvuHT90j/bP/kEGjWC++83MDiT8PJSF8cZM+DECaOj0VzNZ+s+o5xv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\nlFJKKVfSIkUppZRSrqRFilJKKaVc6f8BeWmOKIcIw5wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f01fc159be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_sin = np.sin(x)\n",
    "y_cos = np.cos(x)\n",
    "# Plot the points using matplotlib\n",
    "plt.plot(x, y_sin)\n",
    "plt.plot(x, y_cos)\n",
    "plt.xlabel('x axis label')\n",
    "plt.ylabel('y axis label')\n",
    "plt.title('Sine and Cosine')\n",
    "plt.legend(['Sine', 'Cosine'])\n",
    "\n",
    "# Show the figure.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}