Preliminaries_Numpy_Pandas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Funktions, Conditionals, and Iteration in Python\n",
    "\n",
    "Let us create a Python function, and call it from a loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def HelloWorldXY(x, y):\n",
    "    if (x < 10):\n",
    "        print(\"Hello World, x was < 10\")\n",
    "    elif (x < 20):\n",
    "        print(\"Hello World, x was >= 10 but < 20\")\n",
    "    else:\n",
    "        print(\"Hello World, x was >= 20\")\n",
    "    return x + y\n",
    "\n",
    "print(HelloWorldXY(1,2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us call the function `HelloWorldXY()` from a loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--- Now running with i: 8\n"
     ]
    },
    {
     "ename": "NameError",
     "evalue": "name 'HelloWorldXY' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-7ea2350df544>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m25\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# i=8, 13, 18, 23 (start, stop, step)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"\\n--- Now running with i: {}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mHelloWorldXY\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Result from HelloWorld: {}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'HelloWorldXY' is not defined"
     ]
    }
   ],
   "source": [
    "for i in range(8, 25, 5): # i=8, 13, 18, 23 (start, stop, step)\n",
    "    print(\"\\n--- Now running with i: {}\".format(i))\n",
    "    r = HelloWorldXY(i,i)\n",
    "    print(\"Result from HelloWorld: {}\".format(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want a loop starting at 0 to 2 (exclusive) you could do any of the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterate over the items. `range(2)` is like a list [0,1].\n",
      "0\n",
      "1\n",
      "Iterate over an actual list.\n",
      "0\n",
      "1\n",
      "While works\n",
      "0\n",
      "1\n",
      "Python supports standard key words like continue and break\n",
      "Entered while\n",
      "while broken\n"
     ]
    }
   ],
   "source": [
    "print(\"Iterate over the items. `range(2)` is like a list [0,1].\")\n",
    "for i in range(2):\n",
    "    print(i)\n",
    "\n",
    "print(\"Iterate over an actual list.\")\n",
    "for i in [0,1]:\n",
    "    print(i)\n",
    "\n",
    "print(\"While works\")\n",
    "i = 0\n",
    "while i < 2:\n",
    "    print(i)\n",
    "    i += 1\n",
    "    \n",
    "print(\"Python supports standard key words like continue and break\")\n",
    "while True:\n",
    "    print(\"Entered while\")\n",
    "    break\n",
    "print(\"while broken\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Data in Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape scaler () \n",
      "Shape vector (3,) \n",
      "Shape matrix (3, 3) \n",
      "Shape tensor (3, 3, 2, 1)\n",
      "Type scalar or array <class 'numpy.ndarray'> \n",
      "Type after addition with integer <class 'numpy.int64'>\n",
      "v[1:] =  [ 2 10] \n",
      "m[1:][2:] = \n",
      " [[5 6]\n",
      " [8 9]]\n",
      "[ 1  2 10] [[ 1  2 10]] [[ 1  2 10]]\n",
      "(3,) (1, 3) (1, 3)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Scalar\n",
    "s = np.array(5)\n",
    "# Vector\n",
    "v = np.array([1, 2, 10])\n",
    "# Matrix\n",
    "m = np.array([[1,2,3], \n",
    "              [4,5,6], \n",
    "              [7,8,9]])\n",
    "# Tensor:\n",
    "t = np.array([[[[1],[2]], [[3],[4]], [[5],[6]]],\n",
    "              [[[7],[8]], [[9],[10]], [[11],[12]]],\n",
    "              [[[13],[14]], [[15],[16]], [[17],[17]]]])\n",
    "\n",
    "# Shape\n",
    "print(\"Shape scaler\", s.shape, \"\\nShape vector\", v.shape, \"\\nShape matrix\", m.shape, \"\\nShape tensor\", t.shape)\n",
    "\n",
    "# Type\n",
    "print(\"Type scalar or array\", type(s), \"\\nType after addition with integer\", type(s + 3))\n",
    "\n",
    "# Slicing\n",
    "print(\"v[1:] = \", v[1:], \"\\nm[1:][2:] = \\n\", m[1:,1:])\n",
    "\n",
    "# Reshape arrays\n",
    "x = v.reshape(1, 3)\n",
    "y = v[None, :]\n",
    "print(v, x, y)\n",
    "print(v.shape, x.shape, y.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Element-wise Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6, 7, 8, 9, 10]\n",
      "[ 6  7  8  9 10]\n",
      "[30 35 40 45 50] \n",
      " [30 35 40 45 50] \n",
      "\n",
      "a =\n",
      " [[1 3]\n",
      " [5 7]] \n",
      "b =\n",
      " [[2 4]\n",
      " [6 8]]\n",
      "a + b =\n",
      " [[ 3  7]\n",
      " [11 15]]\n",
      "a * b =\n",
      " [[ 2 12]\n",
      " [30 56]]\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (2,2) (5,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-7ddd6b5f4e75>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"a * b =\\n\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0;31m# Shape mismatch:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"a * values =\\n\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mvalues\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,2) (5,) "
     ]
    }
   ],
   "source": [
    "# The Python way:\n",
    "values = [1, 2, 3, 4, 5]\n",
    "for i in range(len(values)):\n",
    "    values[i] += 5\n",
    "    \n",
    "print(values)\n",
    "\n",
    "# The Numpy way:\n",
    "values = np.array([1, 2, 3, 4, 5])\n",
    "values += 5\n",
    "\n",
    "print(values)\n",
    "\n",
    "# Multiplication\n",
    "x = np.multiply(values, 5)\n",
    "y = values * 5\n",
    "print(x, \"\\n\", y, \"\\n\")\n",
    "\n",
    "# Element wise matrix operations\n",
    "a = np.array([[1,3],[5,7]])\n",
    "b = np.array([[2,4],[6,8]])\n",
    "print(\"a =\\n\", a, \"\\nb =\\n\", b)\n",
    "print(\"a + b =\\n\", a + b)\n",
    "print(\"a * b =\\n\", a * b)\n",
    "# Shape mismatch:\n",
    "print(\"a * values =\\n\", a * values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy Matrix Multiplication\n",
    "Recap element-wise multiplication:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m =\n",
      " [[1 2 3]\n",
      " [4 5 6]] \n",
      "n =\n",
      " [[0.25 0.5  0.75]\n",
      " [1.   1.25 1.5 ]]\n",
      "x =\n",
      " [[0.25 1.   2.25]\n",
      " [4.   6.25 9.  ]] \n",
      "y =\n",
      " [[0.25 1.   2.25]\n",
      " [4.   6.25 9.  ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise recap:\n",
    "m = np.array([[1,2,3],[4,5,6]])\n",
    "# Scalar multiplication\n",
    "n = m * 0.25\n",
    "# Python Elementwise matrix multiplication\n",
    "x = m * n\n",
    "# Numpy Elementwise matrix multiplication\n",
    "y = np.multiply(m, n)\n",
    "\n",
    "print(\"m =\\n\", m, \"\\nn =\\n\", n)\n",
    "print(\"x =\\n\", x, \"\\ny =\\n\", y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Product:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =\n",
      " [[1 2 3 4]\n",
      " [5 6 7 8]] \n",
      "a.shape =\n",
      " (2, 4) \n",
      "b =\n",
      " [[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]] \n",
      "b.shape =\n",
      " (4, 3)\n",
      "c = \n",
      " [[ 70  80  90]\n",
      " [158 184 210]] \n",
      "c.shape =\n",
      " (2, 3)\n",
      "d = \n",
      " [[ 70  80  90]\n",
      " [158 184 210]] \n",
      "d.shape =\n",
      " (2, 3)\n"
     ]
    }
   ],
   "source": [
    "\"\"\" Using np.matmul \"\"\"\n",
    "a = np.array([[1,2,3,4],[5,6,7,8]])\n",
    "b = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])\n",
    "\n",
    "print(\"a =\\n\", a, \"\\na.shape =\\n\", a.shape, \"\\nb =\\n\", b, \"\\nb.shape =\\n\", b.shape)\n",
    "\n",
    "# Matrix product\n",
    "c = np.matmul(a, b)\n",
    "print(\"c = \\n\", c, \"\\nc.shape =\\n\", c.shape)\n",
    "\n",
    "# Dimension mismatch:\n",
    "# print(np.matmul(b, a))\n",
    "\"\"\" Using np.dot \"\"\"\n",
    "d = np.dot(a, b)\n",
    "print(\"d = \\n\", d, \"\\nd.shape =\\n\", d.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transpose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m = \n",
      " [[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]] \n",
      "m.T = \n",
      " [[ 1  5  9]\n",
      " [ 2  6 10]\n",
      " [ 3  7 11]\n",
      " [ 4  8 12]]\n",
      "m = \n",
      " [[  1   2   3   4]\n",
      " [  5   6   7 200]\n",
      " [  9  10  11  12]] \n",
      "m_t = \n",
      " [[  1   5   9]\n",
      " [  2   6  10]\n",
      " [  3   7  11]\n",
      " [  4 200  12]]\n",
      "entries [3][1], [1][3], respectively are edited in both matrices\n"
     ]
    }
   ],
   "source": [
    "m = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
    "print(\"m = \\n\", m,\"\\nm.T = \\n\", m.T)\n",
    "\n",
    "# note how the transposed matrix is not a copy of the original:\n",
    "m_t = m.T\n",
    "m_t[3][1] = 200\n",
    "print(\"m = \\n\", m, \"\\nm_t = \\n\", m_t)\n",
    "print(\"entries [3][1], [1][3], respectively are edited in both matrices\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A real use case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.27  0.45  0.64  0.31]] (1, 4)\n",
      "[[ 0.02   0.001 -0.03   0.036]\n",
      " [ 0.04  -0.003  0.025  0.009]\n",
      " [ 0.012 -0.045  0.28  -0.067]] (3, 4)\n",
      "Matrix multiplication gives:\n",
      " [[-0.01299  0.00664  0.13494]] \n",
      "or, equivalently:\n",
      " [[-0.01299]\n",
      " [ 0.00664]\n",
      " [ 0.13494]]\n"
     ]
    }
   ],
   "source": [
    "inputs = np.array([[-0.27, 0.45, 0.64, 0.31]])\n",
    "print(inputs, inputs.shape)\n",
    "\n",
    "weights = np.array([[0.02, 0.001, -0.03, 0.036], \n",
    "                    [0.04, -0.003, 0.025, 0.009], \n",
    "                    [0.012, -0.045, 0.28, -0.067]])\n",
    "print(weights, weights.shape)\n",
    "\n",
    "print(\"Matrix multiplication gives:\\n\", np.matmul(inputs, weights.T), \"\\nor, equivalently:\\n\", np.matmul(weights, inputs.T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some more useful Numpy methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Showing some basic math on arrays\n",
      "Max: 4\n",
      "Average: 2.0\n",
      "Max index: 2\n",
      "\n",
      "Use numpy to create a [3,3] dimension array with random number\n",
      "[[0.92371879 0.58999086 0.76979433]\n",
      " [0.48733651 0.44698554 0.91494542]\n",
      " [0.59130531 0.69632003 0.32785335]]\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nShowing some basic math on arrays\")\n",
    "\n",
    "b = np.array([0,1,4,3,2])\n",
    "print(\"Max: {}\".format(np.max(b)))\n",
    "print(\"Average: {}\".format(np.average(b)))\n",
    "print(\"Max index: {}\".format(np.argmax(b)))\n",
    "\n",
    "print(\"\\nUse numpy to create a [3,3] dimension array with random number\")\n",
    "c = np.random.rand(3, 3)\n",
    "print(c)"
   ]
  }
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