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1 | 1 | { |
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2 | 2 | "metadata": { |
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3 | "name": "", | |
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3 | "name": "Cython Magics", | |
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4 | 4 | "signature": "sha256:c357b93e9480d6347c6677862bf43750745cef4b30129c5bc53cb879a19d4074" |
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5 | 5 | }, |
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6 | 6 | "nbformat": 3, |
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7 | 7 | "nbformat_minor": 0, |
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8 | 8 | "worksheets": [ |
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9 | 9 | { |
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10 | 10 | "cells": [ |
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11 | 11 | { |
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12 | 12 | "cell_type": "heading", |
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13 | 13 | "level": 1, |
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14 | 14 | "metadata": {}, |
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15 | 15 | "source": [ |
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16 | 16 | "Cython Magic Functions" |
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17 | 17 | ] |
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18 | 18 | }, |
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19 | 19 | { |
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20 | 20 | "cell_type": "heading", |
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21 | 21 | "level": 2, |
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22 | 22 | "metadata": {}, |
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23 | 23 | "source": [ |
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24 | 24 | "Loading the extension" |
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25 | 25 | ] |
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26 | 26 | }, |
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27 | 27 | { |
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28 | 28 | "cell_type": "markdown", |
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29 | 29 | "metadata": {}, |
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30 | 30 | "source": [ |
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31 | 31 | "IPython has a `cythonmagic` extension that contains a number of magic functions for working with Cython code. This extension can be loaded using the `%load_ext` magic as follows:" |
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32 | 32 | ] |
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33 | 33 | }, |
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34 | 34 | { |
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35 | 35 | "cell_type": "code", |
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36 | 36 | "collapsed": false, |
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37 | 37 | "input": [ |
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38 | 38 | "%load_ext cythonmagic" |
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39 | 39 | ], |
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40 | 40 | "language": "python", |
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41 | 41 | "metadata": {}, |
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42 | 42 | "outputs": [], |
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43 | 43 | "prompt_number": 1 |
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44 | 44 | }, |
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45 | 45 | { |
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46 | 46 | "cell_type": "heading", |
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47 | 47 | "level": 2, |
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48 | 48 | "metadata": {}, |
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49 | 49 | "source": [ |
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50 | 50 | "The %cython_inline magic" |
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51 | 51 | ] |
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52 | 52 | }, |
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53 | 53 | { |
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54 | 54 | "cell_type": "markdown", |
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55 | 55 | "metadata": {}, |
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56 | 56 | "source": [ |
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57 | 57 | "The `%%cython_inline` magic uses `Cython.inline` to compile a Cython expression. This allows you to enter and run a function body with Cython code. Use a bare `return` statement to return values. " |
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58 | 58 | ] |
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59 | 59 | }, |
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60 | 60 | { |
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61 | 61 | "cell_type": "code", |
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62 | 62 | "collapsed": false, |
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63 | 63 | "input": [ |
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64 | 64 | "a = 10\n", |
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65 | 65 | "b = 20" |
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66 | 66 | ], |
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67 | 67 | "language": "python", |
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68 | 68 | "metadata": {}, |
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69 | 69 | "outputs": [], |
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70 | 70 | "prompt_number": 2 |
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71 | 71 | }, |
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72 | 72 | { |
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73 | 73 | "cell_type": "code", |
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74 | 74 | "collapsed": false, |
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75 | 75 | "input": [ |
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76 | 76 | "%%cython_inline\n", |
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77 | 77 | "return a+b" |
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78 | 78 | ], |
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79 | 79 | "language": "python", |
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80 | 80 | "metadata": {}, |
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81 | 81 | "outputs": [ |
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82 | 82 | { |
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83 | 83 | "metadata": {}, |
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84 | 84 | "output_type": "pyout", |
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85 | 85 | "prompt_number": 3, |
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86 | 86 | "text": [ |
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87 | 87 | "30" |
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88 | 88 | ] |
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89 | 89 | } |
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90 | 90 | ], |
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91 | 91 | "prompt_number": 3 |
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92 | 92 | }, |
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93 | 93 | { |
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94 | 94 | "cell_type": "heading", |
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95 | 95 | "level": 2, |
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96 | 96 | "metadata": {}, |
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97 | 97 | "source": [ |
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98 | 98 | "The %cython_pyximport magic" |
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99 | 99 | ] |
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100 | 100 | }, |
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101 | 101 | { |
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102 | 102 | "cell_type": "markdown", |
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103 | 103 | "metadata": {}, |
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104 | 104 | "source": [ |
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105 | 105 | "The `%%cython_pyximport` magic allows you to enter arbitrary Cython code into a cell. That Cython code is written as a `.pyx` file in the current working directory and then imported using `pyximport`. You have the specify the name of the module that the Code will appear in. All symbols from the module are imported automatically by the magic function." |
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106 | 106 | ] |
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107 | 107 | }, |
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108 | 108 | { |
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109 | 109 | "cell_type": "code", |
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110 | 110 | "collapsed": false, |
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111 | 111 | "input": [ |
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112 | 112 | "%%cython_pyximport foo\n", |
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113 | 113 | "def f(x):\n", |
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114 | 114 | " return 4.0*x" |
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115 | 115 | ], |
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116 | 116 | "language": "python", |
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117 | 117 | "metadata": {}, |
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118 | 118 | "outputs": [], |
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119 | 119 | "prompt_number": 4 |
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120 | 120 | }, |
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121 | 121 | { |
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122 | 122 | "cell_type": "code", |
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123 | 123 | "collapsed": false, |
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124 | 124 | "input": [ |
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125 | 125 | "f(10)" |
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126 | 126 | ], |
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127 | 127 | "language": "python", |
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128 | 128 | "metadata": {}, |
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129 | 129 | "outputs": [ |
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130 | 130 | { |
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131 | 131 | "metadata": {}, |
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132 | 132 | "output_type": "pyout", |
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133 | 133 | "prompt_number": 5, |
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134 | 134 | "text": [ |
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135 | 135 | "40.0" |
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136 | 136 | ] |
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137 | 137 | } |
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138 | 138 | ], |
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139 | 139 | "prompt_number": 5 |
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140 | 140 | }, |
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141 | 141 | { |
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142 | 142 | "cell_type": "heading", |
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143 | 143 | "level": 2, |
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144 | 144 | "metadata": {}, |
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145 | 145 | "source": [ |
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146 | 146 | "The %cython magic" |
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147 | 147 | ] |
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148 | 148 | }, |
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149 | 149 | { |
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150 | 150 | "cell_type": "markdown", |
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151 | 151 | "metadata": {}, |
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152 | 152 | "source": [ |
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153 | 153 | "Probably the most important magic is the `%cython` magic. This is similar to the `%%cython_pyximport` magic, but doesn't require you to specify a module name. Instead, the `%%cython` magic uses manages everything using temporary files in the `~/.cython/magic` directory. All of the symbols in the Cython module are imported automatically by the magic.\n", |
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154 | 154 | "\n", |
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155 | 155 | "Here is a simple example of a Black-Scholes options pricing algorithm written in Cython. Please note that this example might not compile on non-POSIX systems (e.g., Windows) because of a missing `erf` symbol." |
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156 | 156 | ] |
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157 | 157 | }, |
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158 | 158 | { |
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159 | 159 | "cell_type": "code", |
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160 | 160 | "collapsed": false, |
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161 | 161 | "input": [ |
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162 | 162 | "%%cython\n", |
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163 | 163 | "cimport cython\n", |
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164 | 164 | "from libc.math cimport exp, sqrt, pow, log, erf\n", |
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165 | 165 | "\n", |
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166 | 166 | "@cython.cdivision(True)\n", |
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167 | 167 | "cdef double std_norm_cdf_cy(double x) nogil:\n", |
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168 | 168 | " return 0.5*(1+erf(x/sqrt(2.0)))\n", |
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169 | 169 | "\n", |
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170 | 170 | "@cython.cdivision(True)\n", |
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171 | 171 | "def black_scholes_cy(double s, double k, double t, double v,\n", |
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172 | 172 | " double rf, double div, double cp):\n", |
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173 | 173 | " \"\"\"Price an option using the Black-Scholes model.\n", |
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174 | 174 | " \n", |
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175 | 175 | " s : initial stock price\n", |
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176 | 176 | " k : strike price\n", |
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177 | 177 | " t : expiration time\n", |
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178 | 178 | " v : volatility\n", |
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179 | 179 | " rf : risk-free rate\n", |
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180 | 180 | " div : dividend\n", |
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181 | 181 | " cp : +1/-1 for call/put\n", |
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182 | 182 | " \"\"\"\n", |
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183 | 183 | " cdef double d1, d2, optprice\n", |
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184 | 184 | " with nogil:\n", |
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185 | 185 | " d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))\n", |
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186 | 186 | " d2 = d1 - v*sqrt(t)\n", |
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187 | 187 | " optprice = cp*s*exp(-div*t)*std_norm_cdf_cy(cp*d1) - \\\n", |
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188 | 188 | " cp*k*exp(-rf*t)*std_norm_cdf_cy(cp*d2)\n", |
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189 | 189 | " return optprice" |
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190 | 190 | ], |
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191 | 191 | "language": "python", |
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192 | 192 | "metadata": {}, |
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193 | 193 | "outputs": [], |
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194 | 194 | "prompt_number": 6 |
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195 | 195 | }, |
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196 | 196 | { |
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197 | 197 | "cell_type": "code", |
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198 | 198 | "collapsed": false, |
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199 | 199 | "input": [ |
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200 | 200 | "black_scholes_cy(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" |
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201 | 201 | ], |
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202 | 202 | "language": "python", |
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203 | 203 | "metadata": {}, |
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204 | 204 | "outputs": [ |
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205 | 205 | { |
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206 | 206 | "metadata": {}, |
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207 | 207 | "output_type": "pyout", |
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208 | 208 | "prompt_number": 7, |
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209 | 209 | "text": [ |
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210 | 210 | "10.327861752731728" |
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211 | 211 | ] |
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212 | 212 | } |
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213 | 213 | ], |
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214 | 214 | "prompt_number": 7 |
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215 | 215 | }, |
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216 | 216 | { |
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217 | 217 | "cell_type": "markdown", |
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218 | 218 | "metadata": {}, |
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219 | 219 | "source": [ |
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220 | 220 | "For comparison, the same code is implemented here in pure python." |
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221 | 221 | ] |
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222 | 222 | }, |
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223 | 223 | { |
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224 | 224 | "cell_type": "code", |
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225 | 225 | "collapsed": false, |
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226 | 226 | "input": [ |
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227 | 227 | "from math import exp, sqrt, pow, log, erf\n", |
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228 | 228 | "\n", |
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229 | 229 | "def std_norm_cdf_py(x):\n", |
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230 | 230 | " return 0.5*(1+erf(x/sqrt(2.0)))\n", |
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231 | 231 | "\n", |
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232 | 232 | "def black_scholes_py(s, k, t, v, rf, div, cp):\n", |
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233 | 233 | " \"\"\"Price an option using the Black-Scholes model.\n", |
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234 | 234 | " \n", |
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235 | 235 | " s : initial stock price\n", |
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236 | 236 | " k : strike price\n", |
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237 | 237 | " t : expiration time\n", |
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238 | 238 | " v : volatility\n", |
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239 | 239 | " rf : risk-free rate\n", |
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240 | 240 | " div : dividend\n", |
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241 | 241 | " cp : +1/-1 for call/put\n", |
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242 | 242 | " \"\"\"\n", |
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243 | 243 | " d1 = (log(s/k)+(rf-div+0.5*pow(v,2))*t)/(v*sqrt(t))\n", |
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244 | 244 | " d2 = d1 - v*sqrt(t)\n", |
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245 | 245 | " optprice = cp*s*exp(-div*t)*std_norm_cdf_py(cp*d1) - \\\n", |
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246 | 246 | " cp*k*exp(-rf*t)*std_norm_cdf_py(cp*d2)\n", |
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247 | 247 | " return optprice" |
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248 | 248 | ], |
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249 | 249 | "language": "python", |
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250 | 250 | "metadata": {}, |
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251 | 251 | "outputs": [], |
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252 | 252 | "prompt_number": 8 |
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253 | 253 | }, |
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254 | 254 | { |
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255 | 255 | "cell_type": "code", |
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256 | 256 | "collapsed": false, |
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257 | 257 | "input": [ |
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258 | 258 | "black_scholes_py(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" |
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259 | 259 | ], |
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260 | 260 | "language": "python", |
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261 | 261 | "metadata": {}, |
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262 | 262 | "outputs": [ |
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263 | 263 | { |
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264 | 264 | "metadata": {}, |
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265 | 265 | "output_type": "pyout", |
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266 | 266 | "prompt_number": 9, |
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267 | 267 | "text": [ |
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268 | 268 | "10.327861752731728" |
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269 | 269 | ] |
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270 | 270 | } |
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271 | 271 | ], |
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272 | 272 | "prompt_number": 9 |
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273 | 273 | }, |
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274 | 274 | { |
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275 | 275 | "cell_type": "markdown", |
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276 | 276 | "metadata": {}, |
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277 | 277 | "source": [ |
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278 | 278 | "Below we see the runtime of the two functions: the Cython version is nearly a factor of 10 faster." |
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279 | 279 | ] |
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280 | 280 | }, |
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281 | 281 | { |
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282 | 282 | "cell_type": "code", |
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283 | 283 | "collapsed": false, |
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284 | 284 | "input": [ |
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285 | 285 | "%timeit black_scholes_cy(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" |
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286 | 286 | ], |
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287 | 287 | "language": "python", |
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288 | 288 | "metadata": {}, |
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289 | 289 | "outputs": [ |
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290 | 290 | { |
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291 | 291 | "output_type": "stream", |
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292 | 292 | "stream": "stdout", |
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293 | 293 | "text": [ |
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294 | 294 | "1000000 loops, best of 3: 319 ns per loop\n" |
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295 | 295 | ] |
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296 | 296 | } |
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297 | 297 | ], |
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298 | 298 | "prompt_number": 10 |
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299 | 299 | }, |
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300 | 300 | { |
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301 | 301 | "cell_type": "code", |
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302 | 302 | "collapsed": false, |
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303 | 303 | "input": [ |
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304 | 304 | "%timeit black_scholes_py(100.0, 100.0, 1.0, 0.3, 0.03, 0.0, -1)" |
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305 | 305 | ], |
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306 | 306 | "language": "python", |
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307 | 307 | "metadata": {}, |
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308 | 308 | "outputs": [ |
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309 | 309 | { |
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310 | 310 | "output_type": "stream", |
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311 | 311 | "stream": "stdout", |
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312 | 312 | "text": [ |
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313 | 313 | "100000 loops, best of 3: 2.28 \u00b5s per loop\n" |
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314 | 314 | ] |
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315 | 315 | } |
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316 | 316 | ], |
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317 | 317 | "prompt_number": 11 |
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318 | 318 | }, |
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319 | 319 | { |
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320 | 320 | "cell_type": "heading", |
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321 | 321 | "level": 2, |
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322 | 322 | "metadata": {}, |
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323 | 323 | "source": [ |
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324 | 324 | "External libraries" |
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325 | 325 | ] |
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326 | 326 | }, |
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327 | 327 | { |
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328 | 328 | "cell_type": "markdown", |
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329 | 329 | "metadata": {}, |
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330 | 330 | "source": [ |
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331 | 331 | "Cython allows you to specify additional libraries to be linked with your extension, you can do so with the `-l` flag (also spelled `--lib`). Note that this flag can be passed more than once to specify multiple libraries, such as `-lm -llib2 --lib lib3`. Here's a simple example of how to access the system math library:" |
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332 | 332 | ] |
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333 | 333 | }, |
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334 | 334 | { |
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335 | 335 | "cell_type": "code", |
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336 | 336 | "collapsed": false, |
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337 | 337 | "input": [ |
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338 | 338 | "%%cython -lm\n", |
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339 | 339 | "from libc.math cimport sin\n", |
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340 | 340 | "print 'sin(1)=', sin(1)" |
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341 | 341 | ], |
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342 | 342 | "language": "python", |
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343 | 343 | "metadata": {}, |
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344 | 344 | "outputs": [ |
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345 | 345 | { |
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346 | 346 | "output_type": "stream", |
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347 | 347 | "stream": "stdout", |
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348 | 348 | "text": [ |
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349 | 349 | "sin(1)= 0.841470984808\n" |
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350 | 350 | ] |
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351 | 351 | } |
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352 | 352 | ], |
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353 | 353 | "prompt_number": 12 |
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354 | 354 | }, |
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355 | 355 | { |
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356 | 356 | "cell_type": "markdown", |
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357 | 357 | "metadata": {}, |
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358 | 358 | "source": [ |
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359 | 359 | "You can similarly use the `-I/--include` flag to add include directories to the search path, and `-c/--compile-args` to add extra flags that are passed to Cython via the `extra_compile_args` of the distutils `Extension` class. Please see [the Cython docs on C library usage](http://docs.cython.org/src/tutorial/clibraries.html) for more details on the use of these flags." |
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360 | 360 | ] |
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361 | 361 | } |
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362 | 362 | ], |
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363 | 363 | "metadata": {} |
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364 | 364 | } |
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365 | 365 | ] |
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366 | 366 | } |
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