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Updating example notebooks to v3 format.
Brian Granger -
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1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "00_notebook_tour"
3 "name": "00_notebook_tour"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# A brief tour of the IPython notebook",
12 "# A brief tour of the IPython notebook",
13 "",
13 "",
14 "This document will give you a brief tour of the capabilities of the IPython notebook. ",
14 "This document will give you a brief tour of the capabilities of the IPython notebook. ",
15 "You can view its contents by scrolling around, or execute each cell by typing `Shift-Enter`.",
15 "You can view its contents by scrolling around, or execute each cell by typing `Shift-Enter`.",
16 "After you conclude this brief high-level tour, you should read the accompanying notebook ",
16 "After you conclude this brief high-level tour, you should read the accompanying notebook ",
17 "titled `01_notebook_introduction`, which takes a more step-by-step approach to the features of the",
17 "titled `01_notebook_introduction`, which takes a more step-by-step approach to the features of the",
18 "system. ",
18 "system. ",
19 "",
19 "",
20 "The rest of the notebooks in this directory illustrate various other aspects and ",
20 "The rest of the notebooks in this directory illustrate various other aspects and ",
21 "capabilities of the IPython notebook; some of them may require additional libraries to be executed.",
21 "capabilities of the IPython notebook; some of them may require additional libraries to be executed.",
22 "",
22 "",
23 "**NOTE:** This notebook *must* be run from its own directory, so you must ``cd``",
23 "**NOTE:** This notebook *must* be run from its own directory, so you must ``cd``",
24 "to this directory and then start the notebook, but do *not* use the ``--notebook-dir``",
24 "to this directory and then start the notebook, but do *not* use the ``--notebook-dir``",
25 "option to run it from another location.",
25 "option to run it from another location.",
26 "",
26 "",
27 "The first thing you need to know is that you are still controlling the same old IPython you're used to,",
27 "The first thing you need to know is that you are still controlling the same old IPython you're used to,",
28 "so things like shell aliases and magic commands still work:"
28 "so things like shell aliases and magic commands still work:"
29 ]
29 ]
30 },
30 },
31 {
31 {
32 "cell_type": "code",
32 "cell_type": "code",
33 "collapsed": false,
33 "collapsed": false,
34 "input": [
34 "input": [
35 "pwd"
35 "pwd"
36 ],
36 ],
37 "language": "python",
37 "language": "python",
38 "outputs": [
38 "outputs": [
39 {
39 {
40 "output_type": "pyout",
40 "output_type": "pyout",
41 "prompt_number": 1,
41 "prompt_number": 1,
42 "text": [
42 "text": [
43 "u'/home/fperez/ipython/ipython/docs/examples/notebooks'"
43 "u'/home/fperez/ipython/ipython/docs/examples/notebooks'"
44 ]
44 ]
45 }
45 }
46 ],
46 ],
47 "prompt_number": 1
47 "prompt_number": 1
48 },
48 },
49 {
49 {
50 "cell_type": "code",
50 "cell_type": "code",
51 "collapsed": false,
51 "collapsed": false,
52 "input": [
52 "input": [
53 "ls"
53 "ls"
54 ],
54 ],
55 "language": "python",
55 "language": "python",
56 "outputs": [
56 "outputs": [
57 {
57 {
58 "output_type": "stream",
58 "output_type": "stream",
59 "stream": "stdout",
59 "stream": "stdout",
60 "text": [
60 "text": [
61 "00_notebook_tour.ipynb python-logo.svg",
61 "00_notebook_tour.ipynb python-logo.svg",
62 "01_notebook_introduction.ipynb sympy.ipynb",
62 "01_notebook_introduction.ipynb sympy.ipynb",
63 "animation.m4v sympy_quantum_computing.ipynb",
63 "animation.m4v sympy_quantum_computing.ipynb",
64 "display_protocol.ipynb trapezoid_rule.ipynb",
64 "display_protocol.ipynb trapezoid_rule.ipynb",
65 "formatting.ipynb"
65 "formatting.ipynb"
66 ]
66 ]
67 }
67 }
68 ],
68 ],
69 "prompt_number": 2
69 "prompt_number": 2
70 },
70 },
71 {
71 {
72 "cell_type": "code",
72 "cell_type": "code",
73 "collapsed": false,
73 "collapsed": false,
74 "input": [
74 "input": [
75 "message = 'The IPython notebook is great!'",
75 "message = 'The IPython notebook is great!'",
76 "# note: the echo command does not run on Windows, it's a unix command.",
76 "# note: the echo command does not run on Windows, it's a unix command.",
77 "!echo $message"
77 "!echo $message"
78 ],
78 ],
79 "language": "python",
79 "language": "python",
80 "outputs": [
80 "outputs": [
81 {
81 {
82 "output_type": "stream",
82 "output_type": "stream",
83 "stream": "stdout",
83 "stream": "stdout",
84 "text": [
84 "text": [
85 "The IPython notebook is great!"
85 "The IPython notebook is great!"
86 ]
86 ]
87 }
87 }
88 ],
88 ],
89 "prompt_number": 3
89 "prompt_number": 3
90 },
90 },
91 {
91 {
92 "cell_type": "markdown",
92 "cell_type": "markdown",
93 "source": [
93 "source": [
94 "Plots with matplotlib: do *not* execute the next below if you do not have matplotlib installed or didn't start up ",
94 "Plots with matplotlib: do *not* execute the next below if you do not have matplotlib installed or didn't start up ",
95 "this notebook with the `--pylab` option, as the code will not work."
95 "this notebook with the `--pylab` option, as the code will not work."
96 ]
96 ]
97 },
97 },
98 {
98 {
99 "cell_type": "code",
99 "cell_type": "code",
100 "collapsed": false,
100 "collapsed": false,
101 "input": [
101 "input": [
102 "x = linspace(0, 3*pi, 500)",
102 "x = linspace(0, 3*pi, 500)",
103 "plot(x, sin(x**2))",
103 "plot(x, sin(x**2))",
104 "title('A simple chirp');"
104 "title('A simple chirp');"
105 ],
105 ],
106 "language": "python",
106 "language": "python",
107 "outputs": [
107 "outputs": [
108 {
108 {
109 "output_type": "display_data",
109 "output_type": "display_data",
110 "png": 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wZcoUR8LXhfffB6ZPd77BdCMKSp/X0wfUnmJFERTpOx0qYoUOT19lwTVeTz9q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\nLNDayk76Y8eSf1mUfo8e5PXrfgrmhTDpn3feeXj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110 "png": 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wZcoUR8LXhfffB6ZPd77BdCMKSp/X0wfUnmJFERTpOx0qYoUOT19lwTVeTz9q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\nLNDayk76Y8eSf1mUfo8e5PXrfgrmhTDpn3feeXj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111 }
111 }
112 ],
112 ],
113 "prompt_number": 4
113 "prompt_number": 4
114 },
114 },
115 {
115 {
116 "cell_type": "markdown",
116 "cell_type": "markdown",
117 "source": [
117 "source": [
118 "You can paste blocks of input with prompt markers, such as those from",
118 "You can paste blocks of input with prompt markers, such as those from",
119 "[the official Python tutorial](http://docs.python.org/tutorial/interpreter.html#interactive-mode)"
119 "[the official Python tutorial](http://docs.python.org/tutorial/interpreter.html#interactive-mode)"
120 ]
120 ]
121 },
121 },
122 {
122 {
123 "cell_type": "code",
123 "cell_type": "code",
124 "collapsed": false,
124 "collapsed": false,
125 "input": [
125 "input": [
126 ">>> the_world_is_flat = 1",
126 ">>> the_world_is_flat = 1",
127 ">>> if the_world_is_flat:",
127 ">>> if the_world_is_flat:",
128 "... print \"Be careful not to fall off!\""
128 "... print \"Be careful not to fall off!\""
129 ],
129 ],
130 "language": "python",
130 "language": "python",
131 "outputs": [
131 "outputs": [
132 {
132 {
133 "output_type": "stream",
133 "output_type": "stream",
134 "stream": "stdout",
134 "stream": "stdout",
135 "text": [
135 "text": [
136 "Be careful not to fall off!"
136 "Be careful not to fall off!"
137 ]
137 ]
138 }
138 }
139 ],
139 ],
140 "prompt_number": 5
140 "prompt_number": 5
141 },
141 },
142 {
142 {
143 "cell_type": "markdown",
143 "cell_type": "markdown",
144 "source": [
144 "source": [
145 "Errors are shown in informative ways:"
145 "Errors are shown in informative ways:"
146 ]
146 ]
147 },
147 },
148 {
148 {
149 "cell_type": "code",
149 "cell_type": "code",
150 "collapsed": false,
150 "collapsed": false,
151 "input": [
151 "input": [
152 "%run non_existent_file"
152 "%run non_existent_file"
153 ],
153 ],
154 "language": "python",
154 "language": "python",
155 "outputs": [
155 "outputs": [
156 {
156 {
157 "output_type": "stream",
157 "output_type": "stream",
158 "stream": "stderr",
158 "stream": "stderr",
159 "text": [
159 "text": [
160 "ERROR: File `non_existent_file.py` not found."
160 "ERROR: File `non_existent_file.py` not found."
161 ]
161 ]
162 }
162 }
163 ],
163 ],
164 "prompt_number": 6
164 "prompt_number": 6
165 },
165 },
166 {
166 {
167 "cell_type": "code",
167 "cell_type": "code",
168 "collapsed": false,
168 "collapsed": false,
169 "input": [
169 "input": [
170 "x = 1",
170 "x = 1",
171 "y = 4",
171 "y = 4",
172 "z = y/(1-x)"
172 "z = y/(1-x)"
173 ],
173 ],
174 "language": "python",
174 "language": "python",
175 "outputs": [
175 "outputs": [
176 {
176 {
177 "ename": "ZeroDivisionError",
177 "ename": "ZeroDivisionError",
178 "evalue": "integer division or modulo by zero",
178 "evalue": "integer division or modulo by zero",
179 "output_type": "pyerr",
179 "output_type": "pyerr",
180 "traceback": [
180 "traceback": [
181 "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)",
181 "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mZeroDivisionError\u001b[0m Traceback (most recent call last)",
182 "\u001b[0;32m/home/fperez/ipython/ipython/docs/examples/notebooks/<ipython-input-7-dc39888fd1d2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
182 "\u001b[0;32m/home/fperez/ipython/ipython/docs/examples/notebooks/<ipython-input-7-dc39888fd1d2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
183 "\u001b[0;31mZeroDivisionError\u001b[0m: integer division or modulo by zero"
183 "\u001b[0;31mZeroDivisionError\u001b[0m: integer division or modulo by zero"
184 ]
184 ]
185 }
185 }
186 ],
186 ],
187 "prompt_number": 7
187 "prompt_number": 7
188 },
188 },
189 {
189 {
190 "cell_type": "markdown",
190 "cell_type": "markdown",
191 "source": [
191 "source": [
192 "When IPython needs to display additional information (such as providing details on an object via `x?`",
192 "When IPython needs to display additional information (such as providing details on an object via `x?`",
193 "it will automatically invoke a pager at the bottom of the screen:"
193 "it will automatically invoke a pager at the bottom of the screen:"
194 ]
194 ]
195 },
195 },
196 {
196 {
197 "cell_type": "code",
197 "cell_type": "code",
198 "collapsed": true,
198 "collapsed": true,
199 "input": [
199 "input": [
200 "magic"
200 "magic"
201 ],
201 ],
202 "language": "python",
202 "language": "python",
203 "outputs": [],
203 "outputs": [],
204 "prompt_number": 8
204 "prompt_number": 8
205 },
205 },
206 {
206 {
207 "cell_type": "markdown",
207 "cell_type": "markdown",
208 "source": [
208 "source": [
209 "## Non-blocking output of kernel",
209 "## Non-blocking output of kernel",
210 "",
210 "",
211 "If you execute the next cell, you will see the output arriving as it is generated, not all at the end."
211 "If you execute the next cell, you will see the output arriving as it is generated, not all at the end."
212 ]
212 ]
213 },
213 },
214 {
214 {
215 "cell_type": "code",
215 "cell_type": "code",
216 "collapsed": false,
216 "collapsed": false,
217 "input": [
217 "input": [
218 "import time, sys",
218 "import time, sys",
219 "for i in range(8):",
219 "for i in range(8):",
220 " print i,",
220 " print i,",
221 " time.sleep(0.5)"
221 " time.sleep(0.5)"
222 ],
222 ],
223 "language": "python",
223 "language": "python",
224 "outputs": [
224 "outputs": [
225 {
225 {
226 "output_type": "stream",
226 "output_type": "stream",
227 "stream": "stdout",
227 "stream": "stdout",
228 "text": [
228 "text": [
229 "0 "
229 "0 "
230 ]
230 ]
231 },
231 },
232 {
232 {
233 "output_type": "stream",
233 "output_type": "stream",
234 "stream": "stdout",
234 "stream": "stdout",
235 "text": [
235 "text": [
236 "1 "
236 "1 "
237 ]
237 ]
238 },
238 },
239 {
239 {
240 "output_type": "stream",
240 "output_type": "stream",
241 "stream": "stdout",
241 "stream": "stdout",
242 "text": [
242 "text": [
243 "2 "
243 "2 "
244 ]
244 ]
245 },
245 },
246 {
246 {
247 "output_type": "stream",
247 "output_type": "stream",
248 "stream": "stdout",
248 "stream": "stdout",
249 "text": [
249 "text": [
250 "3 "
250 "3 "
251 ]
251 ]
252 },
252 },
253 {
253 {
254 "output_type": "stream",
254 "output_type": "stream",
255 "stream": "stdout",
255 "stream": "stdout",
256 "text": [
256 "text": [
257 "4 "
257 "4 "
258 ]
258 ]
259 },
259 },
260 {
260 {
261 "output_type": "stream",
261 "output_type": "stream",
262 "stream": "stdout",
262 "stream": "stdout",
263 "text": [
263 "text": [
264 "5 "
264 "5 "
265 ]
265 ]
266 },
266 },
267 {
267 {
268 "output_type": "stream",
268 "output_type": "stream",
269 "stream": "stdout",
269 "stream": "stdout",
270 "text": [
270 "text": [
271 "6 "
271 "6 "
272 ]
272 ]
273 },
273 },
274 {
274 {
275 "output_type": "stream",
275 "output_type": "stream",
276 "stream": "stdout",
276 "stream": "stdout",
277 "text": [
277 "text": [
278 "7"
278 "7"
279 ]
279 ]
280 }
280 }
281 ],
281 ],
282 "prompt_number": 9
282 "prompt_number": 9
283 },
283 },
284 {
284 {
285 "cell_type": "markdown",
285 "cell_type": "markdown",
286 "source": [
286 "source": [
287 "## Clean crash and restart",
287 "## Clean crash and restart",
288 "",
288 "",
289 "We call the low-level system libc.time routine with the wrong argument via",
289 "We call the low-level system libc.time routine with the wrong argument via",
290 "ctypes to segfault the Python interpreter:"
290 "ctypes to segfault the Python interpreter:"
291 ]
291 ]
292 },
292 },
293 {
293 {
294 "cell_type": "code",
294 "cell_type": "code",
295 "collapsed": true,
295 "collapsed": true,
296 "input": [
296 "input": [
297 "from ctypes import CDLL",
297 "from ctypes import CDLL",
298 "# This will crash a linux system; equivalent calls can be made on Windows or Mac",
298 "# This will crash a linux system; equivalent calls can be made on Windows or Mac",
299 "libc = CDLL(\"libc.so.6\") ",
299 "libc = CDLL(\"libc.so.6\") ",
300 "libc.time(-1) # BOOM!!"
300 "libc.time(-1) # BOOM!!"
301 ],
301 ],
302 "language": "python",
302 "language": "python",
303 "outputs": [],
303 "outputs": [],
304 "prompt_number": "*"
304 "prompt_number": "*"
305 },
305 },
306 {
306 {
307 "cell_type": "markdown",
307 "cell_type": "markdown",
308 "source": [
308 "source": [
309 "## Markdown cells can contain formatted text and code",
309 "## Markdown cells can contain formatted text and code",
310 "",
310 "",
311 "You can *italicize*, **boldface**",
311 "You can *italicize*, **boldface**",
312 "",
312 "",
313 "* build",
313 "* build",
314 "* lists",
314 "* lists",
315 "",
315 "",
316 "and embed code meant for illustration instead of execution in Python:",
316 "and embed code meant for illustration instead of execution in Python:",
317 "",
317 "",
318 " def f(x):",
318 " def f(x):",
319 " \"\"\"a docstring\"\"\"",
319 " \"\"\"a docstring\"\"\"",
320 " return x**2",
320 " return x**2",
321 "",
321 "",
322 "or other languages:",
322 "or other languages:",
323 "",
323 "",
324 " if (i=0; i<n; i++) {",
324 " if (i=0; i<n; i++) {",
325 " printf(\"hello %d\\n\", i);",
325 " printf(\"hello %d\\n\", i);",
326 " x += 4;",
326 " x += 4;",
327 " }"
327 " }"
328 ]
328 ]
329 },
329 },
330 {
330 {
331 "cell_type": "markdown",
331 "cell_type": "markdown",
332 "source": [
332 "source": [
333 "Courtesy of MathJax, you can include mathematical expressions both inline: ",
333 "Courtesy of MathJax, you can include mathematical expressions both inline: ",
334 "$e^{i\\pi} + 1 = 0$ and displayed:",
334 "$e^{i\\pi} + 1 = 0$ and displayed:",
335 "",
335 "",
336 "$$e^x=\\sum_{i=0}^\\infty \\frac{1}{i!}x^i$$"
336 "$$e^x=\\sum_{i=0}^\\infty \\frac{1}{i!}x^i$$"
337 ]
337 ]
338 },
338 },
339 {
339 {
340 "cell_type": "markdown",
340 "cell_type": "markdown",
341 "source": [
341 "source": [
342 "## Rich displays: include anyting a browser can show",
342 "## Rich displays: include anyting a browser can show",
343 "",
343 "",
344 "Note that we have an actual protocol for this, see the `display_protocol` notebook for further details.",
344 "Note that we have an actual protocol for this, see the `display_protocol` notebook for further details.",
345 "",
345 "",
346 "### Images"
346 "### Images"
347 ]
347 ]
348 },
348 },
349 {
349 {
350 "cell_type": "code",
350 "cell_type": "code",
351 "collapsed": false,
351 "collapsed": false,
352 "input": [
352 "input": [
353 "from IPython.core.display import Image",
353 "from IPython.core.display import Image",
354 "Image(filename='../../source/_static/logo.png')"
354 "Image(filename='../../source/_static/logo.png')"
355 ],
355 ],
356 "language": "python",
356 "language": "python",
357 "outputs": [
357 "outputs": [
358 {
358 {
359 "output_type": "pyout",
359 "output_type": "pyout",
360 "png": 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360 "png": 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361 "prompt_number": 1,
361 "prompt_number": 1,
362 "text": [
362 "text": [
363 "&lt;IPython.core.display.Image at 0x41d4690&gt;"
363 "&lt;IPython.core.display.Image at 0x41d4690&gt;"
364 ]
364 ]
365 }
365 }
366 ],
366 ],
367 "prompt_number": 1
367 "prompt_number": 1
368 },
368 },
369 {
369 {
370 "cell_type": "markdown",
370 "cell_type": "markdown",
371 "source": [
371 "source": [
372 "An image can also be displayed from raw data or a url"
372 "An image can also be displayed from raw data or a url"
373 ]
373 ]
374 },
374 },
375 {
375 {
376 "cell_type": "code",
376 "cell_type": "code",
377 "collapsed": false,
377 "collapsed": false,
378 "input": [
378 "input": [
379 "Image('http://python.org/images/python-logo.gif')"
379 "Image('http://python.org/images/python-logo.gif')"
380 ],
380 ],
381 "language": "python",
381 "language": "python",
382 "outputs": [
382 "outputs": [
383 {
383 {
384 "html": [
384 "html": [
385 "<img src=\"http://python.org/images/python-logo.gif\" />"
385 "<img src=\"http://python.org/images/python-logo.gif\" />"
386 ],
386 ],
387 "output_type": "pyout",
387 "output_type": "pyout",
388 "prompt_number": 2,
388 "prompt_number": 2,
389 "text": [
389 "text": [
390 "&lt;IPython.core.display.Image at 0x41d4550&gt;"
390 "&lt;IPython.core.display.Image at 0x41d4550&gt;"
391 ]
391 ]
392 }
392 }
393 ],
393 ],
394 "prompt_number": 2
394 "prompt_number": 2
395 },
395 },
396 {
396 {
397 "cell_type": "markdown",
397 "cell_type": "markdown",
398 "source": [
398 "source": [
399 "SVG images are also supported out of the box (since modern browsers do a good job of rendering them):"
399 "SVG images are also supported out of the box (since modern browsers do a good job of rendering them):"
400 ]
400 ]
401 },
401 },
402 {
402 {
403 "cell_type": "code",
403 "cell_type": "code",
404 "collapsed": false,
404 "collapsed": false,
405 "input": [
405 "input": [
406 "from IPython.core.display import SVG",
406 "from IPython.core.display import SVG",
407 "SVG(filename='python-logo.svg')"
407 "SVG(filename='python-logo.svg')"
408 ],
408 ],
409 "language": "python",
409 "language": "python",
410 "outputs": [
410 "outputs": [
411 {
411 {
412 "output_type": "pyout",
412 "output_type": "pyout",
413 "prompt_number": 3,
413 "prompt_number": 3,
414 "svg": [
414 "svg": [
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415 "<svg height=\"115.02pt\" id=\"svg2\" inkscape:version=\"0.43\" sodipodi:docbase=\"/home/sdeibel\" sodipodi:docname=\"logo-python-generic.svg\" sodipodi:version=\"0.32\" version=\"1.0\" width=\"388.84pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:cc=\"http://web.resource.org/cc/\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:inkscape=\"http://www.inkscape.org/namespaces/inkscape\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\" xmlns:sodipodi=\"http://inkscape.sourceforge.net/DTD/sodipodi-0.dtd\" xmlns:svg=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">",
416 " <metadata id=\"metadata2193\">",
416 " <metadata id=\"metadata2193\">",
417 " <rdf:RDF>",
417 " <rdf:RDF>",
418 " <cc:Work rdf:about=\"\">",
418 " <cc:Work rdf:about=\"\">",
419 " <dc:format>image/svg+xml</dc:format>",
419 " <dc:format>image/svg+xml</dc:format>",
420 " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>",
420 " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>",
421 " </cc:Work>",
421 " </cc:Work>",
422 " </rdf:RDF>",
422 " </rdf:RDF>",
423 " </metadata>",
423 " </metadata>",
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424 " <sodipodi:namedview bordercolor=\"#666666\" borderopacity=\"1.0\" id=\"base\" inkscape:current-layer=\"svg2\" inkscape:cx=\"243.02499\" inkscape:cy=\"71.887497\" inkscape:pageopacity=\"0.0\" inkscape:pageshadow=\"2\" inkscape:window-height=\"543\" inkscape:window-width=\"791\" inkscape:window-x=\"0\" inkscape:window-y=\"0\" inkscape:zoom=\"1.4340089\" pagecolor=\"#ffffff\"/>",
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426 " <linearGradient id=\"linearGradient2795\">",
427 " <stop id=\"stop2797\" offset=\"0\" style=\"stop-color:#b8b8b8;stop-opacity:0.49803922\"/>",
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428 " <stop id=\"stop2799\" offset=\"1\" style=\"stop-color:#7f7f7f;stop-opacity:0\"/>",
428 " <stop id=\"stop2799\" offset=\"1\" style=\"stop-color:#7f7f7f;stop-opacity:0\"/>",
429 " </linearGradient>",
429 " </linearGradient>",
430 " <linearGradient id=\"linearGradient2787\">",
430 " <linearGradient id=\"linearGradient2787\">",
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432 " <stop id=\"stop2791\" offset=\"1\" style=\"stop-color:#7f7f7f;stop-opacity:0\"/>",
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474 " </g>",
474 " </g>",
475 "</svg>"
475 "</svg>"
476 ],
476 ],
477 "text": [
477 "text": [
478 "&lt;IPython.core.display.SVG at 0x41d4910&gt;"
478 "&lt;IPython.core.display.SVG at 0x41d4910&gt;"
479 ]
479 ]
480 }
480 }
481 ],
481 ],
482 "prompt_number": 3
482 "prompt_number": 3
483 },
483 },
484 {
484 {
485 "cell_type": "markdown",
485 "cell_type": "markdown",
486 "source": [
486 "source": [
487 "### Video"
487 "### Video"
488 ]
488 ]
489 },
489 },
490 {
490 {
491 "cell_type": "markdown",
491 "cell_type": "markdown",
492 "source": [
492 "source": [
493 "And more exotic objects can also be displayed, as long as their representation supports ",
493 "And more exotic objects can also be displayed, as long as their representation supports ",
494 "the IPython display protocol.",
494 "the IPython display protocol.",
495 "",
495 "",
496 "For example, videos hosted externally on YouTube are easy to load (and writing a similar wrapper for other",
496 "For example, videos hosted externally on YouTube are easy to load (and writing a similar wrapper for other",
497 "hosted content is trivial):"
497 "hosted content is trivial):"
498 ]
498 ]
499 },
499 },
500 {
500 {
501 "cell_type": "code",
501 "cell_type": "code",
502 "collapsed": false,
502 "collapsed": false,
503 "input": [
503 "input": [
504 "from IPython.lib.display import YouTubeVideo",
504 "from IPython.lib.display import YouTubeVideo",
505 "# a talk about IPython at Sage Days at U. Washington, Seattle.",
505 "# a talk about IPython at Sage Days at U. Washington, Seattle.",
506 "# Video credit: William Stein.",
506 "# Video credit: William Stein.",
507 "YouTubeVideo('1j_HxD4iLn8')"
507 "YouTubeVideo('1j_HxD4iLn8')"
508 ],
508 ],
509 "language": "python",
509 "language": "python",
510 "outputs": [
510 "outputs": [
511 {
511 {
512 "html": [
512 "html": [
513 "",
513 "",
514 " <iframe",
514 " <iframe",
515 " width=\"400\"",
515 " width=\"400\"",
516 " height=\"300\"",
516 " height=\"300\"",
517 " src=\"http://www.youtube.com/embed/1j_HxD4iLn8\"",
517 " src=\"http://www.youtube.com/embed/1j_HxD4iLn8\"",
518 " frameborder=\"0\"",
518 " frameborder=\"0\"",
519 " allowfullscreen",
519 " allowfullscreen",
520 " ></iframe>",
520 " ></iframe>",
521 " "
521 " "
522 ],
522 ],
523 "output_type": "pyout",
523 "output_type": "pyout",
524 "prompt_number": 4,
524 "prompt_number": 4,
525 "text": [
525 "text": [
526 "&lt;IPython.lib.display.YouTubeVideo at 0x41d4310&gt;"
526 "&lt;IPython.lib.display.YouTubeVideo at 0x41d4310&gt;"
527 ]
527 ]
528 }
528 }
529 ],
529 ],
530 "prompt_number": 4
530 "prompt_number": 4
531 },
531 },
532 {
532 {
533 "cell_type": "markdown",
533 "cell_type": "markdown",
534 "source": [
534 "source": [
535 "Using the nascent video capabilities of modern browsers, you may also be able to display local",
535 "Using the nascent video capabilities of modern browsers, you may also be able to display local",
536 "videos. At the moment this doesn't work very well in all browsers, so it may or may not work for you;",
536 "videos. At the moment this doesn't work very well in all browsers, so it may or may not work for you;",
537 "we will continue testing this and looking for ways to make it more robust. ",
537 "we will continue testing this and looking for ways to make it more robust. ",
538 "",
538 "",
539 "The following cell loads a local file called `animation.m4v`, encodes the raw video as base64 for http",
539 "The following cell loads a local file called `animation.m4v`, encodes the raw video as base64 for http",
540 "transport, and uses the HTML5 video tag to load it. On Chrome 15 it works correctly, displaying a control",
540 "transport, and uses the HTML5 video tag to load it. On Chrome 15 it works correctly, displaying a control",
541 "bar at the bottom with a play/pause button and a location slider."
541 "bar at the bottom with a play/pause button and a location slider."
542 ]
542 ]
543 },
543 },
544 {
544 {
545 "cell_type": "code",
545 "cell_type": "code",
546 "collapsed": false,
546 "collapsed": false,
547 "input": [
547 "input": [
548 "from IPython.core.display import HTML",
548 "from IPython.core.display import HTML",
549 "video = open(\"animation.m4v\", \"rb\").read()",
549 "video = open(\"animation.m4v\", \"rb\").read()",
550 "video_encoded = video.encode(\"base64\")",
550 "video_encoded = video.encode(\"base64\")",
551 "video_tag = '<video controls alt=\"test\" src=\"data:video/x-m4v;base64,{0}\">'.format(video_encoded)",
551 "video_tag = '<video controls alt=\"test\" src=\"data:video/x-m4v;base64,{0}\">'.format(video_encoded)",
552 "HTML(data=video_tag)"
552 "HTML(data=video_tag)"
553 ],
553 ],
554 "language": "python",
554 "language": "python",
555 "outputs": [
555 "outputs": [
556 {
556 {
557 "html": [
557 "html": [
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558 "<video controls alt=\"test\" src=\"data:video/x-m4v;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAAqiW1kYXQAAAKMBgX//4jcRem9",
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767 "\">"
767 "\">"
768 ],
768 ],
769 "output_type": "pyout",
769 "output_type": "pyout",
770 "prompt_number": 5,
770 "prompt_number": 5,
771 "text": [
771 "text": [
772 "&lt;IPython.core.display.HTML at 0x423a550&gt;"
772 "&lt;IPython.core.display.HTML at 0x423a550&gt;"
773 ]
773 ]
774 }
774 }
775 ],
775 ],
776 "prompt_number": 5
776 "prompt_number": 5
777 },
777 },
778 {
778 {
779 "cell_type": "markdown",
779 "cell_type": "markdown",
780 "source": [
780 "source": [
781 "## Local Files",
781 "## Local Files",
782 "",
782 "",
783 "The above examples embed images and video from the notebook filesystem in the output",
783 "The above examples embed images and video from the notebook filesystem in the output",
784 "areas of code cells. It is also possible to request these files directly in markdown cells",
784 "areas of code cells. It is also possible to request these files directly in markdown cells",
785 "if they reside in the notebook directory via relative urls prefixed with `files/`:",
785 "if they reside in the notebook directory via relative urls prefixed with `files/`:",
786 "",
786 "",
787 " files/[subdirectory/]<filename>",
787 " files/[subdirectory/]<filename>",
788 "",
788 "",
789 "",
789 "",
790 "For example, in the example notebook folder, we have the Python logo, addressed as:",
790 "For example, in the example notebook folder, we have the Python logo, addressed as:",
791 "",
791 "",
792 " <img src=\"files/python-logo.svg\" />",
792 " <img src=\"files/python-logo.svg\" />",
793 "",
793 "",
794 "<img src=\"/files/python-logo.svg\" />",
794 "<img src=\"/files/python-logo.svg\" />",
795 "",
795 "",
796 "and a video with the HTML5 video tag:",
796 "and a video with the HTML5 video tag:",
797 "",
797 "",
798 " <video controls src=\"files/animation.m4v\" />",
798 " <video controls src=\"files/animation.m4v\" />",
799 "",
799 "",
800 "<video controls src=\"/files/animation.m4v\" />",
800 "<video controls src=\"/files/animation.m4v\" />",
801 "",
801 "",
802 "These do not embed the data into the notebook file,",
802 "These do not embed the data into the notebook file,",
803 "and require that the files exist when you are viewing the notebook.",
803 "and require that the files exist when you are viewing the notebook.",
804 "",
804 "",
805 "### Security of local files",
805 "### Security of local files",
806 "",
806 "",
807 "Note that this means that the IPython notebook server also acts as a generic file server",
807 "Note that this means that the IPython notebook server also acts as a generic file server",
808 "for files inside the same tree as your notebooks. Access is not granted outside the",
808 "for files inside the same tree as your notebooks. Access is not granted outside the",
809 "notebook folder so you have strict control over what files are visible, but for this",
809 "notebook folder so you have strict control over what files are visible, but for this",
810 "reason it is highly recommended that you do not run the notebook server with a notebook",
810 "reason it is highly recommended that you do not run the notebook server with a notebook",
811 "directory at a high level in your filesystem (e.g. your home directory).",
811 "directory at a high level in your filesystem (e.g. your home directory).",
812 "",
812 "",
813 "When you run the notebook in a password-protected manner, local file access is restricted",
813 "When you run the notebook in a password-protected manner, local file access is restricted",
814 "to authenticated users unless read-only views are active."
814 "to authenticated users unless read-only views are active."
815 ]
815 ]
816 },
816 },
817 {
817 {
818 "cell_type": "markdown",
818 "cell_type": "markdown",
819 "source": [
819 "source": [
820 "### External sites",
820 "### External sites",
821 "",
821 "",
822 "You can even embed an entire page from another site in an iframe; for example this is today's Wikipedia",
822 "You can even embed an entire page from another site in an iframe; for example this is today's Wikipedia",
823 "page for mobile users:"
823 "page for mobile users:"
824 ]
824 ]
825 },
825 },
826 {
826 {
827 "cell_type": "code",
827 "cell_type": "code",
828 "collapsed": false,
828 "collapsed": false,
829 "input": [
829 "input": [
830 "HTML('<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350>')"
830 "HTML('<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350>')"
831 ],
831 ],
832 "language": "python",
832 "language": "python",
833 "outputs": [
833 "outputs": [
834 {
834 {
835 "html": [
835 "html": [
836 "<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350>"
836 "<iframe src=http://en.mobile.wikipedia.org/?useformat=mobile width=700 height=350>"
837 ],
837 ],
838 "output_type": "pyout",
838 "output_type": "pyout",
839 "prompt_number": 6,
839 "prompt_number": 6,
840 "text": [
840 "text": [
841 "&lt;IPython.core.display.HTML at 0x41d4710&gt;"
841 "&lt;IPython.core.display.HTML at 0x41d4710&gt;"
842 ]
842 ]
843 }
843 }
844 ],
844 ],
845 "prompt_number": 6
845 "prompt_number": 6
846 },
846 },
847 {
847 {
848 "cell_type": "markdown",
848 "cell_type": "markdown",
849 "source": [
849 "source": [
850 "### Mathematics",
850 "### Mathematics",
851 "",
851 "",
852 "And we also support the display of mathematical expressions typeset in LaTeX, which is rendered",
852 "And we also support the display of mathematical expressions typeset in LaTeX, which is rendered",
853 "in the browser thanks to the [MathJax library](http://mathjax.org). ",
853 "in the browser thanks to the [MathJax library](http://mathjax.org). ",
854 "",
854 "",
855 "Note that this is *different* from the above examples. Above we were typing mathematical expressions",
855 "Note that this is *different* from the above examples. Above we were typing mathematical expressions",
856 "in Markdown cells (along with normal text) and letting the browser render them; now we are displaying",
856 "in Markdown cells (along with normal text) and letting the browser render them; now we are displaying",
857 "the output of a Python computation as a LaTeX expression wrapped by the `Math()` object so the browser",
857 "the output of a Python computation as a LaTeX expression wrapped by the `Math()` object so the browser",
858 "renders it:"
858 "renders it:"
859 ]
859 ]
860 },
860 },
861 {
861 {
862 "cell_type": "code",
862 "cell_type": "code",
863 "collapsed": false,
863 "collapsed": false,
864 "input": [
864 "input": [
865 "from IPython.core.display import Math",
865 "from IPython.core.display import Math",
866 "Math(r'$F(k) = \\int_{-\\infty}^{\\infty} f(x) e^{2\\pi i k} dx$')"
866 "Math(r'$F(k) = \\int_{-\\infty}^{\\infty} f(x) e^{2\\pi i k} dx$')"
867 ],
867 ],
868 "language": "python",
868 "language": "python",
869 "outputs": [
869 "outputs": [
870 {
870 {
871 "latex": [
871 "latex": [
872 "$F(k) = \\int_{-\\infty}^{\\infty} f(x) e^{2\\pi i k} dx$"
872 "$F(k) = \\int_{-\\infty}^{\\infty} f(x) e^{2\\pi i k} dx$"
873 ],
873 ],
874 "output_type": "pyout",
874 "output_type": "pyout",
875 "prompt_number": 8,
875 "prompt_number": 8,
876 "text": [
876 "text": [
877 "&lt;IPython.core.display.Math at 0x45840d0&gt;"
877 "&lt;IPython.core.display.Math at 0x45840d0&gt;"
878 ]
878 ]
879 }
879 }
880 ],
880 ],
881 "prompt_number": 8
881 "prompt_number": 8
882 },
882 },
883 {
883 {
884 "cell_type": "markdown",
884 "cell_type": "markdown",
885 "source": [
885 "source": [
886 "# Loading external codes",
886 "# Loading external codes",
887 "* Drag and drop a ``.py`` in the dashboard",
887 "* Drag and drop a ``.py`` in the dashboard",
888 "* Use ``%loadpy`` with any local or remote url: [the Matplotlib Gallery!](http://matplotlib.sourceforge.net/gallery.html)",
888 "* Use ``%loadpy`` with any local or remote url: [the Matplotlib Gallery!](http://matplotlib.sourceforge.net/gallery.html)",
889 "",
889 "",
890 "In this notebook we've kept the output saved so you can see the result, but you should run the next",
890 "In this notebook we've kept the output saved so you can see the result, but you should run the next",
891 "cell yourself (with an active internet connection)."
891 "cell yourself (with an active internet connection)."
892 ]
892 ]
893 },
893 },
894 {
894 {
895 "cell_type": "code",
895 "cell_type": "code",
896 "collapsed": true,
896 "collapsed": true,
897 "input": [
897 "input": [
898 "%loadpy http://matplotlib.sourceforge.net/mpl_examples/pylab_examples/integral_demo.py"
898 "%loadpy http://matplotlib.sourceforge.net/mpl_examples/pylab_examples/integral_demo.py"
899 ],
899 ],
900 "language": "python",
900 "language": "python",
901 "outputs": [],
901 "outputs": [],
902 "prompt_number": 8
902 "prompt_number": 8
903 },
903 },
904 {
904 {
905 "cell_type": "code",
905 "cell_type": "code",
906 "collapsed": false,
906 "collapsed": false,
907 "input": [
907 "input": [
908 "#!/usr/bin/env python",
908 "#!/usr/bin/env python",
909 "",
909 "",
910 "# implement the example graphs/integral from pyx",
910 "# implement the example graphs/integral from pyx",
911 "from pylab import *",
911 "from pylab import *",
912 "from matplotlib.patches import Polygon",
912 "from matplotlib.patches import Polygon",
913 "",
913 "",
914 "def func(x):",
914 "def func(x):",
915 " return (x-3)*(x-5)*(x-7)+85",
915 " return (x-3)*(x-5)*(x-7)+85",
916 "",
916 "",
917 "ax = subplot(111)",
917 "ax = subplot(111)",
918 "",
918 "",
919 "a, b = 2, 9 # integral area",
919 "a, b = 2, 9 # integral area",
920 "x = arange(0, 10, 0.01)",
920 "x = arange(0, 10, 0.01)",
921 "y = func(x)",
921 "y = func(x)",
922 "plot(x, y, linewidth=1)",
922 "plot(x, y, linewidth=1)",
923 "",
923 "",
924 "# make the shaded region",
924 "# make the shaded region",
925 "ix = arange(a, b, 0.01)",
925 "ix = arange(a, b, 0.01)",
926 "iy = func(ix)",
926 "iy = func(ix)",
927 "verts = [(a,0)] + zip(ix,iy) + [(b,0)]",
927 "verts = [(a,0)] + zip(ix,iy) + [(b,0)]",
928 "poly = Polygon(verts, facecolor='0.8', edgecolor='k')",
928 "poly = Polygon(verts, facecolor='0.8', edgecolor='k')",
929 "ax.add_patch(poly)",
929 "ax.add_patch(poly)",
930 "",
930 "",
931 "text(0.5 * (a + b), 30,",
931 "text(0.5 * (a + b), 30,",
932 " r\"$\\int_a^b f(x)\\mathrm{d}x$\", horizontalalignment='center',",
932 " r\"$\\int_a^b f(x)\\mathrm{d}x$\", horizontalalignment='center',",
933 " fontsize=20)",
933 " fontsize=20)",
934 "",
934 "",
935 "axis([0,10, 0, 180])",
935 "axis([0,10, 0, 180])",
936 "figtext(0.9, 0.05, 'x')",
936 "figtext(0.9, 0.05, 'x')",
937 "figtext(0.1, 0.9, 'y')",
937 "figtext(0.1, 0.9, 'y')",
938 "ax.set_xticks((a,b))",
938 "ax.set_xticks((a,b))",
939 "ax.set_xticklabels(('a','b'))",
939 "ax.set_xticklabels(('a','b'))",
940 "ax.set_yticks([])",
940 "ax.set_yticks([])",
941 "show()"
941 "show()"
942 ],
942 ],
943 "language": "python",
943 "language": "python",
944 "outputs": [
944 "outputs": [
945 {
945 {
946 "output_type": "display_data",
946 "output_type": "display_data",
947 "png": 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947 "png": 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948 }
948 }
949 ],
949 ],
950 "prompt_number": 9
950 "prompt_number": 9
951 },
951 },
952 {
952 {
953 "cell_type": "code",
953 "cell_type": "code",
954 "collapsed": true,
954 "collapsed": true,
955 "input": [],
955 "input": [],
956 "language": "python",
956 "language": "python",
957 "outputs": []
957 "outputs": []
958 }
958 }
959 ]
959 ]
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1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "01_notebook_introduction"
3 "name": "01_notebook_introduction"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# An introduction to the IPython notebook",
12 "# An introduction to the IPython notebook",
13 "",
13 "",
14 "The IPython web notebook is a frontend that allows for new modes",
14 "The IPython web notebook is a frontend that allows for new modes",
15 "of interaction with IPython: this web-based interface allows you to execute Python and IPython",
15 "of interaction with IPython: this web-based interface allows you to execute Python and IPython",
16 "commands in each input cell just like you would at the IPython terminal or Qt console, but you can",
16 "commands in each input cell just like you would at the IPython terminal or Qt console, but you can",
17 "also save an entire session as a document in a file with the `.ipynb` extension.",
17 "also save an entire session as a document in a file with the `.ipynb` extension.",
18 "",
18 "",
19 "The document you are reading now is precisely an example of one such notebook, and we will show you",
19 "The document you are reading now is precisely an example of one such notebook, and we will show you",
20 "here how to best use this new interface.",
20 "here how to best use this new interface.",
21 "",
21 "",
22 "The first thing to understand is that a notebook consists of a sequence of 'cells' that can contain ",
22 "The first thing to understand is that a notebook consists of a sequence of 'cells' that can contain ",
23 "either text (such as this one) or code meant for execution (such as the next one):",
23 "either text (such as this one) or code meant for execution (such as the next one):",
24 "",
24 "",
25 "* Text cells can be written using [Markdown syntax](http://daringfireball.net/projects/markdown/syntax) ",
25 "* Text cells can be written using [Markdown syntax](http://daringfireball.net/projects/markdown/syntax) ",
26 "(in a future release we will also provide support for reStructuredText and Sphinx integration, and we ",
26 "(in a future release we will also provide support for reStructuredText and Sphinx integration, and we ",
27 "welcome help from interested contributors to make that happen).",
27 "welcome help from interested contributors to make that happen).",
28 "",
28 "",
29 "* Code cells take IPython input (i.e. Python code, `%magics`, `!system calls`, etc) like IPython at",
29 "* Code cells take IPython input (i.e. Python code, `%magics`, `!system calls`, etc) like IPython at",
30 "the terminal or at the Qt Console. The only difference is that in order to execute a cell, you *must*",
30 "the terminal or at the Qt Console. The only difference is that in order to execute a cell, you *must*",
31 "use `Shift-Enter`, as pressing `Enter` will add a new line of text to the cell. When you type ",
31 "use `Shift-Enter`, as pressing `Enter` will add a new line of text to the cell. When you type ",
32 "`Shift-Enter`, the cell content is executed, output displayed and a new cell is created below. Try",
32 "`Shift-Enter`, the cell content is executed, output displayed and a new cell is created below. Try",
33 "it now by putting your cursor on the next cell and typing `Shift-Enter`:"
33 "it now by putting your cursor on the next cell and typing `Shift-Enter`:"
34 ]
34 ]
35 },
35 },
36 {
36 {
37 "cell_type": "code",
37 "cell_type": "code",
38 "collapsed": false,
38 "collapsed": false,
39 "input": [
39 "input": [
40 "\"This is the new IPython notebook\""
40 "\"This is the new IPython notebook\""
41 ],
41 ],
42 "language": "python",
42 "language": "python",
43 "outputs": [
43 "outputs": [
44 {
44 {
45 "output_type": "pyout",
45 "output_type": "pyout",
46 "prompt_number": 1,
46 "prompt_number": 1,
47 "text": [
47 "text": [
48 "'This is the new IPython notebook'"
48 "'This is the new IPython notebook'"
49 ]
49 ]
50 }
50 }
51 ],
51 ],
52 "prompt_number": 1
52 "prompt_number": 1
53 },
53 },
54 {
54 {
55 "cell_type": "markdown",
55 "cell_type": "markdown",
56 "source": [
56 "source": [
57 "You can re-execute the same cell over and over as many times as you want. Simply put your",
57 "You can re-execute the same cell over and over as many times as you want. Simply put your",
58 "cursor in the cell again, edit at will, and type `Shift-Enter` to execute. ",
58 "cursor in the cell again, edit at will, and type `Shift-Enter` to execute. ",
59 "",
59 "",
60 "**Tip:** A cell can also be executed",
60 "**Tip:** A cell can also be executed",
61 "*in-place*, where IPython executes its content but leaves the cursor in the same cell. This is done by",
61 "*in-place*, where IPython executes its content but leaves the cursor in the same cell. This is done by",
62 "typing `Ctrl-Enter` instead, and is useful if you want to quickly run a command to check something ",
62 "typing `Ctrl-Enter` instead, and is useful if you want to quickly run a command to check something ",
63 "before tping the real content you want to leave in the cell. For example, in the next cell, try issuing",
63 "before tping the real content you want to leave in the cell. For example, in the next cell, try issuing",
64 "several system commands in-place with `Ctrl-Enter`, such as `pwd` and then `ls`:"
64 "several system commands in-place with `Ctrl-Enter`, such as `pwd` and then `ls`:"
65 ]
65 ]
66 },
66 },
67 {
67 {
68 "cell_type": "code",
68 "cell_type": "code",
69 "collapsed": false,
69 "collapsed": false,
70 "input": [
70 "input": [
71 "ls"
71 "ls"
72 ],
72 ],
73 "language": "python",
73 "language": "python",
74 "outputs": [
74 "outputs": [
75 {
75 {
76 "output_type": "stream",
76 "output_type": "stream",
77 "stream": "stdout",
77 "stream": "stdout",
78 "text": [
78 "text": [
79 "00_notebook_tour.ipynb formatting.ipynb sympy_quantum_computing.ipynb",
79 "00_notebook_tour.ipynb formatting.ipynb sympy_quantum_computing.ipynb",
80 "01_notebook_introduction.ipynb python-logo.svg trapezoid_rule.ipynb",
80 "01_notebook_introduction.ipynb python-logo.svg trapezoid_rule.ipynb",
81 "display_protocol.ipynb sympy.ipynb"
81 "display_protocol.ipynb sympy.ipynb"
82 ]
82 ]
83 }
83 }
84 ],
84 ],
85 "prompt_number": 2
85 "prompt_number": 2
86 },
86 },
87 {
87 {
88 "cell_type": "markdown",
88 "cell_type": "markdown",
89 "source": [
89 "source": [
90 "In a cell, you can type anything from a single python expression to an arbitrarily long amount of code ",
90 "In a cell, you can type anything from a single python expression to an arbitrarily long amount of code ",
91 "(although for reasons of readability, you should probably limit this to a few dozen lines):"
91 "(although for reasons of readability, you should probably limit this to a few dozen lines):"
92 ]
92 ]
93 },
93 },
94 {
94 {
95 "cell_type": "code",
95 "cell_type": "code",
96 "collapsed": false,
96 "collapsed": false,
97 "input": [
97 "input": [
98 "def f(x):",
98 "def f(x):",
99 " \"\"\"My function",
99 " \"\"\"My function",
100 " x : parameter\"\"\"",
100 " x : parameter\"\"\"",
101 " ",
101 " ",
102 " return x+1",
102 " return x+1",
103 "",
103 "",
104 "print \"f(3) = \", f(3)"
104 "print \"f(3) = \", f(3)"
105 ],
105 ],
106 "language": "python",
106 "language": "python",
107 "outputs": [
107 "outputs": [
108 {
108 {
109 "output_type": "stream",
109 "output_type": "stream",
110 "stream": "stdout",
110 "stream": "stdout",
111 "text": [
111 "text": [
112 "f(3) = 4"
112 "f(3) = 4"
113 ]
113 ]
114 }
114 }
115 ],
115 ],
116 "prompt_number": 3
116 "prompt_number": 3
117 },
117 },
118 {
118 {
119 "cell_type": "markdown",
119 "cell_type": "markdown",
120 "source": [
120 "source": [
121 "## User interface",
121 "## User interface",
122 "",
122 "",
123 "When you start a new notebook server with `ipython notebook`, your",
123 "When you start a new notebook server with `ipython notebook`, your",
124 "browser should open into the *Dashboard*, a page listing all notebooks",
124 "browser should open into the *Dashboard*, a page listing all notebooks",
125 "available in the current directory as well as letting you create new",
125 "available in the current directory as well as letting you create new",
126 "notebooks. In this page, you can also drag and drop existing `.py` files",
126 "notebooks. In this page, you can also drag and drop existing `.py` files",
127 "over the file list to import them as notebooks (see the manual for ",
127 "over the file list to import them as notebooks (see the manual for ",
128 "[further details on how these files are ",
128 "[further details on how these files are ",
129 "interpreted](http://ipython.org/ipython-doc/stable/interactive/htmlnotebook.html)).",
129 "interpreted](http://ipython.org/ipython-doc/stable/interactive/htmlnotebook.html)).",
130 "",
130 "",
131 "Once you open an existing notebook (like this one) or create a new one,",
131 "Once you open an existing notebook (like this one) or create a new one,",
132 "you are in the main notebook interface, which consists of a main editing",
132 "you are in the main notebook interface, which consists of a main editing",
133 "area (where these cells are contained) as well as a collapsible left panel, ",
133 "area (where these cells are contained) as well as a collapsible left panel, ",
134 "a permanent header area at the top, and a pager that rises from the",
134 "a permanent header area at the top, and a pager that rises from the",
135 "bottom when needed and can be collapsed again."
135 "bottom when needed and can be collapsed again."
136 ]
136 ]
137 },
137 },
138 {
138 {
139 "cell_type": "markdown",
139 "cell_type": "markdown",
140 "source": [
140 "source": [
141 "### Main editing area",
141 "### Main editing area",
142 "",
142 "",
143 "Here, you can move with the arrow keys or using the ",
143 "Here, you can move with the arrow keys or using the ",
144 "scroll bars. The cursor enters code cells immediately, but only selects",
144 "scroll bars. The cursor enters code cells immediately, but only selects",
145 "text (markdown) cells without entering in them; to enter a text cell,",
145 "text (markdown) cells without entering in them; to enter a text cell,",
146 "use `Enter`, and `Shift-Enter` to exit it again (just like to execute a ",
146 "use `Enter`, and `Shift-Enter` to exit it again (just like to execute a ",
147 "code cell)."
147 "code cell)."
148 ]
148 ]
149 },
149 },
150 {
150 {
151 "cell_type": "markdown",
151 "cell_type": "markdown",
152 "source": [
152 "source": [
153 "### Left panel",
153 "### Left panel",
154 "",
154 "",
155 "This panel contains a number of panes that can be",
155 "This panel contains a number of panes that can be",
156 "collapsed vertically by clicking on their title bar, and the whole panel",
156 "collapsed vertically by clicking on their title bar, and the whole panel",
157 "can also be collapsed by clicking on the vertical divider (note that you",
157 "can also be collapsed by clicking on the vertical divider (note that you",
158 "can not *drag* the divider, for now you can only click on it).",
158 "can not *drag* the divider, for now you can only click on it).",
159 "",
159 "",
160 "The *Notebook* section contains actions that pertain to the whole notebook,",
160 "The *Notebook* section contains actions that pertain to the whole notebook,",
161 "such as downloading the current notebook either in its original format",
161 "such as downloading the current notebook either in its original format",
162 "or as a `.py` script, and printing it. When you click the `Print` button,",
162 "or as a `.py` script, and printing it. When you click the `Print` button,",
163 "a new HTML page opens with a static copy of the notebook; you can then",
163 "a new HTML page opens with a static copy of the notebook; you can then",
164 "use your web browser's mechanisms to save or print this file.",
164 "use your web browser's mechanisms to save or print this file.",
165 "",
165 "",
166 "The *Cell* section lets you manipulate individual cells, and the names should ",
166 "The *Cell* section lets you manipulate individual cells, and the names should ",
167 "be fairly self-explanatory.",
167 "be fairly self-explanatory.",
168 "",
168 "",
169 "The *Kernel* section lets you signal the kernel executing your code. ",
169 "The *Kernel* section lets you signal the kernel executing your code. ",
170 "`Interrupt` does the equivalent of hitting `Ctrl-C` at a terminal, and",
170 "`Interrupt` does the equivalent of hitting `Ctrl-C` at a terminal, and",
171 "`Restart` fully kills the kernel process and starts a fresh one. Obviously",
171 "`Restart` fully kills the kernel process and starts a fresh one. Obviously",
172 "this means that all your previous variables are destroyed, but it also",
172 "this means that all your previous variables are destroyed, but it also",
173 "makes it easy to get a fresh kernel in which to re-execute a notebook, perhaps",
173 "makes it easy to get a fresh kernel in which to re-execute a notebook, perhaps",
174 "after changing an extension module for which Python's `reload` mechanism",
174 "after changing an extension module for which Python's `reload` mechanism",
175 "does not work. If you check the 'Kill kernel upon exit' box, when you ",
175 "does not work. If you check the 'Kill kernel upon exit' box, when you ",
176 "close the page IPython will automatically shut down the running kernel;",
176 "close the page IPython will automatically shut down the running kernel;",
177 "otherwise the kernels won't close until you stop the whole ",
177 "otherwise the kernels won't close until you stop the whole ",
178 "",
178 "",
179 "The *Help* section contains links to the documentation of some projects",
179 "The *Help* section contains links to the documentation of some projects",
180 "closely related to IPython as well as the minimal keybindings you need to",
180 "closely related to IPython as well as the minimal keybindings you need to",
181 "know. But you should use `Ctrl-m h` (or click the `QuickHelp` button at",
181 "know. But you should use `Ctrl-m h` (or click the `QuickHelp` button at",
182 "the top) and learn some of the other keybindings, as it will make your ",
182 "the top) and learn some of the other keybindings, as it will make your ",
183 "workflow much more fluid and efficient.",
183 "workflow much more fluid and efficient.",
184 "",
184 "",
185 "The *Configuration* section at the bottom lets you change some values",
185 "The *Configuration* section at the bottom lets you change some values",
186 "related to the display of tooltips and the behavior of the tab completer."
186 "related to the display of tooltips and the behavior of the tab completer."
187 ]
187 ]
188 },
188 },
189 {
189 {
190 "cell_type": "markdown",
190 "cell_type": "markdown",
191 "source": [
191 "source": [
192 "### Header bar",
192 "### Header bar",
193 "",
193 "",
194 "The header area at the top allows you to rename an existing ",
194 "The header area at the top allows you to rename an existing ",
195 "notebook and open up a short help tooltip. This area also indicates",
195 "notebook and open up a short help tooltip. This area also indicates",
196 "with a red **Busy** mark on the right whenever the kernel is busy executing",
196 "with a red **Busy** mark on the right whenever the kernel is busy executing",
197 "code."
197 "code."
198 ]
198 ]
199 },
199 },
200 {
200 {
201 "cell_type": "markdown",
201 "cell_type": "markdown",
202 "source": [
202 "source": [
203 "### The pager at the bottom",
203 "### The pager at the bottom",
204 "",
204 "",
205 "Whenever IPython needs to display additional ",
205 "Whenever IPython needs to display additional ",
206 "information, such as when you type `somefunction?` in a cell, the notebook",
206 "information, such as when you type `somefunction?` in a cell, the notebook",
207 "opens a pane at the bottom where this information is shown. You can keep",
207 "opens a pane at the bottom where this information is shown. You can keep",
208 "this pager pane open for reference (it doesn't block input in the main area)",
208 "this pager pane open for reference (it doesn't block input in the main area)",
209 "or dismiss it by clicking on its divider bar."
209 "or dismiss it by clicking on its divider bar."
210 ]
210 ]
211 },
211 },
212 {
212 {
213 "cell_type": "markdown",
213 "cell_type": "markdown",
214 "source": [
214 "source": [
215 "### Tab completion and tooltips",
215 "### Tab completion and tooltips",
216 "",
216 "",
217 "The notebook uses the same underlying machinery for tab completion that ",
217 "The notebook uses the same underlying machinery for tab completion that ",
218 "IPython uses at the terminal, but displays the information differently.",
218 "IPython uses at the terminal, but displays the information differently.",
219 "Whey you complete with the `Tab` key, IPython shows a drop list with all",
219 "Whey you complete with the `Tab` key, IPython shows a drop list with all",
220 "available completions. If you type more characters while this list is open,",
220 "available completions. If you type more characters while this list is open,",
221 "IPython automatically eliminates from the list options that don't match the",
221 "IPython automatically eliminates from the list options that don't match the",
222 "new characters; once there is only one option left you can hit `Tab` once",
222 "new characters; once there is only one option left you can hit `Tab` once",
223 "more (or `Enter`) to complete. You can also select the completion you",
223 "more (or `Enter`) to complete. You can also select the completion you",
224 "want with the arrow keys or the mouse, and then hit `Enter`.",
224 "want with the arrow keys or the mouse, and then hit `Enter`.",
225 "",
225 "",
226 "In addition, if you hit `Tab` inside of open parentheses, IPython will ",
226 "In addition, if you hit `Tab` inside of open parentheses, IPython will ",
227 "search for the docstring of the last object left of the parens and will",
227 "search for the docstring of the last object left of the parens and will",
228 "display it on a tooltip. For example, type `list(<TAB>` and you will",
228 "display it on a tooltip. For example, type `list(<TAB>` and you will",
229 "see the docstring for the builtin `list` constructor:"
229 "see the docstring for the builtin `list` constructor:"
230 ]
230 ]
231 },
231 },
232 {
232 {
233 "cell_type": "code",
233 "cell_type": "code",
234 "collapsed": true,
234 "collapsed": true,
235 "input": [
235 "input": [
236 "# Position your cursor after the ( and hit the Tab key:",
236 "# Position your cursor after the ( and hit the Tab key:",
237 "list("
237 "list("
238 ],
238 ],
239 "language": "python",
239 "language": "python",
240 "outputs": []
240 "outputs": []
241 },
241 },
242 {
242 {
243 "cell_type": "markdown",
243 "cell_type": "markdown",
244 "source": [
244 "source": [
245 "## The frontend/kernel model",
245 "## The frontend/kernel model",
246 "",
246 "",
247 "The IPython notebook works on a client/server model where an *IPython kernel*",
247 "The IPython notebook works on a client/server model where an *IPython kernel*",
248 "starts in a separate process and acts as a server to executes the code you type,",
248 "starts in a separate process and acts as a server to executes the code you type,",
249 "while the web browser provides acts as a client, providing a front end environment",
249 "while the web browser provides acts as a client, providing a front end environment",
250 "for you to type. But one kernel is capable of simultaneously talking to more than",
250 "for you to type. But one kernel is capable of simultaneously talking to more than",
251 "one client, and they do not all need to be of the same kind. All IPython frontends",
251 "one client, and they do not all need to be of the same kind. All IPython frontends",
252 "are capable of communicating with a kernel, and any number of them can be active",
252 "are capable of communicating with a kernel, and any number of them can be active",
253 "at the same time. In addition to allowing you to have, for example, more than one",
253 "at the same time. In addition to allowing you to have, for example, more than one",
254 "browser session active, this lets you connect clients with different user interface features.",
254 "browser session active, this lets you connect clients with different user interface features.",
255 "",
255 "",
256 "For example, you may want to connect a Qt console to your kernel and use it as a help",
256 "For example, you may want to connect a Qt console to your kernel and use it as a help",
257 "browser, calling `??` on objects in the Qt console (whose pager is more flexible than the",
257 "browser, calling `??` on objects in the Qt console (whose pager is more flexible than the",
258 "one in the notebook). You can start a new Qt console connected to your current kernel by ",
258 "one in the notebook). You can start a new Qt console connected to your current kernel by ",
259 "using the `%qtconsole` magic, this will automatically detect the necessary connection",
259 "using the `%qtconsole` magic, this will automatically detect the necessary connection",
260 "information.",
260 "information.",
261 "",
261 "",
262 "If you want to open one manually, or want to open a text console from a terminal, you can ",
262 "If you want to open one manually, or want to open a text console from a terminal, you can ",
263 "get your kernel's connection information with the `%connect_info` magic:"
263 "get your kernel's connection information with the `%connect_info` magic:"
264 ]
264 ]
265 },
265 },
266 {
266 {
267 "cell_type": "code",
267 "cell_type": "code",
268 "collapsed": false,
268 "collapsed": false,
269 "input": [
269 "input": [
270 "%connect_info"
270 "%connect_info"
271 ],
271 ],
272 "language": "python",
272 "language": "python",
273 "outputs": [
273 "outputs": [
274 {
274 {
275 "output_type": "stream",
275 "output_type": "stream",
276 "stream": "stdout",
276 "stream": "stdout",
277 "text": [
277 "text": [
278 "{",
278 "{",
279 " \"stdin_port\": 53970, ",
279 " \"stdin_port\": 53970, ",
280 " \"ip\": \"127.0.0.1\", ",
280 " \"ip\": \"127.0.0.1\", ",
281 " \"hb_port\": 53971, ",
281 " \"hb_port\": 53971, ",
282 " \"key\": \"30daac61-6b73-4bae-a7d9-9dca538794d5\", ",
282 " \"key\": \"30daac61-6b73-4bae-a7d9-9dca538794d5\", ",
283 " \"shell_port\": 53968, ",
283 " \"shell_port\": 53968, ",
284 " \"iopub_port\": 53969",
284 " \"iopub_port\": 53969",
285 "}",
285 "}",
286 "",
286 "",
287 "Paste the above JSON into a file, and connect with:",
287 "Paste the above JSON into a file, and connect with:",
288 " $> ipython <app> --existing <file>",
288 " $> ipython <app> --existing <file>",
289 "or, if you are local, you can connect with just:",
289 "or, if you are local, you can connect with just:",
290 " $> ipython <app> --existing kernel-dd85d1cc-c335-44f4-bed8-f1a2173a819a.json ",
290 " $> ipython <app> --existing kernel-dd85d1cc-c335-44f4-bed8-f1a2173a819a.json ",
291 "or even just:",
291 "or even just:",
292 " $> ipython <app> --existing ",
292 " $> ipython <app> --existing ",
293 "if this is the most recent IPython session you have started."
293 "if this is the most recent IPython session you have started."
294 ]
294 ]
295 }
295 }
296 ],
296 ],
297 "prompt_number": 4
297 "prompt_number": 4
298 },
298 },
299 {
299 {
300 "cell_type": "markdown",
300 "cell_type": "markdown",
301 "source": [
301 "source": [
302 "## The kernel's `raw_input` and `%debug`",
302 "## The kernel's `raw_input` and `%debug`",
303 "",
303 "",
304 "The one feature the notebook currently doesn't support as a client is the ability to send data to the kernel's",
304 "The one feature the notebook currently doesn't support as a client is the ability to send data to the kernel's",
305 "standard input socket. That is, if the kernel requires information to be typed interactively by calling the",
305 "standard input socket. That is, if the kernel requires information to be typed interactively by calling the",
306 "builtin `raw_input` function, the notebook will be blocked. This happens for example if you run a script",
306 "builtin `raw_input` function, the notebook will be blocked. This happens for example if you run a script",
307 "that queries interactively for parameters, and very importantly, is how the interactive IPython debugger that ",
307 "that queries interactively for parameters, and very importantly, is how the interactive IPython debugger that ",
308 "activates when you type `%debug` works.",
308 "activates when you type `%debug` works.",
309 "",
309 "",
310 "So, in order to be able to use `%debug` or anything else that requires `raw_input`, you can either use a Qt ",
310 "So, in order to be able to use `%debug` or anything else that requires `raw_input`, you can either use a Qt ",
311 "console or a terminal console:",
311 "console or a terminal console:",
312 "",
312 "",
313 "- From the notebook, typing `%qtconsole` finds all the necessary connection data for you.",
313 "- From the notebook, typing `%qtconsole` finds all the necessary connection data for you.",
314 "- From the terminal, first type `%connect_info` while still in the notebook, and then copy and paste the ",
314 "- From the terminal, first type `%connect_info` while still in the notebook, and then copy and paste the ",
315 "resulting information, using `qtconsole` or `console` depending on which type of client you want."
315 "resulting information, using `qtconsole` or `console` depending on which type of client you want."
316 ]
316 ]
317 },
317 },
318 {
318 {
319 "cell_type": "markdown",
319 "cell_type": "markdown",
320 "source": [
320 "source": [
321 "## Display of complex objects",
321 "## Display of complex objects",
322 "",
322 "",
323 "As the 'tour' notebook shows, the IPython notebook has fairly sophisticated display capabilities. In addition",
323 "As the 'tour' notebook shows, the IPython notebook has fairly sophisticated display capabilities. In addition",
324 "to the examples there, you can study the `display_protocol` notebook in this same examples folder, to ",
324 "to the examples there, you can study the `display_protocol` notebook in this same examples folder, to ",
325 "learn how to customize arbitrary objects (in your own code or external libraries) to display in the notebook",
325 "learn how to customize arbitrary objects (in your own code or external libraries) to display in the notebook",
326 "in any way you want, including graphical forms or mathematical expressions."
326 "in any way you want, including graphical forms or mathematical expressions."
327 ]
327 ]
328 },
328 },
329 {
329 {
330 "cell_type": "markdown",
330 "cell_type": "markdown",
331 "source": [
331 "source": [
332 "## Plotting support",
332 "## Plotting support",
333 "",
333 "",
334 "As we've explained already, the notebook is just another frontend talking to the same IPython kernel that",
334 "As we've explained already, the notebook is just another frontend talking to the same IPython kernel that",
335 "you're already familiar with, so the same options for plotting support apply.",
335 "you're already familiar with, so the same options for plotting support apply.",
336 "",
336 "",
337 "If you start the notebook with `--pylab`, you will get matplotlib's floating, interactive windows and you",
337 "If you start the notebook with `--pylab`, you will get matplotlib's floating, interactive windows and you",
338 "can call the `display` function to paste figures into the notebook document. If you start it with ",
338 "can call the `display` function to paste figures into the notebook document. If you start it with ",
339 "`--pylab inline`, all plots will appear inline automatically. In this regard, the notebook works identically",
339 "`--pylab inline`, all plots will appear inline automatically. In this regard, the notebook works identically",
340 "to the Qt console.",
340 "to the Qt console.",
341 "",
341 "",
342 "Note that if you start the notebook server with pylab support, *all* kernels are automatically started in",
342 "Note that if you start the notebook server with pylab support, *all* kernels are automatically started in",
343 "pylab mode and with the same choice of backend (i.e. floating windows or inline figures). But you can also",
343 "pylab mode and with the same choice of backend (i.e. floating windows or inline figures). But you can also",
344 "start the notebook server simply by typing `ipython notebook`, and then selectively turn on pylab support ",
344 "start the notebook server simply by typing `ipython notebook`, and then selectively turn on pylab support ",
345 "only for the notebooks you want by using the `%pylab` magic (see its docstring for details)."
345 "only for the notebooks you want by using the `%pylab` magic (see its docstring for details)."
346 ]
346 ]
347 },
347 },
348 {
348 {
349 "cell_type": "code",
349 "cell_type": "code",
350 "collapsed": false,
350 "collapsed": false,
351 "input": [
351 "input": [
352 "%pylab inline",
352 "%pylab inline",
353 "plot(rand(100))"
353 "plot(rand(100))"
354 ],
354 ],
355 "language": "python",
355 "language": "python",
356 "outputs": [
356 "outputs": [
357 {
357 {
358 "output_type": "stream",
358 "output_type": "stream",
359 "stream": "stdout",
359 "stream": "stdout",
360 "text": [
360 "text": [
361 "",
361 "",
362 "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].",
362 "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].",
363 "For more information, type 'help(pylab)'."
363 "For more information, type 'help(pylab)'."
364 ]
364 ]
365 },
365 },
366 {
366 {
367 "output_type": "pyout",
367 "output_type": "pyout",
368 "prompt_number": 5,
368 "prompt_number": 5,
369 "text": [
369 "text": [
370 "[<matplotlib.lines.Line2D at 0x11165bcd0>]"
370 "[<matplotlib.lines.Line2D at 0x11165bcd0>]"
371 ]
371 ]
372 },
372 },
373 {
373 {
374 "output_type": "display_data",
374 "output_type": "display_data",
375 "png": 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VuTa33grccQe50Tc18dvh7sMqBF9SEk9lVT8FrzMPPlc8eK8g68gIuf7Fxfwn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\nWXuGgto0Y8fyPy8Kgn/nHf57cSj4zZu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375 "png": 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KENI/dkzdg4/aoskrBQ+Ya9OYpuCp/w5kB1k7O0nQMmkFr0Lwfgp+dJTc1GgKm/szBwYI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\nWXuGgto0Y8fyPy8Kgn/nHf57cSj4zZu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376 }
376 }
377 ],
377 ],
378 "prompt_number": 5
378 "prompt_number": 5
379 },
379 },
380 {
380 {
381 "cell_type": "markdown",
381 "cell_type": "markdown",
382 "source": [
382 "source": [
383 "## Security",
383 "## Security",
384 "",
384 "",
385 "By default the notebook only listens on localhost, so it does not expose your computer to attacks coming from",
385 "By default the notebook only listens on localhost, so it does not expose your computer to attacks coming from",
386 "the internet. By default the notebook does not require any authentication, but you can configure it to",
386 "the internet. By default the notebook does not require any authentication, but you can configure it to",
387 "ask for a password before allowing access to the files. ",
387 "ask for a password before allowing access to the files. ",
388 "",
388 "",
389 "Furthermore, you can require the notebook to encrypt all communications by using SSL and making all connections",
389 "Furthermore, you can require the notebook to encrypt all communications by using SSL and making all connections",
390 "using the https protocol instead of plain http. This is a good idea if you decide to run your notebook on",
390 "using the https protocol instead of plain http. This is a good idea if you decide to run your notebook on",
391 "addresses that are visible from the internet. For further details on how to configure this, see the",
391 "addresses that are visible from the internet. For further details on how to configure this, see the",
392 "[security section](http://ipython.org/ipython-doc/stable/interactive/htmlnotebook.html#security) of the ",
392 "[security section](http://ipython.org/ipython-doc/stable/interactive/htmlnotebook.html#security) of the ",
393 "manual.",
393 "manual.",
394 "",
394 "",
395 "Finally, note that you can also run a notebook with the `--read-only` flag, which lets you provide access",
395 "Finally, note that you can also run a notebook with the `--read-only` flag, which lets you provide access",
396 "to your notebook documents to others without letting them execute code (which can be useful to broadcast",
396 "to your notebook documents to others without letting them execute code (which can be useful to broadcast",
397 "a computation to colleagues or students, for example). The read-only flag behaves differently depending",
397 "a computation to colleagues or students, for example). The read-only flag behaves differently depending",
398 "on whether the server has a password or not:",
398 "on whether the server has a password or not:",
399 "",
399 "",
400 "- Passwordless server: users directly see all notebooks in read-only mode.",
400 "- Passwordless server: users directly see all notebooks in read-only mode.",
401 "- Password-protected server: users can see all notebooks in read-only mode, but a login button is available",
401 "- Password-protected server: users can see all notebooks in read-only mode, but a login button is available",
402 "and once a user authenticates, he or she obtains write/execute privileges.",
402 "and once a user authenticates, he or she obtains write/execute privileges.",
403 "",
403 "",
404 "The first case above makes it easy to broadcast on the fly an existing notebook by simply starting a *second* ",
404 "The first case above makes it easy to broadcast on the fly an existing notebook by simply starting a *second* ",
405 "notebook server in the same directory as the first, but in read-only mode. This can be done without having",
405 "notebook server in the same directory as the first, but in read-only mode. This can be done without having",
406 "to configure a password first (which requires calling a hashing function and editing a configuration file)."
406 "to configure a password first (which requires calling a hashing function and editing a configuration file)."
407 ]
407 ]
408 },
408 },
409 {
409 {
410 "cell_type": "code",
410 "cell_type": "code",
411 "collapsed": true,
411 "collapsed": true,
412 "input": [],
412 "input": [],
413 "language": "python",
413 "language": "python",
414 "outputs": []
414 "outputs": []
415 }
415 }
416 ]
416 ]
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@@ -1,375 +1,375 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "display_protocol"
3 "name": "display_protocol"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# Using the IPython display protocol for your own objects",
12 "# Using the IPython display protocol for your own objects",
13 "",
13 "",
14 "IPython extends the idea of the ``__repr__`` method in Python to support multiple representations for a given",
14 "IPython extends the idea of the ``__repr__`` method in Python to support multiple representations for a given",
15 "object, which clients can use to display the object according to their capabilities. An object can return multiple",
15 "object, which clients can use to display the object according to their capabilities. An object can return multiple",
16 "representations of itself by implementing special methods, and you can also define at runtime custom display ",
16 "representations of itself by implementing special methods, and you can also define at runtime custom display ",
17 "functions for existing objects whose methods you can't or won't modify. In this notebook, we show how both approaches work.",
17 "functions for existing objects whose methods you can't or won't modify. In this notebook, we show how both approaches work.",
18 "",
18 "",
19 "<br/>",
19 "<br/>",
20 "**Note:** this notebook has had all output cells stripped out so we can include it in the IPython documentation with ",
20 "**Note:** this notebook has had all output cells stripped out so we can include it in the IPython documentation with ",
21 "a minimal file size. You'll need to manually execute the cells to see the output (you can run all of them with the ",
21 "a minimal file size. You'll need to manually execute the cells to see the output (you can run all of them with the ",
22 "\"Run All\" button, or execute each individually). You must start this notebook with",
22 "\"Run All\" button, or execute each individually). You must start this notebook with",
23 "<pre>",
23 "<pre>",
24 "ipython notebook --pylab inline",
24 "ipython notebook --pylab inline",
25 "</pre>",
25 "</pre>",
26 "",
26 "",
27 "to ensure pylab support is available for plots.",
27 "to ensure pylab support is available for plots.",
28 "",
28 "",
29 "## Custom-built classes with dedicated ``_repr_*_`` methods",
29 "## Custom-built classes with dedicated ``_repr_*_`` methods",
30 "",
30 "",
31 "In our first example, we illustrate how objects can expose directly to IPython special representations of",
31 "In our first example, we illustrate how objects can expose directly to IPython special representations of",
32 "themselves, by providing methods such as ``_repr_svg_``, ``_repr_png_``, ``_repr_latex_``, etc. For a full",
32 "themselves, by providing methods such as ``_repr_svg_``, ``_repr_png_``, ``_repr_latex_``, etc. For a full",
33 "list of the special ``_repr_*_`` methods supported, see the code in ``IPython.core.displaypub``.",
33 "list of the special ``_repr_*_`` methods supported, see the code in ``IPython.core.displaypub``.",
34 "",
34 "",
35 "As an illustration, we build a class that holds data generated by sampling a Gaussian distribution with given mean ",
35 "As an illustration, we build a class that holds data generated by sampling a Gaussian distribution with given mean ",
36 "and variance. The class can display itself in a variety of ways: as a LaTeX expression or as an image in PNG or SVG ",
36 "and variance. The class can display itself in a variety of ways: as a LaTeX expression or as an image in PNG or SVG ",
37 "format. Each frontend can then decide which representation it can handle.",
37 "format. Each frontend can then decide which representation it can handle.",
38 "Further, we illustrate how to expose directly to the user the ability to directly access the various alternate ",
38 "Further, we illustrate how to expose directly to the user the ability to directly access the various alternate ",
39 "representations (since by default displaying the object itself will only show one, and which is shown will depend on the ",
39 "representations (since by default displaying the object itself will only show one, and which is shown will depend on the ",
40 "required representations that even cache necessary data in cases where it may be expensive to compute.",
40 "required representations that even cache necessary data in cases where it may be expensive to compute.",
41 "",
41 "",
42 "The next cell defines the Gaussian class:"
42 "The next cell defines the Gaussian class:"
43 ]
43 ]
44 },
44 },
45 {
45 {
46 "cell_type": "code",
46 "cell_type": "code",
47 "collapsed": false,
47 "collapsed": false,
48 "input": [
48 "input": [
49 "from IPython.core.pylabtools import print_figure",
49 "from IPython.core.pylabtools import print_figure",
50 "from IPython.core.display import Image, SVG, Math",
50 "from IPython.core.display import Image, SVG, Math",
51 "",
51 "",
52 "class Gaussian(object):",
52 "class Gaussian(object):",
53 " \"\"\"A simple object holding data sampled from a Gaussian distribution.",
53 " \"\"\"A simple object holding data sampled from a Gaussian distribution.",
54 " \"\"\"",
54 " \"\"\"",
55 " def __init__(self, mean=0, std=1, size=1000):",
55 " def __init__(self, mean=0, std=1, size=1000):",
56 " self.data = np.random.normal(mean, std, size)",
56 " self.data = np.random.normal(mean, std, size)",
57 " self.mean = mean",
57 " self.mean = mean",
58 " self.std = std",
58 " self.std = std",
59 " self.size = size",
59 " self.size = size",
60 " # For caching plots that may be expensive to compute",
60 " # For caching plots that may be expensive to compute",
61 " self._png_data = None",
61 " self._png_data = None",
62 " self._svg_data = None",
62 " self._svg_data = None",
63 " ",
63 " ",
64 " def _figure_data(self, format):",
64 " def _figure_data(self, format):",
65 " fig, ax = plt.subplots()",
65 " fig, ax = plt.subplots()",
66 " ax.plot(self.data, 'o')",
66 " ax.plot(self.data, 'o')",
67 " ax.set_title(self._repr_latex_())",
67 " ax.set_title(self._repr_latex_())",
68 " data = print_figure(fig, format)",
68 " data = print_figure(fig, format)",
69 " # We MUST close the figure, otherwise IPython's display machinery",
69 " # We MUST close the figure, otherwise IPython's display machinery",
70 " # will pick it up and send it as output, resulting in a double display",
70 " # will pick it up and send it as output, resulting in a double display",
71 " plt.close(fig)",
71 " plt.close(fig)",
72 " return data",
72 " return data",
73 " ",
73 " ",
74 " # Here we define the special repr methods that provide the IPython display protocol",
74 " # Here we define the special repr methods that provide the IPython display protocol",
75 " # Note that for the two figures, we cache the figure data once computed.",
75 " # Note that for the two figures, we cache the figure data once computed.",
76 " ",
76 " ",
77 " def _repr_png_(self):",
77 " def _repr_png_(self):",
78 " if self._png_data is None:",
78 " if self._png_data is None:",
79 " self._png_data = self._figure_data('png')",
79 " self._png_data = self._figure_data('png')",
80 " return self._png_data",
80 " return self._png_data",
81 "",
81 "",
82 "",
82 "",
83 " def _repr_svg_(self):",
83 " def _repr_svg_(self):",
84 " if self._svg_data is None:",
84 " if self._svg_data is None:",
85 " self._svg_data = self._figure_data('svg')",
85 " self._svg_data = self._figure_data('svg')",
86 " return self._svg_data",
86 " return self._svg_data",
87 " ",
87 " ",
88 " def _repr_latex_(self):",
88 " def _repr_latex_(self):",
89 " return r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,",
89 " return r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,",
90 " self.std, self.size)",
90 " self.std, self.size)",
91 " ",
91 " ",
92 " # We expose as properties some of the above reprs, so that the user can see them",
92 " # We expose as properties some of the above reprs, so that the user can see them",
93 " # directly (since otherwise the client dictates which one it shows by default)",
93 " # directly (since otherwise the client dictates which one it shows by default)",
94 " @property",
94 " @property",
95 " def png(self):",
95 " def png(self):",
96 " return Image(self._repr_png_(), embed=True)",
96 " return Image(self._repr_png_(), embed=True)",
97 " ",
97 " ",
98 " @property",
98 " @property",
99 " def svg(self):",
99 " def svg(self):",
100 " return SVG(self._repr_svg_())",
100 " return SVG(self._repr_svg_())",
101 " ",
101 " ",
102 " @property",
102 " @property",
103 " def latex(self):",
103 " def latex(self):",
104 " return Math(self._repr_svg_())",
104 " return Math(self._repr_svg_())",
105 " ",
105 " ",
106 " # An example of using a property to display rich information, in this case",
106 " # An example of using a property to display rich information, in this case",
107 " # the histogram of the distribution. We've hardcoded the format to be png",
107 " # the histogram of the distribution. We've hardcoded the format to be png",
108 " # in this case, but in production code it would be trivial to make it an option",
108 " # in this case, but in production code it would be trivial to make it an option",
109 " @property",
109 " @property",
110 " def hist(self):",
110 " def hist(self):",
111 " fig, ax = plt.subplots()",
111 " fig, ax = plt.subplots()",
112 " ax.hist(self.data, bins=100)",
112 " ax.hist(self.data, bins=100)",
113 " ax.set_title(self._repr_latex_())",
113 " ax.set_title(self._repr_latex_())",
114 " data = print_figure(fig, 'png')",
114 " data = print_figure(fig, 'png')",
115 " plt.close(fig)",
115 " plt.close(fig)",
116 " return Image(data, embed=True)"
116 " return Image(data, embed=True)"
117 ],
117 ],
118 "language": "python",
118 "language": "python",
119 "outputs": [],
119 "outputs": [],
120 "prompt_number": 1
120 "prompt_number": 1
121 },
121 },
122 {
122 {
123 "cell_type": "markdown",
123 "cell_type": "markdown",
124 "source": [
124 "source": [
125 "Now, we create an instance of the Gaussian distribution, whose default representation will be its LaTeX form:"
125 "Now, we create an instance of the Gaussian distribution, whose default representation will be its LaTeX form:"
126 ]
126 ]
127 },
127 },
128 {
128 {
129 "cell_type": "code",
129 "cell_type": "code",
130 "collapsed": false,
130 "collapsed": false,
131 "input": [
131 "input": [
132 "x = Gaussian()",
132 "x = Gaussian()",
133 "x"
133 "x"
134 ],
134 ],
135 "language": "python",
135 "language": "python",
136 "outputs": [],
136 "outputs": [],
137 "prompt_number": 2
137 "prompt_number": 2
138 },
138 },
139 {
139 {
140 "cell_type": "markdown",
140 "cell_type": "markdown",
141 "source": [
141 "source": [
142 "We can view the data in png or svg formats:"
142 "We can view the data in png or svg formats:"
143 ]
143 ]
144 },
144 },
145 {
145 {
146 "cell_type": "code",
146 "cell_type": "code",
147 "collapsed": false,
147 "collapsed": false,
148 "input": [
148 "input": [
149 "x.png"
149 "x.png"
150 ],
150 ],
151 "language": "python",
151 "language": "python",
152 "outputs": [],
152 "outputs": [],
153 "prompt_number": 3
153 "prompt_number": 3
154 },
154 },
155 {
155 {
156 "cell_type": "code",
156 "cell_type": "code",
157 "collapsed": false,
157 "collapsed": false,
158 "input": [
158 "input": [
159 "x.svg"
159 "x.svg"
160 ],
160 ],
161 "language": "python",
161 "language": "python",
162 "outputs": [],
162 "outputs": [],
163 "prompt_number": 4
163 "prompt_number": 4
164 },
164 },
165 {
165 {
166 "cell_type": "markdown",
166 "cell_type": "markdown",
167 "source": [
167 "source": [
168 "Since IPython only displays by default as an ``Out[]`` cell the result of the last computation, we can use the",
168 "Since IPython only displays by default as an ``Out[]`` cell the result of the last computation, we can use the",
169 "``display()`` function to show more than one representation in a single cell:"
169 "``display()`` function to show more than one representation in a single cell:"
170 ]
170 ]
171 },
171 },
172 {
172 {
173 "cell_type": "code",
173 "cell_type": "code",
174 "collapsed": false,
174 "collapsed": false,
175 "input": [
175 "input": [
176 "display(x.png)",
176 "display(x.png)",
177 "display(x.svg)"
177 "display(x.svg)"
178 ],
178 ],
179 "language": "python",
179 "language": "python",
180 "outputs": [],
180 "outputs": [],
181 "prompt_number": 5
181 "prompt_number": 5
182 },
182 },
183 {
183 {
184 "cell_type": "markdown",
184 "cell_type": "markdown",
185 "source": [
185 "source": [
186 "Now let's create a new Gaussian with different parameters"
186 "Now let's create a new Gaussian with different parameters"
187 ]
187 ]
188 },
188 },
189 {
189 {
190 "cell_type": "code",
190 "cell_type": "code",
191 "collapsed": false,
191 "collapsed": false,
192 "input": [
192 "input": [
193 "x2 = Gaussian(0.5, 0.2, 2000)",
193 "x2 = Gaussian(0.5, 0.2, 2000)",
194 "x2"
194 "x2"
195 ],
195 ],
196 "language": "python",
196 "language": "python",
197 "outputs": [],
197 "outputs": [],
198 "prompt_number": 6
198 "prompt_number": 6
199 },
199 },
200 {
200 {
201 "cell_type": "markdown",
201 "cell_type": "markdown",
202 "source": [
202 "source": [
203 "We can easily compare them by displaying their histograms"
203 "We can easily compare them by displaying their histograms"
204 ]
204 ]
205 },
205 },
206 {
206 {
207 "cell_type": "code",
207 "cell_type": "code",
208 "collapsed": false,
208 "collapsed": false,
209 "input": [
209 "input": [
210 "display(x.hist)",
210 "display(x.hist)",
211 "display(x2.hist)"
211 "display(x2.hist)"
212 ],
212 ],
213 "language": "python",
213 "language": "python",
214 "outputs": [],
214 "outputs": [],
215 "prompt_number": 7
215 "prompt_number": 7
216 },
216 },
217 {
217 {
218 "cell_type": "markdown",
218 "cell_type": "markdown",
219 "source": [
219 "source": [
220 "## Adding IPython display support to existing objects",
220 "## Adding IPython display support to existing objects",
221 "",
221 "",
222 "When you are directly writing your own classes, you can adapt them for display in IPython by ",
222 "When you are directly writing your own classes, you can adapt them for display in IPython by ",
223 "following the above example. But in practice, we often need to work with existing code we",
223 "following the above example. But in practice, we often need to work with existing code we",
224 "can't modify. ",
224 "can't modify. ",
225 "",
225 "",
226 "We now illustrate how to add these kinds of extended display capabilities to existing objects.",
226 "We now illustrate how to add these kinds of extended display capabilities to existing objects.",
227 "We will use the numpy polynomials and change their default representation to be a formatted",
227 "We will use the numpy polynomials and change their default representation to be a formatted",
228 "LaTeX expression.",
228 "LaTeX expression.",
229 "",
229 "",
230 "First, consider how a numpy polynomial object renders by default:"
230 "First, consider how a numpy polynomial object renders by default:"
231 ]
231 ]
232 },
232 },
233 {
233 {
234 "cell_type": "code",
234 "cell_type": "code",
235 "collapsed": false,
235 "collapsed": false,
236 "input": [
236 "input": [
237 "p = np.polynomial.Polynomial([1,2,3], [-10, 10])",
237 "p = np.polynomial.Polynomial([1,2,3], [-10, 10])",
238 "p"
238 "p"
239 ],
239 ],
240 "language": "python",
240 "language": "python",
241 "outputs": [],
241 "outputs": [],
242 "prompt_number": 8
242 "prompt_number": 8
243 },
243 },
244 {
244 {
245 "cell_type": "markdown",
245 "cell_type": "markdown",
246 "source": [
246 "source": [
247 "Next, we define a function that pretty-prints a polynomial as a LaTeX string:"
247 "Next, we define a function that pretty-prints a polynomial as a LaTeX string:"
248 ]
248 ]
249 },
249 },
250 {
250 {
251 "cell_type": "code",
251 "cell_type": "code",
252 "collapsed": true,
252 "collapsed": true,
253 "input": [
253 "input": [
254 "def poly2latex(p):",
254 "def poly2latex(p):",
255 " terms = ['%.2g' % p.coef[0]]",
255 " terms = ['%.2g' % p.coef[0]]",
256 " if len(p) > 1:",
256 " if len(p) > 1:",
257 " term = 'x'",
257 " term = 'x'",
258 " c = p.coef[1]",
258 " c = p.coef[1]",
259 " if c!=1:",
259 " if c!=1:",
260 " term = ('%.2g ' % c) + term",
260 " term = ('%.2g ' % c) + term",
261 " terms.append(term)",
261 " terms.append(term)",
262 " if len(p) > 2:",
262 " if len(p) > 2:",
263 " for i in range(2, len(p)):",
263 " for i in range(2, len(p)):",
264 " term = 'x^%d' % i",
264 " term = 'x^%d' % i",
265 " c = p.coef[i]",
265 " c = p.coef[i]",
266 " if c!=1:",
266 " if c!=1:",
267 " term = ('%.2g ' % c) + term",
267 " term = ('%.2g ' % c) + term",
268 " terms.append(term)",
268 " terms.append(term)",
269 " px = '$P(x)=%s$' % '+'.join(terms)",
269 " px = '$P(x)=%s$' % '+'.join(terms)",
270 " dom = r', domain: $[%.2g,\\ %.2g]$' % tuple(p.domain)",
270 " dom = r', domain: $[%.2g,\\ %.2g]$' % tuple(p.domain)",
271 " return px+dom"
271 " return px+dom"
272 ],
272 ],
273 "language": "python",
273 "language": "python",
274 "outputs": [],
274 "outputs": [],
275 "prompt_number": 9
275 "prompt_number": 9
276 },
276 },
277 {
277 {
278 "cell_type": "markdown",
278 "cell_type": "markdown",
279 "source": [
279 "source": [
280 "This produces, on our polynomial ``p``, the following:"
280 "This produces, on our polynomial ``p``, the following:"
281 ]
281 ]
282 },
282 },
283 {
283 {
284 "cell_type": "code",
284 "cell_type": "code",
285 "collapsed": false,
285 "collapsed": false,
286 "input": [
286 "input": [
287 "poly2latex(p)"
287 "poly2latex(p)"
288 ],
288 ],
289 "language": "python",
289 "language": "python",
290 "outputs": [],
290 "outputs": [],
291 "prompt_number": 10
291 "prompt_number": 10
292 },
292 },
293 {
293 {
294 "cell_type": "markdown",
294 "cell_type": "markdown",
295 "source": [
295 "source": [
296 "Note that this did *not* produce a formated LaTeX object, because it is simply a string ",
296 "Note that this did *not* produce a formated LaTeX object, because it is simply a string ",
297 "with LaTeX code. In order for this to be interpreted as a mathematical expression, it",
297 "with LaTeX code. In order for this to be interpreted as a mathematical expression, it",
298 "must be properly wrapped into a Math object:"
298 "must be properly wrapped into a Math object:"
299 ]
299 ]
300 },
300 },
301 {
301 {
302 "cell_type": "code",
302 "cell_type": "code",
303 "collapsed": false,
303 "collapsed": false,
304 "input": [
304 "input": [
305 "from IPython.core.display import Math",
305 "from IPython.core.display import Math",
306 "Math(poly2latex(p))"
306 "Math(poly2latex(p))"
307 ],
307 ],
308 "language": "python",
308 "language": "python",
309 "outputs": [],
309 "outputs": [],
310 "prompt_number": 11
310 "prompt_number": 11
311 },
311 },
312 {
312 {
313 "cell_type": "markdown",
313 "cell_type": "markdown",
314 "source": [
314 "source": [
315 "But we can configure IPython to do this automatically for us as follows. We hook into the",
315 "But we can configure IPython to do this automatically for us as follows. We hook into the",
316 "IPython display system and instruct it to use ``poly2latex`` for the latex mimetype, when",
316 "IPython display system and instruct it to use ``poly2latex`` for the latex mimetype, when",
317 "encountering objects of the ``Polynomial`` type defined in the",
317 "encountering objects of the ``Polynomial`` type defined in the",
318 "``numpy.polynomial.polynomial`` module:"
318 "``numpy.polynomial.polynomial`` module:"
319 ]
319 ]
320 },
320 },
321 {
321 {
322 "cell_type": "code",
322 "cell_type": "code",
323 "collapsed": true,
323 "collapsed": true,
324 "input": [
324 "input": [
325 "ip = get_ipython()",
325 "ip = get_ipython()",
326 "latex_formatter = ip.display_formatter.formatters['text/latex']",
326 "latex_formatter = ip.display_formatter.formatters['text/latex']",
327 "latex_formatter.for_type_by_name('numpy.polynomial.polynomial',",
327 "latex_formatter.for_type_by_name('numpy.polynomial.polynomial',",
328 " 'Polynomial', poly2latex)"
328 " 'Polynomial', poly2latex)"
329 ],
329 ],
330 "language": "python",
330 "language": "python",
331 "outputs": [],
331 "outputs": [],
332 "prompt_number": 12
332 "prompt_number": 12
333 },
333 },
334 {
334 {
335 "cell_type": "markdown",
335 "cell_type": "markdown",
336 "source": [
336 "source": [
337 "For more examples on how to use the above system, and how to bundle similar print functions",
337 "For more examples on how to use the above system, and how to bundle similar print functions",
338 "into a convenient IPython extension, see the ``IPython/extensions/sympyprinting.py`` file. ",
338 "into a convenient IPython extension, see the ``IPython/extensions/sympyprinting.py`` file. ",
339 "The machinery that defines the display system is in the ``display.py`` and ``displaypub.py`` ",
339 "The machinery that defines the display system is in the ``display.py`` and ``displaypub.py`` ",
340 "files in ``IPython/core``.",
340 "files in ``IPython/core``.",
341 "",
341 "",
342 "Once our special printer has been loaded, all polynomials will be represented by their ",
342 "Once our special printer has been loaded, all polynomials will be represented by their ",
343 "mathematical form instead:"
343 "mathematical form instead:"
344 ]
344 ]
345 },
345 },
346 {
346 {
347 "cell_type": "code",
347 "cell_type": "code",
348 "collapsed": false,
348 "collapsed": false,
349 "input": [
349 "input": [
350 "p"
350 "p"
351 ],
351 ],
352 "language": "python",
352 "language": "python",
353 "outputs": [],
353 "outputs": [],
354 "prompt_number": 13
354 "prompt_number": 13
355 },
355 },
356 {
356 {
357 "cell_type": "code",
357 "cell_type": "code",
358 "collapsed": false,
358 "collapsed": false,
359 "input": [
359 "input": [
360 "p2 = np.polynomial.Polynomial([-20, 71, -15, 1])",
360 "p2 = np.polynomial.Polynomial([-20, 71, -15, 1])",
361 "p2"
361 "p2"
362 ],
362 ],
363 "language": "python",
363 "language": "python",
364 "outputs": [],
364 "outputs": [],
365 "prompt_number": 14
365 "prompt_number": 14
366 },
366 },
367 {
367 {
368 "cell_type": "code",
368 "cell_type": "code",
369 "collapsed": true,
369 "collapsed": true,
370 "input": [],
370 "input": [],
371 "language": "python",
371 "language": "python",
372 "outputs": [],
372 "outputs": [],
373 "prompt_number": 14
373 "prompt_number": 14
374 }
374 }
375 ]
375 ]
Show file before | Show file after | Hide comments
@@ -1,122 +1,122 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "formatting"
3 "name": "formatting"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# Examples of basic formatting in the notebook",
12 "# Examples of basic formatting in the notebook",
13 "",
13 "",
14 "Normal and formatted text cells such as this one use the ",
14 "Normal and formatted text cells such as this one use the ",
15 "[Markdown](http://daringfireball.net/projects/markdown/basics) syntax.",
15 "[Markdown](http://daringfireball.net/projects/markdown/basics) syntax.",
16 "",
16 "",
17 "",
17 "",
18 "# Title (h1)",
18 "# Title (h1)",
19 "",
19 "",
20 "## Heading (h2)",
20 "## Heading (h2)",
21 "",
21 "",
22 "### Heading (h3)",
22 "### Heading (h3)",
23 "",
23 "",
24 "Here is a paragraph of text.",
24 "Here is a paragraph of text.",
25 "",
25 "",
26 "* One.",
26 "* One.",
27 " - Sublist",
27 " - Sublist",
28 " - Here we go",
28 " - Here we go",
29 " - Sublist",
29 " - Sublist",
30 " - Here we go",
30 " - Here we go",
31 " - Here we go",
31 " - Here we go",
32 "* Two.",
32 "* Two.",
33 " - Sublist",
33 " - Sublist",
34 "* Three.",
34 "* Three.",
35 " - Sublist",
35 " - Sublist",
36 "",
36 "",
37 "Now another list:",
37 "Now another list:",
38 "",
38 "",
39 "---",
39 "---",
40 "",
40 "",
41 "1. Here we go",
41 "1. Here we go",
42 " 1. Sublist",
42 " 1. Sublist",
43 " 2. Sublist",
43 " 2. Sublist",
44 "2. There we go",
44 "2. There we go",
45 "3. Now this",
45 "3. Now this",
46 "",
46 "",
47 "And another paragraph.",
47 "And another paragraph.",
48 "",
48 "",
49 "### Heading (h3)",
49 "### Heading (h3)",
50 "",
50 "",
51 "#### Heading (h4)",
51 "#### Heading (h4)",
52 "",
52 "",
53 "##### Heading (h5)",
53 "##### Heading (h5)",
54 "",
54 "",
55 "###### Heading (h6)",
55 "###### Heading (h6)",
56 "",
56 "",
57 "## Heading (h2)"
57 "## Heading (h2)"
58 ]
58 ]
59 },
59 },
60 {
60 {
61 "cell_type": "markdown",
61 "cell_type": "markdown",
62 "source": [
62 "source": [
63 "# Heading (h1)",
63 "# Heading (h1)",
64 "",
64 "",
65 "## Heading (h2)",
65 "## Heading (h2)",
66 "",
66 "",
67 "### Heading (h3)",
67 "### Heading (h3)",
68 "",
68 "",
69 "#### Heading (h4)",
69 "#### Heading (h4)",
70 "",
70 "",
71 "##### Heading (h5)",
71 "##### Heading (h5)",
72 "",
72 "",
73 "###### Heading (h6)",
73 "###### Heading (h6)",
74 "",
74 "",
75 "Now for a simple code example:",
75 "Now for a simple code example:",
76 "",
76 "",
77 " for i in range(10):",
77 " for i in range(10):",
78 " print i",
78 " print i",
79 "",
79 "",
80 "Now more text"
80 "Now more text"
81 ]
81 ]
82 },
82 },
83 {
83 {
84 "cell_type": "markdown",
84 "cell_type": "markdown",
85 "source": [
85 "source": [
86 "## Heading (h2)",
86 "## Heading (h2)",
87 "",
87 "",
88 "Here is text.",
88 "Here is text.",
89 "",
89 "",
90 "> This is a *block* quote. This is a block quote. This is a block quote. ",
90 "> This is a *block* quote. This is a block quote. This is a block quote. ",
91 "> This is a **block** quote. This is a block quote. This is a block quote. ",
91 "> This is a **block** quote. This is a block quote. This is a block quote. ",
92 "> This is a `block` quote. This is a block quote. This is a block quote. ",
92 "> This is a `block` quote. This is a block quote. This is a block quote. ",
93 "> This is a block quote. This is a block quote. This is a block quote. ",
93 "> This is a block quote. This is a block quote. This is a block quote. ",
94 "> This is a block quote. This is a block quote. This is a block quote. ",
94 "> This is a block quote. This is a block quote. This is a block quote. ",
95 "> This is a block quote. This is a block quote. This is a block quote. ",
95 "> This is a block quote. This is a block quote. This is a block quote. ",
96 "",
96 "",
97 "Here is text",
97 "Here is text",
98 "",
98 "",
99 "<table>",
99 "<table>",
100 "<tr>",
100 "<tr>",
101 "<th>Header 1</th>",
101 "<th>Header 1</th>",
102 "<th>Header 2</th>",
102 "<th>Header 2</th>",
103 "</tr>",
103 "</tr>",
104 "<tr>",
104 "<tr>",
105 "<td>row 1, cell 1</td>",
105 "<td>row 1, cell 1</td>",
106 "<td>row 1, cell 2</td>",
106 "<td>row 1, cell 2</td>",
107 "</tr>",
107 "</tr>",
108 "<tr>",
108 "<tr>",
109 "<td>row 2, cell 1</td>",
109 "<td>row 2, cell 1</td>",
110 "<td>row 2, cell 2</td>",
110 "<td>row 2, cell 2</td>",
111 "</tr>",
111 "</tr>",
112 "</table>"
112 "</table>"
113 ]
113 ]
114 },
114 },
115 {
115 {
116 "cell_type": "code",
116 "cell_type": "code",
117 "collapsed": true,
117 "collapsed": true,
118 "input": [],
118 "input": [],
119 "language": "python",
119 "language": "python",
120 "outputs": [],
120 "outputs": [],
121 "prompt_number": "&nbsp;"
121 "prompt_number": "&nbsp;"
122 }
122 }
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@@ -1,322 +1,322 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "sympy"
3 "name": "sympy"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# SymPy: Open Source Symbolic Mathematics",
12 "# SymPy: Open Source Symbolic Mathematics",
13 "",
13 "",
14 "This notebook uses the [SymPy](http://sympy.org) package to perform symbolic manipulations,",
14 "This notebook uses the [SymPy](http://sympy.org) package to perform symbolic manipulations,",
15 "and combined with numpy and matplotlib, also displays numerical visualizations of symbolically",
15 "and combined with numpy and matplotlib, also displays numerical visualizations of symbolically",
16 "constructed expressions.",
16 "constructed expressions.",
17 "",
17 "",
18 "We first load sympy printing and plotting support, as well as all of sympy:"
18 "We first load sympy printing and plotting support, as well as all of sympy:"
19 ]
19 ]
20 },
20 },
21 {
21 {
22 "cell_type": "code",
22 "cell_type": "code",
23 "collapsed": false,
23 "collapsed": false,
24 "input": [
24 "input": [
25 "%load_ext sympyprinting",
25 "%load_ext sympyprinting",
26 "%pylab inline",
26 "%pylab inline",
27 "",
27 "",
28 "from __future__ import division",
28 "from __future__ import division",
29 "import sympy as sym",
29 "import sympy as sym",
30 "from sympy import *",
30 "from sympy import *",
31 "x, y, z = symbols(\"x y z\")",
31 "x, y, z = symbols(\"x y z\")",
32 "k, m, n = symbols(\"k m n\", integer=True)",
32 "k, m, n = symbols(\"k m n\", integer=True)",
33 "f, g, h = map(Function, 'fgh')"
33 "f, g, h = map(Function, 'fgh')"
34 ],
34 ],
35 "language": "python",
35 "language": "python",
36 "outputs": [
36 "outputs": [
37 {
37 {
38 "output_type": "stream",
38 "output_type": "stream",
39 "stream": "stdout",
39 "stream": "stdout",
40 "text": [
40 "text": [
41 "",
41 "",
42 "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].",
42 "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].",
43 "For more information, type 'help(pylab)'."
43 "For more information, type 'help(pylab)'."
44 ]
44 ]
45 }
45 }
46 ],
46 ],
47 "prompt_number": 1
47 "prompt_number": 1
48 },
48 },
49 {
49 {
50 "cell_type": "markdown",
50 "cell_type": "markdown",
51 "source": [
51 "source": [
52 "<h2>Elementary operations</h2>"
52 "<h2>Elementary operations</h2>"
53 ]
53 ]
54 },
54 },
55 {
55 {
56 "cell_type": "code",
56 "cell_type": "code",
57 "collapsed": false,
57 "collapsed": false,
58 "input": [
58 "input": [
59 "Rational(3,2)*pi + exp(I*x) / (x**2 + y)"
59 "Rational(3,2)*pi + exp(I*x) / (x**2 + y)"
60 ],
60 ],
61 "language": "python",
61 "language": "python",
62 "outputs": [
62 "outputs": [
63 {
63 {
64 "latex": [
64 "latex": [
65 "$$\\frac{3}{2} \\pi + \\frac{e^{\\mathbf{\\imath} x}}{x^{2} + y}$$"
65 "$$\\frac{3}{2} \\pi + \\frac{e^{\\mathbf{\\imath} x}}{x^{2} + y}$$"
66 ],
66 ],
67 "output_type": "pyout",
67 "output_type": "pyout",
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69 "prompt_number": 2,
69 "prompt_number": 2,
70 "text": [
70 "text": [
71 "",
71 "",
72 " \u2148\u22c5x ",
72 " \u2148\u22c5x ",
73 "3\u22c5\u03c0 \u212f ",
73 "3\u22c5\u03c0 \u212f ",
74 "\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500",
74 "\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500",
75 " 2 2 ",
75 " 2 2 ",
76 " x + y"
76 " x + y"
77 ]
77 ]
78 }
78 }
79 ],
79 ],
80 "prompt_number": 2
80 "prompt_number": 2
81 },
81 },
82 {
82 {
83 "cell_type": "code",
83 "cell_type": "code",
84 "collapsed": false,
84 "collapsed": false,
85 "input": [
85 "input": [
86 "exp(I*x).subs(x,pi).evalf()"
86 "exp(I*x).subs(x,pi).evalf()"
87 ],
87 ],
88 "language": "python",
88 "language": "python",
89 "outputs": [
89 "outputs": [
90 {
90 {
91 "latex": [
91 "latex": [
92 "$$-1.0$$"
92 "$$-1.0$$"
93 ],
93 ],
94 "output_type": "pyout",
94 "output_type": "pyout",
95 "png": "iVBORw0KGgoAAAANSUhEUgAAACsAAAASCAYAAADCKCelAAAABHNCSVQICAgIfAhkiAAAAU1JREFU\nSInt1csrBlEcxvGPWxKFhcsCK5QFJVlYsfJPsLKQjf8CG8qejVKWkhUbsRBZuWzct0okxQK5LGam\npmmU923evMpTp9N5njm/+c7MmXP4QyopQM0WbKM9j3mzuMEjKjCP+yzhIlVjGOf4zHFuGS4xHvOm\nsInSTOhi6sIaZrArd9gRvAgeOFJHWGcsC8DvtCR32ENspfhXWI0Gmb/iPFSOHlykZJcYigbFANsk\n+NGfUrJn1KOS4oBtDvvnlCzy6igO2Jew/0jJKuJZMcCe4fWbrBpvuCNY3JG6seDnB8UhJvIEjOsN\np4K1mVQNboW7Sxz2BAMZ3DwfHaM14ZWhF3uR8RvLoBVVCe8Igwm/H7WYKyTMuuCzNaZkfXjHRsKv\nFxzTkzFvAfuFAGzEjmBj/wzbAw4wGruuDdeYTqnRiWUshm0FDYWA/def1heszTze5axPeQAAAABJ\nRU5ErkJggg==\n",
95 "png": "iVBORw0KGgoAAAANSUhEUgAAACsAAAASCAYAAADCKCelAAAABHNCSVQICAgIfAhkiAAAAU1JREFU\nSInt1csrBlEcxvGPWxKFhcsCK5QFJVlYsfJPsLKQjf8CG8qejVKWkhUbsRBZuWzct0okxQK5LGam\npmmU923evMpTp9N5njm/+c7MmXP4QyopQM0WbKM9j3mzuMEjKjCP+yzhIlVjGOf4zHFuGS4xHvOm\nsInSTOhi6sIaZrArd9gRvAgeOFJHWGcsC8DvtCR32ENspfhXWI0Gmb/iPFSOHlykZJcYigbFANsk\n+NGfUrJn1KOS4oBtDvvnlCzy6igO2Jew/0jJKuJZMcCe4fWbrBpvuCNY3JG6seDnB8UhJvIEjOsN\np4K1mVQNboW7Sxz2BAMZ3DwfHaM14ZWhF3uR8RvLoBVVCe8Igwm/H7WYKyTMuuCzNaZkfXjHRsKv\nFxzTkzFvAfuFAGzEjmBj/wzbAw4wGruuDdeYTqnRiWUshm0FDYWA/def1heszTze5axPeQAAAABJ\nRU5ErkJggg==\n",
96 "prompt_number": 4,
96 "prompt_number": 4,
97 "text": [
97 "text": [
98 "-1.00000000000000"
98 "-1.00000000000000"
99 ]
99 ]
100 }
100 }
101 ],
101 ],
102 "prompt_number": 4
102 "prompt_number": 4
103 },
103 },
104 {
104 {
105 "cell_type": "code",
105 "cell_type": "code",
106 "collapsed": true,
106 "collapsed": true,
107 "input": [
107 "input": [
108 "e = x + 2*y"
108 "e = x + 2*y"
109 ],
109 ],
110 "language": "python",
110 "language": "python",
111 "outputs": [],
111 "outputs": [],
112 "prompt_number": 5
112 "prompt_number": 5
113 },
113 },
114 {
114 {
115 "cell_type": "code",
115 "cell_type": "code",
116 "collapsed": false,
116 "collapsed": false,
117 "input": [
117 "input": [
118 "srepr(e)"
118 "srepr(e)"
119 ],
119 ],
120 "language": "python",
120 "language": "python",
121 "outputs": [
121 "outputs": [
122 {
122 {
123 "output_type": "pyout",
123 "output_type": "pyout",
124 "prompt_number": 6,
124 "prompt_number": 6,
125 "text": [
125 "text": [
126 "Add(Symbol('x'), Mul(Integer(2), Symbol('y')))"
126 "Add(Symbol('x'), Mul(Integer(2), Symbol('y')))"
127 ]
127 ]
128 }
128 }
129 ],
129 ],
130 "prompt_number": 6
130 "prompt_number": 6
131 },
131 },
132 {
132 {
133 "cell_type": "code",
133 "cell_type": "code",
134 "collapsed": false,
134 "collapsed": false,
135 "input": [
135 "input": [
136 "exp(pi * sqrt(163)).evalf(50)"
136 "exp(pi * sqrt(163)).evalf(50)"
137 ],
137 ],
138 "language": "python",
138 "language": "python",
139 "outputs": [
139 "outputs": [
140 {
140 {
141 "latex": [
141 "latex": [
142 "$$262537412640768743.99999999999925007259719818568888$$"
142 "$$262537412640768743.99999999999925007259719818568888$$"
143 ],
143 ],
144 "output_type": "pyout",
144 "output_type": "pyout",
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146 "prompt_number": 7,
146 "prompt_number": 7,
147 "text": [
147 "text": [
148 "262537412640768743.99999999999925007259719818568888"
148 "262537412640768743.99999999999925007259719818568888"
149 ]
149 ]
150 }
150 }
151 ],
151 ],
152 "prompt_number": 7
152 "prompt_number": 7
153 },
153 },
154 {
154 {
155 "cell_type": "markdown",
155 "cell_type": "markdown",
156 "source": [
156 "source": [
157 "<h2>Algebra<h2>"
157 "<h2>Algebra<h2>"
158 ]
158 ]
159 },
159 },
160 {
160 {
161 "cell_type": "code",
161 "cell_type": "code",
162 "collapsed": false,
162 "collapsed": false,
163 "input": [
163 "input": [
164 "eq = ((x+y)**2 * (x+1))",
164 "eq = ((x+y)**2 * (x+1))",
165 "eq"
165 "eq"
166 ],
166 ],
167 "language": "python",
167 "language": "python",
168 "outputs": [
168 "outputs": [
169 {
169 {
170 "latex": [
170 "latex": [
171 "$$\\left(x + 1\\right) \\left(x + y\\right)^{2}$$"
171 "$$\\left(x + 1\\right) \\left(x + y\\right)^{2}$$"
172 ],
172 ],
173 "output_type": "pyout",
173 "output_type": "pyout",
174 "png": "iVBORw0KGgoAAAANSUhEUgAAAHQAAAAbCAYAAACtOKuoAAAABHNCSVQICAgIfAhkiAAAA/tJREFU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\nAElFTkSuQmCC\n",
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175 "prompt_number": 8,
175 "prompt_number": 8,
176 "text": [
176 "text": [
177 "",
177 "",
178 " 2",
178 " 2",
179 "(x + 1)\u22c5(x + y) "
179 "(x + 1)\u22c5(x + y) "
180 ]
180 ]
181 }
181 }
182 ],
182 ],
183 "prompt_number": 8
183 "prompt_number": 8
184 },
184 },
185 {
185 {
186 "cell_type": "code",
186 "cell_type": "code",
187 "collapsed": false,
187 "collapsed": false,
188 "input": [
188 "input": [
189 "expand(eq)"
189 "expand(eq)"
190 ],
190 ],
191 "language": "python",
191 "language": "python",
192 "outputs": [
192 "outputs": [
193 {
193 {
194 "latex": [
194 "latex": [
195 "$$x^{3} + 2 x^{2} y + x^{2} + x y^{2} + 2 x y + y^{2}$$"
195 "$$x^{3} + 2 x^{2} y + x^{2} + x y^{2} + 2 x y + y^{2}$$"
196 ],
196 ],
197 "output_type": "pyout",
197 "output_type": "pyout",
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198 "png": "iVBORw0KGgoAAAANSUhEUgAAAQ0AAAAbCAYAAABm6to6AAAABHNCSVQICAgIfAhkiAAABQhJREFU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\n",
199 "prompt_number": 9,
199 "prompt_number": 9,
200 "text": [
200 "text": [
201 "",
201 "",
202 " 3 2 2 2 2",
202 " 3 2 2 2 2",
203 "x + 2\u22c5x \u22c5y + x + x\u22c5y + 2\u22c5x\u22c5y + y "
203 "x + 2\u22c5x \u22c5y + x + x\u22c5y + 2\u22c5x\u22c5y + y "
204 ]
204 ]
205 }
205 }
206 ],
206 ],
207 "prompt_number": 9
207 "prompt_number": 9
208 },
208 },
209 {
209 {
210 "cell_type": "code",
210 "cell_type": "code",
211 "collapsed": false,
211 "collapsed": false,
212 "input": [
212 "input": [
213 "a = 1/x + (x*sin(x) - 1)/x",
213 "a = 1/x + (x*sin(x) - 1)/x",
214 "a"
214 "a"
215 ],
215 ],
216 "language": "python",
216 "language": "python",
217 "outputs": [
217 "outputs": [
218 {
218 {
219 "latex": [
219 "latex": [
220 "$$\\frac{x \\operatorname{sin}\\left(x\\right) -1}{x} + \\frac{1}{x}$$"
220 "$$\\frac{x \\operatorname{sin}\\left(x\\right) -1}{x} + \\frac{1}{x}$$"
221 ],
221 ],
222 "output_type": "pyout",
222 "output_type": "pyout",
223 "png": "iVBORw0KGgoAAAANSUhEUgAAAFwAAAAbCAYAAADxsuiMAAAABHNCSVQICAgIfAhkiAAAAolJREFU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\n1YVPJWzHYFHp/atRo0aNquc3S/HNyBXE+1kAAAAASUVORK5CYII=\n",
223 "png": "iVBORw0KGgoAAAANSUhEUgAAAFwAAAAbCAYAAADxsuiMAAAABHNCSVQICAgIfAhkiAAAAolJREFU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\n1YVPJWzHYFHp/atRo0aNquc3S/HNyBXE+1kAAAAASUVORK5CYII=\n",
224 "prompt_number": 10,
224 "prompt_number": 10,
225 "text": [
225 "text": [
226 "",
226 "",
227 "x\u22c5sin(x) - 1 1",
227 "x\u22c5sin(x) - 1 1",
228 "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500",
228 "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500",
229 " x x"
229 " x x"
230 ]
230 ]
231 }
231 }
232 ],
232 ],
233 "prompt_number": 10
233 "prompt_number": 10
234 },
234 },
235 {
235 {
236 "cell_type": "code",
236 "cell_type": "code",
237 "collapsed": false,
237 "collapsed": false,
238 "input": [
238 "input": [
239 "simplify(a)"
239 "simplify(a)"
240 ],
240 ],
241 "language": "python",
241 "language": "python",
242 "outputs": [
242 "outputs": [
243 {
243 {
244 "latex": [
244 "latex": [
245 "$$\\operatorname{sin}\\left(x\\right)$$"
245 "$$\\operatorname{sin}\\left(x\\right)$$"
246 ],
246 ],
247 "output_type": "pyout",
247 "output_type": "pyout",
248 "png": "iVBORw0KGgoAAAANSUhEUgAAADAAAAASCAYAAAAdZl26AAAABHNCSVQICAgIfAhkiAAAAnNJREFU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\n89kW1gAAAABJRU5ErkJggg==\n",
248 "png": "iVBORw0KGgoAAAANSUhEUgAAADAAAAASCAYAAAAdZl26AAAABHNCSVQICAgIfAhkiAAAAnNJREFU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\n89kW1gAAAABJRU5ErkJggg==\n",
249 "prompt_number": 11,
249 "prompt_number": 11,
250 "text": [
250 "text": [
251 "sin(x)"
251 "sin(x)"
252 ]
252 ]
253 }
253 }
254 ],
254 ],
255 "prompt_number": 11
255 "prompt_number": 11
256 },
256 },
257 {
257 {
258 "cell_type": "code",
258 "cell_type": "code",
259 "collapsed": false,
259 "collapsed": false,
260 "input": [
260 "input": [
261 "eq = Eq(x**3 + 2*x**2 + 4*x + 8, 0)",
261 "eq = Eq(x**3 + 2*x**2 + 4*x + 8, 0)",
262 "eq"
262 "eq"
263 ],
263 ],
264 "language": "python",
264 "language": "python",
265 "outputs": [
265 "outputs": [
266 {
266 {
267 "latex": [
267 "latex": [
268 "$$x^{3} + 2 x^{2} + 4 x + 8 = 0$$"
268 "$$x^{3} + 2 x^{2} + 4 x + 8 = 0$$"
269 ],
269 ],
270 "output_type": "pyout",
270 "output_type": "pyout",
271 "png": "iVBORw0KGgoAAAANSUhEUgAAALIAAAAZCAYAAACVUXRFAAAABHNCSVQICAgIfAhkiAAABSRJREFU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\nX/JnRRiZjdxGAAAAAElFTkSuQmCC\n",
271 "png": "iVBORw0KGgoAAAANSUhEUgAAALIAAAAZCAYAAACVUXRFAAAABHNCSVQICAgIfAhkiAAABSRJREFU\neJzt2nnsHVMUwPHPrz+UtlpNiKK6KJFaSkQsjajtD0sliFRCE0uF8I9dbN2oiCKI0NhfEZTYUoJY\n/7DE9gciSC2xhFhraS1Ff/44M/p+09f2zXtvOn0y32QyM3fu3HvOzJ1zzzl3qKj4H9DT4n37YCyG\nYxLm4dlOCVUCe+JQbIDxmIF3SpWoYq3wOY5PjqdhCQaWJ05bDMGNdedT8CuGlSNOxdpkJwxOjo/G\n77p3IE/AcoxLzoeiD5NLk6iiFO7FxWUL0QY9wrVI3awdxUAeX5pEFblp1UeG3XA4RuIM/NYRiZpj\nB1wlfNpheAWzsbgDbd+Nb3FOB9pqlXOxPq4oUYZGDMcF6BXPvRcz8UXB/Y4U7/tr/CyezbX4oZOd\nnIK3sFEnG10N2+MljErOh+PdZNuyzbanYa72PvB2GY2lmFWiDI3YBAuwRV3ZBLwnBlpR9OIjMc5S\n5uBpDGin4T3xjchaENaxDwe30eYErNdk3UcwMVM2MZHh+jZkmCwGMvFRjmmjrTz6ZLlF6DKrjf6b\nJY+cU3FJg/K5OLtjEq3McfjTipgMthPP6KS0oJUR/T0W4avkfBcsE1a5Vc7W/Fc9EXdg47qy14Wy\nB7XY/yRsjicwAkfqb3nykkefeo7C8230m5c8cu4mMlXZoP4fxWZ4zsPLYpZKWYRPdCAgP1L4cRdh\nobDS7VDTvAV8WfjjIzLlPwvfNi/biHRbX2Yb2kJbKTX5LfoQ3JYcry2LXNO8nFOEXAuEOweDhEtX\nVGC8nsgo3dzg2tP4sb5iPTvgRPHVDcOpYsBuKizWBfhMTO9lMUm89J/qykaJgfd4pm4z+nyiv3Uv\niwutObhr9v0UwaNi0WsK9sX5OEYExe8X1OfmIl5Z0uDaUvFBDcSf9QN5NE4WD2Y5HhDuwpkiG/Aq\nXhA+XJn8rf8ghtOFzPUDoVv0gV3Fy/p4NXXK1mcZjsCDOAR3CVfs7dXcc4dwSfJwJl5MjtNZd2mD\nemnZJiJm+4+r9bdMj+LN5HhrXJrcVAQ1rQdX24pBMDtT3i36DMB8kUpMaeRaFKFPTb7nfqxYBT1M\nzGR9yb6orMVOVu1m3Z9c2yx7YWzm/Etc3mnJVkFNawN5Q7whIucs3aLPadg/U9bo5RWhT03zcp4g\nLHDKYJHLXS7y+EWwvgjiZzW4tlDMEj3095E/rTveHluJqaqTzBdZjiyjsEciWJZpGmdEenAnnsL0\nBte7QZ8Rwu+d10Rf7ejTied+qlj4SlmKs/AhbhKW8bsm5WmWv/CBFcFlPUNEcN+3ugZOE1/CoLqy\ncauo2wlq8lvkOVYewCesou66qs9UPCPchHR7QrycD5Lzoxrc1yl9mpVzsLC8jVyXHvxi5RkDbhXu\nT55tUqaNu/FwpqxXxElPZjscKH5d3Dk5f0x/J36ImEaKoibfQD5R+IRZbk/23aZPPWOs7FoUpU9N\n83K+Ln5JyLK3WN0rinPFUnT9yvFe4hkdmBakrsV+Ilh6JykbI7IDRBAyA9cVKGweDhDr7k/hnrry\ngcJq0F36ZBma2bNu6HOZiEUWidmCCPJmiExDUdwulqdPxg1J2Ul4Dc+lldKB/Jr4i+1A4S/tjmtE\nKmcx7lNcfjIvD4kp7rgG1+Yk+27SJ2WosLSp1T1DWLsrRTqqbH0WJn3MFFN7r/Bhp1uRPSmCxWIF\nb7pwVQhXp9HsUDo17f3bsK5R0x361HSHnGukrb+HOsgv+KNsITpIt+jTLXJWVFRUVFRUVFRUVOTk\nX/JnRRiZjdxGAAAAAElFTkSuQmCC\n",
272 "prompt_number": 12,
272 "prompt_number": 12,
273 "text": [
273 "text": [
274 "",
274 "",
275 " 3 2 ",
275 " 3 2 ",
276 "x + 2\u22c5x + 4\u22c5x + 8 = 0"
276 "x + 2\u22c5x + 4\u22c5x + 8 = 0"
277 ]
277 ]
278 }
278 }
279 ],
279 ],
280 "prompt_number": 12
280 "prompt_number": 12
281 },
281 },
282 {
282 {
283 "cell_type": "code",
283 "cell_type": "code",
284 "collapsed": false,
284 "collapsed": false,
285 "input": [
285 "input": [
286 "solve(eq, x)"
286 "solve(eq, x)"
287 ],
287 ],
288 "language": "python",
288 "language": "python",
289 "outputs": [
289 "outputs": [
290 {
290 {
291 "output_type": "pyout",
291 "output_type": "pyout",
292 "prompt_number": 13,
292 "prompt_number": 13,
293 "text": [
293 "text": [
294 "[-2, -2\u22c5\u2148, 2\u22c5\u2148]"
294 "[-2, -2\u22c5\u2148, 2\u22c5\u2148]"
295 ]
295 ]
296 }
296 }
297 ],
297 ],
298 "prompt_number": 13
298 "prompt_number": 13
299 },
299 },
300 {
300 {
301 "cell_type": "code",
301 "cell_type": "code",
302 "collapsed": false,
302 "collapsed": false,
303 "input": [
303 "input": [
304 "a, b = symbols('a b')",
304 "a, b = symbols('a b')",
305 "Sum(6*n**2 + 2**n, (n, a, b))"
305 "Sum(6*n**2 + 2**n, (n, a, b))"
306 ],
306 ],
307 "language": "python",
307 "language": "python",
308 "outputs": [
308 "outputs": [
309 {
309 {
310 "latex": [
310 "latex": [
311 "$$\\sum_{n=a}^{b} \\left(2^{n} + 6 n^{2}\\right)$$"
311 "$$\\sum_{n=a}^{b} \\left(2^{n} + 6 n^{2}\\right)$$"
312 ],
312 ],
313 "output_type": "pyout",
313 "output_type": "pyout",
314 "png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAAA4CAYAAAA2PDy+AAAABHNCSVQICAgIfAhkiAAABt1JREFU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\nTkSuQmCC\n",
314 "png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAAA4CAYAAAA2PDy+AAAABHNCSVQICAgIfAhkiAAABt1JREFU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\nTkSuQmCC\n",
315 "prompt_number": 14,
315 "prompt_number": 14,
316 "text": [
316 "text": [
317 "",
317 "",
318 " b ",
318 " b ",
319 " ___ ",
319 " ___ ",
320 " \u2572 ",
320 " \u2572 ",
321 " \u2572 \u239b n 2\u239e",
321 " \u2572 \u239b n 2\u239e",
322 " \u2571 \u239d2 + 6\u22c5n \u23a0",
322 " \u2571 \u239d2 + 6\u22c5n \u23a0",
@@ -325,299 +325,299 b''
325 "n = a "
325 "n = a "
326 ]
326 ]
327 }
327 }
328 ],
328 ],
329 "prompt_number": 14
329 "prompt_number": 14
330 },
330 },
331 {
331 {
332 "cell_type": "markdown",
332 "cell_type": "markdown",
333 "source": [
333 "source": [
334 "<h2>Calculus</h2>"
334 "<h2>Calculus</h2>"
335 ]
335 ]
336 },
336 },
337 {
337 {
338 "cell_type": "code",
338 "cell_type": "code",
339 "collapsed": false,
339 "collapsed": false,
340 "input": [
340 "input": [
341 "limit((sin(x)-x)/x**3, x, 0)"
341 "limit((sin(x)-x)/x**3, x, 0)"
342 ],
342 ],
343 "language": "python",
343 "language": "python",
344 "outputs": [
344 "outputs": [
345 {
345 {
346 "latex": [
346 "latex": [
347 "$$- \\frac{1}{6}$$"
347 "$$- \\frac{1}{6}$$"
348 ],
348 ],
349 "output_type": "pyout",
349 "output_type": "pyout",
350 "png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAeCAYAAADZ7LXbAAAABHNCSVQICAgIfAhkiAAAAPpJREFU\nSInt1aFKBFEUh/Gfq0WDCO6iguhoMwg2k6YFi7DRaBKMvoDZavYhDBaDLyBo2CfQJhgMgm6wjGHu\nLOOAgnIWXHa/cs+ce/n+3GHmXoaMOdxgpT4xFRRwhCbaaAQ5vyVHVm8OPHUc8j9DJoM8hzjBFtaw\niNsg96gxUak3cVHr/UQXx78N+St5gGNIiHhdJR1MYwazOA90o7hHzlKd4SMFhdHAE1YrvfXqgoib\ncQNLih3sYhtXeAhw9zlQfMY76Xker1guF0Scwm9pvE/jC3rYjwzpKnZSPdFzvAe4v3CNvVS38IyF\ncjLqP2niFI9Jfom7IPeYAfAJyood4uaM00cAAAAASUVORK5CYII=\n",
350 "png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAeCAYAAADZ7LXbAAAABHNCSVQICAgIfAhkiAAAAPpJREFU\nSInt1aFKBFEUh/Gfq0WDCO6iguhoMwg2k6YFi7DRaBKMvoDZavYhDBaDLyBo2CfQJhgMgm6wjGHu\nLOOAgnIWXHa/cs+ce/n+3GHmXoaMOdxgpT4xFRRwhCbaaAQ5vyVHVm8OPHUc8j9DJoM8hzjBFtaw\niNsg96gxUak3cVHr/UQXx78N+St5gGNIiHhdJR1MYwazOA90o7hHzlKd4SMFhdHAE1YrvfXqgoib\ncQNLih3sYhtXeAhw9zlQfMY76Xker1guF0Scwm9pvE/jC3rYjwzpKnZSPdFzvAe4v3CNvVS38IyF\ncjLqP2niFI9Jfom7IPeYAfAJyood4uaM00cAAAAASUVORK5CYII=\n",
351 "prompt_number": 15,
351 "prompt_number": 15,
352 "text": [
352 "text": [
353 "-1/6"
353 "-1/6"
354 ]
354 ]
355 }
355 }
356 ],
356 ],
357 "prompt_number": 15
357 "prompt_number": 15
358 },
358 },
359 {
359 {
360 "cell_type": "code",
360 "cell_type": "code",
361 "collapsed": false,
361 "collapsed": false,
362 "input": [
362 "input": [
363 "(1/cos(x)).series(x, 0, 6)"
363 "(1/cos(x)).series(x, 0, 6)"
364 ],
364 ],
365 "language": "python",
365 "language": "python",
366 "outputs": [
366 "outputs": [
367 {
367 {
368 "latex": [
368 "latex": [
369 "$$1 + \\frac{1}{2} x^{2} + \\frac{5}{24} x^{4} + \\operatorname{\\mathcal{O}}\\left(x^{6}\\right)$$"
369 "$$1 + \\frac{1}{2} x^{2} + \\frac{5}{24} x^{4} + \\operatorname{\\mathcal{O}}\\left(x^{6}\\right)$$"
370 ],
370 ],
371 "output_type": "pyout",
371 "output_type": "pyout",
372 "png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAAAfCAYAAABedqnDAAAABHNCSVQICAgIfAhkiAAABlFJREFU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\nVzAtLS0tLS0tLS0tLS0t+B+WXJxZxtS3TgAAAABJRU5ErkJggg==\n",
372 "png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAAAfCAYAAABedqnDAAAABHNCSVQICAgIfAhkiAAABlFJREFU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\nVzAtLS0tLS0tLS0tLS0t+B+WXJxZxtS3TgAAAABJRU5ErkJggg==\n",
373 "prompt_number": 16,
373 "prompt_number": 16,
374 "text": [
374 "text": [
375 "",
375 "",
376 " 2 4 ",
376 " 2 4 ",
377 " x 5\u22c5x \u239b 6\u239e",
377 " x 5\u22c5x \u239b 6\u239e",
378 "1 + \u2500\u2500 + \u2500\u2500\u2500\u2500 + O\u239dx \u23a0",
378 "1 + \u2500\u2500 + \u2500\u2500\u2500\u2500 + O\u239dx \u23a0",
379 " 2 24 "
379 " 2 24 "
380 ]
380 ]
381 }
381 }
382 ],
382 ],
383 "prompt_number": 16
383 "prompt_number": 16
384 },
384 },
385 {
385 {
386 "cell_type": "code",
386 "cell_type": "code",
387 "collapsed": false,
387 "collapsed": false,
388 "input": [
388 "input": [
389 "diff(cos(x**2)**2 / (1+x), x)"
389 "diff(cos(x**2)**2 / (1+x), x)"
390 ],
390 ],
391 "language": "python",
391 "language": "python",
392 "outputs": [
392 "outputs": [
393 {
393 {
394 "latex": [
394 "latex": [
395 "$$- 4 \\frac{x \\operatorname{sin}\\left(x^{2}\\right) \\operatorname{cos}\\left(x^{2}\\right)}{x + 1} - \\frac{\\operatorname{cos}^{2}\\left(x^{2}\\right)}{\\left(x + 1\\right)^{2}}$$"
395 "$$- 4 \\frac{x \\operatorname{sin}\\left(x^{2}\\right) \\operatorname{cos}\\left(x^{2}\\right)}{x + 1} - \\frac{\\operatorname{cos}^{2}\\left(x^{2}\\right)}{\\left(x + 1\\right)^{2}}$$"
396 ],
396 ],
397 "output_type": "pyout",
397 "output_type": "pyout",
398 "png": "iVBORw0KGgoAAAANSUhEUgAAAMIAAAAoCAYAAACsPiXVAAAABHNCSVQICAgIfAhkiAAABhBJREFU\neJzt3G2sHUUZwPEf5YIU29tGpVawpQgCGmluYhAiNMEQJJIgbwGNVktiFAOYkIi8BAgXDKBADMYY\nEpUg1ER5k7dPakT4IGLEaKgxolZFCWCjUahKgWL58OzhbE/PObt7z569d3vm/+XuzszOPM+zZ3Zm\nnpnnkkgk7DHfAjTEGvylRLlFuBj/x6u4MZd3ALbglZpl68ca7ZJ3FIbpkGeNybHJWFiFT5Ys+2Ec\nll3fg8NzeUtweY1yDaJt8o7KMB06jN0mi0pW3mbOx3dKln0HTsmuN+PQXN5/8DROr0+0vrRN3lEZ\npkOHSbNJ7azFBRXKvwFLs+sfYP+e/D3w9RrkGkTb5K2DIh0asUnbRoS1eKJC+ZPx4wrlX8JWrMPD\neKYnf4cYXldXqLMKbZO3Dop0aMQmbesIT+oOe2V4H35bsY1lOA7XDcj/M2Yq1lmWtslbF8N0aMQm\nbesILwklyrKv8BxUYT2+hMU4oU/+ZuF9GAdtk7cuhunQiE2mKjZQhQuxl5175TFiMbMWj2Eljs/K\n/ikrc7LwEmwRP/wHRYc9G0fjq3gW5+C9uEYsiFbhbfh8rr19+sg1TIajM3mvwp5ieO3ln3h7T9pn\nxVfoKWzH3bn0aWwT7r8LhVuvn45NylsXVfVmV92XGq5D22yyEwfiv5jNpU3jU9n1afh5dn2bUIRY\n6DyeXe+HB3LlV2AjzsRnsDf+gI/k6n++R45HxReligxFnCtedIerdTv7KWJeSnTQ/EfgrkzWQTo2\nJW9dVNWb4boPok022YVviEXJbC5tH/HjJYatS/o8NyV+3JvERshbsvSlwgBPi+FuqRja/pp79gPC\naHk24oiKMhTxFd3h9mDxdVmS3b8Ry/ukw334nME6NiFvXcxFb4brPohGbDKONcLpeKhP+ja8nF2f\noOsJWJ4rs10Md1fgKN1pzlZ8XBh1UVbX8T3tnCmG5mW6O+YP4ZCKMhSxCj/Nrj+IXwj/NDEK/rtP\n+mJdL8YgHZuQty7mojfDdR9EIzapuyMswUn4Xp+8Dwl/8Bq8B7/K2v9Ylr9azP1fFT/4W/DH3PPr\nxfB3lhhtejvCWfguPprlw704sYIMReyHv+N/2f0zopN2mBId8tme9Itwu5i6DdNx3PLWRVW9Nyl+\nv4NoxCZ7lny4LFfia/iXmBY9ovs1WCeGuBVZ2kx2fzdeFAacwkHCaG/CN3N1HyK+9r8Ri7MviKGx\n8/V5txg2H8dzWdq2rJ3t+FsJGYq4FjfjH9n977M6Dhfb+kfifvHiZ/AuHJvp9sUSOo5b3rqoqjfF\nug+iLTZ5nRlcmrvvXSPMF51DWKNyGM6ooZ4i2iZvE7TGJovEtGXvXNpC6QiJRCF1rRHOwbd1FzGJ\nRKvIb6gdIdyeZWMUfi18sSvF/PzmekVLjJm5vu/dkjoCc9Zjg3ChddhLeI+exO+E5+CeGtpK1MOo\n731HcZEE4dpKa4REaxjXWaPpnr+JRJOUDf8cG9P4ifDR7siE+BlObVqQxERTJvwzMWaW40cWdjDM\n7s4FYlcbrhcdI1Ej5xfkf1psKu4Q66RJY/ECabcoXDMxIrMly01iRzhRnD6dD1aIM2a9rLPzaYeB\ntC1CrS6OwSdwg9hyPw/fF8EeieqsECc6NzfQVr+p5xZxdil/XLsoXHPiGSWwY7ZkG5M2IlymHg/h\nKFPPKRGV1uE8sZ81KFxzl4cnjZdFsAdxJv7e7HpDT7m3ikVXfvPpWDuHDm4VEVmTzv54oYZ6igJ1\nOqdVr+2Tt12ccCCOZBeFayZy/FIcIaZcYMdsyXonbUT4Vs/9XKeesyXbG2Tf3oOfpZnENcKogR2J\nXcn/+KaF336jCJ29SPxDra3qDxDq5Tm8eS4PTuLUaCXeKTb5LhMHybbhjhrq3iAWaHCTCBy5qYZ6\nFzrLctfzOfVcLUJGE2OmjuCQ3ZE7B6Q3PfUcJEchkzg1GoUvz7cAC5RHhfuU+Zt67msE923dMcuJ\nyWSTcGv+0Ggxxcfpxrj3Y4PoZDMi9nml+AdfsvZvlaZGiXnm/brToLky16nngXaf+OxEIpFIJBKJ\nRCKRSCQWBq8BH7XPIH70GuoAAAAASUVORK5CYII=\n",
398 "png": "iVBORw0KGgoAAAANSUhEUgAAAMIAAAAoCAYAAACsPiXVAAAABHNCSVQICAgIfAhkiAAABhBJREFU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\nRCKRSCQWBq8BH7XPIH70GuoAAAAASUVORK5CYII=\n",
399 "prompt_number": 17,
399 "prompt_number": 17,
400 "text": [
400 "text": [
401 "",
401 "",
402 " 2 ",
402 " 2 ",
403 " \u239b 2\u239e \u239b 2\u239e \u239b 2\u239e",
403 " \u239b 2\u239e \u239b 2\u239e \u239b 2\u239e",
404 " 4\u22c5x\u22c5sin\u239dx \u23a0\u22c5cos\u239dx \u23a0 cos \u239dx \u23a0",
404 " 4\u22c5x\u22c5sin\u239dx \u23a0\u22c5cos\u239dx \u23a0 cos \u239dx \u23a0",
405 "- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500",
405 "- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500",
406 " x + 1 2",
406 " x + 1 2",
407 " (x + 1) "
407 " (x + 1) "
408 ]
408 ]
409 }
409 }
410 ],
410 ],
411 "prompt_number": 17
411 "prompt_number": 17
412 },
412 },
413 {
413 {
414 "cell_type": "code",
414 "cell_type": "code",
415 "collapsed": false,
415 "collapsed": false,
416 "input": [
416 "input": [
417 "integrate(x**2 * cos(x), (x, 0, pi/2))"
417 "integrate(x**2 * cos(x), (x, 0, pi/2))"
418 ],
418 ],
419 "language": "python",
419 "language": "python",
420 "outputs": [
420 "outputs": [
421 {
421 {
422 "latex": [
422 "latex": [
423 "$$-2 + \\frac{1}{4} \\pi^{2}$$"
423 "$$-2 + \\frac{1}{4} \\pi^{2}$$"
424 ],
424 ],
425 "output_type": "pyout",
425 "output_type": "pyout",
426 "png": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAAfCAYAAABNjStyAAAABHNCSVQICAgIfAhkiAAAArVJREFU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\nTp1YfAdxIoFGVphKVAAAAABJRU5ErkJggg==\n",
426 "png": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAAfCAYAAABNjStyAAAABHNCSVQICAgIfAhkiAAAArVJREFU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\nTp1YfAdxIoFGVphKVAAAAABJRU5ErkJggg==\n",
427 "prompt_number": 18,
427 "prompt_number": 18,
428 "text": [
428 "text": [
429 "",
429 "",
430 " 2",
430 " 2",
431 " \u03c0 ",
431 " \u03c0 ",
432 "-2 + \u2500\u2500",
432 "-2 + \u2500\u2500",
433 " 4 "
433 " 4 "
434 ]
434 ]
435 }
435 }
436 ],
436 ],
437 "prompt_number": 18
437 "prompt_number": 18
438 },
438 },
439 {
439 {
440 "cell_type": "code",
440 "cell_type": "code",
441 "collapsed": false,
441 "collapsed": false,
442 "input": [
442 "input": [
443 "eqn = Eq(Derivative(f(x),x,x) + 9*f(x), 1)",
443 "eqn = Eq(Derivative(f(x),x,x) + 9*f(x), 1)",
444 "display(eqn)",
444 "display(eqn)",
445 "dsolve(eqn, f(x))"
445 "dsolve(eqn, f(x))"
446 ],
446 ],
447 "language": "python",
447 "language": "python",
448 "outputs": [
448 "outputs": [
449 {
449 {
450 "latex": [
450 "latex": [
451 "$$9 \\operatorname{f}\\left(x\\right) + \\frac{\\partial^{2}}{\\partial^{2} x} \\operatorname{f}\\left(x\\right) = 1$$"
451 "$$9 \\operatorname{f}\\left(x\\right) + \\frac{\\partial^{2}}{\\partial^{2} x} \\operatorname{f}\\left(x\\right) = 1$$"
452 ],
452 ],
453 "output_type": "display_data",
453 "output_type": "display_data",
454 "png": "iVBORw0KGgoAAAANSUhEUgAAAI4AAAAnCAYAAADZ7nAuAAAABHNCSVQICAgIfAhkiAAABX5JREFU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\n",
454 "png": "iVBORw0KGgoAAAANSUhEUgAAAI4AAAAnCAYAAADZ7nAuAAAABHNCSVQICAgIfAhkiAAABX5JREFU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\n",
455 "text": [
455 "text": [
456 "",
456 "",
457 " 2 ",
457 " 2 ",
458 " d ",
458 " d ",
459 "9\u22c5f(x) + \u2500\u2500\u2500(f(x)) = 1",
459 "9\u22c5f(x) + \u2500\u2500\u2500(f(x)) = 1",
460 " 2 ",
460 " 2 ",
461 " dx "
461 " dx "
462 ]
462 ]
463 },
463 },
464 {
464 {
465 "latex": [
465 "latex": [
466 "$$\\operatorname{f}\\left(x\\right) = C_{1} \\operatorname{sin}\\left(3 x\\right) + C_{2} \\operatorname{cos}\\left(3 x\\right) + \\frac{1}{9}$$"
466 "$$\\operatorname{f}\\left(x\\right) = C_{1} \\operatorname{sin}\\left(3 x\\right) + C_{2} \\operatorname{cos}\\left(3 x\\right) + \\frac{1}{9}$$"
467 ],
467 ],
468 "output_type": "pyout",
468 "output_type": "pyout",
469 "png": "iVBORw0KGgoAAAANSUhEUgAAAQUAAAAeCAYAAAAl8At9AAAABHNCSVQICAgIfAhkiAAACFtJREFU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\n",
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470 "prompt_number": 19,
470 "prompt_number": 19,
471 "text": [
471 "text": [
472 "f(x) = C\u2081\u22c5sin(3\u22c5x) + C\u2082\u22c5cos(3\u22c5x) + 1/9"
472 "f(x) = C\u2081\u22c5sin(3\u22c5x) + C\u2082\u22c5cos(3\u22c5x) + 1/9"
473 ]
473 ]
474 }
474 }
475 ],
475 ],
476 "prompt_number": 19
476 "prompt_number": 19
477 },
477 },
478 {
478 {
479 "cell_type": "markdown",
479 "cell_type": "markdown",
480 "source": [
480 "source": [
481 "# Illustrating Taylor series",
481 "# Illustrating Taylor series",
482 "",
482 "",
483 "We will define a function to compute the Taylor series expansions of a symbolically defined expression at",
483 "We will define a function to compute the Taylor series expansions of a symbolically defined expression at",
484 "various orders and visualize all the approximations together with the original function"
484 "various orders and visualize all the approximations together with the original function"
485 ]
485 ]
486 },
486 },
487 {
487 {
488 "cell_type": "code",
488 "cell_type": "code",
489 "collapsed": true,
489 "collapsed": true,
490 "input": [
490 "input": [
491 "# You can change the default figure size to be a bit larger if you want,",
491 "# You can change the default figure size to be a bit larger if you want,",
492 "# uncomment the next line for that:",
492 "# uncomment the next line for that:",
493 "#plt.rc('figure', figsize=(10, 6))"
493 "#plt.rc('figure', figsize=(10, 6))"
494 ],
494 ],
495 "language": "python",
495 "language": "python",
496 "outputs": [],
496 "outputs": [],
497 "prompt_number": 20
497 "prompt_number": 20
498 },
498 },
499 {
499 {
500 "cell_type": "code",
500 "cell_type": "code",
501 "collapsed": true,
501 "collapsed": true,
502 "input": [
502 "input": [
503 "def plot_taylor_approximations(func, x0=None, orders=(2, 4), xrange=(0,1), yrange=None, npts=200):",
503 "def plot_taylor_approximations(func, x0=None, orders=(2, 4), xrange=(0,1), yrange=None, npts=200):",
504 " \"\"\"Plot the Taylor series approximations to a function at various orders.",
504 " \"\"\"Plot the Taylor series approximations to a function at various orders.",
505 "",
505 "",
506 " Parameters",
506 " Parameters",
507 " ----------",
507 " ----------",
508 " func : a sympy function",
508 " func : a sympy function",
509 " x0 : float",
509 " x0 : float",
510 " Origin of the Taylor series expansion. If not given, x0=xrange[0].",
510 " Origin of the Taylor series expansion. If not given, x0=xrange[0].",
511 " orders : list",
511 " orders : list",
512 " List of integers with the orders of Taylor series to show. Default is (2, 4).",
512 " List of integers with the orders of Taylor series to show. Default is (2, 4).",
513 " xrange : 2-tuple or array.",
513 " xrange : 2-tuple or array.",
514 " Either an (xmin, xmax) tuple indicating the x range for the plot (default is (0, 1)),",
514 " Either an (xmin, xmax) tuple indicating the x range for the plot (default is (0, 1)),",
515 " or the actual array of values to use.",
515 " or the actual array of values to use.",
516 " yrange : 2-tuple",
516 " yrange : 2-tuple",
517 " (ymin, ymax) tuple indicating the y range for the plot. If not given,",
517 " (ymin, ymax) tuple indicating the y range for the plot. If not given,",
518 " the full range of values will be automatically used. ",
518 " the full range of values will be automatically used. ",
519 " npts : int",
519 " npts : int",
520 " Number of points to sample the x range with. Default is 200.",
520 " Number of points to sample the x range with. Default is 200.",
521 " \"\"\"",
521 " \"\"\"",
522 " if not callable(func):",
522 " if not callable(func):",
523 " raise ValueError('func must be callable')",
523 " raise ValueError('func must be callable')",
524 " if isinstance(xrange, (list, tuple)):",
524 " if isinstance(xrange, (list, tuple)):",
525 " x = np.linspace(float(xrange[0]), float(xrange[1]), npts)",
525 " x = np.linspace(float(xrange[0]), float(xrange[1]), npts)",
526 " else:",
526 " else:",
527 " x = xrange",
527 " x = xrange",
528 " if x0 is None: x0 = x[0]",
528 " if x0 is None: x0 = x[0]",
529 " xs = sym.Symbol('x')",
529 " xs = sym.Symbol('x')",
530 " # Make a numpy-callable form of the original function for plotting",
530 " # Make a numpy-callable form of the original function for plotting",
531 " fx = func(xs)",
531 " fx = func(xs)",
532 " f = sym.lambdify(xs, fx, modules=['numpy'])",
532 " f = sym.lambdify(xs, fx, modules=['numpy'])",
533 " # We could use latex(fx) instead of str(), but matploblib gets confused",
533 " # We could use latex(fx) instead of str(), but matploblib gets confused",
534 " # with some of the (valid) latex constructs sympy emits. So we play it safe.",
534 " # with some of the (valid) latex constructs sympy emits. So we play it safe.",
535 " plot(x, f(x), label=str(fx), lw=2)",
535 " plot(x, f(x), label=str(fx), lw=2)",
536 " # Build the Taylor approximations, plotting as we go",
536 " # Build the Taylor approximations, plotting as we go",
537 " apps = {}",
537 " apps = {}",
538 " for order in orders:",
538 " for order in orders:",
539 " app = fx.series(xs, x0, n=order).removeO()",
539 " app = fx.series(xs, x0, n=order).removeO()",
540 " apps[order] = app",
540 " apps[order] = app",
541 " # Must be careful here: if the approximation is a constant, we can't",
541 " # Must be careful here: if the approximation is a constant, we can't",
542 " # blindly use lambdify as it won't do the right thing. In that case, ",
542 " # blindly use lambdify as it won't do the right thing. In that case, ",
543 " # evaluate the number as a float and fill the y array with that value.",
543 " # evaluate the number as a float and fill the y array with that value.",
544 " if isinstance(app, sym.numbers.Number):",
544 " if isinstance(app, sym.numbers.Number):",
545 " y = np.zeros_like(x)",
545 " y = np.zeros_like(x)",
546 " y.fill(app.evalf())",
546 " y.fill(app.evalf())",
547 " else:",
547 " else:",
548 " fa = sym.lambdify(xs, app, modules=['numpy'])",
548 " fa = sym.lambdify(xs, app, modules=['numpy'])",
549 " y = fa(x)",
549 " y = fa(x)",
550 " tex = sym.latex(app).replace('$', '')",
550 " tex = sym.latex(app).replace('$', '')",
551 " plot(x, y, label=r'$n=%s:\\, %s$' % (order, tex) )",
551 " plot(x, y, label=r'$n=%s:\\, %s$' % (order, tex) )",
552 " ",
552 " ",
553 " # Plot refinements",
553 " # Plot refinements",
554 " if yrange is not None:",
554 " if yrange is not None:",
555 " plt.ylim(*yrange)",
555 " plt.ylim(*yrange)",
556 " grid()",
556 " grid()",
557 " legend(loc='best').get_frame().set_alpha(0.8)"
557 " legend(loc='best').get_frame().set_alpha(0.8)"
558 ],
558 ],
559 "language": "python",
559 "language": "python",
560 "outputs": [],
560 "outputs": [],
561 "prompt_number": 21
561 "prompt_number": 21
562 },
562 },
563 {
563 {
564 "cell_type": "markdown",
564 "cell_type": "markdown",
565 "source": [
565 "source": [
566 "With this function defined, we can now use it for any sympy function or expression"
566 "With this function defined, we can now use it for any sympy function or expression"
567 ]
567 ]
568 },
568 },
569 {
569 {
570 "cell_type": "code",
570 "cell_type": "code",
571 "collapsed": false,
571 "collapsed": false,
572 "input": [
572 "input": [
573 "plot_taylor_approximations(sin, 0, [2, 4, 6], (0, 2*pi), (-2,2))"
573 "plot_taylor_approximations(sin, 0, [2, 4, 6], (0, 2*pi), (-2,2))"
574 ],
574 ],
575 "language": "python",
575 "language": "python",
576 "outputs": [
576 "outputs": [
577 {
577 {
578 "output_type": "display_data",
578 "output_type": "display_data",
579 "png": 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MwoMQYO5cIDSUbroyMlKom7t3aZROTAzQqBGwaxcwaBB1dx1NTcUPT5/Crn59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\n8+bNePHiBaZOnYozZ84AAIKDgzFt2jQUFRVh1qx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579 "png": 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MwoMQYO5cIDSUbroyMlKom7t3aZROTAzQqBGwaxcwaBB1dx1NTcUPT5/Crn59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\nnD9fO428zKjZfSQzPJKiEEL28/FC+9a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580 }
580 }
581 ],
581 ],
582 "prompt_number": 22
582 "prompt_number": 22
583 },
583 },
584 {
584 {
585 "cell_type": "code",
585 "cell_type": "code",
586 "collapsed": false,
586 "collapsed": false,
587 "input": [
587 "input": [
588 "plot_taylor_approximations(cos, 0, [2, 4, 6], (0, 2*pi), (-2,2))"
588 "plot_taylor_approximations(cos, 0, [2, 4, 6], (0, 2*pi), (-2,2))"
589 ],
589 ],
590 "language": "python",
590 "language": "python",
591 "outputs": [
591 "outputs": [
592 {
592 {
593 "output_type": "display_data",
593 "output_type": "display_data",
594 "png": 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4q3ZtmpQtq7YUq+fyZejXD5KTlTN6c+eqrUhSGMhcN9bOqlXKqamjR3Ot2SaE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\ndow29M7OzjRr1kyvvsUhK6WW/cR6ax8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594 "png": 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4q3ZtmpQtq7YUq+fyZejXD5KTlTN6c+eqrUhSGMhcN9bOqlXKqamjR3Ot2SaE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\ndow29M7OzjRr1kyvvsUhK6WW/cR6ax8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595 }
595 }
596 ],
596 ],
597 "prompt_number": 23
597 "prompt_number": 23
598 },
598 },
599 {
599 {
600 "cell_type": "markdown",
600 "cell_type": "markdown",
601 "source": [
601 "source": [
602 "This shows easily how a Taylor series is useless beyond its convergence radius, illustrated by ",
602 "This shows easily how a Taylor series is useless beyond its convergence radius, illustrated by ",
603 "a simple function that has singularities on the real axis:"
603 "a simple function that has singularities on the real axis:"
604 ]
604 ]
605 },
605 },
606 {
606 {
607 "cell_type": "code",
607 "cell_type": "code",
608 "collapsed": false,
608 "collapsed": false,
609 "input": [
609 "input": [
610 "# For an expression made from elementary functions, we must first make it into",
610 "# For an expression made from elementary functions, we must first make it into",
611 "# a callable function, the simplest way is to use the Python lambda construct.",
611 "# a callable function, the simplest way is to use the Python lambda construct.",
612 "plot_taylor_approximations(lambda x: 1/cos(x), 0, [2,4,6], (0, 2*pi), (-5,5))"
612 "plot_taylor_approximations(lambda x: 1/cos(x), 0, [2,4,6], (0, 2*pi), (-5,5))"
613 ],
613 ],
614 "language": "python",
614 "language": "python",
615 "outputs": [
615 "outputs": [
616 {
616 {
617 "output_type": "display_data",
617 "output_type": "display_data",
618 "png": 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GloMfwPXLDcs9QJa1A+zrFwIP4BwOh8MoPICbQaPRyC3BKrh+eWF5LjLL2gH2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\nIQwG86sqpdRfVsvmzZslK7cy5H7+1mK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618 "png": 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Dd+wA7tyRrlyOZfAAbgZTPlpMDD2OGUODeFm2ZGbiUG4ulolIS//E1HCDAZg/n5rrP/wA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\nIQwG86sqpdRfVsvmzZslK7cy5H7+1mK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619 }
619 }
620 ],
620 ],
621 "prompt_number": 24
621 "prompt_number": 24
622 }
622 }
623 ]
623 ]
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@@ -2,7 +2,7 b''
2 "metadata": {
2 "metadata": {
3 "name": "sympy_quantum_computing"
3 "name": "sympy_quantum_computing"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
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@@ -1,115 +1,115 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "trapezoid_rule"
3 "name": "trapezoid_rule"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "Basic numerical integration: the trapezoid rule",
12 "Basic numerical integration: the trapezoid rule",
13 "===============================================",
13 "===============================================",
14 "",
14 "",
15 "A simple illustration of the trapezoid rule for definite integration:",
15 "A simple illustration of the trapezoid rule for definite integration:",
16 "",
16 "",
17 "$$",
17 "$$",
18 "\\int_{a}^{b} f(x)\\, dx \\approx \\frac{1}{2} \\sum_{k=1}^{N} \\left( x_{k} - x_{k-1} \\right) \\left( f(x_{k}) + f(x_{k-1}) \\right).",
18 "\\int_{a}^{b} f(x)\\, dx \\approx \\frac{1}{2} \\sum_{k=1}^{N} \\left( x_{k} - x_{k-1} \\right) \\left( f(x_{k}) + f(x_{k-1}) \\right).",
19 "$$",
19 "$$",
20 "<br>",
20 "<br>",
21 "First, we define a simple function and sample it between 0 and 10 at 200 points"
21 "First, we define a simple function and sample it between 0 and 10 at 200 points"
22 ]
22 ]
23 },
23 },
24 {
24 {
25 "cell_type": "code",
25 "cell_type": "code",
26 "collapsed": true,
26 "collapsed": true,
27 "input": [
27 "input": [
28 "def f(x):",
28 "def f(x):",
29 " return (x-3)*(x-5)*(x-7)+85",
29 " return (x-3)*(x-5)*(x-7)+85",
30 "",
30 "",
31 "x = linspace(0, 10, 200)",
31 "x = linspace(0, 10, 200)",
32 "y = f(x)"
32 "y = f(x)"
33 ],
33 ],
34 "language": "python",
34 "language": "python",
35 "outputs": [],
35 "outputs": [],
36 "prompt_number": 1
36 "prompt_number": 1
37 },
37 },
38 {
38 {
39 "cell_type": "markdown",
39 "cell_type": "markdown",
40 "source": [
40 "source": [
41 "Choose a region to integrate over and take only a few points in that region"
41 "Choose a region to integrate over and take only a few points in that region"
42 ]
42 ]
43 },
43 },
44 {
44 {
45 "cell_type": "code",
45 "cell_type": "code",
46 "collapsed": true,
46 "collapsed": true,
47 "input": [
47 "input": [
48 "a, b = 1, 9",
48 "a, b = 1, 9",
49 "xint = x[logical_and(x>=a, x<=b)][::30]",
49 "xint = x[logical_and(x>=a, x<=b)][::30]",
50 "yint = y[logical_and(x>=a, x<=b)][::30]"
50 "yint = y[logical_and(x>=a, x<=b)][::30]"
51 ],
51 ],
52 "language": "python",
52 "language": "python",
53 "outputs": [],
53 "outputs": [],
54 "prompt_number": 2
54 "prompt_number": 2
55 },
55 },
56 {
56 {
57 "cell_type": "markdown",
57 "cell_type": "markdown",
58 "source": [
58 "source": [
59 "Plot both the function and the area below it in the trapezoid approximation"
59 "Plot both the function and the area below it in the trapezoid approximation"
60 ]
60 ]
61 },
61 },
62 {
62 {
63 "cell_type": "code",
63 "cell_type": "code",
64 "collapsed": false,
64 "collapsed": false,
65 "input": [
65 "input": [
66 "plot(x, y, lw=2)",
66 "plot(x, y, lw=2)",
67 "axis([0, 10, 0, 140])",
67 "axis([0, 10, 0, 140])",
68 "fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)",
68 "fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)",
69 "text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);"
69 "text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);"
70 ],
70 ],
71 "language": "python",
71 "language": "python",
72 "outputs": [
72 "outputs": [
73 {
73 {
74 "output_type": "display_data",
74 "output_type": "display_data",
75 "png": 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75 "png": 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x4gTLli3jm2++qXlAjabOXwLmrrwcRo1Sxmh/4gnYvr2q22NZWRmbNm3CysqK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\nAElFTkSuQmCC\n"
76 }
76 }
77 ],
77 ],
78 "prompt_number": 3
78 "prompt_number": 3
79 },
79 },
80 {
80 {
81 "cell_type": "markdown",
81 "cell_type": "markdown",
82 "source": [
82 "source": [
83 "Compute the integral both at high accuracy and with the trapezoid approximation"
83 "Compute the integral both at high accuracy and with the trapezoid approximation"
84 ]
84 ]
85 },
85 },
86 {
86 {
87 "cell_type": "code",
87 "cell_type": "code",
88 "collapsed": false,
88 "collapsed": false,
89 "input": [
89 "input": [
90 "from scipy.integrate import quad, trapz",
90 "from scipy.integrate import quad, trapz",
91 "integral, error = quad(f, 1, 9)",
91 "integral, error = quad(f, 1, 9)",
92 "print \"The integral is:\", integral, \"+/-\", error",
92 "print \"The integral is:\", integral, \"+/-\", error",
93 "print \"The trapezoid approximation with\", len(xint), \"points is:\", trapz(yint, xint)"
93 "print \"The trapezoid approximation with\", len(xint), \"points is:\", trapz(yint, xint)"
94 ],
94 ],
95 "language": "python",
95 "language": "python",
96 "outputs": [
96 "outputs": [
97 {
97 {
98 "output_type": "stream",
98 "output_type": "stream",
99 "stream": "stdout",
99 "stream": "stdout",
100 "text": [
100 "text": [
101 "The integral is: 680.0 +/- 7.54951656745e-12",
101 "The integral is: 680.0 +/- 7.54951656745e-12",
102 "The trapezoid approximation with 6 points is: 621.286411141"
102 "The trapezoid approximation with 6 points is: 621.286411141"
103 ]
103 ]
104 }
104 }
105 ],
105 ],
106 "prompt_number": 4
106 "prompt_number": 4
107 },
107 },
108 {
108 {
109 "cell_type": "code",
109 "cell_type": "code",
110 "collapsed": true,
110 "collapsed": true,
111 "input": [],
111 "input": [],
112 "language": "python",
112 "language": "python",
113 "outputs": []
113 "outputs": []
114 }
114 }
115 ]
115 ]
Show file before | Show file after | Hide comments
@@ -1,89 +1,89 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "helloworld"
3 "name": "helloworld"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# Distributed hello world",
12 "# Distributed hello world",
13 "",
13 "",
14 "Originally by Ken Kinder (ken at kenkinder dom com)"
14 "Originally by Ken Kinder (ken at kenkinder dom com)"
15 ]
15 ]
16 },
16 },
17 {
17 {
18 "cell_type": "code",
18 "cell_type": "code",
19 "collapsed": true,
19 "collapsed": true,
20 "input": [
20 "input": [
21 "from IPython.parallel import Client"
21 "from IPython.parallel import Client"
22 ],
22 ],
23 "language": "python",
23 "language": "python",
24 "outputs": [],
24 "outputs": [],
25 "prompt_number": 1
25 "prompt_number": 1
26 },
26 },
27 {
27 {
28 "cell_type": "code",
28 "cell_type": "code",
29 "collapsed": true,
29 "collapsed": true,
30 "input": [
30 "input": [
31 "rc = Client()",
31 "rc = Client()",
32 "view = rc.load_balanced_view()"
32 "view = rc.load_balanced_view()"
33 ],
33 ],
34 "language": "python",
34 "language": "python",
35 "outputs": [],
35 "outputs": [],
36 "prompt_number": 2
36 "prompt_number": 2
37 },
37 },
38 {
38 {
39 "cell_type": "code",
39 "cell_type": "code",
40 "collapsed": true,
40 "collapsed": true,
41 "input": [
41 "input": [
42 "def sleep_and_echo(t, msg):",
42 "def sleep_and_echo(t, msg):",
43 " import time",
43 " import time",
44 " time.sleep(t)",
44 " time.sleep(t)",
45 " return msg"
45 " return msg"
46 ],
46 ],
47 "language": "python",
47 "language": "python",
48 "outputs": [],
48 "outputs": [],
49 "prompt_number": 3
49 "prompt_number": 3
50 },
50 },
51 {
51 {
52 "cell_type": "code",
52 "cell_type": "code",
53 "collapsed": true,
53 "collapsed": true,
54 "input": [
54 "input": [
55 "world = view.apply_async(sleep_and_echo, 3, 'World!')",
55 "world = view.apply_async(sleep_and_echo, 3, 'World!')",
56 "hello = view.apply_async(sleep_and_echo, 2, 'Hello')"
56 "hello = view.apply_async(sleep_and_echo, 2, 'Hello')"
57 ],
57 ],
58 "language": "python",
58 "language": "python",
59 "outputs": [],
59 "outputs": [],
60 "prompt_number": 4
60 "prompt_number": 4
61 },
61 },
62 {
62 {
63 "cell_type": "code",
63 "cell_type": "code",
64 "collapsed": false,
64 "collapsed": false,
65 "input": [
65 "input": [
66 "print \"Submitted tasks:\", hello.msg_ids, world.msg_ids",
66 "print \"Submitted tasks:\", hello.msg_ids, world.msg_ids",
67 "print hello.get(), world.get()"
67 "print hello.get(), world.get()"
68 ],
68 ],
69 "language": "python",
69 "language": "python",
70 "outputs": [
70 "outputs": [
71 {
71 {
72 "output_type": "stream",
72 "output_type": "stream",
73 "stream": "stdout",
73 "stream": "stdout",
74 "text": [
74 "text": [
75 "Submitted tasks: ['dd1052e0-aa75-4b25-9d35-ecbdaf6e3ed7'] ['1b46aa21-20d1-459c-bc36-2d8d03336f74']",
75 "Submitted tasks: ['dd1052e0-aa75-4b25-9d35-ecbdaf6e3ed7'] ['1b46aa21-20d1-459c-bc36-2d8d03336f74']",
76 "Hello"
76 "Hello"
77 ]
77 ]
78 },
78 },
79 {
79 {
80 "output_type": "stream",
80 "output_type": "stream",
81 "stream": "stdout",
81 "stream": "stdout",
82 "text": [
82 "text": [
83 " World!"
83 " World!"
84 ]
84 ]
85 }
85 }
86 ],
86 ],
87 "prompt_number": 5
87 "prompt_number": 5
88 }
88 }
89 ]
89 ]
Show file before | Show file after | Hide comments
@@ -1,221 +1,221 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "parallel_mpi"
3 "name": "parallel_mpi"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# Simple usage of a set of MPI engines",
12 "# Simple usage of a set of MPI engines",
13 "",
13 "",
14 "This example assumes you've started a cluster of N engines (4 in this example) as part",
14 "This example assumes you've started a cluster of N engines (4 in this example) as part",
15 "of an MPI world. ",
15 "of an MPI world. ",
16 "",
16 "",
17 "Our documentation describes [how to create an MPI profile](http://ipython.org/ipython-doc/dev/parallel/parallel_process.html#using-ipcluster-in-mpiexec-mpirun-mode)",
17 "Our documentation describes [how to create an MPI profile](http://ipython.org/ipython-doc/dev/parallel/parallel_process.html#using-ipcluster-in-mpiexec-mpirun-mode)",
18 "and explains [basic MPI usage of the IPython cluster](http://ipython.org/ipython-doc/dev/parallel/parallel_mpi.html).",
18 "and explains [basic MPI usage of the IPython cluster](http://ipython.org/ipython-doc/dev/parallel/parallel_mpi.html).",
19 "",
19 "",
20 "",
20 "",
21 "For the simplest possible way to start 4 engines that belong to the same MPI world, ",
21 "For the simplest possible way to start 4 engines that belong to the same MPI world, ",
22 "you can run this in a terminal or antoher notebook:",
22 "you can run this in a terminal or antoher notebook:",
23 "",
23 "",
24 "<pre>",
24 "<pre>",
25 "ipcluster start --engines=MPI -n 4",
25 "ipcluster start --engines=MPI -n 4",
26 "</pre>",
26 "</pre>",
27 "",
27 "",
28 "Note: to run the above in a notebook, use a *new* notebook and prepend the command with `!`, but do not run",
28 "Note: to run the above in a notebook, use a *new* notebook and prepend the command with `!`, but do not run",
29 "it in *this* notebook, as this command will block until you shut down the cluster. To stop the cluster, use ",
29 "it in *this* notebook, as this command will block until you shut down the cluster. To stop the cluster, use ",
30 "the 'Interrupt' button on the left, which is the equivalent of sending `Ctrl-C` to the kernel.",
30 "the 'Interrupt' button on the left, which is the equivalent of sending `Ctrl-C` to the kernel.",
31 "",
31 "",
32 "Once the cluster is running, we can connect to it and open a view into it:"
32 "Once the cluster is running, we can connect to it and open a view into it:"
33 ]
33 ]
34 },
34 },
35 {
35 {
36 "cell_type": "code",
36 "cell_type": "code",
37 "collapsed": true,
37 "collapsed": true,
38 "input": [
38 "input": [
39 "from IPython.parallel import Client",
39 "from IPython.parallel import Client",
40 "c = Client()",
40 "c = Client()",
41 "view = c[:]"
41 "view = c[:]"
42 ],
42 ],
43 "language": "python",
43 "language": "python",
44 "outputs": [],
44 "outputs": [],
45 "prompt_number": 21
45 "prompt_number": 21
46 },
46 },
47 {
47 {
48 "cell_type": "markdown",
48 "cell_type": "markdown",
49 "source": [
49 "source": [
50 "Let's define a simple function that gets the MPI rank from each engine."
50 "Let's define a simple function that gets the MPI rank from each engine."
51 ]
51 ]
52 },
52 },
53 {
53 {
54 "cell_type": "code",
54 "cell_type": "code",
55 "collapsed": true,
55 "collapsed": true,
56 "input": [
56 "input": [
57 "@view.remote(block=True)",
57 "@view.remote(block=True)",
58 "def mpi_rank():",
58 "def mpi_rank():",
59 " from mpi4py import MPI",
59 " from mpi4py import MPI",
60 " comm = MPI.COMM_WORLD",
60 " comm = MPI.COMM_WORLD",
61 " return comm.Get_rank()"
61 " return comm.Get_rank()"
62 ],
62 ],
63 "language": "python",
63 "language": "python",
64 "outputs": [],
64 "outputs": [],
65 "prompt_number": 22
65 "prompt_number": 22
66 },
66 },
67 {
67 {
68 "cell_type": "code",
68 "cell_type": "code",
69 "collapsed": false,
69 "collapsed": false,
70 "input": [
70 "input": [
71 "mpi_rank()"
71 "mpi_rank()"
72 ],
72 ],
73 "language": "python",
73 "language": "python",
74 "outputs": [
74 "outputs": [
75 {
75 {
76 "output_type": "pyout",
76 "output_type": "pyout",
77 "prompt_number": 23,
77 "prompt_number": 23,
78 "text": [
78 "text": [
79 "[3, 0, 2, 1]"
79 "[3, 0, 2, 1]"
80 ]
80 ]
81 }
81 }
82 ],
82 ],
83 "prompt_number": 23
83 "prompt_number": 23
84 },
84 },
85 {
85 {
86 "cell_type": "markdown",
86 "cell_type": "markdown",
87 "source": [
87 "source": [
88 "For interactive convenience, we load the parallel magic extensions and make this view",
88 "For interactive convenience, we load the parallel magic extensions and make this view",
89 "the active one for the automatic parallelism magics.",
89 "the active one for the automatic parallelism magics.",
90 "",
90 "",
91 "This is not necessary and in production codes likely won't be used, as the engines will ",
91 "This is not necessary and in production codes likely won't be used, as the engines will ",
92 "load their own MPI codes separately. But it makes it easy to illustrate everything from",
92 "load their own MPI codes separately. But it makes it easy to illustrate everything from",
93 "within a single notebook here."
93 "within a single notebook here."
94 ]
94 ]
95 },
95 },
96 {
96 {
97 "cell_type": "code",
97 "cell_type": "code",
98 "collapsed": true,
98 "collapsed": true,
99 "input": [
99 "input": [
100 "%load_ext parallelmagic",
100 "%load_ext parallelmagic",
101 "view.activate()"
101 "view.activate()"
102 ],
102 ],
103 "language": "python",
103 "language": "python",
104 "outputs": [],
104 "outputs": [],
105 "prompt_number": 4
105 "prompt_number": 4
106 },
106 },
107 {
107 {
108 "cell_type": "markdown",
108 "cell_type": "markdown",
109 "source": [
109 "source": [
110 "Use the autopx magic to make the rest of this cell execute on the engines instead",
110 "Use the autopx magic to make the rest of this cell execute on the engines instead",
111 "of locally"
111 "of locally"
112 ]
112 ]
113 },
113 },
114 {
114 {
115 "cell_type": "code",
115 "cell_type": "code",
116 "collapsed": true,
116 "collapsed": true,
117 "input": [
117 "input": [
118 "view.block = True"
118 "view.block = True"
119 ],
119 ],
120 "language": "python",
120 "language": "python",
121 "outputs": [],
121 "outputs": [],
122 "prompt_number": 24
122 "prompt_number": 24
123 },
123 },
124 {
124 {
125 "cell_type": "code",
125 "cell_type": "code",
126 "collapsed": false,
126 "collapsed": false,
127 "input": [
127 "input": [
128 "%autopx"
128 "%autopx"
129 ],
129 ],
130 "language": "python",
130 "language": "python",
131 "outputs": [
131 "outputs": [
132 {
132 {
133 "output_type": "stream",
133 "output_type": "stream",
134 "stream": "stdout",
134 "stream": "stdout",
135 "text": [
135 "text": [
136 "%autopx enabled"
136 "%autopx enabled"
137 ]
137 ]
138 }
138 }
139 ],
139 ],
140 "prompt_number": 32
140 "prompt_number": 32
141 },
141 },
142 {
142 {
143 "cell_type": "markdown",
143 "cell_type": "markdown",
144 "source": [
144 "source": [
145 "With autopx enabled, the next cell will actually execute *entirely on each engine*:"
145 "With autopx enabled, the next cell will actually execute *entirely on each engine*:"
146 ]
146 ]
147 },
147 },
148 {
148 {
149 "cell_type": "code",
149 "cell_type": "code",
150 "collapsed": true,
150 "collapsed": true,
151 "input": [
151 "input": [
152 "from mpi4py import MPI",
152 "from mpi4py import MPI",
153 "",
153 "",
154 "comm = MPI.COMM_WORLD",
154 "comm = MPI.COMM_WORLD",
155 "size = comm.Get_size()",
155 "size = comm.Get_size()",
156 "rank = comm.Get_rank()",
156 "rank = comm.Get_rank()",
157 "",
157 "",
158 "if rank == 0:",
158 "if rank == 0:",
159 " data = [(i+1)**2 for i in range(size)]",
159 " data = [(i+1)**2 for i in range(size)]",
160 "else:",
160 "else:",
161 " data = None",
161 " data = None",
162 "data = comm.scatter(data, root=0)",
162 "data = comm.scatter(data, root=0)",
163 "",
163 "",
164 "assert data == (rank+1)**2, 'data=%s, rank=%s' % (data, rank)"
164 "assert data == (rank+1)**2, 'data=%s, rank=%s' % (data, rank)"
165 ],
165 ],
166 "language": "python",
166 "language": "python",
167 "outputs": [],
167 "outputs": [],
168 "prompt_number": 29
168 "prompt_number": 29
169 },
169 },
170 {
170 {
171 "cell_type": "markdown",
171 "cell_type": "markdown",
172 "source": [
172 "source": [
173 "Though the assertion at the end of the previous block validated the code, we can now ",
173 "Though the assertion at the end of the previous block validated the code, we can now ",
174 "pull the 'data' variable from all the nodes for local inspection.",
174 "pull the 'data' variable from all the nodes for local inspection.",
175 "First, don't forget to toggle off `autopx` mode so code runs again in the notebook:"
175 "First, don't forget to toggle off `autopx` mode so code runs again in the notebook:"
176 ]
176 ]
177 },
177 },
178 {
178 {
179 "cell_type": "code",
179 "cell_type": "code",
180 "collapsed": false,
180 "collapsed": false,
181 "input": [
181 "input": [
182 "%autopx"
182 "%autopx"
183 ],
183 ],
184 "language": "python",
184 "language": "python",
185 "outputs": [
185 "outputs": [
186 {
186 {
187 "output_type": "stream",
187 "output_type": "stream",
188 "stream": "stdout",
188 "stream": "stdout",
189 "text": [
189 "text": [
190 "%autopx disabled"
190 "%autopx disabled"
191 ]
191 ]
192 }
192 }
193 ],
193 ],
194 "prompt_number": 33
194 "prompt_number": 33
195 },
195 },
196 {
196 {
197 "cell_type": "code",
197 "cell_type": "code",
198 "collapsed": false,
198 "collapsed": false,
199 "input": [
199 "input": [
200 "view['data']"
200 "view['data']"
201 ],
201 ],
202 "language": "python",
202 "language": "python",
203 "outputs": [
203 "outputs": [
204 {
204 {
205 "output_type": "pyout",
205 "output_type": "pyout",
206 "prompt_number": 34,
206 "prompt_number": 34,
207 "text": [
207 "text": [
208 "[16, 1, 9, 4]"
208 "[16, 1, 9, 4]"
209 ]
209 ]
210 }
210 }
211 ],
211 ],
212 "prompt_number": 34
212 "prompt_number": 34
213 },
213 },
214 {
214 {
215 "cell_type": "code",
215 "cell_type": "code",
216 "collapsed": true,
216 "collapsed": true,
217 "input": [],
217 "input": [],
218 "language": "python",
218 "language": "python",
219 "outputs": []
219 "outputs": []
220 }
220 }
221 ]
221 ]
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@@ -1,89 +1,118 b''
1 {
1 {
2 "nbformat": 2,
2 "metadata": {
3 "metadata": {
3 "name": "task1"
4 "name": "task_1"
4 },
5 },
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "source": "# Simple task farming example",
10 "cell_type": "markdown",
11 "cell_type": "markdown"
11 "source": [
12 },
12 "# Simple task farming example"
13 {
13 ]
14 "cell_type": "code",
14 },
15 "language": "python",
15 {
16 "outputs": [],
16 "cell_type": "code",
17 "collapsed": true,
17 "collapsed": true,
18 "prompt_number": 3,
18 "input": [
19 "input": "from IPython.parallel import Client"
19 "from IPython.parallel import Client"
20 },
20 ],
21 {
21 "language": "python",
22 "source": "A `Client.load_balanced_view` is used to get the object used for working with load balanced tasks.",
22 "outputs": [],
23 "cell_type": "markdown"
23 "prompt_number": 3
24 },
24 },
25 {
25 {
26 "cell_type": "code",
26 "cell_type": "markdown",
27 "language": "python",
27 "source": [
28 "outputs": [],
28 "A `Client.load_balanced_view` is used to get the object used for working with load balanced tasks."
29 "collapsed": true,
29 ]
30 "prompt_number": 4,
30 },
31 "input": "rc = Client()\nv = rc.load_balanced_view()"
31 {
32 },
32 "cell_type": "code",
33 {
33 "collapsed": true,
34 "source": "Set the variable `d` on all engines:",
34 "input": [
35 "cell_type": "markdown"
35 "rc = Client()",
36 },
36 "v = rc.load_balanced_view()"
37 {
37 ],
38 "cell_type": "code",
38 "language": "python",
39 "language": "python",
39 "outputs": [],
40 "outputs": [],
40 "prompt_number": 4
41 "collapsed": true,
41 },
42 "prompt_number": 5,
42 {
43 "input": "rc[:]['d'] = 30"
43 "cell_type": "markdown",
44 },
44 "source": [
45 {
45 "Set the variable `d` on all engines:"
46 "source": "Define a function that will be our task:",
46 ]
47 "cell_type": "markdown"
47 },
48 },
48 {
49 {
49 "cell_type": "code",
50 "cell_type": "code",
50 "collapsed": true,
51 "language": "python",
51 "input": [
52 "outputs": [],
52 "rc[:]['d'] = 30"
53 "collapsed": true,
53 ],
54 "prompt_number": 6,
54 "language": "python",
55 "input": "def task(a):\n return a, 10*d, a*10*d"
55 "outputs": [],
56 },
56 "prompt_number": 5
57 {
57 },
58 "source": "Run the task once:",
58 {
59 "cell_type": "markdown"
59 "cell_type": "markdown",
60 },
60 "source": [
61 {
61 "Define a function that will be our task:"
62 "cell_type": "code",
62 ]
63 "language": "python",
63 },
64 "outputs": [],
64 {
65 "collapsed": true,
65 "cell_type": "code",
66 "prompt_number": 7,
66 "collapsed": true,
67 "input": "ar = v.apply(task, 5)"
67 "input": [
68 },
68 "def task(a):",
69 {
69 " return a, 10*d, a*10*d"
70 "source": "Print the results:",
70 ],
71 "cell_type": "markdown"
71 "language": "python",
72 },
72 "outputs": [],
73 {
73 "prompt_number": 6
74 "cell_type": "code",
74 },
75 "language": "python",
75 {
76 "outputs": [
76 "cell_type": "markdown",
77 {
77 "source": [
78 "output_type": "stream",
78 "Run the task once:"
79 "text": "a, b, c: [5, 300, 1500]"
79 ]
80 }
80 },
81 ],
81 {
82 "collapsed": false,
82 "cell_type": "code",
83 "prompt_number": 8,
83 "collapsed": true,
84 "input": "print \"a, b, c: \", ar.get()"
84 "input": [
85 }
85 "ar = v.apply(task, 5)"
86 ]
86 ],
87 }
87 "language": "python",
88 ]
88 "outputs": [],
89 "prompt_number": 7
90 },
91 {
92 "cell_type": "markdown",
93 "source": [
94 "Print the results:"
95 ]
96 },
97 {
98 "cell_type": "code",
99 "collapsed": false,
100 "input": [
101 "print \"a, b, c: \", ar.get()"
102 ],
103 "language": "python",
104 "outputs": [
105 {
106 "output_type": "stream",
107 "stream": "stdout",
108 "text": [
109 "a, b, c: [5, 300, 1500]"
110 ]
111 }
112 ],
113 "prompt_number": 8
114 }
115 ]
116 }
117 ]
89 } No newline at end of file
118 }
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@@ -1,106 +1,106 b''
1 {
1 {
2 "metadata": {
2 "metadata": {
3 "name": "taskmap"
3 "name": "taskmap"
4 },
4 },
5 "nbformat": 2,
5 "nbformat": 3,
6 "worksheets": [
6 "worksheets": [
7 {
7 {
8 "cells": [
8 "cells": [
9 {
9 {
10 "cell_type": "markdown",
10 "cell_type": "markdown",
11 "source": [
11 "source": [
12 "# Load balanced map and parallel function decorator"
12 "# Load balanced map and parallel function decorator"
13 ]
13 ]
14 },
14 },
15 {
15 {
16 "cell_type": "code",
16 "cell_type": "code",
17 "collapsed": true,
17 "collapsed": true,
18 "input": [
18 "input": [
19 "from IPython.parallel import Client"
19 "from IPython.parallel import Client"
20 ],
20 ],
21 "language": "python",
21 "language": "python",
22 "outputs": [],
22 "outputs": [],
23 "prompt_number": 1
23 "prompt_number": 1
24 },
24 },
25 {
25 {
26 "cell_type": "code",
26 "cell_type": "code",
27 "collapsed": false,
27 "collapsed": false,
28 "input": [
28 "input": [
29 "rc = Client()",
29 "rc = Client()",
30 "v = rc.load_balanced_view()"
30 "v = rc.load_balanced_view()"
31 ],
31 ],
32 "language": "python",
32 "language": "python",
33 "outputs": [],
33 "outputs": [],
34 "prompt_number": 3
34 "prompt_number": 3
35 },
35 },
36 {
36 {
37 "cell_type": "code",
37 "cell_type": "code",
38 "collapsed": false,
38 "collapsed": false,
39 "input": [
39 "input": [
40 "result = v.map(lambda x: 2*x, range(10))",
40 "result = v.map(lambda x: 2*x, range(10))",
41 "print \"Simple, default map: \", list(result)"
41 "print \"Simple, default map: \", list(result)"
42 ],
42 ],
43 "language": "python",
43 "language": "python",
44 "outputs": [
44 "outputs": [
45 {
45 {
46 "output_type": "stream",
46 "output_type": "stream",
47 "stream": "stdout",
47 "stream": "stdout",
48 "text": [
48 "text": [
49 "Simple, default map: "
49 "Simple, default map: "
50 ]
50 ]
51 },
51 },
52 {
52 {
53 "output_type": "stream",
53 "output_type": "stream",
54 "stream": "stdout",
54 "stream": "stdout",
55 "text": [
55 "text": [
56 "[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
56 "[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
57 ]
57 ]
58 }
58 }
59 ],
59 ],
60 "prompt_number": 4
60 "prompt_number": 4
61 },
61 },
62 {
62 {
63 "cell_type": "code",
63 "cell_type": "code",
64 "collapsed": false,
64 "collapsed": false,
65 "input": [
65 "input": [
66 "ar = v.map_async(lambda x: 2*x, range(10))",
66 "ar = v.map_async(lambda x: 2*x, range(10))",
67 "print \"Submitted tasks, got ids: \", ar.msg_ids",
67 "print \"Submitted tasks, got ids: \", ar.msg_ids",
68 "result = ar.get()",
68 "result = ar.get()",
69 "print \"Using a mapper: \", result"
69 "print \"Using a mapper: \", result"
70 ],
70 ],
71 "language": "python",
71 "language": "python",
72 "outputs": [
72 "outputs": [
73 {
73 {
74 "output_type": "stream",
74 "output_type": "stream",
75 "stream": "stdout",
75 "stream": "stdout",
76 "text": [
76 "text": [
77 "Submitted tasks, got ids: ['5100a4c7-73a4-4832-aa91-e774f6f3ede8', 'd0cae1cf-2b32-4092-9eb7-f17b43fb3849', 'e08d3ee2-f221-47fe-9556-ed938e692030', '065585e4-cdf9-4240-a5fe-e44b2ae5d023', 'd2162f23-68e5-4318-ba1e-e34fd03a72ac', '5b3b835f-2099-4a70-9896-d1aa810c77e6', 'e2c2a823-bd44-4f91-8db3-c154d0d86e56', '991e0c25-f98a-44b5-9d9e-889d4180b9a5', '4ad41221-28bd-482f-a300-97c404648161', '5b730eb3-e0bb-4cdd-b228-c3b8d158828a']",
77 "Submitted tasks, got ids: ['5100a4c7-73a4-4832-aa91-e774f6f3ede8', 'd0cae1cf-2b32-4092-9eb7-f17b43fb3849', 'e08d3ee2-f221-47fe-9556-ed938e692030', '065585e4-cdf9-4240-a5fe-e44b2ae5d023', 'd2162f23-68e5-4318-ba1e-e34fd03a72ac', '5b3b835f-2099-4a70-9896-d1aa810c77e6', 'e2c2a823-bd44-4f91-8db3-c154d0d86e56', '991e0c25-f98a-44b5-9d9e-889d4180b9a5', '4ad41221-28bd-482f-a300-97c404648161', '5b730eb3-e0bb-4cdd-b228-c3b8d158828a']",
78 "Using a mapper: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
78 "Using a mapper: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
79 ]
79 ]
80 }
80 }
81 ],
81 ],
82 "prompt_number": 5
82 "prompt_number": 5
83 },
83 },
84 {
84 {
85 "cell_type": "code",
85 "cell_type": "code",
86 "collapsed": false,
86 "collapsed": false,
87 "input": [
87 "input": [
88 "@v.parallel(block=True)",
88 "@v.parallel(block=True)",
89 "def f(x): return 2*x",
89 "def f(x): return 2*x",
90 "",
90 "",
91 "result = f.map(range(10))",
91 "result = f.map(range(10))",
92 "print \"Using a parallel function: \", result"
92 "print \"Using a parallel function: \", result"
93 ],
93 ],
94 "language": "python",
94 "language": "python",
95 "outputs": [
95 "outputs": [
96 {
96 {
97 "output_type": "stream",
97 "output_type": "stream",
98 "stream": "stdout",
98 "stream": "stdout",
99 "text": [
99 "text": [
100 "Using a parallel function: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
100 "Using a parallel function: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
101 ]
101 ]
102 }
102 }
103 ],
103 ],
104 "prompt_number": 6
104 "prompt_number": 6
105 }
105 }
106 ]
106 ]
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