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Converting notebooks to JSON format.
Brian E. Granger -
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@@ -281,7 +281,7 b' class NotebookHandler(web.RequestHandler):'
281 last_mod, name, data = nbm.get_notebook(notebook_id, format)
281 last_mod, name, data = nbm.get_notebook(notebook_id, format)
282 if format == u'json':
282 if format == u'json':
283 self.set_header('Content-Type', 'application/json')
283 self.set_header('Content-Type', 'application/json')
284 self.set_header('Content-Disposition','attachment; filename="%s.json"' % name)
284 self.set_header('Content-Disposition','attachment; filename="%s.ipynb"' % name)
285 elif format == u'py':
285 elif format == u'py':
286 self.set_header('Content-Type', 'application/x-python')
286 self.set_header('Content-Type', 'application/x-python')
287 self.set_header('Content-Disposition','attachment; filename="%s.py"' % name)
287 self.set_header('Content-Disposition','attachment; filename="%s.py"' % name)
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@@ -1,68 +1,63 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 {
2 <notebook>
2 "nbformat": 2,
3 <name>helloworld</name>
3 "name": "helloworld",
4 <nbformat>2</nbformat>
4 "worksheets": [
5 <worksheets>
5 {
6 <worksheet>
6 "cells": [
7 <cells>
7 {
8 <markdowncell>
8 "source": "# Distributed hello world\n\nOriginally by Ken Kinder (ken at kenkinder dom com)",
9 <source># Distributed hello world
9 "cell_type": "markdown"
10
10 },
11 Originally by Ken Kinder (ken at kenkinder dom com)</source>
11 {
12 </markdowncell>
12 "cell_type": "code",
13 <codecell>
13 "language": "python",
14 <input>from IPython.parallel import Client</input>
14 "outputs": [],
15 <language>python</language>
15 "collapsed": true,
16 <prompt_number>3</prompt_number>
16 "prompt_number": 3,
17 <collapsed>1</collapsed>
17 "input": "from IPython.parallel import Client"
18 <outputs />
18 },
19 </codecell>
19 {
20 <codecell>
20 "cell_type": "code",
21 <input>rc = Client()
21 "language": "python",
22 view = rc.load_balanced_view()</input>
22 "outputs": [],
23 <language>python</language>
23 "collapsed": true,
24 <prompt_number>4</prompt_number>
24 "prompt_number": 4,
25 <collapsed>1</collapsed>
25 "input": "rc = Client()\nview = rc.load_balanced_view()"
26 <outputs />
26 },
27 </codecell>
27 {
28 <codecell>
28 "cell_type": "code",
29 <input>def sleep_and_echo(t, msg):
29 "language": "python",
30 import time
30 "outputs": [],
31 time.sleep(t)
31 "collapsed": true,
32 return msg</input>
32 "prompt_number": 5,
33 <language>python</language>
33 "input": "def sleep_and_echo(t, msg):\n import time\n time.sleep(t)\n return msg"
34 <prompt_number>5</prompt_number>
34 },
35 <collapsed>1</collapsed>
35 {
36 <outputs />
36 "cell_type": "code",
37 </codecell>
37 "language": "python",
38 <codecell>
38 "outputs": [],
39 <input>world = view.apply_async(sleep_and_echo, 3, 'World!')
39 "collapsed": true,
40 hello = view.apply_async(sleep_and_echo, 2, 'Hello')
40 "prompt_number": 6,
41 </input>
41 "input": "world = view.apply_async(sleep_and_echo, 3, 'World!')\nhello = view.apply_async(sleep_and_echo, 2, 'Hello')\n"
42 <language>python</language>
42 },
43 <prompt_number>6</prompt_number>
43 {
44 <collapsed>1</collapsed>
44 "cell_type": "code",
45 <outputs />
45 "language": "python",
46 </codecell>
46 "outputs": [
47 <codecell>
47 {
48 <input>print "Submitted tasks:", hello.msg_ids, world.msg_ids
48 "output_type": "stream",
49 print hello.get(), world.get()</input>
49 "text": "Submitted tasks: [&apos;9e533683-d54e-4588-929e-984dd3eb6dc4&apos;] [&apos;90395f15-723f-44df-a743-a5d88cdeb6a0&apos;]\nHello"
50 <language>python</language>
50 },
51 <prompt_number>7</prompt_number>
51 {
52 <collapsed>0</collapsed>
52 "output_type": "stream",
53 <outputs>
53 "text": "World!"
54 <output>
54 }
55 <output_type>stream</output_type>
55 ],
56 <text>Submitted tasks: [&amp;apos;9e533683-d54e-4588-929e-984dd3eb6dc4&amp;apos;] [&amp;apos;90395f15-723f-44df-a743-a5d88cdeb6a0&amp;apos;]
56 "collapsed": false,
57 Hello</text>
57 "prompt_number": 7,
58 </output>
58 "input": "print \"Submitted tasks:\", hello.msg_ids, world.msg_ids\nprint hello.get(), world.get()"
59 <output>
59 }
60 <output_type>stream</output_type>
60 ]
61 <text>World!</text>
61 }
62 </output>
62 ]
63 </outputs>
63 } No newline at end of file
64 </codecell>
65 </cells>
66 </worksheet>
67 </worksheets>
68 </notebook>
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@@ -1,2054 +1,241 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 {
2 <notebook>
2 "nbformat": 2,
3 <name>mcpricer</name>
3 "name": "mcpricer",
4 <nbformat>2</nbformat>
4 "worksheets": [
5 <worksheets>
5 {
6 <worksheet>
6 "cells": [
7 <cells>
7 {
8 <markdowncell>
8 "source": "# Parallel Monto-Carlo options pricing",
9 <source># Parallel Monto-Carlo options pricing</source>
9 "cell_type": "markdown"
10 </markdowncell>
10 },
11 <markdowncell>
11 {
12 <source>## Problem setup</source>
12 "source": "## Problem setup",
13 </markdowncell>
13 "cell_type": "markdown"
14 <codecell>
14 },
15 <input>import sys
15 {
16 import time
16 "cell_type": "code",
17 from IPython.parallel import Client
17 "language": "python",
18 import numpy as np
18 "outputs": [],
19 from mckernel import price_options
19 "collapsed": true,
20 from matplotlib import pyplot as plt</input>
20 "prompt_number": 1,
21 <language>python</language>
21 "input": "import sys\nimport time\nfrom IPython.parallel import Client\nimport numpy as np\nfrom mckernel import price_options\nfrom matplotlib import pyplot as plt"
22 <prompt_number>1</prompt_number>
22 },
23 <collapsed>1</collapsed>
23 {
24 <outputs />
24 "cell_type": "code",
25 </codecell>
25 "language": "python",
26 <codecell>
26 "outputs": [],
27 <input>cluster_profile = "default"
27 "collapsed": true,
28 price = 100.0 # Initial price
28 "prompt_number": 2,
29 rate = 0.05 # Interest rate
29 "input": "cluster_profile = \"default\"\nprice = 100.0 # Initial price\nrate = 0.05 # Interest rate\ndays = 260 # Days to expiration\npaths = 10000 # Number of MC paths\nn_strikes = 5 # Number of strike values\nmin_strike = 90.0 # Min strike price\nmax_strike = 110.0 # Max strike price\nn_sigmas = 5 # Number of volatility values\nmin_sigma = 0.1 # Min volatility\nmax_sigma = 0.4 # Max volatility"
30 days = 260 # Days to expiration
30 },
31 paths = 10000 # Number of MC paths
31 {
32 n_strikes = 5 # Number of strike values
32 "cell_type": "code",
33 min_strike = 90.0 # Min strike price
33 "language": "python",
34 max_strike = 110.0 # Max strike price
34 "outputs": [],
35 n_sigmas = 5 # Number of volatility values
35 "collapsed": true,
36 min_sigma = 0.1 # Min volatility
36 "prompt_number": 3,
37 max_sigma = 0.4 # Max volatility</input>
37 "input": "strike_vals = np.linspace(min_strike, max_strike, n_strikes)\nsigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)"
38 <language>python</language>
38 },
39 <prompt_number>2</prompt_number>
39 {
40 <collapsed>1</collapsed>
40 "source": "## Parallel computation across strike prices and volatilities",
41 <outputs />
41 "cell_type": "markdown"
42 </codecell>
42 },
43 <codecell>
43 {
44 <input>strike_vals = np.linspace(min_strike, max_strike, n_strikes)
44 "source": "The Client is used to setup the calculation and works with all engines.",
45 sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)</input>
45 "cell_type": "markdown"
46 <language>python</language>
46 },
47 <prompt_number>3</prompt_number>
47 {
48 <collapsed>1</collapsed>
48 "cell_type": "code",
49 <outputs />
49 "language": "python",
50 </codecell>
50 "outputs": [],
51 <markdowncell>
51 "collapsed": true,
52 <source>## Parallel computation across strike prices and volatilities</source>
52 "prompt_number": 4,
53 </markdowncell>
53 "input": "c = Client(profile=cluster_profile)"
54 <markdowncell>
54 },
55 <source>The Client is used to setup the calculation and works with all engines.</source>
55 {
56 </markdowncell>
56 "source": "A LoadBalancedView is an interface to the engines that provides dynamic load \nbalancing at the expense of not knowing which engine will execute the code.",
57 <codecell>
57 "cell_type": "markdown"
58 <input>c = Client(profile=cluster_profile)</input>
58 },
59 <language>python</language>
59 {
60 <prompt_number>4</prompt_number>
60 "cell_type": "code",
61 <collapsed>1</collapsed>
61 "language": "python",
62 <outputs />
62 "outputs": [],
63 </codecell>
63 "collapsed": true,
64 <markdowncell>
64 "prompt_number": 5,
65 <source>A LoadBalancedView is an interface to the engines that provides dynamic load
65 "input": "view = c.load_balanced_view()"
66 balancing at the expense of not knowing which engine will execute the code.</source>
66 },
67 </markdowncell>
67 {
68 <codecell>
68 "cell_type": "code",
69 <input>view = c.load_balanced_view()</input>
69 "language": "python",
70 <language>python</language>
70 "outputs": [
71 <prompt_number>5</prompt_number>
71 {
72 <collapsed>1</collapsed>
72 "output_type": "stream",
73 <outputs />
73 "text": "Strike prices: [ 90. 95. 100. 105. 110.]\nVolatilities: [ 0.1 0.175 0.25 0.325 0.4 ]"
74 </codecell>
74 }
75 <codecell>
75 ],
76 <input>print "Strike prices: ", strike_vals
76 "collapsed": false,
77 print "Volatilities: ", sigma_vals</input>
77 "prompt_number": 6,
78 <language>python</language>
78 "input": "print \"Strike prices: \", strike_vals\nprint \"Volatilities: \", sigma_vals"
79 <prompt_number>6</prompt_number>
79 },
80 <collapsed>0</collapsed>
80 {
81 <outputs>
81 "source": "Submit tasks for each (strike, sigma) pair.",
82 <output>
82 "cell_type": "markdown"
83 <output_type>stream</output_type>
83 },
84 <text>Strike prices: [ 90. 95. 100. 105. 110.]
84 {
85 Volatilities: [ 0.1 0.175 0.25 0.325 0.4 ]</text>
85 "cell_type": "code",
86 </output>
86 "language": "python",
87 </outputs>
87 "outputs": [],
88 </codecell>
88 "collapsed": true,
89 <markdowncell>
89 "prompt_number": 7,
90 <source>Submit tasks for each (strike, sigma) pair.</source>
90 "input": "t1 = time.time()\nasync_results = []\nfor strike in strike_vals:\n for sigma in sigma_vals:\n ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)\n async_results.append(ar)"
91 </markdowncell>
91 },
92 <codecell>
92 {
93 <input>t1 = time.time()
93 "cell_type": "code",
94 async_results = []
94 "language": "python",
95 for strike in strike_vals:
95 "outputs": [
96 for sigma in sigma_vals:
96 {
97 ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)
97 "output_type": "stream",
98 async_results.append(ar)</input>
98 "text": "Submitted tasks: 25"
99 <language>python</language>
99 }
100 <prompt_number>7</prompt_number>
100 ],
101 <collapsed>1</collapsed>
101 "collapsed": false,
102 <outputs />
102 "prompt_number": 8,
103 </codecell>
103 "input": "print \"Submitted tasks: \", len(async_results)"
104 <codecell>
104 },
105 <input>print "Submitted tasks: ", len(async_results)</input>
105 {
106 <language>python</language>
106 "source": "Block until all tasks are completed.",
107 <prompt_number>8</prompt_number>
107 "cell_type": "markdown"
108 <collapsed>0</collapsed>
108 },
109 <outputs>
109 {
110 <output>
110 "cell_type": "code",
111 <output_type>stream</output_type>
111 "language": "python",
112 <text>Submitted tasks: 25</text>
112 "outputs": [
113 </output>
113 {
114 </outputs>
114 "output_type": "stream",
115 </codecell>
115 "text": "Parallel calculation completed, time = 2.57819604874 s"
116 <markdowncell>
116 }
117 <source>Block until all tasks are completed.</source>
117 ],
118 </markdowncell>
118 "collapsed": false,
119 <codecell>
119 "prompt_number": 9,
120 <input>c.wait(async_results)
120 "input": "c.wait(async_results)\nt2 = time.time()\nt = t2-t1\n\nprint \"Parallel calculation completed, time = %s s\" % t"
121 t2 = time.time()
121 },
122 t = t2-t1
122 {
123
123 "source": "## Process and visualize results",
124 print "Parallel calculation completed, time = %s s" % t</input>
124 "cell_type": "markdown"
125 <language>python</language>
125 },
126 <prompt_number>9</prompt_number>
126 {
127 <collapsed>0</collapsed>
127 "source": "Get the results using the `get` method:",
128 <outputs>
128 "cell_type": "markdown"
129 <output>
129 },
130 <output_type>stream</output_type>
130 {
131 <text>Parallel calculation completed, time = 2.57819604874 s</text>
131 "cell_type": "code",
132 </output>
132 "language": "python",
133 </outputs>
133 "outputs": [],
134 </codecell>
134 "collapsed": true,
135 <markdowncell>
135 "prompt_number": 10,
136 <source>## Process and visualize results</source>
136 "input": "results = [ar.get() for ar in async_results]\n"
137 </markdowncell>
137 },
138 <markdowncell>
138 {
139 <source>Get the results using the `get` method:</source>
139 "source": "Assemble the result into a structured NumPy array.",
140 </markdowncell>
140 "cell_type": "markdown"
141 <codecell>
141 },
142 <input>results = [ar.get() for ar in async_results]
142 {
143 </input>
143 "cell_type": "code",
144 <language>python</language>
144 "language": "python",
145 <prompt_number>10</prompt_number>
145 "outputs": [],
146 <collapsed>1</collapsed>
146 "collapsed": true,
147 <outputs />
147 "prompt_number": 11,
148 </codecell>
148 "input": "prices = np.empty(n_strikes*n_sigmas,\n dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]\n)\n\nfor i, price in enumerate(results):\n prices[i] = tuple(price)\n \nprices.shape = (n_strikes, n_sigmas)\nstrike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals)"
149 <markdowncell>
149 },
150 <source>Assemble the result into a structured NumPy array.</source>
150 {
151 </markdowncell>
151 "source": "Plot the value of the European call in (volatility, strike) space.",
152 <codecell>
152 "cell_type": "markdown"
153 <input>prices = np.empty(n_strikes*n_sigmas,
153 },
154 dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]
154 {
155 )
155 "cell_type": "code",
156
156 "language": "python",
157 for i, price in enumerate(results):
157 "outputs": [
158 prices[i] = tuple(price)
158 {
159
159 "output_type": "pyout",
160 prices.shape = (n_strikes, n_sigmas)
160 "prompt_number": 12,
161 strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals)</input>
161 "text": "&lt;matplotlib.text.Text at 0x2c54750&gt;"
162 <language>python</language>
162 },
163 <prompt_number>11</prompt_number>
163 {
164 <collapsed>1</collapsed>
164 "output_type": "display_data",
165 <outputs />
165 "png": 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lF/exgIFcET0xzCKg1XZm6uuyWcPR0ZG6ujqcna93yK6rq0OttvIO8mMzod9G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\nA4CDCGcAcBDhDAAOIpwBwEFfFzJgnth8qvoAAAAASUVORK5CYII=\n"
166 </codecell>
166 }
167 <markdowncell>
167 ],
168 <source>Plot the value of the European call in (volatility, strike) space.</source>
168 "collapsed": false,
169 </markdowncell>
169 "prompt_number": 12,
170 <codecell>
170 "input": "plt.contourf(sigma_mesh, strike_mesh, prices['ecall'])\nplt.axis('tight')\nplt.colorbar()\nplt.title('European Call')\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")"
171 <input>plt.contourf(sigma_mesh, strike_mesh, prices['ecall'])
171 },
172 plt.axis('tight')
172 {
173 plt.colorbar()
173 "source": "Plot the value of the Asian call in (volatility, strike) space.",
174 plt.title('European Call')
174 "cell_type": "markdown"
175 plt.xlabel("Volatility")
175 },
176 plt.ylabel("Strike Price")</input>
176 {
177 <language>python</language>
177 "cell_type": "code",
178 <prompt_number>12</prompt_number>
178 "language": "python",
179 <collapsed>0</collapsed>
179 "outputs": [
180 <outputs>
180 {
181 <output>
181 "output_type": "pyout",
182 <output_type>pyout</output_type>
182 "prompt_number": 13,
183 <text>&amp;lt;matplotlib.text.Text at 0x2c54750&amp;gt;</text>
183 "text": "&lt;matplotlib.text.Text at 0x2e14610&gt;"
184 <prompt_number>12</prompt_number>
184 },
185 </output>
185 {
186 <output>
186 "output_type": "display_data",
187 <output_type>display_data</output_type>
187 "png": 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ebtVCtksyoi8YjotW0SWqRzQbY4xAu8VjtYoHQ1lBiGgZDkdm/1nGU4Ghu6Ho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\nHnpIf+ncBiNEaGfb+rR5EKD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188 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVdjQUFBRWFDQVlBQUFETkJKYVNBQUFBQkhOQ1NWUUlD
188 }
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189 ],
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192 "input": "plt.contourf(sigma_mesh, strike_mesh, prices['acall'])\nplt.axis('tight')\nplt.colorbar()\nplt.title(\"Asian Call\")\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")"
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193 },
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194 {
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195 "source": "Plot the value of the European put in (volatility, strike) space.",
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196 "cell_type": "markdown"
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197 },
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198 {
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200 "language": "python",
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201 "outputs": [
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202 {
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203 "output_type": "pyout",
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204 "prompt_number": 14,
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205 "text": "&lt;matplotlib.text.Text at 0x32ee190&gt;"
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206 },
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207 {
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208 "output_type": "display_data",
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209 "png": 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Sk9ylGKXZlDOc/aiplrsU2Zk3mzK5SMuAGwfkLsWwZE+FPSfA8OOgQ+UWwTj+PV3W7dlW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\nH1+m+kgqUZ4V2FmJMDdUZQWQ9DuYcgk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210 }
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211 ],
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212 "collapsed": false,
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213 "prompt_number": 14,
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214 "input": "plt.contourf(sigma_mesh, strike_mesh, prices['eput'])\nplt.axis('tight')\nplt.colorbar()\nplt.title(\"European Put\")\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")"
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215 },
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216 {
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217 "source": "Plot the value of the Asian put in (volatility, strike) space.",
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218 "cell_type": "markdown"
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219 },
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220 {
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221 "cell_type": "code",
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222 "language": "python",
223 bEpTWVNGCmhmSFBmLzRUV1piUjZYUzgvdnJyUFAvODgwUkdSckp6NTA2bVRwM2FhUjJkdWVPT08x
223 "outputs": [
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224 {
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225 "output_type": "pyout",
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226 "prompt_number": 15,
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227 "text": "&lt;matplotlib.text.Text at 0x3487c50&gt;"
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228 },
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229 {
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230 "output_type": "display_data",
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231 "png": 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AHMWw/9Yh3UGGLv5JfQYd1d+zjtF6lOIFMRUuyGadpGWUwmtNb5Bz5v+s38lh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\nJIgXZ47jOAnixZnjOE6C/g98ZDDk0wdCzQAAAABJRU5ErkJggg==\n"
232 Qkl1S2loZzBhRkRiN1FFREJsQlVWS1JnUllJZ0NNWnoKN05neERodzRRRXBLQ2l0WHJpUWtKSVRZ
232 }
233 MkZpOXR0VjAvUlRUYWU5YVpIdFg3TVZWZkVFUUROSFRmZzd1a29TK24rRmRYVjNiL2NSZgpVMVBE
233 ],
234 dmZmZXk2dXZ2b29rU2J6d3dndXNYNzllN3hvVkRlZlUxRlEyYk5qUWR2dlFvVU1rSnllMysxeHJ1
234 "collapsed": false,
235 MVM0QkREMmNBcS9POUlKCkR6aUc3dHBQWFQrNUcrYnNnemt4WFQvUDdDSUd3NFJxY0xsMXNxSTVD
235 "prompt_number": 15,
236 MkRPSXdyVjFFMjJYck9zOXFIU0w1TTlQdGVvMHpTWnRyQU8KVEpUVzlYZ2ZOZWlmT2NQYm1jLzcy
236 "input": "plt.contourf(sigma_mesh, strike_mesh, prices['aput'])\nplt.axis('tight')\nplt.colorbar()\nplt.title(\"Asian Put\")\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")\n"
237 clZyM0hYWFhkeC8vLzFNbkRpUmZmdjJVVjVlVGx4Y0hBQm56cHdoS1NtSm9xSWkvUDM5Mjkydgoy
237 }
238 Y1A1NW5lTGxKUVVubjMyV1U2ZE9zV0pFeWRRcVZTNHVibVp1eVNMNTVFU1Q4VGdPbHdidDhBMXBh
238 ]
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615 </png>
616 </output>
617 </outputs>
618 </codecell>
619 <markdowncell>
620 <source>Plot the value of the Asian call in (volatility, strike) space.</source>
621 </markdowncell>
622 <codecell>
623 <input>plt.contourf(sigma_mesh, strike_mesh, prices['acall'])
624 plt.axis('tight')
625 plt.colorbar()
626 plt.title("Asian Call")
627 plt.xlabel("Volatility")
628 plt.ylabel("Strike Price")</input>
629 <language>python</language>
630 <prompt_number>13</prompt_number>
631 <collapsed>0</collapsed>
632 <outputs>
633 <output>
634 <output_type>pyout</output_type>
635 <text>&amp;lt;matplotlib.text.Text at 0x2e14610&amp;gt;</text>
636 <prompt_number>13</prompt_number>
637 </output>
638 <output>
639 <output_type>display_data</output_type>
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1087 </png>
1088 </output>
1089 </outputs>
1090 </codecell>
1091 <markdowncell>
1092 <source>Plot the value of the European put in (volatility, strike) space.</source>
1093 </markdowncell>
1094 <codecell>
1095 <input>plt.contourf(sigma_mesh, strike_mesh, prices['eput'])
1096 plt.axis('tight')
1097 plt.colorbar()
1098 plt.title("European Put")
1099 plt.xlabel("Volatility")
1100 plt.ylabel("Strike Price")</input>
1101 <language>python</language>
1102 <prompt_number>14</prompt_number>
1103 <collapsed>0</collapsed>
1104 <outputs>
1105 <output>
1106 <output_type>pyout</output_type>
1107 <text>&amp;lt;matplotlib.text.Text at 0x32ee190&amp;gt;</text>
1108 <prompt_number>14</prompt_number>
1109 </output>
1110 <output>
1111 <output_type>display_data</output_type>
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1585 </png>
1586 </output>
1587 </outputs>
1588 </codecell>
1589 <markdowncell>
1590 <source>Plot the value of the Asian put in (volatility, strike) space.</source>
1591 </markdowncell>
1592 <codecell>
1593 <input>plt.contourf(sigma_mesh, strike_mesh, prices['aput'])
1594 plt.axis('tight')
1595 plt.colorbar()
1596 plt.title("Asian Put")
1597 plt.xlabel("Volatility")
1598 plt.ylabel("Strike Price")
1599 </input>
1600 <language>python</language>
1601 <prompt_number>15</prompt_number>
1602 <collapsed>0</collapsed>
1603 <outputs>
1604 <output>
1605 <output_type>pyout</output_type>
1606 <text>&amp;lt;matplotlib.text.Text at 0x3487c50&amp;gt;</text>
1607 <prompt_number>15</prompt_number>
1608 </output>
1609 <output>
1610 <output_type>display_data</output_type>
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2047 </png>
2048 </output>
2049 </outputs>
2050 </codecell>
2051 </cells>
2052 </worksheet>
2053 </worksheets>
2054 </notebook>
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@@ -1,1270 +1,226 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 {
2 <notebook>
2 "nbformat": 2,
3 <name>rmt</name>
3 "name": "rmt",
4 <nbformat>2</nbformat>
4 "worksheets": [
5 <worksheets>
5 {
6 <worksheet>
6 "cells": [
7 <cells>
7 {
8 <markdowncell>
8 "source": "# Eigenvalue distribution of Gaussian orthogonal random matrices",
9 <source># Eigenvalue distribution of Gaussian orthogonal random matrices</source>
9 "cell_type": "markdown"
10 </markdowncell>
10 },
11 <markdowncell>
11 {
12 <source>The eigenvalues of random matrices obey certain statistical laws. Here we construct random matrices
12 "source": "The eigenvalues of random matrices obey certain statistical laws. Here we construct random matrices \nfrom the Gaussian Orthogonal Ensemble (GOE), find their eigenvalues and then investigate the nearest\nneighbor eigenvalue distribution $\\rho(s)$.",
13 from the Gaussian Orthogonal Ensemble (GOE), find their eigenvalues and then investigate the nearest
13 "cell_type": "markdown"
14 neighbor eigenvalue distribution $\rho(s)$.</source>
14 },
15 </markdowncell>
15 {
16 <codecell>
16 "cell_type": "code",
17 <input>from rmtkernel import ensemble_diffs, normalize_diffs, GOE
17 "language": "python",
18 import numpy as np
18 "outputs": [],
19 from IPython.parallel import Client</input>
19 "collapsed": false,
20 <language>python</language>
20 "prompt_number": 1,
21 <prompt_number>1</prompt_number>
21 "input": "from rmtkernel import ensemble_diffs, normalize_diffs, GOE\nimport numpy as np\nfrom IPython.parallel import Client"
22 <collapsed>0</collapsed>
22 },
23 <outputs />
23 {
24 </codecell>
24 "source": "## Wigner's nearest neighbor eigenvalue distribution",
25 <markdowncell>
25 "cell_type": "markdown"
26 <source>## Wigner's nearest neighbor eigenvalue distribution</source>
26 },
27 </markdowncell>
27 {
28 <markdowncell>
28 "source": "The Wigner distribution gives the theoretical result for the nearest neighbor eigenvalue distribution\nfor the GOE:\n\n$$\\rho(s) = \\frac{\\pi s}{2} \\exp(-\\pi s^2/4)$$",
29 <source>The Wigner distribution gives the theoretical result for the nearest neighbor eigenvalue distribution
29 "cell_type": "markdown"
30 for the GOE:
30 },
31
31 {
32 $$\rho(s) = \frac{\pi s}{2} \exp(-\pi s^2/4)$$</source>
32 "cell_type": "code",
33 </markdowncell>
33 "language": "python",
34 <codecell>
34 "outputs": [],
35 <input>def wigner_dist(s):
35 "collapsed": true,
36 """Returns (s, rho(s)) for the Wigner GOE distribution."""
36 "prompt_number": 2,
37 return (np.pi*s/2.0) * np.exp(-np.pi*s**2/4.)</input>
37 "input": "def wigner_dist(s):\n \"\"\"Returns (s, rho(s)) for the Wigner GOE distribution.\"\"\"\n return (np.pi*s/2.0) * np.exp(-np.pi*s**2/4.)"
38 <language>python</language>
38 },
39 <prompt_number>2</prompt_number>
39 {
40 <collapsed>1</collapsed>
40 "cell_type": "code",
41 <outputs />
41 "language": "python",
42 </codecell>
42 "outputs": [],
43 <codecell>
43 "collapsed": true,
44 <input>def generate_wigner_data():
44 "prompt_number": 3,
45 s = np.linspace(0.0,4.0,400)
45 "input": "def generate_wigner_data():\n s = np.linspace(0.0,4.0,400)\n rhos = wigner_dist(s)\n return s, rhos"
46 rhos = wigner_dist(s)
46 },
47 return s, rhos</input>
47 {
48 <language>python</language>
48 "cell_type": "code",
49 <prompt_number>3</prompt_number>
49 "language": "python",
50 <collapsed>1</collapsed>
50 "outputs": [],
51 <outputs />
51 "collapsed": false,
52 </codecell>
52 "prompt_number": 4,
53 <codecell>
53 "input": "s, rhos = generate_wigner_data()"
54 <input>s, rhos = generate_wigner_data()</input>
54 },
55 <language>python</language>
55 {
56 <prompt_number>4</prompt_number>
56 "cell_type": "code",
57 <collapsed>0</collapsed>
57 "language": "python",
58 <outputs />
58 "outputs": [
59 </codecell>
59 {
60 <codecell>
60 "output_type": "pyout",
61 <input>plot(s, rhos)
61 "prompt_number": 17,
62 xlabel('Normalized level spacing s')
62 "text": "&lt;matplotlib.text.Text at 0x3828790&gt;"
63 ylabel('Probability $\rho(s)$')</input>
63 },
64 <language>python</language>
64 {
65 <prompt_number>17</prompt_number>
65 "output_type": "display_data",
66 <collapsed>0</collapsed>
66 "png": 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67 <outputs>
67 }
68 <output>
68 ],
69 <output_type>pyout</output_type>
69 "collapsed": false,
70 <text>&amp;lt;matplotlib.text.Text at 0x3828790&amp;gt;</text>
70 "prompt_number": 17,
71 <prompt_number>17</prompt_number>
71 "input": "plot(s, rhos)\nxlabel('Normalized level spacing s')\nylabel('Probability $\\rho(s)$')"
72 </output>
72 },
73 <output>
73 {
74 <output_type>display_data</output_type>
74 "source": "## Serial calculation of nearest neighbor eigenvalue distribution",
75 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVl3QUFBRU1DQVlBQUFEWGlZR1NBQUFBQkhOQ1NWUUlD
75 "cell_type": "markdown"
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76 },
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77 {
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78 "source": "In this section we numerically construct and diagonalize a large number of GOE random matrices\nand compute the nerest neighbor eigenvalue distribution. This comptation is done on a single core.",
79 UEIKUTRZNW52UG05R2crbnUrcVV4UkZRUWdoaEtoQ0hhMERDQ0dFY0E1U01JUVFRcGhGQ29ZUVFn
79 "cell_type": "markdown"
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80 },
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81 {
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82 "cell_type": "code",
83 WEIwQ2YKUG4zdzlQUWtQRHljOVBUME1zZTR1N3R6NGNJRmpFWWpPVGs1Tkc3Y1dJcUZFRUpvek80
83 "language": "python",
84 Rkl5TWpBMTlmWDlOcmYzOS8wdExTeWh3egpjdVJJcmw2OWlvZUhCNzE3OTJiSmtpWDJqaW1FRU9J
84 "outputs": [],
85 YTliUU9VSkY1OCtaUnIxNDlUcDQ4eVk0ZE80aUtpdUxJa1NQVXFWTzJ2c2xUCmh4QkNWRTkxZWlQ
85 "collapsed": true,
86 cy9vUVJFaExDM3IxN1RhOTM3ZHBGang0OXloeVRtcHJLSTQ4OFF1UEdqUWtMQytQbW0yOW0zNzU5
86 "prompt_number": 6,
87 Rlo1UFVSU0gKLzVvMmJacm1HU1NuWkpTY2tyUGtxN3JzWGpEYzNkMEJ0U2hrWjJlVG5KeE1XRmhZ
87 "input": "def serial_diffs(num, N):\n \"\"\"Compute the nearest neighbor distribution for num NxX matrices.\"\"\"\n diffs = ensemble_diffs(num, N)\n normalized_diffs = normalize_diffs(diffs)\n return normalized_diffs"
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88 },
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89 {
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90 "cell_type": "code",
91 YWZUMWFnOVRnZ2gKYXFQcWZuYkswaUJDQ0NITUlnVkRDQ0dFV2FSZ0NDR0VNSXNVRENHRUVHWnh5
91 "language": "python",
92 Sm5lNHZxS2lpQTlIZGF2aDh4TXVId1ppb3VoUXdlNAo0dzdvMnhlOHZiVk9LWVJ3TlRKS3lva1VG
92 "outputs": [],
93 RUJDQXN5Y0NiZmNBbmZkQldGaDBMZ3g2SFJ3NEFEOC9EUDg5QlBvOVRCNU12VHJwNzRuCmhCQWxx
93 "collapsed": true,
94 dnZaS1FYRFNheGJCNk5HUVdnb1RKc0d3Y0dWSDF0VUJFdVd3T3paY1BQTjhPbW4wSzZkL2JJS0lS
94 "prompt_number": 7,
95 eWJES3QxVVlvQzc3MEgKano0S2l4ZkR0OTlldjFnQU5HZ0FZOGJBYjcrcHpWUGR1c0h5NWZiSks0
95 "input": "serial_nmats = 1000\nserial_matsize = 50"
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96 },
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97 {
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99 "language": "python",
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100 "outputs": [
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101 {
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103 "text": "1 loops, best of 1: 1.19 s per loop"
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104 }
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105 ],
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106 "collapsed": false,
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107 "prompt_number": 8,
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108 "input": "%timeit -r1 -n1 serial_diffs(serial_nmats, serial_matsize)"
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109 },
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110 {
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112 "language": "python",
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113 "outputs": [],
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114 "collapsed": false,
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115 "prompt_number": 9,
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116 "input": "serial_diffs = serial_diffs(serial_nmats, serial_matsize)"
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117 },
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118 {
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119 "source": "The numerical computation agrees with the predictions of Wigner, but it would be nice to get more\nstatistics. For that we will do a parallel computation.",
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120 "cell_type": "markdown"
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121 },
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122 {
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125 "outputs": [
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126 {
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127 "output_type": "pyout",
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128 "prompt_number": 10,
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129 "text": "&lt;matplotlib.text.Text at 0x3475bd0&gt;"
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130 },
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132 "output_type": "display_data",
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133 "png": 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CWKxqWTAyczM5EH8Af2d/raMIU0lpDXtfhSeeB12+1mmEsEjVsmDsu7SPjk06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\nSfn7+yt3d3fl5+en1q5dW2I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134 }
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135 ],
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136 "collapsed": false,
137 SFVhSVVTSgphLzh4UFgzNjlHcWR4KzRmYlNFaEllemR1OWYwZXRldVhmUzRac25UbmoxN01uRGdR
137 "prompt_number": 10,
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138 "input": "hist_data = hist(serial_diffs, bins=30, normed=True)\nplot(s, rhos)\nxlabel('Normalized level spacing s')\nylabel('Probability $P(s)$')"
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139 },
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140 {
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141 "source": "## Parallel calculation of nearest neighbor eigenvalue distribution",
142 N3p6OE1MTDdqV3hsRkNDSm00WnpXREI4UElrZW9NCjc5cE9VZFI1S0ROblFtU2sxbW1FRU5lcTdt
142 "cell_type": "markdown"
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143 },
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144 {
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145 "source": "Here we perform a parallel computation, where each process constructs and diagonalizes a subset of\nthe overall set of random matrices.",
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146 "cell_type": "markdown"
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147 },
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148 {
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149 "cell_type": "code",
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150 "language": "python",
151 RjlpMWF4Y3BLU244OXR0dkZCUVUyQ0tYdzVQK0M4czFiZ3pSMGJMdnR4RE95dXlsUVZhc1dNSHUK
151 "outputs": [],
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152 "collapsed": true,
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154 c2VQSDJmY3VIRVdoNmd1clFyR3Q5L0NoeDlDVXBMZEwrMFNSbzBDClB6K1lNa1hySkVMVVRnNnhI
154 "input": "def parallel_diffs(rc, num, N):\n nengines = len(rc.targets)\n num_per_engine = num/nengines\n print \"Running with\", num_per_engine, \"per engine.\"\n ar = rc.apply_async(ensemble_diffs, num_per_engine, N)\n diffs = np.array(ar.get()).flatten()\n normalized_diffs = normalize_diffs(diffs)\n return normalized_diffs"
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155 },
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156 {
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157 "cell_type": "code",
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158 "language": "python",
159 RDRvaE1tVENBaElZRjE2OVlSSHgvUG1UTm55aDNUdDI5ZnNyS3l5TXJLWXVyVXFSWmZ3MWJXcllQ
159 "outputs": [],
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160 "collapsed": true,
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161 "prompt_number": 12,
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162 "input": "client = Client()\nview = client[:]\nview.run('rmtkernel.py')\nview.block = False"
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163 },
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164 {
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165 "cell_type": "code",
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166 "language": "python",
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167 "outputs": [],
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168 "collapsed": true,
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169 "prompt_number": 13,
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170 "input": "parallel_nmats = 40*serial_nmats\nparallel_matsize = 50"
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171 },
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172 {
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173 "cell_type": "code",
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174 "language": "python",
175 SUo0ZmdzTGhnalJvd2dORFNVRjE5OGtZRURCOUt4WTBkYjVISTQwbjloVzVHUlVGZ0lWaGpJSVlT
175 "outputs": [
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176 {
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177 "output_type": "stream",
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178 "text": "Running with 10000 per engine.\n1 loops, best of 1: 14 s per loop"
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179 },
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180 {
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181 "output_type": "stream"
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182 }
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183 ],
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184 "collapsed": false,
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185 "prompt_number": 14,
186 QjZMQ3NhQUFRTVlPSEFneTVjdngyZzAyaXFUdzlpMFNacWp0UFIvLzZldUVQejc3MW9uRVVLQWhR
186 "input": "%timeit -r1 -n1 parallel_diffs(view, parallel_nmats, parallel_matsize)"
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187 },
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188 {
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189 "cell_type": "code",
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190 "language": "python",
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191 "outputs": [
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192 {
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193 "output_type": "stream",
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194 "text": "Running with 10000 per engine."
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195 }
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196 ],
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197 "collapsed": false,
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198 "prompt_number": 15,
199 SWN4Y2FJNk9tZktGS3VmCld0UkFRWUU2YW0zREJ2RDExVHFORU03THBuMFlKUi9tNGVIaGRPellz
199 "input": "pdiffs = parallel_diffs(view, parallel_nmats, parallel_matsize)"
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200 },
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201 {
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202 "source": "Again, the agreement with the Wigner distribution is excellent, but now we have better\nstatistics.",
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203 "cell_type": "markdown"
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204 },
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205 {
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206 "cell_type": "code",
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207 "language": "python",
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208 "outputs": [
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209 {
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210 "output_type": "pyout",
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211 "prompt_number": 16,
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212 "text": "&lt;matplotlib.text.Text at 0x376c950&gt;"
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213 },
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214 {
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215 "output_type": "display_data",
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216 "png": 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EVW18Ex4dCOqcsCeEU7BoD+Py5cu0bdvW+LxNmzZcvnzZ6qFszXDKIFd3O7oL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\nYgzjDehT9fgt8mPlwZWy+q2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401 </png>
402 </output>
403 </outputs>
404 </codecell>
405 <markdowncell>
406 <source>## Serial calculation of nearest neighbor eigenvalue distribution</source>
407 </markdowncell>
408 <markdowncell>
409 <source>In this section we numerically construct and diagonalize a large number of GOE random matrices
410 and compute the nerest neighbor eigenvalue distribution. This comptation is done on a single core.</source>
411 </markdowncell>
412 <codecell>
413 <input>def serial_diffs(num, N):
414 """Compute the nearest neighbor distribution for num NxX matrices."""
415 diffs = ensemble_diffs(num, N)
416 normalized_diffs = normalize_diffs(diffs)
417 return normalized_diffs</input>
418 <language>python</language>
419 <prompt_number>6</prompt_number>
420 <collapsed>1</collapsed>
421 <outputs />
422 </codecell>
423 <codecell>
424 <input>serial_nmats = 1000
425 serial_matsize = 50</input>
426 <language>python</language>
427 <prompt_number>7</prompt_number>
428 <collapsed>1</collapsed>
429 <outputs />
430 </codecell>
431 <codecell>
432 <input>%timeit -r1 -n1 serial_diffs(serial_nmats, serial_matsize)</input>
433 <language>python</language>
434 <prompt_number>8</prompt_number>
435 <collapsed>0</collapsed>
436 <outputs>
437 <output>
438 <output_type>stream</output_type>
439 <text>1 loops, best of 1: 1.19 s per loop</text>
440 </output>
441 </outputs>
442 </codecell>
443 <codecell>
444 <input>serial_diffs = serial_diffs(serial_nmats, serial_matsize)</input>
445 <language>python</language>
446 <prompt_number>9</prompt_number>
447 <collapsed>0</collapsed>
448 <outputs />
449 </codecell>
450 <markdowncell>
451 <source>The numerical computation agrees with the predictions of Wigner, but it would be nice to get more
452 statistics. For that we will do a parallel computation.</source>
453 </markdowncell>
454 <codecell>
455 <input>hist_data = hist(serial_diffs, bins=30, normed=True)
456 plot(s, rhos)
457 xlabel('Normalized level spacing s')
458 ylabel('Probability $P(s)$')</input>
459 <language>python</language>
460 <prompt_number>10</prompt_number>
461 <collapsed>0</collapsed>
462 <outputs>
463 <output>
464 <output_type>pyout</output_type>
465 <text>&amp;lt;matplotlib.text.Text at 0x3475bd0&amp;gt;</text>
466 <prompt_number>10</prompt_number>
467 </output>
468 <output>
469 <output_type>display_data</output_type>
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802 </png>
803 </output>
804 </outputs>
805 </codecell>
806 <markdowncell>
807 <source>## Parallel calculation of nearest neighbor eigenvalue distribution</source>
808 </markdowncell>
809 <markdowncell>
810 <source>Here we perform a parallel computation, where each process constructs and diagonalizes a subset of
811 the overall set of random matrices.</source>
812 </markdowncell>
813 <codecell>
814 <input>def parallel_diffs(rc, num, N):
815 nengines = len(rc.targets)
816 num_per_engine = num/nengines
817 print "Running with", num_per_engine, "per engine."
818 ar = rc.apply_async(ensemble_diffs, num_per_engine, N)
819 diffs = np.array(ar.get()).flatten()
820 normalized_diffs = normalize_diffs(diffs)
821 return normalized_diffs</input>
822 <language>python</language>
823 <prompt_number>11</prompt_number>
824 <collapsed>1</collapsed>
825 <outputs />
826 </codecell>
827 <codecell>
828 <input>client = Client()
829 view = client[:]
830 view.run('rmtkernel.py')
831 view.block = False</input>
832 <language>python</language>
833 <prompt_number>12</prompt_number>
834 <collapsed>1</collapsed>
835 <outputs />
836 </codecell>
837 <codecell>
838 <input>parallel_nmats = 40*serial_nmats
839 parallel_matsize = 50</input>
840 <language>python</language>
841 <prompt_number>13</prompt_number>
842 <collapsed>1</collapsed>
843 <outputs />
844 </codecell>
845 <codecell>
846 <input>%timeit -r1 -n1 parallel_diffs(view, parallel_nmats, parallel_matsize)</input>
847 <language>python</language>
848 <prompt_number>14</prompt_number>
849 <collapsed>0</collapsed>
850 <outputs>
851 <output>
852 <output_type>stream</output_type>
853 <text>Running with 10000 per engine.
854 1 loops, best of 1: 14 s per loop</text>
855 </output>
856 <output>
857 <output_type>stream</output_type>
858 <text />
859 </output>
860 </outputs>
861 </codecell>
862 <codecell>
863 <input>pdiffs = parallel_diffs(view, parallel_nmats, parallel_matsize)</input>
864 <language>python</language>
865 <prompt_number>15</prompt_number>
866 <collapsed>0</collapsed>
867 <outputs>
868 <output>
869 <output_type>stream</output_type>
870 <text>Running with 10000 per engine.</text>
871 </output>
872 </outputs>
873 </codecell>
874 <markdowncell>
875 <source>Again, the agreement with the Wigner distribution is excellent, but now we have better
876 statistics.</source>
877 </markdowncell>
878 <codecell>
879 <input>hist_data = hist(pdiffs, bins=30, normed=True)
880 plot(s, rhos)
881 xlabel('Normalized level spacing s')
882 ylabel('Probability $P(s)$')</input>
883 <language>python</language>
884 <prompt_number>16</prompt_number>
885 <collapsed>0</collapsed>
886 <outputs>
887 <output>
888 <output_type>pyout</output_type>
889 <text>&amp;lt;matplotlib.text.Text at 0x376c950&amp;gt;</text>
890 <prompt_number>16</prompt_number>
891 </output>
892 <output>
893 <output_type>display_data</output_type>
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1263 </png>
1264 </output>
1265 </outputs>
1266 </codecell>
1267 </cells>
1268 </worksheet>
1269 </worksheets>
1270 </notebook>
Show file before | Show file after | Hide comments
@@ -1,78 +1,87 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 {
2 <notebook>
2 "nbformat": 2,
3 <name>task_1</name>
3 "name": "task_1",
4 <nbformat>2</nbformat>
4 "worksheets": [
5 <worksheets>
5 {
6 <worksheet>
6 "cells": [
7 <cells>
7 {
8 <markdowncell>
8 "source": "# Simple task farming example",
9 <source># Simple task farming example</source>
9 "cell_type": "markdown"
10 </markdowncell>
10 },
11 <codecell>
11 {
12 <input>from IPython.parallel import Client</input>
12 "cell_type": "code",
13 <language>python</language>
13 "language": "python",
14 <prompt_number>3</prompt_number>
14 "outputs": [],
15 <collapsed>1</collapsed>
15 "collapsed": true,
16 <outputs />
16 "prompt_number": 3,
17 </codecell>
17 "input": "from IPython.parallel import Client"
18 <markdowncell>
18 },
19 <source>A `Client.load_balanced_view` is used to get the object used for working with load balanced tasks.</source>
19 {
20 </markdowncell>
20 "source": "A `Client.load_balanced_view` is used to get the object used for working with load balanced tasks.",
21 <codecell>
21 "cell_type": "markdown"
22 <input>rc = Client()
22 },
23 v = rc.load_balanced_view()</input>
23 {
24 <language>python</language>
24 "cell_type": "code",
25 <prompt_number>4</prompt_number>
25 "language": "python",
26 <collapsed>1</collapsed>
26 "outputs": [],
27 <outputs />
27 "collapsed": true,
28 </codecell>
28 "prompt_number": 4,
29 <markdowncell>
29 "input": "rc = Client()\nv = rc.load_balanced_view()"
30 <source>Set the variable `d` on all engines:</source>
30 },
31 </markdowncell>
31 {
32 <codecell>
32 "source": "Set the variable `d` on all engines:",
33 <input>rc[:]['d'] = 30</input>
33 "cell_type": "markdown"
34 <language>python</language>
34 },
35 <prompt_number>5</prompt_number>
35 {
36 <collapsed>1</collapsed>
36 "cell_type": "code",
37 <outputs />
37 "language": "python",
38 </codecell>
38 "outputs": [],
39 <markdowncell>
39 "collapsed": true,
40 <source>Define a function that will be our task:</source>
40 "prompt_number": 5,
41 </markdowncell>
41 "input": "rc[:]['d'] = 30"
42 <codecell>
42 },
43 <input>def task(a):
43 {
44 return a, 10*d, a*10*d</input>
44 "source": "Define a function that will be our task:",
45 <language>python</language>
45 "cell_type": "markdown"
46 <prompt_number>6</prompt_number>
46 },
47 <collapsed>1</collapsed>
47 {
48 <outputs />
48 "cell_type": "code",
49 </codecell>
49 "language": "python",
50 <markdowncell>
50 "outputs": [],
51 <source>Run the task once:</source>
51 "collapsed": true,
52 </markdowncell>
52 "prompt_number": 6,
53 <codecell>
53 "input": "def task(a):\n return a, 10*d, a*10*d"
54 <input>ar = v.apply(task, 5)</input>
54 },
55 <language>python</language>
55 {
56 <prompt_number>7</prompt_number>
56 "source": "Run the task once:",
57 <collapsed>1</collapsed>
57 "cell_type": "markdown"
58 <outputs />
58 },
59 </codecell>
59 {
60 <markdowncell>
60 "cell_type": "code",
61 <source>Print the results:</source>
61 "language": "python",
62 </markdowncell>
62 "outputs": [],
63 <codecell>
63 "collapsed": true,
64 <input>print "a, b, c: ", ar.get()</input>
64 "prompt_number": 7,
65 <language>python</language>
65 "input": "ar = v.apply(task, 5)"
66 <prompt_number>8</prompt_number>
66 },
67 <collapsed>0</collapsed>
67 {
68 <outputs>
68 "source": "Print the results:",
69 <output>
69 "cell_type": "markdown"
70 <output_type>stream</output_type>
70 },
71 <text>a, b, c: [5, 300, 1500]</text>
71 {
72 </output>
72 "cell_type": "code",
73 </outputs>
73 "language": "python",
74 </codecell>
74 "outputs": [
75 </cells>
75 {
76 </worksheet>
76 "output_type": "stream",
77 </worksheets>
77 "text": "a, b, c: [5, 300, 1500]"
78 </notebook>
78 }
79 ],
80 "collapsed": false,
81 "prompt_number": 8,
82 "input": "print \"a, b, c: \", ar.get()"
83 }
84 ]
85 }
86 ]
87 } No newline at end of file
Show file before | Show file after | Hide comments
@@ -1,74 +1,69 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 {
2 <notebook>
2 "nbformat": 2,
3 <name>taskmap</name>
3 "name": "taskmap",
4 <nbformat>2</nbformat>
4 "worksheets": [
5 <worksheets>
5 {
6 <worksheet>
6 "cells": [
7 <cells>
7 {
8 <markdowncell>
8 "source": "# Load balanced map and parallel function decorator",
9 <source># Load balanced map and parallel function decorator</source>
9 "cell_type": "markdown"
10 </markdowncell>
10 },
11 <codecell>
11 {
12 <input>from IPython.parallel import Client</input>
12 "cell_type": "code",
13 <language>python</language>
13 "language": "python",
14 <prompt_number>4</prompt_number>
14 "outputs": [],
15 <collapsed>1</collapsed>
15 "collapsed": true,
16 <outputs />
16 "prompt_number": 4,
17 </codecell>
17 "input": "from IPython.parallel import Client"
18 <codecell>
18 },
19 <input>rc = Client()
19 {
20 v = rc.load_balanced_view()</input>
20 "cell_type": "code",
21 <language>python</language>
21 "language": "python",
22 <prompt_number>5</prompt_number>
22 "outputs": [],
23 <collapsed>1</collapsed>
23 "collapsed": true,
24 <outputs />
24 "prompt_number": 5,
25 </codecell>
25 "input": "rc = Client()\nv = rc.load_balanced_view()"
26 <codecell>
26 },
27 <input>result = v.map(lambda x: 2*x, range(10))
27 {
28 print "Simple, default map: ", list(result)</input>
28 "cell_type": "code",
29 <language>python</language>
29 "language": "python",
30 <prompt_number>6</prompt_number>
30 "outputs": [
31 <collapsed>0</collapsed>
31 {
32 <outputs>
32 "output_type": "stream",
33 <output>
33 "text": "Simple, default map: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
34 <output_type>stream</output_type>
34 }
35 <text>Simple, default map: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]</text>
35 ],
36 </output>
36 "collapsed": false,
37 </outputs>
37 "prompt_number": 6,
38 </codecell>
38 "input": "result = v.map(lambda x: 2*x, range(10))\nprint \"Simple, default map: \", list(result)"
39 <codecell>
39 },
40 <input>ar = v.map_async(lambda x: 2*x, range(10))
40 {
41 print "Submitted tasks, got ids: ", ar.msg_ids
41 "cell_type": "code",
42 result = ar.get()
42 "language": "python",
43 print "Using a mapper: ", result</input>
43 "outputs": [
44 <language>python</language>
44 {
45 <prompt_number>7</prompt_number>
45 "output_type": "stream",
46 <collapsed>0</collapsed>
46 "text": "Submitted tasks, got ids: [&apos;2a25ff3f-f0d0-4428-909a-3fe808ca61f9&apos;, &apos;edd42168-fac2-4b3f-a696-ce61b37aa71d&apos;, &apos;8a548908-7812-44e6-a8b1-68e941bee608&apos;, &apos;26435a77-fe86-49b6-b59f-de864d59c99f&apos;, &apos;6750c7b4-2168-49ec-bcc4-feb1e17c5e53&apos;, &apos;117240d1-5dfc-4783-948f-e9523b2b2f6a&apos;, &apos;6de16d46-f2e2-49bd-8180-e43d1d875529&apos;, &apos;3d372b84-0c68-4315-92c8-a080c68478b7&apos;, &apos;43acedae-e35c-4a17-87f0-9e5e672500f7&apos;, &apos;eb71dd1f-9500-4375-875d-c2c42999848c&apos;]\nUsing a mapper: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
47 <outputs>
47 }
48 <output>
48 ],
49 <output_type>stream</output_type>
49 "collapsed": false,
50 <text>Submitted tasks, got ids: [&amp;apos;2a25ff3f-f0d0-4428-909a-3fe808ca61f9&amp;apos;, &amp;apos;edd42168-fac2-4b3f-a696-ce61b37aa71d&amp;apos;, &amp;apos;8a548908-7812-44e6-a8b1-68e941bee608&amp;apos;, &amp;apos;26435a77-fe86-49b6-b59f-de864d59c99f&amp;apos;, &amp;apos;6750c7b4-2168-49ec-bcc4-feb1e17c5e53&amp;apos;, &amp;apos;117240d1-5dfc-4783-948f-e9523b2b2f6a&amp;apos;, &amp;apos;6de16d46-f2e2-49bd-8180-e43d1d875529&amp;apos;, &amp;apos;3d372b84-0c68-4315-92c8-a080c68478b7&amp;apos;, &amp;apos;43acedae-e35c-4a17-87f0-9e5e672500f7&amp;apos;, &amp;apos;eb71dd1f-9500-4375-875d-c2c42999848c&amp;apos;]
50 "prompt_number": 7,
51 Using a mapper: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]</text>
51 "input": "ar = v.map_async(lambda x: 2*x, range(10))\nprint \"Submitted tasks, got ids: \", ar.msg_ids\nresult = ar.get()\nprint \"Using a mapper: \", result"
52 </output>
52 },
53 </outputs>
53 {
54 </codecell>
54 "cell_type": "code",
55 <codecell>
55 "language": "python",
56 <input>@v.parallel(block=True)
56 "outputs": [
57 def f(x): return 2*x
57 {
58
58 "output_type": "stream",
59 result = f.map(range(10))
59 "text": "Using a parallel function: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]"
60 print "Using a parallel function: ", result</input>
60 }
61 <language>python</language>
61 ],
62 <prompt_number>8</prompt_number>
62 "collapsed": false,
63 <collapsed>0</collapsed>
63 "prompt_number": 8,
64 <outputs>
64 "input": "@v.parallel(block=True)\ndef f(x): return 2*x\n\nresult = f.map(range(10))\nprint \"Using a parallel function: \", result"
65 <output>
65 }
66 <output_type>stream</output_type>
66 ]
67 <text>Using a parallel function: [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]</text>
67 }
68 </output>
68 ]
69 </outputs>
69 } No newline at end of file
70 </codecell>
71 </cells>
72 </worksheet>
73 </worksheets>
74 </notebook>
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This diff has been collapsed as it changes many lines, (886 lines changed) Show them Hide them
@@ -1,606 +1,280 b''
1 <?xml version="1.0" encoding="utf-8"?>
1 {
2 <notebook>
2 "nbformat": 2,
3 <name>basic_quantum</name>
3 "name": "basic_quantum",
4 <nbformat>2</nbformat>
4 "worksheets": [
5 <worksheets>
5 {
6 <worksheet>
6 "cells": [
7 <cells>
7 {
8 <markdowncell>
8 "source": "<h1>Basic Symbolic Quantum Mechanics</h1>",
9 <source>&lt;h1&gt;Basic Symbolic Quantum Mechanics&lt;/h1&gt;</source>
9 "cell_type": "markdown"
10 </markdowncell>
10 },
11 <codecell>
11 {
12 <input>%load_ext sympyprinting</input>
12 "cell_type": "code",
13 <language>python</language>
13 "language": "python",
14 <prompt_number>18</prompt_number>
14 "outputs": [],
15 <collapsed>1</collapsed>
15 "collapsed": true,
16 <outputs />
16 "prompt_number": 18,
17 </codecell>
17 "input": "%load_ext sympyprinting"
18 <codecell>
18 },
19 <input>from sympy import sqrt, symbols, Rational
19 {
20 from sympy import expand, Eq, Symbol, simplify, exp, sin
20 "cell_type": "code",
21 from sympy.physics.quantum import *
21 "language": "python",
22 from sympy.physics.quantum.qubit import *
22 "outputs": [],
23 from sympy.physics.quantum.gate import *
23 "collapsed": true,
24 from sympy.physics.quantum.grover import *
24 "prompt_number": 19,
25 from sympy.physics.quantum.qft import QFT, IQFT, Fourier
25 "input": "from sympy import sqrt, symbols, Rational\nfrom sympy import expand, Eq, Symbol, simplify, exp, sin\nfrom sympy.physics.quantum import *\nfrom sympy.physics.quantum.qubit import *\nfrom sympy.physics.quantum.gate import *\nfrom sympy.physics.quantum.grover import *\nfrom sympy.physics.quantum.qft import QFT, IQFT, Fourier\nfrom sympy.physics.quantum.circuitplot import circuit_plot"
26 from sympy.physics.quantum.circuitplot import circuit_plot</input>
26 },
27 <language>python</language>
27 {
28 <prompt_number>19</prompt_number>
28 "source": "<h2>Bras and Kets</h2>",
29 <collapsed>1</collapsed>
29 "cell_type": "markdown"
30 <outputs />
30 },
31 </codecell>
31 {
32 <markdowncell>
32 "source": "Create symbolic states",
33 <source>&lt;h2&gt;Bras and Kets&lt;/h2&gt;</source>
33 "cell_type": "markdown"
34 </markdowncell>
34 },
35 <markdowncell>
35 {
36 <source>Create symbolic states</source>
36 "cell_type": "code",
37 </markdowncell>
37 "language": "python",
38 <codecell>
38 "outputs": [],
39 <input>phi, psi = Ket('phi'), Ket('psi')
39 "collapsed": true,
40 alpha, beta = symbols('alpha beta', complex=True)</input>
40 "prompt_number": 20,
41 <language>python</language>
41 "input": "phi, psi = Ket('phi'), Ket('psi')\nalpha, beta = symbols('alpha beta', complex=True)"
42 <prompt_number>20</prompt_number>
42 },
43 <collapsed>1</collapsed>
43 {
44 <outputs />
44 "source": "Create a superposition",
45 </codecell>
45 "cell_type": "markdown"
46 <markdowncell>
46 },
47 <source>Create a superposition</source>
47 {
48 </markdowncell>
48 "cell_type": "code",
49 <codecell>
49 "language": "python",
50 <input>state = alpha*psi + beta*phi; state
50 "outputs": [
51 </input>
51 {
52 <language>python</language>
52 "output_type": "pyout",
53 <prompt_number>21</prompt_number>
53 "latex": "$$\\alpha {\\left|\\psi\\right\\rangle } + \\beta {\\left|\\phi\\right\\rangle }$$",
54 <collapsed>0</collapsed>
54 "prompt_number": 21,
55 <outputs>
55 "png": "iVBORw0KGgoAAAANSUhEUgAAAF8AAAAXCAYAAABtR5P0AAAABHNCSVQICAgIfAhkiAAABHBJREFU\naIHt2VmsXWMUB/Dfvb0dqBYtjZCrWvdBOiDVlmpTLTW0UiSGkHjRpoZETSUkTQyJseaIGzFUESXE\nA0rwwJWK4UE0SjwgaFNqnkra4PKw9s7Zd9+99z2nd0By/y/nfGt9a531/771rW/tfRjE/xL3Y8y/\nHUQ/o185NvfCdjSGNTD/JgzNyS7HhF7E0FeYhnYR41pciyaNcbwUB+RklfxaGgyyNxiJP3Kyp7Ac\nVwxgHHksxV+4WMTXjC/wSYN+2vB5TlbJrzeZ3wjG4tsC+SbsgVG99D9tJ+2Ow59Yo5YYnfgNhzXg\np1lsYB6V/AZq8Y9CR4luNZb00v8dO2EzCvPxSE4+XmTx2w34mor3S3Sl/AZq8WcoJ/MWZg5gLCnO\nwmMF8hvxiigZ9WKu8uQq5VdU8ycmgbViHL7Glfgl0Tfh7wK7YTgPR2IDbsnohqod69vFxXRqRr8O\ni/FsCYH+wHjRzYzGQ9guYv8KRyvmmEUrVuB7nISDsAtuwKe5uXXxO1jUqUXJuBn3Jcbpzt2dfD6J\nfTK2l2CS2OXt2C2R76XrhbMav+d+t0VxFtaLjgbnj8rENEpswmqR7Z1YkOjyHFNchJexv1iXexP5\n4diie9fTI782setX5+QniiyYif0y+mxgQ3FX8n0FflDbrNNE2UkxVvfMgKtwSFWAFehocP4iwSeP\n4fhOcKN48c/BR2rJNQ3LMvrn8GCB70p+a8Xij8zJW8XiLxcLv29BYMPFxsBGcVpSXI8hmfEQkWV5\njFHLoEbR0eD8lbmYstiIV5Pv+cWfgB1YmJGtEImb4gHF91s3fmnNb8axeEG0WVlsTj6PEH3slwWO\nd4jjNhlTRM+coknXNmw6Hi7wkc4twwQ8o/hibhP3TB5bxMnNo0Vxa9iCA/FSSQwL8VNO36brM8F0\nvFNi34VfuviTRW3+oMSIaKeWVuhhjiC1PhnvLS7sLCbiiQLbc0XWlOEz5f18B+b1EFuK0UlcRThZ\nXJrrSvST8bHaZdwinhNStInkW1lg241fmkWbEof5hSJqW6fY7e0lQaXoxDa1rJqH1zL6Zblxihax\nue/14L8vMBfH636CWkQJWYPXS2zXq5Vd4kHs3eR7k+ia2vFige9u/NIAfhZH+vic0QLcKo7RuGT+\nKSWBwfOilp6QjCeJ0zQCq8SdsrXA7nQ8XeG3LzED14i2OK37acfyo64lM4914kn9zGQ8XyTTWHGa\nN+CyArtCftk+/2zcJi6ZzUlAb+IC0YLeI148PV4R3FZR867DLNFRrEp07aJ0FGFx8vsDgRGiuViK\nR0Xi7Yk3cL7q/n4bjhFNxGxRZsdgV9ys+N6hH/iV9cAppuLCOvzMUp1t9aCjznm7K67HZajiOESt\nva5CKb/+fKSfr75FWaK49WwE39Q5b644zX2BQ5W/z8milF9vFr9TcbuWYgo+7MFHq6izv/YiDjij\nznmzNfbCrIrjHFGqqtBX/Lqhp9fA7XX4GOg/Uxp9+1nF8c467P8rfxYNYhCDGAT8A+0w3Ws5danI\nAAAAAElFTkSuQmCC\n",
56 <output>
56 "text": "\u03b1\u22c5\u2758\u03c8\u27e9 + \u03b2\u22c5\u2758\u03c6\u27e9"
57 <output_type>pyout</output_type>
57 }
58 <text>α⋅❘ψ⟩ + β⋅❘φ⟩</text>
58 ],
59 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQUY4QUFBQVhDQVlBQUFCdFI1UDBBQUFBQkhOQ1NWUUlD
59 "collapsed": false,
60 QWdJZkFoa2lBQUFCSEJKUkVGVQphSUh0MlZtc1hXTVVCL0RmdmIwZHFCWXRqWkNyV3ZkQk9pRFZs
60 "prompt_number": 21,
61 bXBUTFRXMFVpU0drSGpScG9aRVRTVWtUUXlKc2VhSUd6RlVFU1hFCkEwcnd3SldLNFVFMFNqd2dh
61 "input": "state = alpha*psi + beta*phi; state\n"
62 Rk5xbmtyYTRQS3c5czdaZDkrOTl6Mm5kMEJ5L3kvbmZHdDlhNTMxLzc3MXJXL3RmUmpFL3hMM1k4
62 },
63 eS8KSFVRL28xODVOdmZDZGpTR05URC9KZ3pOeVM3SGhGN0UwRmVZaG5ZUjQxcGNpeWFOY2J3VUIr
63 {
64 UmtsZnhhR2d5eU54aUpQM0t5cDdBYwpWd3hnSEhrc3hWKzRXTVRYakMvd1NZTisydkI1VGxiSnJ6
64 "source": "Dagger the superposition and multiply the original",
65 ZVozd2pHNHRzQytTYnNnVkc5OUQ5dEorMk93NTlZbzVZWW5mZ05oelhnCnAxbHNZQjZWL0FacThZ
65 "cell_type": "markdown"
66 OUNSNGx1TlpiMDB2OGRPMkV6Q3ZQeFNFNCtYbVR4MnczNG1vcjNTM1NsL0FacThXY29KL01XWmc1
66 },
67 Z0xDbk8Kd21NRjhodnhpaWdaOVdLdTh1UXE1VmRVOHljbWdiVmlITDdHbGZnbDBUZmg3d0s3WVRn
67 {
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68 "cell_type": "code",
69 clZ1QjduSVNEc0F0dXdLZTV1WFh4TzFqVXFVWEp1Qm4zSmNicHp0MmRmRDZKCmZUSzJsMkNTMk9Y
69 "language": "python",
70 dDJDMlI3NlhyaGJNYXYrZCt0MFZ4RnRhTGpnYm5qOHJFTkVwc3dtcVI3WjFZa09qeUhGTmNoSmV4
70 "outputs": [
71 djFpWGV4UDUKNGRpaWU5ZlRJNzgyc2V0WDUrUW5paXlZaWYweStteGdRM0ZYOG4wRmZsRGJyTk5F
71 {
72 MlVreFZ2Zk1nS3R3U0ZXQUZlaG9jUDRpd1NlUAo0ZmhPY0tONDhjL0JSMnJKTlEzTE12cm44R0NC
72 "output_type": "pyout",
73 NzBwK2E4WGlqOHpKVzhYaUx4Y0x2MjlCWU1QRnhzQkdjVnBTWEk4aG1mRVFrV1Y1CmpGSExvRWJS
73 "latex": "$$\\left(\\overline{\\alpha} {\\left\\langle \\psi\\right|} + \\overline{\\beta} {\\left\\langle \\phi\\right|}\\right) \\left(\\alpha {\\left|\\psi\\right\\rangle } + \\beta {\\left|\\phi\\right\\rangle }\\right)$$",
74 MGVEOGxibVlzdGlJVjVQditjV2ZnQjFZbUpHdEVJbWI0Z0hGOTFzM2Ztbk5iOGF4ZUVHMFdWbHNU
74 "prompt_number": 22,
75 ajZQRUgzc2x3V08KZDRqak5obFRSTStjb2tuWE5tdzZIaTd3a2M0dHd3UThvL2hpYmhQM1RCNWJ4
75 "png": "iVBORw0KGgoAAAANSUhEUgAAANoAAAAaCAYAAADR9UJvAAAABHNCSVQICAgIfAhkiAAACHpJREFU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\n2Kc62Q7y4E4AAAAASUVORK5CYII=\n",
76 TW5ObzBWeGE5aUNBL0ZTU1F3TDhWTk8zNmJyTThGMAp2Rk5pMzRWZnV2aVRSVzMrb01TSWFLZVdW
76 "text": "\u239b\u23bd \u23bd \u239e \n\u239d\u03b1\u22c5\u27e8\u03c8\u2758 + \u03b2\u22c5\u27e8\u03c6\u2758\u23a0\u22c5(\u03b1\u22c5\u2758\u03c8\u27e9 + \u03b2\u22c5\u2758\u03c6\u27e9)"
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77 }
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78 ],
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79 "collapsed": false,
80 aWEydkZpZ2U5dS9OSUFmaFpIK3ZpYzBRTGNLbzdSdUdUKwpLU1dCd2ZPaWxwNlFqQ2VKMHpRQ3E4
80 "prompt_number": 22,
81 U2RzclhBN25ROFhlRzNMekVEMTRpMk9LMzdhY2Z5bzY0bE00OTE0a245ekdROFh5VFRXSEdhCk4r
81 "input": "ip = Dagger(state)*state; ip\n"
82 Q3lBcnRDZnRrKy8yemNKaTZaelVsQWIrSUMwWUxlSTE0OFBWNFIzRlpSODY3RExORlJyRXAwN2FK
82 },
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83 {
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84 "source": "Distribute",
85 NDlXd0UzOVE1YjY0NHpYMkJRNVcvejhtaWxGOXZGcjlUY2J1V1lnbys3TUZIcTZpenYvWWlEamlq
85 "cell_type": "markdown"
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86 },
87 WWhDREdBVDhBKzB3M1dzNWRhbkkKQUFBQUFFbEZUa1N1UW1DQwo=
87 {
88 </png>
88 "cell_type": "code",
89 <latex>$$\alpha {\left|\psi\right\rangle } + \beta {\left|\phi\right\rangle }$$</latex>
89 "language": "python",
90 <prompt_number>21</prompt_number>
90 "outputs": [
91 </output>
91 {
92 </outputs>
92 "output_type": "pyout",
93 </codecell>
93 "latex": "$$\\alpha \\overline{\\alpha} \\left\\langle \\psi \\right. {\\left|\\psi\\right\\rangle } + \\alpha \\overline{\\beta} \\left\\langle \\phi \\right. {\\left|\\psi\\right\\rangle } + \\beta \\overline{\\alpha} \\left\\langle \\psi \\right. {\\left|\\phi\\right\\rangle } + \\beta \\overline{\\beta} \\left\\langle \\phi \\right. {\\left|\\phi\\right\\rangle }$$",
94 <markdowncell>
94 "prompt_number": 23,
95 <source>Dagger the superposition and multiply the original</source>
95 "png": "iVBORw0KGgoAAAANSUhEUgAAAU8AAAAaCAYAAAA3+d4CAAAABHNCSVQICAgIfAhkiAAAB9VJREFU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\nVapUevofz4SOwufiq5gAAAAASUVORK5CYII=\n",
96 </markdowncell>
96 "text": "\u23bd \u23bd \u23bd \u23bd \n\u03b1\u22c5\u03b1\u22c5\u27e8\u03c8\u2758\u03c8\u27e9 + \u03b1\u22c5\u03b2\u22c5\u27e8\u03c6\u2758\u03c8\u27e9 + \u03b2\u22c5\u03b1\u22c5\u27e8\u03c8\u2758\u03c6\u27e9 + \u03b2\u22c5\u03b2\u22c5\u27e8\u03c6\u2758\u03c6\u27e9"
97 <codecell>
97 }
98 <input>ip = Dagger(state)*state; ip
98 ],
99 </input>
99 "collapsed": false,
100 <language>python</language>
100 "prompt_number": 23,
101 <prompt_number>22</prompt_number>
101 "input": "qapply(expand(ip))\n"
102 <collapsed>0</collapsed>
102 },
103 <outputs>
103 {
104 <output>
104 "source": "<h2>Operators</h2>",
105 <output_type>pyout</output_type>
105 "cell_type": "markdown"
106 <text>⎛⎽ ⎽ ⎞
106 },
107 ⎝α⋅⟨ψ❘ + β⋅⟨φ❘⎠⋅(α⋅❘ψ⟩ + β⋅❘φ⟩)</text>
107 {
108 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQU5vQUFBQWFDQVlBQUFEUjlVSnZBQUFBQkhOQ1NWUUlD
108 "source": "Create symbolic operators",
109 QWdJZkFoa2lBQUFDSHBKUkVGVQplSnp0bkhlTVZFVWN4ejkzUjBmZ3dEdWFvaWg0b0lKS1FNQ1du
109 "cell_type": "markdown"
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110 },
111 RmhqUWVYT1AzN3p2TGV6TS9ObTN0dTdOYnFmNUxLN00vTm1mci85dmpmbE4zTmJRWms0aHdHekxY
111 {
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112 "cell_type": "code",
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113 "language": "python",
114 RC9vWjFoU2M4Vng1UlU3QWJNQXVZQURjQ1JoaksrUGw1dVNjOFowdm9BCjI0RTlQZW85Rk9qblVj
114 "outputs": [],
115 NkZ5UVlYSnEwT0FvN09hRWRXWEhybEF1b3hhZVh5cnhZNHlwVFJ4cEIyTUREUVlGRGFRRUUxVUFj
115 "collapsed": true,
116 MFdmTGoKVkFIOVBjcTFKbU9Bb2NDVHdDYms1bCtQM05nZnF6SWhQZzRNYUhzTGNDZHdOWENCbzl3
116 "prompt_number": 24,
117 SVplZTFBWFZueGFiVmFtQSs4R29yMmhMSApSeTlmVEZxNS9Oc0duQTU4QzZ4TXF2dzY0T1pBZzF4
117 "input": "A = Operator('A')\nB = Operator('B')\nC = Operator('C')"
118 Y0NSem9XWFlFc2pZMGtjdGdRN2VVMXgwR1hHVkkzNnFsKy9wWUE5eGd5Y3RaCjBrY0JuenZxckFa
118 },
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119 {
120 SGdrb1B4UG8KYThuTHBiU2hPK0pUS0YyQld3enAvWkdSNjJUMU9jVEhVekJQTzhIdTM2NnFQVnNF
120 "source": "Test commutativity",
121 OGk1VmJ6R3cyV0RDcFZVUDRONE1kcVRSekZldgpuR2Q5THEyUy9KdWk1NXVpamtPQVpaN0dKREVS
121 "cell_type": "markdown"
122 ZURxZ2ZCOWdjNUhhanFoU2Y2R2NCVHhtU0o4TnZBTThxejZIK0RnU1dCcG94M2JnCkIyQi9RMTR0
122 },
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123 {
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124 "cell_type": "code",
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125 "language": "python",
126 SnVvMFhGdGlGNDZXYlI2QUpnRzNPalpWbFo4OVhJUm9wWEx2eWJnUytUaGZ3QUtSN1E2CllJZWgw
126 "outputs": [
127 b2c5Z0JYQUlOWEE5Y0NGNUFkSnJsQ3ZvNEVQS0x3SlppTTN6a2ZBUGJIMDRUU1BwSlhLeUFzdGRy
127 {
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128 "output_type": "pyout",
129 UXh1RWZJRUwxTVpORnFMYkEzcmJNUDZLdVhpMUN0a3Z4YgpoMzNxeVVUZ0swdGVUM1d4dmc4eERl
129 "prompt_number": 25,
130 a3RlaUVPWHFQU0g2UndYZEdONWtETFhFVEFpSm5JZWlUaU5HU1JINUd6R1oxQURiQW84SnBUCmtT
130 "text": "False"
131 bTB6bDdJUXhYNVlQSXhZaXJTeTBjaW4wcHpXTGdDaVV5ZEdTdWZjOWh6Sy9uZlJjUnk1R0V6RWFx
131 }
132 WGJrTVdyU0tPQjg2ejJPY2kKVkROZnZjRDhQWWRxRmVIeWJ5cXhUbEFmMGJZaFRwcldibmNqVTQ4
132 ],
133 NVd2cEtWWDQwRXVKZmdBemozd00vYTJWcmtDbElXeVFNR3Y4eQpkMFhXSXhITGtkNjRGT3lMaEhG
133 "collapsed": false,
134 MU5pRVJyRHJzUG9MMCtQT0FjNEZmVmRxaHdOdnFmUlB3R1RLUDk2RWRvbzFPVDJXRGlSQzlUQlJE
134 "prompt_number": 25,
135 CnE1ZVFhV3RMNDZPWGpTeGF1ZnhiUjJ6L1UxK2pyVUdHd243a2g1U3JnQk9BaGNCUDJqWHJZOFpW
135 "input": "A*B == B*A\n"
136 QWw4Z3ZjRjZDdG1nWHNjaFEvdkMKbUIxL2FHV0h4L0o5R0lyMDN2b1EzeFk0QURucG9yTUp1Q1Nn
136 },
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137 {
138 V2pXcHNoMW85ajFPUzJzVzE4dEdGcTFjL24yTGRIUkE0WU8ySGVrQkJwTC9vSTFFOW10V0dScUxo
138 "source": "Distribute A+B squared",
139 QjRQCkhLTGV2d2FjRHp4a0tBL05EK0pHOVhrRXN0YUpxRVNtTjZiMmJLeEJwa1c2YU4yUlhuMmE0
139 "cell_type": "markdown"
140 WnBmRFdtdVNOazRWZi9yd0Z2WWZUeUUKL0I1ZWo5QWRqRXc1WDNhMEZhY0djNCs5SGRnSFdiREhD
140 },
141 ZFhMUlJhdCtpRWpzZWtoZytKbzVxdVhqU3hhdWZ6YkIzbllBUE1tNXhyawpRWXZ2ZlAraVhqY1VG
141 {
142 djhubWpNZitGRzliMExtd2tkaWRyS2EvSjcwY0dTOUV6RVovOTQrb2hINDJwRCtPL0FiOXJXblRq
142 "cell_type": "code",
143 MHlyZEtwClFIclNwNUFGTTloOVhJbEVyaUxpWmRvQTl5R1JzWS93WXpmTXZmSldKTkNoRTZxWGl5
143 "language": "python",
144 eGFUUWZ1ZDlSZERNM3E4ZGZMUkJhdFhQNE4KUnZRQnpHdXgxUlFlUFZtTjlHZ2p0ZlE2NERZazRs
144 "outputs": [
145 T3Qwb2FyMXdYWVR3NHNRWHFTNkpvdXlCU25EWEl5WlJ1eWQxUUtoaUMrNnZQNgpXNUJOMFl0amFU
145 {
146 WWY1eU1oOGQ3cTh5amdQVVRRQnVTaE1aMWdNTkVMMlhRMW5RNVppZ2lxazBZdkcybTE2b3lzSVRj
146 "output_type": "pyout",
147 YThvcEppRjRtCjVwTk9xeVQvQmhFTGhwaEd0R1hJdkRWT0kzQ2NNcW9yTWlUMlJBUzdDT2tCcmxM
147 "latex": "$$A B + \\left(A\\right)^{2} + B A + \\left(B\\right)^{2}$$",
148 bGxxaHJma09HNEFFVTlxeUxrTkR6NDhERHlEQjcKQXhMcGVvVFNCVUZBMWdlWEl5SGVDbVJLTkFy
148 "prompt_number": 26,
149 eGRUVDUwd1Niais4aGkrc0daSjlyQ0hKVERrRDhmU1hBbnJIWXY0OFhNSi91VDZPWApqYlJhVGNZ
149 "png": "iVBORw0KGgoAAAANSUhEUgAAAMAAAAAZCAYAAABn7SHgAAAABHNCSVQICAgIfAhkiAAABONJREFU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\nuwAAAABJRU5ErkJggg==\n",
150 ZWFDa21JWHFaU0t0VmtuK0RnWnRjRGJkSEZweTJucTRQc21iUXFhWnd2Nkl2Y0llanJVcEUrS2sw
150 "text": "2 2\nA\u22c5B + A + B\u22c5A + B"
151 OTVnMmNnbjVOa0pDCnhiM0pQN0hkRHRrcmNaSGs0ekRnZHBMM2szS1c5RVhBQkV0ZUZUSjY5WGZV
151 }
152 RzZLWHpRWUkwNnFDc0VDV2pxOW1hZlRLT2ZKOHRVcnkKcncvd1Nid2UwOVJ4QnhJSnVnZnpodW9X
152 ],
153 WW91OEdEOVF1RkRkakF5eFhTMEdOU0pmekVKYWJxcllpUHZrUkp4Njh1ZnpmNUE4OVVueQpzUTc1
153 "collapsed": false,
154 dDZNZG5qYkVHWVk4eUxialF6dVJUV2pYT2loRUx4Y2hXbzBsZWFSTWFzdEhzM3JDOVhMaHExV1Nm
154 "prompt_number": 26,
155 M09SWUU2aTVsVklhTFVZCnY1RXhITGpNa1crTFRPcmtNdGhnNnRGTjNFbTZVL0F1SCs5QXdyOUo1
155 "input": "expand((A+B)**2)"
156 TFRQN1pESXBzOHArR2N3YjZpR290dWc0NnZWQXNUK0xQaG8KbGthdm5DUFBWeXVYZnhPUXFIdmVJ
156 },
157 R2I3S1lPZHlPNzRCTEwvYnNWeTdEZExEZWJlMXNTbEdXendiYU1kOEZlSytsMCt4dmRrWE9qKwp6
157 {
158 VUpPYmZpc1YwOUhUb2owU0NvWWFFTWNYNjMyQXo2bGNLOHRGSisyMHVqbDh0RkhLNWQvWFpEamFC
158 "source": "Create a commutator",
159 UHduMFVCY3ZxNGMyS3BaR3h6Cit2Wmt2em1LU2Uva0lsWnNQcWF0TS9TNkRyVHNqL240YXRXSjdL
159 "cell_type": "markdown"
160 T1pMMW4wU2x1Znk3K094RTdzbHlsVHBreVpNbVhLbENtVGdyOEIKMktjNjJRN3k0RTRBQUFBQVNV
160 },
161 Vk9SSzVDWUlJPQo=
161 {
162 </png>
162 "cell_type": "code",
163 <latex>$$\left(\overline{\alpha} {\left\langle \psi\right|} + \overline{\beta} {\left\langle \phi\right|}\right) \left(\alpha {\left|\psi\right\rangle } + \beta {\left|\phi\right\rangle }\right)$$</latex>
163 "language": "python",
164 <prompt_number>22</prompt_number>
164 "outputs": [
165 </output>
165 {
166 </outputs>
166 "output_type": "pyout",
167 </codecell>
167 "latex": "$$\\left[A,B\\right]$$",
168 <markdowncell>
168 "prompt_number": 27,
169 <source>Distribute</source>
169 "png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAAWCAYAAAC/kK73AAAABHNCSVQICAgIfAhkiAAAAkhJREFU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\nvA1Pse5//Nv4Bfpvd5tNLRluAAAAAElFTkSuQmCC\n",
170 </markdowncell>
170 "text": "[A,B]"
171 <codecell>
171 }
172 <input>qapply(expand(ip))
172 ],
173 </input>
173 "collapsed": false,
174 <language>python</language>
174 "prompt_number": 27,
175 <prompt_number>23</prompt_number>
175 "input": "comm = Commutator(A,B); comm\n"
176 <collapsed>0</collapsed>
176 },
177 <outputs>
177 {
178 <output>
178 "source": "Carry out the commutator",
179 <output_type>pyout</output_type>
179 "cell_type": "markdown"
180 <text>⎽ ⎽ ⎽ ⎽
180 },
181 α⋅α⋅⟨ψ❘ψ⟩ + α⋅β⋅⟨φ❘ψ⟩ + β⋅α⋅⟨ψ❘φ⟩ + β⋅β⋅⟨φ❘φ⟩</text>
181 {
182 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQVU4QUFBQWFDQVlBQUFBMytkNENBQUFBQkhOQ1NWUUlD
182 "cell_type": "code",
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183 "language": "python",
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184 "outputs": [
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185 {
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186 "output_type": "pyout",
187 MGdCN0JLeHRtclpKeU5NdVY2VUJaSgpEVFVaR0djWU94YzRLbUw3Q0tCQjBXZFVubGxlbnM2a091
187 "latex": "$$A B - B A$$",
188 QnM0QzdnZnVCbW9HdE1yQ25uNFFpTHNBNEV4aHBlV3VYdDQ2aHhxalZmCjBERTJqYzNUdTJxdXJp
188 "prompt_number": 28,
189 ZlBldURsaEw5aENXMHZCRFlZOW5NeXNNWCtNQlB6ZkFoY25rTHV2SFFFY0Nmd0czQVRjdXpOd01x
189 "png": "iVBORw0KGgoAAAANSUhEUgAAAE4AAAASCAYAAAD15uiRAAAABHNCSVQICAgIfAhkiAAAAi5JREFU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\nrkJggg==\n",
190 WWVGUE8KcHdDYlVqaStvakUyNGRXWmZCdzFUclgyc01hVG10Zzh2YXZtNm5yMTNRUE10R2pYQkh6
190 "text": "A\u22c5B - B\u22c5A"
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191 }
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192 ],
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193 "collapsed": false,
194 YXVWaERXTk4KYk43ZVZYT3R4Y216QWFsNS9Hb1lYd0hXcDlCdlVwNVBrYW1EeTUxNHZVTmJFeDBD
194 "prompt_number": 28,
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195 "input": "comm.doit()"
196 Vmx5alFOY0QwNENweUp0NEQzZ1UyQmVUWEJ1L0VIZzRZdnQ0NU9uWUI4QmpnZTFECmFGdEFPeHVw
196 },
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197 {
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198 "source": "Create a more fancy commutator",
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200 },
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201 {
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202 "cell_type": "code",
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203 "language": "python",
204 TzhpdWhqMEkrVHI3dzhERHBQbXNabTZWMmJITDRTdWQ0SC9FMzFPclFSaUJIbUkwL0R4bGpHCkF6
204 "outputs": [
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205 {
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206 "output_type": "pyout",
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207 "latex": "$$\\left[A B,B + C\\right]$$",
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208 "prompt_number": 29,
209 CkRXelRzcXNRL3lSMENMRGQrNE40emlCVHBFbkFkWUZ0VXhGdXdmZXhCZGdkMFQ1cnhtbnhyV0RP
209 "png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAAAWCAYAAAA/45nkAAAABHNCSVQICAgIfAhkiAAAA3tJREFU\naIHt2E2sXVMUB/DfexqvUvr0QxXFQI2k8dn4at+A1wglkfiImRIhEhEDDBrVCNLGM2qjHRA6EMSE\ngfhIkSt9jU7E90cISaWEpBJaDarFYO3b3l7n3LPP6733Te5/ss/Za+3/XufstdZeezPAtGKo7f1N\n/ImteKpi7Docgwc76GzCpTgPf+H91MJcnISX8Sh+r2F3r3iPBiO4Idl1rviPI9iMl7AWD+FjXIb9\nRSSNzMmW4G+8kKG7EP9iQ4HsyiR7K3PefvBOBRfhc2zBFeLHS+3j2IjfMC6cfGYZUSNjsiG8Lj7w\n3Qz9m5LutSXyT5N8XgZXL3nn4YyaNhCevV95JhjCJP4QP/6oF2AV7sNefJGhvxEHMLtANjPx/ILh\nDK5e8l4vvqsObheLfEeF3hq8k56PWIAZNSecg1uxAveINFCFMXyIPQWyO3E87sU/NW3pFW8uzhbp\nbweeqdD9TjhLJRoV8s0ix8F2sfoj5epOxEFMtPWPCq/Yrdp7+sVbNwK2ie8fz9C9EIvT85QjYKmI\ngGbe/zm1C7GzZMxykQLOxPrUN0vk7Z1J/mUNG3rNm4s5uByf4O0M/Q9yiRsl/cN4z5Gb1CbhARd3\n4JsQoXdCgexh7MPKXON6zFsnAlaKb3+u5hy0RUDuBnWXOBt839LXGgFlGBN1794C2bo0/7P+fx6p\nQq94c9F0us8ydOfqUInlpKAFWI2vsaylf1FqyxZgFi5QfqA7KEqzBcnA3Rm2dIN3lWJPH8WxSd6O\n5/Fky3sz5f6YYe9qPJahh+IUtAVXF/Q3w3BtCdeKJL+xRL40ySdzjesxb50UdFaa44kKvcW4v62v\nVgpaJk68bxTIdqW2LALGUrutQDZDVCvwdMn4U3vE2w18K6rA6xTvQ8QirRF7ZTYaLc9L8BNOLtE9\nTXjBKyXyHfimoH8RXhRp4raSsc1T7gNd5u2EumXobLEIkzi9pX8Ut4hCoahEryxD54tS8xyHq59x\nhz2euFxanp6vEd64Po17TZRp54sLsu0iioj6vZkeLhEbaRF24QcRgRM4rku83cQeXCUOfRuEA3yF\nX0XBUuQ8lWh0ybhu4ZE+zjWVq4ipYEpl6HRgWHh1v7BP/66uD6HuXVA/cTde7eN8W/s41yG0R8AB\nESL9CMVOmC/y/kfTbEc3cbP4t6fo3QXhAAMMMEAd/Af3QOJHSnIYNwAAAABJRU5ErkJggg==\n",
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210 "text": "[A\u22c5B,B + C]"
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211 }
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212 ],
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213 "collapsed": false,
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214 "prompt_number": 29,
215 TzI5cnFPOWNSWWc5YURnZzQ2aU1HNVZ4SnJ5S3FxUGJjYkpWeDRlQnAwbgpOYkZaZWpkVnJuNlI5
215 "input": "comm = Commutator(A*B,B+C); comm"
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216 },
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217 {
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218 "source": "Expand the commutator",
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219 "cell_type": "markdown"
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220 },
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221 {
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222 "cell_type": "code",
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223 "language": "python",
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224 "outputs": [
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225 {
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226 "output_type": "pyout",
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227 "latex": "$$\\left[A,B\\right] B + \\left[A,C\\right] B + A \\left[B,C\\right]$$",
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228 "prompt_number": 30,
229 NjZwcTU3NDJrZlVyMjNiCnlDUlBiK0svMFZCcjlVc2hSeHpudnFSejhTd1M0elI0YVpXMWowM0dL
229 "png": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAAWCAYAAABAHklQAAAABHNCSVQICAgIfAhkiAAABOVJREFU\neJztm0toXUUYx3+JCWnF+KrU+kYLYtHahY+gJKWIr9q6EVypFHRRxYAFn3RjXFnBjYKK1EgEURc+\nUNCIQh0fQVxpiwuRgO83ilItautj8c3h3hxnzpk58829t3J+EE4y38x3vu9/58ycOzOBlpaWvjBU\n+vtV4HfgdeChmrb3AocAdzS47wxwOTAB/A0sAPusbRw4GXjJ1vvBlm8DNgCjwCYlnzmI0RDSdCwY\nAq4EJoFzkfzHgOeAB4HVwAc2pkHXr446vXz6z5AvPw39MYE3WwvsB56KDLKbUST55x22s6z/PcBw\nyWYy+NTERNTV0PFUe895pAOM2/Jh4HrgSeBTYDogvkHQr4oQvUyFLUd+avp7DV0MAa8A/wC7IoIs\nc4H1caPHPm/tZ5fKTQafPo4GTgmsW2AC62nouAXYCzyKzAYuHrf3OCMgPm39oJmGLkL1MhU27fyS\n9G8ygm0BXgN+BVY1aF+w3l7f8NjXAH8Bn/fR54XA1RH3jyFVxylgFvngtyJ5uZgHvgI+CvCZ4zPR\n0lCj32nmp66/qbEfhQQ+AiwCPwUE6eNl4GuP7SpktLjPYTMZfPrYDNwWUR/CZr5UHY8EPkNyXV5T\n9xzgicD4tPWDZhqWidHLVNi08suiv9dgeQS4yP6+gAQ7VtPGxTDwM/B0qfxQ4CZru5P/LghVxZji\n00euhy9Vx522zXRdReAkZPapiy+HfqDz8MXoZTzlmvmp6D8S0LjgPGQEKt63v7PXVcgoEMM64Ahk\nBNlhy5YBlyArVZcB7w2Azxxo6LgZ+a6xM6DuF/anjkHVT6vfaeaXQ//KUeNNZDm24GHk6Z8IcVzi\nFtv2dIftBuBPZKUoJsYUnz60Zz4NHVfb+u9GxlVgPOU59IO0ma+JXsZTrpWfmv6hCy5bkT2K7i+i\n3SNQLOuB74GPHbZZ4BtE5HGHvZc+tdHQseh0HwbUHWNpx61iEPXT7Hda+anpH/LauRLYjgQ92VV+\nor02Xal7q8K+Fwn6NGB3D3xeB9zqaHM4IuC1DtszdF5fQtDSsXjV8i0cdHMzsukcQupnoq2hdr/T\n6nO59HdO2XPARkf5JmT6vTvUuWWNbbfNYz/O2j8hfMEl1acPzdfOOXR0HAV+Q05jVHEYcL+j3DjK\ncukHzV8752iml3GUaeanpn/da+cksus/77B9aa+uEej4Cp/FXsvbHvuMvT6GCBJCDp+aaOq4H5kx\nppCVNBcrkGNNDwTGN2j6NdXLR9P8eqU/sHTUWAt8CxzrqXuCDfSFUvk65GzbrKfds8hGaflEwEok\n4APAXYExavn0oTHz5dBxBOkAi8ixqILlwKXI0vyKwPggn34Qr2FTvQqMo6xJftn1d33nOwZZ1j2T\nzmrTxXRGHOg8+QBXICPKDmQT80fkLNv5yBRejCQvIoJOIKcBFpAlXpApepkt2wC84wm8TA6fWuTS\nEaSzXIOszm1HVvAWgV+QfKfxn7joZpD0S9XLRUp+vdB/CSa2QQX3KPrqxmTy6yLXJnsM2joaZX91\naGyyx2CU/WXTP+fp9H6dfNdkH/K60k8Odh0HQcMUsukfc8Ilho3A+5l895JdpP3nRir/Bx37rWEK\nWfUvP9UHkH0J35JsqM8p3P8zlcLtSGx/KPvVRkND0NfxYNEvlVb/lpaWlpaWlpaWlg7/Ap2JCsCY\nEBHmAAAAAElFTkSuQmCC\n",
230 VThQYXhpN2prZVczaTBhMTFLbFNwVXFWYXBVcVZLbFNwVXEKVmFwVWV2b2Z6NFNPd3VmaXE1Z0FB
230 "text": "[A,B]\u22c5B + [A,C]\u22c5B + A\u22c5[B,C]"
231 QUFBU1VWT1JLNUNZSUk9Cg==
231 }
232 </png>
232 ],
233 <latex>$$\alpha \overline{\alpha} \left\langle \psi \right. {\left|\psi\right\rangle } + \alpha \overline{\beta} \left\langle \phi \right. {\left|\psi\right\rangle } + \beta \overline{\alpha} \left\langle \psi \right. {\left|\phi\right\rangle } + \beta \overline{\beta} \left\langle \phi \right. {\left|\phi\right\rangle }$$</latex>
233 "collapsed": false,
234 <prompt_number>23</prompt_number>
234 "prompt_number": 30,
235 </output>
235 "input": "comm.expand(commutator=True)"
236 </outputs>
236 },
237 </codecell>
237 {
238 <markdowncell>
238 "source": "Carry out and expand the commutators",
239 <source>&lt;h2&gt;Operators&lt;/h2&gt;</source>
239 "cell_type": "markdown"
240 </markdowncell>
240 },
241 <markdowncell>
241 {
242 <source>Create symbolic operators</source>
242 "cell_type": "code",
243 </markdowncell>
243 "language": "python",
244 <codecell>
244 "outputs": [
245 <input>A = Operator('A')
245 {
246 B = Operator('B')
246 "output_type": "pyout",
247 C = Operator('C')</input>
247 "latex": "$$A B C + A \\left(B\\right)^{2} - B A B - C A B$$",
248 <language>python</language>
248 "prompt_number": 31,
249 <prompt_number>24</prompt_number>
249 "png": "iVBORw0KGgoAAAANSUhEUgAAAO8AAAAZCAYAAADZu3m9AAAABHNCSVQICAgIfAhkiAAABbRJREFU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\n",
250 <collapsed>1</collapsed>
250 "text": "2 \nA\u22c5B\u22c5C + A\u22c5B - B\u22c5A\u22c5B - C\u22c5A\u22c5B"
251 <outputs />
251 }
252 </codecell>
252 ],
253 <markdowncell>
253 "collapsed": false,
254 <source>Test commutativity</source>
254 "prompt_number": 31,
255 </markdowncell>
255 "input": "_.doit().expand()\n"
256 <codecell>
256 },
257 <input>A*B == B*A
257 {
258 </input>
258 "source": "Take the dagger",
259 <language>python</language>
259 "cell_type": "markdown"
260 <prompt_number>25</prompt_number>
260 },
261 <collapsed>0</collapsed>
261 {
262 <outputs>
262 "cell_type": "code",
263 <output>
263 "language": "python",
264 <output_type>pyout</output_type>
264 "outputs": [
265 <text>False</text>
265 {
266 <prompt_number>25</prompt_number>
266 "output_type": "pyout",
267 </output>
267 "latex": "$$- B^{\\dagger} A^{\\dagger} B^{\\dagger} - B^{\\dagger} A^{\\dagger} C^{\\dagger} + \\left(B^{\\dagger}\\right)^{2} A^{\\dagger} + C^{\\dagger} B^{\\dagger} A^{\\dagger}$$",
268 </outputs>
268 "prompt_number": 32,
269 </codecell>
269 "png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAAaCAYAAACTk2bRAAAABHNCSVQICAgIfAhkiAAABwZJREFU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\n",
270 <markdowncell>
270 "text": "2 \n \u2020 \u2020 \u2020 \u2020 \u2020 \u2020 \u239b \u2020\u239e \u2020 \u2020 \u2020 \u2020\n- B \u22c5A \u22c5B - B \u22c5A \u22c5C + \u239dB \u23a0 \u22c5A + C \u22c5B \u22c5A"
271 <source>Distribute A+B squared</source>
271 }
272 </markdowncell>
272 ],
273 <codecell>
273 "collapsed": false,
274 <input>expand((A+B)**2)</input>
274 "prompt_number": 32,
275 <language>python</language>
275 "input": "Dagger(_)"
276 <prompt_number>26</prompt_number>
276 }
277 <collapsed>0</collapsed>
277 ]
278 <outputs>
278 }
279 <output>
279 ]
280 <output_type>pyout</output_type>
280 } No newline at end of file
281 <text>2 2
282 A⋅B + A + B⋅A + B</text>
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315 </png>
316 <latex>$$A B + \left(A\right)^{2} + B A + \left(B\right)^{2}$$</latex>
317 <prompt_number>26</prompt_number>
318 </output>
319 </outputs>
320 </codecell>
321 <markdowncell>
322 <source>Create a commutator</source>
323 </markdowncell>
324 <codecell>
325 <input>comm = Commutator(A,B); comm
326 </input>
327 <language>python</language>
328 <prompt_number>27</prompt_number>
329 <collapsed>0</collapsed>
330 <outputs>
331 <output>
332 <output_type>pyout</output_type>
333 <text>[A,B]</text>
334 <png>aVZCT1J3MEtHZ29BQUFBTlNVaEVVZ0FBQUM0QUFBQVdDQVlBQUFDL2tLNzNBQUFBQkhOQ1NWUUlD
335 QWdJZkFoa2lBQUFBa2hKUkVGVQpTSW50MTgyTFRXRWNCL0RQdk9XbEpwVEdZTEt3VUZNenpZWm1N
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350 </png>
351 <latex>$$\left[A,B\right]$$</latex>
352 <prompt_number>27</prompt_number>
353 </output>
354 </outputs>
355 </codecell>
356 <markdowncell>
357 <source>Carry out the commutator</source>
358 </markdowncell>
359 <codecell>
360 <input>comm.doit()</input>
361 <language>python</language>
362 <prompt_number>28</prompt_number>
363 <collapsed>0</collapsed>
364 <outputs>
365 <output>
366 <output_type>pyout</output_type>
367 <text>A⋅B - B⋅A</text>
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384 </png>
385 <latex>$$A B - B A$$</latex>
386 <prompt_number>28</prompt_number>
387 </output>
388 </outputs>
389 </codecell>
390 <markdowncell>
391 <source>Create a more fancy commutator</source>
392 </markdowncell>
393 <codecell>
394 <input>comm = Commutator(A*B,B+C); comm</input>
395 <language>python</language>
396 <prompt_number>29</prompt_number>
397 <collapsed>0</collapsed>
398 <outputs>
399 <output>
400 <output_type>pyout</output_type>
401 <text>[A⋅B,B + C]</text>
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425 </png>
426 <latex>$$\left[A B,B + C\right]$$</latex>
427 <prompt_number>29</prompt_number>
428 </output>
429 </outputs>
430 </codecell>
431 <markdowncell>
432 <source>Expand the commutator</source>
433 </markdowncell>
434 <codecell>
435 <input>comm.expand(commutator=True)</input>
436 <language>python</language>
437 <prompt_number>30</prompt_number>
438 <collapsed>0</collapsed>
439 <outputs>
440 <output>
441 <output_type>pyout</output_type>
442 <text>[A,B]⋅B + [A,C]⋅B + A⋅[B,C]</text>
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475 </png>
476 <latex>$$\left[A,B\right] B + \left[A,C\right] B + A \left[B,C\right]$$</latex>
477 <prompt_number>30</prompt_number>
478 </output>
479 </outputs>
480 </codecell>
481 <markdowncell>
482 <source>Carry out and expand the commutators</source>
483 </markdowncell>
484 <codecell>
485 <input>_.doit().expand()
486 </input>
487 <language>python</language>
488 <prompt_number>31</prompt_number>
489 <collapsed>0</collapsed>
490 <outputs>
491 <output>
492 <output_type>pyout</output_type>
493 <text>2
494 A⋅B⋅C + A⋅B - B⋅A⋅B - C⋅A⋅B</text>
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532 </png>
533 <latex>$$A B C + A \left(B\right)^{2} - B A B - C A B$$</latex>
534 <prompt_number>31</prompt_number>
535 </output>
536 </outputs>
537 </codecell>
538 <markdowncell>
539 <source>Take the dagger</source>
540 </markdowncell>
541 <codecell>
542 <input>Dagger(_)</input>
543 <language>python</language>
544 <prompt_number>32</prompt_number>
545 <collapsed>0</collapsed>
546 <outputs>
547 <output>
548 <output_type>pyout</output_type>
549 <text>2
550 † † † † † † ⎛ †⎞ † † † †
551 - B ⋅A ⋅B - B ⋅A ⋅C + ⎝B ⎠ ⋅A + C ⋅B ⋅A</text>
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597 </png>
598 <latex>$$- B^{\dagger} A^{\dagger} B^{\dagger} - B^{\dagger} A^{\dagger} C^{\dagger} + \left(B^{\dagger}\right)^{2} A^{\dagger} + C^{\dagger} B^{\dagger} A^{\dagger}$$</latex>
599 <prompt_number>32</prompt_number>
600 </output>
601 </outputs>
602 </codecell>
603 </cells>
604 </worksheet>
605 </worksheets>
606 </notebook>
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