|
15 | 15 | }, |
16 | 16 | { |
17 | 17 | "cell_type": "code", |
18 | | - "execution_count": 4, |
| 18 | + "execution_count": 1, |
19 | 19 | "metadata": { |
20 | 20 | "collapsed": true |
21 | 21 | }, |
|
39 | 39 | }, |
40 | 40 | { |
41 | 41 | "cell_type": "code", |
42 | | - "execution_count": 31, |
| 42 | + "execution_count": 2, |
43 | 43 | "metadata": { |
44 | | - "collapsed": true |
| 44 | + "collapsed": false |
45 | 45 | }, |
46 | 46 | "outputs": [], |
47 | 47 | "source": [ |
|
71 | 71 | }, |
72 | 72 | { |
73 | 73 | "cell_type": "code", |
74 | | - "execution_count": 32, |
| 74 | + "execution_count": 3, |
75 | 75 | "metadata": { |
76 | 76 | "collapsed": false |
77 | 77 | }, |
|
90 | 90 | }, |
91 | 91 | { |
92 | 92 | "cell_type": "code", |
93 | | - "execution_count": 33, |
| 93 | + "execution_count": 4, |
94 | 94 | "metadata": { |
95 | 95 | "collapsed": false |
96 | 96 | }, |
|
99 | 99 | "name": "stdout", |
100 | 100 | "output_type": "stream", |
101 | 101 | "text": [ |
102 | | - "The sample average is 1.23623083705 and the sample variance 1.30830563846 based on 40 samples for N(1,1)\n" |
| 102 | + "The sample average is 0.650211887244 and the sample variance 0.843164549377 based on 40 samples for N(1,1)\n" |
103 | 103 | ] |
104 | 104 | } |
105 | 105 | ], |
|
169 | 169 | "output_type": "stream", |
170 | 170 | "text": [ |
171 | 171 | "Identical samples:\n", |
172 | | - " [-0.14653656 -0.47307654 -0.03942304 0.12535728 0.02529963 1.34499499\n", |
173 | | - " -0.05358885 -0.2939091 1.94854913 0.41751495] and\n", |
174 | | - " [-0.14653656 -0.47307654 -0.03942304 0.12535728 0.02529963 1.34499499\n", |
175 | | - " -0.05358885 -0.2939091 1.94854913 0.41751495]\n", |
176 | | - "Covariance of samples [[ 0.9457889 -0.01289219]\n", |
177 | | - " [-0.01289219 0.93458634]]\n" |
| 172 | + " [ 0.81489992 0.76143959 0.07694935 -0.61195669 -1.1646947 -2.31956454\n", |
| 173 | + " 0.5642974 -1.10766594 0.43282974 -0.20260256] and\n", |
| 174 | + " [ 0.81489992 0.76143959 0.07694935 -0.61195669 -1.1646947 -2.31956454\n", |
| 175 | + " 0.5642974 -1.10766594 0.43282974 -0.20260256]\n", |
| 176 | + "Covariance of samples [[ 0.95500506 -0.00345936]\n", |
| 177 | + " [-0.00345936 1.05820756]]\n" |
178 | 178 | ] |
179 | 179 | } |
180 | 180 | ], |
|
196 | 196 | }, |
197 | 197 | { |
198 | 198 | "cell_type": "code", |
199 | | - "execution_count": 30, |
| 199 | + "execution_count": 12, |
200 | 200 | "metadata": { |
201 | 201 | "collapsed": false |
202 | 202 | }, |
|
205 | 205 | "name": "stdout", |
206 | 206 | "output_type": "stream", |
207 | 207 | "text": [ |
208 | | - "sr= [[-2.5796549 -0.80784927 -0.88291778 1.15429748 1.60292571 -0.94056234]\n", |
209 | | - " [ 2.85426974 0.47565126 0.78506184 2.05482599 0.10387867 0.52951015]\n", |
210 | | - " [-0.63850658 -0.82684445 -0.31751491 -0.11278389 1.38274907 -0.12146601]\n", |
211 | | - " [-0.69092677 0.31169424 0.57306888 -0.50967253 1.14489301 1.12292133]\n", |
212 | | - " [-1.23597204 -0.59336124 0.28783502 2.08356145 1.11139071 0.04475031]] \n", |
213 | | - "sr4= [[-1.23597204 -0.59336124 0.28783502 2.08356145 1.11139071 0.04475031]] ar=\n", |
214 | | - " [array([[-2.5796549 , -0.80784927, -0.88291778, 1.15429748, 1.60292571,\n", |
215 | | - " -0.94056234]]), array([[ 2.85426974, 0.47565126, 0.78506184, 2.05482599, 0.10387867,\n", |
216 | | - " 0.52951015]]), array([[-0.63850658, -0.82684445, -0.31751491, -0.11278389, 1.38274907,\n", |
217 | | - " -0.12146601]]), array([[-0.69092677, 0.31169424, 0.57306888, -0.50967253, 1.14489301,\n", |
218 | | - " 1.12292133]]), array([[-1.23597204, -0.59336124, 0.28783502, 2.08356145, 1.11139071,\n", |
219 | | - " 0.04475031]])]\n" |
| 208 | + "sr= [[ 0.90390365 0.65476072 -0.42647782 0.47217152 0.0518215 -0.32324357]\n", |
| 209 | + " [-0.24180847 -0.35042203 -1.21377586 -0.32739907 -1.74333538 -0.0759546 ]\n", |
| 210 | + " [ 1.27268467 -0.02500331 -0.0904326 -0.82035676 2.3166674 0.37689438]\n", |
| 211 | + " [ 0.05270123 -0.1900696 -0.66663564 -0.58521261 -0.03028957 -0.44856859]] \n", |
| 212 | + "sr4= [[ 0.05270123 -0.1900696 -0.66663564 -0.58521261 -0.03028957 -0.44856859]] ar=\n", |
| 213 | + " [array([[ 0.90390365, 0.65476072, -0.42647782, 0.47217152, 0.0518215 ,\n", |
| 214 | + " -0.32324357]]), array([[-0.24180847, -0.35042203, -1.21377586, -0.32739907, -1.74333538,\n", |
| 215 | + " -0.0759546 ]]), array([[ 1.27268467, -0.02500331, -0.0904326 , -0.82035676, 2.3166674 ,\n", |
| 216 | + " 0.37689438]]), array([[ 0.05270123, -0.1900696 , -0.66663564, -0.58521261, -0.03028957,\n", |
| 217 | + " -0.44856859]])]\n" |
220 | 218 | ] |
221 | 219 | } |
222 | 220 | ], |
|
225 | 223 | " \"\"\"\n", |
226 | 224 | " A4.4 Page 166\n", |
227 | 225 | " \"\"\"\n", |
228 | | - " N=5\n", |
| 226 | + " N=4\n", |
229 | 227 | " M=6\n", |
230 | 228 | " sr=np.zeros((N,M))\n", |
231 | 229 | " stream={}; init_state={}\n", |
|
238 | 236 | " stream[j].set_state(init_state[j])# reset state of jth rng\n", |
239 | 237 | " return stream[j].randn(1,M)\n", |
240 | 238 | " #\n", |
241 | | - " sr4=srandn(4) # reproduces the 4th row \n", |
| 239 | + " sr4=srandn(N-1) # reproduces the 4th row \n", |
242 | 240 | " #\n", |
243 | 241 | " from ipyparallel import Client\n", |
244 | 242 | " import os\n", |
|
255 | 253 | }, |
256 | 254 | { |
257 | 255 | "cell_type": "code", |
258 | | - "execution_count": 15, |
| 256 | + "execution_count": 13, |
259 | 257 | "metadata": { |
260 | 258 | "collapsed": false |
261 | 259 | }, |
|
298 | 296 | }, |
299 | 297 | { |
300 | 298 | "cell_type": "code", |
301 | | - "execution_count": 8, |
| 299 | + "execution_count": 14, |
302 | 300 | "metadata": { |
303 | 301 | "collapsed": false |
304 | 302 | }, |
|
307 | 305 | "name": "stdout", |
308 | 306 | "output_type": "stream", |
309 | 307 | "text": [ |
310 | | - "Uniform sample from unit ball at origin [ 0.54476269 -0.71305309]\n", |
311 | | - "Uniform sample from unit sphere at origin [-0.64960659 0.73582129 0.19125456]\n", |
312 | | - "Uniform sample of unit ball [-0.66832045 -0.39539924] using 2 attempts (rejection sampling)\n" |
| 308 | + "Uniform sample from unit ball at origin [ 0.51655396 0.28705832]\n", |
| 309 | + "Uniform sample from unit sphere at origin [ 0.5821194 0.25029924 0.7736196 ]\n", |
| 310 | + "Uniform sample of unit ball [-0.10768545 -0.98238243] using 1 attempts (rejection sampling)\n" |
313 | 311 | ] |
314 | 312 | } |
315 | 313 | ], |
|
331 | 329 | }, |
332 | 330 | { |
333 | 331 | "cell_type": "code", |
334 | | - "execution_count": 9, |
| 332 | + "execution_count": 15, |
335 | 333 | "metadata": { |
336 | 334 | "collapsed": false |
337 | 335 | }, |
|
356 | 354 | }, |
357 | 355 | { |
358 | 356 | "cell_type": "code", |
359 | | - "execution_count": 10, |
| 357 | + "execution_count": 16, |
360 | 358 | "metadata": { |
361 | 359 | "collapsed": false |
362 | 360 | }, |
|
365 | 363 | "name": "stdout", |
366 | 364 | "output_type": "stream", |
367 | 365 | "text": [ |
368 | | - "Multivariate Gaussian sample [ 0.52466687 1.12560085]\n" |
| 366 | + "Multivariate Gaussian sample [-0.43260261 1.69354539]\n" |
369 | 367 | ] |
370 | 368 | } |
371 | 369 | ], |
|
384 | 382 | }, |
385 | 383 | { |
386 | 384 | "cell_type": "code", |
387 | | - "execution_count": 11, |
| 385 | + "execution_count": 31, |
388 | 386 | "metadata": { |
389 | 387 | "collapsed": false |
390 | 388 | }, |
|
396 | 394 | " A4.9 Page 174\n", |
397 | 395 | " \"\"\"\n", |
398 | 396 | " d=baru0.size\n", |
399 | | - " N=T // Dt\n", |
| 397 | + " N=int(T // Dt)\n", |
400 | 398 | " u=np.zeros((M,d)) \n", |
401 | 399 | " for j in range(M):\n", |
402 | 400 | " u0=baru0 + epsilon * np.random.uniform(-1,1,baru0.size)\n", |
|
421 | 419 | }, |
422 | 420 | { |
423 | 421 | "cell_type": "code", |
424 | | - "execution_count": 12, |
| 422 | + "execution_count": 32, |
425 | 423 | "metadata": { |
426 | 424 | "collapsed": false |
427 | 425 | }, |
|
430 | 428 | "name": "stdout", |
431 | 429 | "output_type": "stream", |
432 | 430 | "text": [ |
433 | | - "mean 1.48488796481 sd 0.0284883420065\n" |
| 431 | + "mean 1.50227354061 sd 0.02939864970796154\n" |
434 | 432 | ] |
435 | 433 | } |
436 | 434 | ], |
|
452 | 450 | }, |
453 | 451 | { |
454 | 452 | "cell_type": "code", |
455 | | - "execution_count": 13, |
| 453 | + "execution_count": 33, |
456 | 454 | "metadata": { |
457 | 455 | "collapsed": true |
458 | 456 | }, |
459 | 457 | "outputs": [], |
460 | 458 | "source": [ |
461 | 459 | "def pop_monte_anti(M,T,Dt,baru0,epsilon):\n", |
462 | 460 | " d=baru0.size\n", |
463 | | - " N=T // Dt\n", |
| 461 | + " N=int(T // Dt)\n", |
464 | 462 | " u=np.zeros((2*M,d)) \n", |
465 | 463 | " for j in range(M):\n", |
466 | 464 | " u0=baru0 + epsilon * np.random.uniform(-1,1,baru0.size)\n", |
|
482 | 480 | }, |
483 | 481 | { |
484 | 482 | "cell_type": "code", |
485 | | - "execution_count": 14, |
| 483 | + "execution_count": 44, |
486 | 484 | "metadata": { |
487 | 485 | "collapsed": false |
488 | 486 | }, |
|
491 | 489 | "name": "stdout", |
492 | 490 | "output_type": "stream", |
493 | 491 | "text": [ |
494 | | - "mean 1.49625648822 sd 0.0286472044095\n" |
| 492 | + "mean 1.49540169969 sd 0.026396530226\n" |
495 | 493 | ] |
496 | 494 | } |
497 | 495 | ], |
|
502 | 500 | "bar_x,sig95=pop_monte_anti(M,T,Dt,baru0,epsilon)\n", |
503 | 501 | "print(\"mean\",bar_x,\"sd\",sig95)" |
504 | 502 | ] |
505 | | - }, |
506 | | - { |
507 | | - "cell_type": "code", |
508 | | - "execution_count": null, |
509 | | - "metadata": { |
510 | | - "collapsed": true |
511 | | - }, |
512 | | - "outputs": [], |
513 | | - "source": [] |
514 | 503 | } |
515 | 504 | ], |
516 | 505 | "metadata": { |
517 | 506 | "kernelspec": { |
518 | | - "display_name": "Python 2", |
| 507 | + "display_name": "Python 3", |
519 | 508 | "language": "python", |
520 | | - "name": "python2" |
| 509 | + "name": "python3" |
521 | 510 | }, |
522 | 511 | "language_info": { |
523 | 512 | "codemirror_mode": { |
524 | 513 | "name": "ipython", |
525 | | - "version": 2 |
| 514 | + "version": 3 |
526 | 515 | }, |
527 | 516 | "file_extension": ".py", |
528 | 517 | "mimetype": "text/x-python", |
529 | 518 | "name": "python", |
530 | 519 | "nbconvert_exporter": "python", |
531 | | - "pygments_lexer": "ipython2", |
532 | | - "version": "2.7.11" |
| 520 | + "pygments_lexer": "ipython3", |
| 521 | + "version": "3.5.1" |
533 | 522 | } |
534 | 523 | }, |
535 | 524 | "nbformat": 4, |
|
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