hw2: added plots to report
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\documentclass{scrartcl}
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\usepackage[utf8]{inputenc}
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\usepackage{float}
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\usepackage{graphicx}
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\usepackage{subcaption}
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\usepackage{amsmath}
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@ -72,6 +73,18 @@ use semilogy) as functions of the iterations.}
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The solution of this task can be found in Section 1.5 of the script \texttt{main.m}.
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\begin{figure}[H]
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{\textwidth}{\input{obvalues}}
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\caption{Objective function values w.r.t. iteration number}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{\textwidth}{\input{gnorms}}
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\caption{Norm of the gradient w.r.t. iteration number \\ (y-axis is log scaled)}
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\end{subfigure}
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\caption{Plots for Exercise 1.4.}
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\end{figure}
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\subsection{Finally, explain why the Conjugate Gradient method is a Krylov subspace method.}
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Because theorem 5.3 holds, which itself holds mainly because of this (5.10, page 106 [127]):
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@ -104,6 +117,26 @@ and plot it with respect to the number of iteration.}
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The solution of this task can be found in section 2.3 of the \texttt{main.m} MATLAB script.
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\begin{figure}[H]
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a1}}
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\caption{First matrix}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a2}}
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\caption{Second matrix}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a3}}
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\caption{Third matrix}
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\end{subfigure}
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\begin{subfigure}{0.5\textwidth}
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\resizebox{\textwidth}{!}{\input{a4}}
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\caption{Fourth matrix}
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\end{subfigure}
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\caption{Plots of logarithm energy norm of the error per iteration. Minus infinity logarithms not shown in the plot.}
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\end{figure}
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\subsection{Comment on the convergence of the method for the different matrices. What can you say observing
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the number of iterations obtained and the number of clusters of the eigenvalues of the related
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matrix?}
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|
||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
272 0.0048677895829831\\
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||||
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|
||||
274 0.00480378674614987\\
|
||||
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||||
276 0.00474006690008788\\
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||||
277 0.00470831349244334\\
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||||
278 0.00467663130722396\\
|
||||
279 0.00464502050490086\\
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||||
280 0.00461348124703293\\
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||||
281 0.00458201369628163\\
|
||||
282 0.00455061801642291\\
|
||||
283 0.0045192943723595\\
|
||||
284 0.00448804293013615\\
|
||||
285 0.0044568638569488\\
|
||||
286 0.00442575732116265\\
|
||||
287 0.00439472349232172\\
|
||||
288 0.00436376254116446\\
|
||||
289 0.00433287463963956\\
|
||||
290 0.00430205996091684\\
|
||||
291 0.00427131867940353\\
|
||||
292 0.00424065097076077\\
|
||||
293 0.0042100570119147\\
|
||||
294 0.00417953698107631\\
|
||||
295 0.00414909105775303\\
|
||||
296 0.00411871942276631\\
|
||||
297 0.00408842225826936\\
|
||||
298 0.00405819974775964\\
|
||||
299 0.0040280520761\\
|
||||
300 0.00399797942953172\\
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||||
301 0.00396798199569348\\
|
||||
302 0.00393805996364055\\
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||||
303 0.00390821352385935\\
|
||||
304 0.0038784428682873\\
|
||||
305 0.00384874819033299\\
|
||||
306 0.00381912968489116\\
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||||
307 0.00378958754836631\\
|
||||
308 0.00376012197868838\\
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||||
309 0.00373073317533429\\
|
||||
310 0.00370142133934982\\
|
||||
311 0.00367218667336645\\
|
||||
312 0.00364302938162671\\
|
||||
313 0.00361394967000176\\
|
||||
314 0.00358494774601489\\
|
||||
315 0.00355602381886526\\
|
||||
316 0.00352717809944686\\
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||||
317 0.00349841080037579\\
|
||||
318 0.00346972213601006\\
|
||||
319 0.00344111232247518\\
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||||
320 0.00341258157769011\\
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||||
321 0.00338413012138901\\
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||||
322 0.00335575817514826\\
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||||
323 0.00332746596241382\\
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||||
324 0.00329925370852406\\
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||||
325 0.00327112164074077\\
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||||
326 0.00324306998827306\\
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||||
327 0.00321509898230687\\
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||||
328 0.00318720885603513\\
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||||
329 0.0031593998446833\\
|
||||
330 0.00313167218554325\\
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||||
331 0.00310402611800003\\
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||||
332 0.00307646188356444\\
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||||
333 0.00304897972590616\\
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||||
334 0.00302157989088305\\
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||||
335 0.00299426262657563\\
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||||
336 0.00296702818332233\\
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||||
337 0.00293987681375033\\
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||||
338 0.00291280877281477\\
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||||
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||||
340 0.00285892370851336\\
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||||
341 0.00283210720701309\\
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||||
342 0.0028053750779542\\
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||||
343 0.00277872758847611\\
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||||
344 0.00275216500827033\\
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||||
345 0.00272568760962288\\
|
||||
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||||
347 0.00267298945937576\\
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||||
348 0.00264676926570329\\
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||||
349 0.00262063536953265\\
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||||
350 0.00259458805676995\\
|
||||
351 0.00256862761618329\\
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||||
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|
||||
353 0.00251696852119695\\
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||||
354 0.00249127045907285\\
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||||
355 0.0024656604537759\\
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||||
356 0.00244013880912067\\
|
||||
357 0.00241470583208676\\
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||||
358 0.00238936183287563\\
|
||||
359 0.00236410712496877\\
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||||
360 0.00233894202518255\\
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||||
361 0.0023138668537316\\
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||||
362 0.00228888193428664\\
|
||||
363 0.00226398759403862\\
|
||||
364 0.00223918416376428\\
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||||
365 0.00221447197788892\\
|
||||
366 0.00218985137455768\\
|
||||
367 0.00216532269570178\\
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||||
368 0.00214088628711106\\
|
||||
369 0.00211654249850854\\
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||||
370 0.00209229168362315\\
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||||
371 0.00206813420026647\\
|
||||
372 0.0020440704104159\\
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||||
373 0.00202010068029071\\
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||||
374 0.00199622538044178\\
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||||
375 0.00197244488583009\\
|
||||
376 0.00194875957592076\\
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||||
377 0.001925169834773\\
|
||||
378 0.00190167605113088\\
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||||
379 0.00187827861852296\\
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||||
380 0.00185497793535806\\
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||||
381 0.00183177440502798\\
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||||
382 0.00180866843601563\\
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||||
383 0.00178566044199606\\
|
||||
384 0.00176275084195269\\
|
||||
385 0.00173994006029262\\
|
||||
386 0.00171722852695989\\
|
||||
387 0.00169461667756041\\
|
||||
388 0.00167210495348647\\
|
||||
389 0.00164969380204556\\
|
||||
390 0.00162738367659497\\
|
||||
391 0.00160517503667887\\
|
||||
392 0.00158306834816748\\
|
||||
393 0.0015610640834086\\
|
||||
394 0.0015391627213757\\
|
||||
395 0.00151736474782592\\
|
||||
396 0.00149567065545892\\
|
||||
397 0.0014740809440871\\
|
||||
398 0.00145259612080798\\
|
||||
399 0.00143121670018043\\
|
||||
400 0.00140994320441235\\
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||||
401 0.00138877616355118\\
|
||||
402 0.00136771611567928\\
|
||||
403 0.00134676360712423\\
|
||||
404 0.0013259191926667\\
|
||||
405 0.00130518343576434\\
|
||||
406 0.00128455690877751\\
|
||||
407 0.00126404019320747\\
|
||||
408 0.00124363387994308\\
|
||||
409 0.00122333856951558\\
|
||||
410 0.00120315487236122\\
|
||||
411 0.00118308340910146\\
|
||||
412 0.00116312481082477\\
|
||||
413 0.00114327971938729\\
|
||||
414 0.0011235487877217\\
|
||||
415 0.00110393268015729\\
|
||||
416 0.00108443207275845\\
|
||||
417 0.00106504765367342\\
|
||||
418 0.00104578012349787\\
|
||||
419 0.00102663019565582\\
|
||||
420 0.00100759859679339\\
|
||||
421 0.000988686067195324\\
|
||||
422 0.000969893361216197\\
|
||||
423 0.00095122124773175\\
|
||||
424 0.000932670510608069\\
|
||||
425 0.000914241949201074\\
|
||||
426 0.000895936378867371\\
|
||||
427 0.000877754631508528\\
|
||||
428 0.000859697556137518\\
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||||
429 0.000841766019473127\\
|
||||
430 0.000823960906565026\\
|
||||
431 0.000806283121448403\\
|
||||
432 0.000788733587831909\\
|
||||
433 0.000771313249822707\\
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||||
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||||
435 0.000736864043657104\\
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||||
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|
||||
437 0.000702943493760668\\
|
||||
438 0.000686184065011434\\
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||||
439 0.000669559970537391\\
|
||||
440 0.000653072321041874\\
|
||||
441 0.000636722255029885\\
|
||||
442 0.000620510939986573\\
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||||
443 0.000604439573630549\\
|
||||
444 0.000588509385236614\\
|
||||
445 0.00057272163704996\\
|
||||
446 0.000557077625787128\\
|
||||
447 0.000541578684230604\\
|
||||
448 0.000526226182934612\\
|
||||
449 0.000511021532042753\\
|
||||
450 0.000495966183230885\\
|
||||
451 0.000481061631787299\\
|
||||
452 0.000466309418840188\\
|
||||
453 0.000451711133747819\\
|
||||
454 0.000437268416668315\\
|
||||
455 0.000422982961323787\\
|
||||
456 0.000408856517981088\\
|
||||
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|
||||
458 0.000381087970655137\\
|
||||
459 0.000367449680220597\\
|
||||
460 0.000353978036748788\\
|
||||
461 0.000340675127175451\\
|
||||
462 0.000327543118842089\\
|
||||
463 0.000314584264791908\\
|
||||
464 0.00030180090957059\\
|
||||
465 0.000289195495589093\\
|
||||
466 0.000276770570127334\\
|
||||
467 0.000264528793057209\\
|
||||
468 0.000252472945386399\\
|
||||
469 0.00024060593873623\\
|
||||
470 0.000228930825897021\\
|
||||
471 0.00021745081260729\\
|
||||
472 0.000206169270765922\\
|
||||
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|
||||
474 0.000184216010914346\\
|
||||
475 0.000173552011227236\\
|
||||
476 0.000163101960414044\\
|
||||
477 0.000152870328142166\\
|
||||
478 0.000142861876255546\\
|
||||
479 0.000133081692029448\\
|
||||
480 0.000123535226978182\\
|
||||
481 0.000114228342456702\\
|
||||
482 0.000105167363667044\\
|
||||
483 9.63591441704975e-05\\
|
||||
484 8.78111436770309e-05\\
|
||||
485 7.9531522846157e-05\\
|
||||
486 7.15292601814999e-05\\
|
||||
487 6.38142980942563e-05\\
|
||||
488 5.63977281764285e-05\\
|
||||
489 4.9292030273616e-05\\
|
||||
490 4.25113871340903e-05\\
|
||||
491 3.6072108144126e-05\\
|
||||
492 2.99932155320352e-05\\
|
||||
493 2.4297281571859e-05\\
|
||||
494 1.90116702899788e-05\\
|
||||
495 1.4170462377942e-05\\
|
||||
496 9.81758432223143e-06\\
|
||||
497 6.01201802407357e-06\\
|
||||
498 2.83409247558248e-06\\
|
||||
499 4.26545343219991e-16\\
|
||||
};
|
||||
\end{axis}
|
||||
\end{tikzpicture}%
|
||||
|
|
@ -26,11 +26,13 @@ if plots
|
|||
plot(0:(size(ys,1)-1), ys);
|
||||
sgtitle("Objective function values per iteration");
|
||||
axis([-1 500 -inf +inf]);
|
||||
%matlab2tikz('showInfo', false, './obvalues.tex');
|
||||
|
||||
figure;
|
||||
semilogy(0:(size(gnorms,1)-1), gnorms);
|
||||
sgtitle("Log of gradient norm per iteration");
|
||||
axis([-1 500 -inf +inf]);
|
||||
%matlab2tikz('showInfo', false, './gnorms.tex');
|
||||
end
|
||||
%% 2.1 - Matrix definitions
|
||||
|
||||
|
|
@ -56,12 +58,16 @@ n = 10;
|
|||
if plots
|
||||
enl_plot(x1, xs1, A1);
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A1)");
|
||||
%matlab2tikz('showInfo', false, './a1.tex');
|
||||
enl_plot(x2, xs2, A2);
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A2)");
|
||||
%matlab2tikz('showInfo', false, './a2.tex');
|
||||
enl_plot(x3, xs3, A3)
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A3)");
|
||||
%matlab2tikz('showInfo', false, './a3.tex');
|
||||
enl_plot(x4, xs4, A4);
|
||||
sgtitle("Log energy norm of the error per iter. (matrix A4)");
|
||||
%matlab2tikz('showInfo', false, './a4.tex');
|
||||
end
|
||||
|
||||
function enl_plot(xsol, xs, A)
|
||||
|
|
|
|||
|
|
@ -0,0 +1,520 @@
|
|||
% This file was created by matlab2tikz.
|
||||
%
|
||||
\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
|
||||
%
|
||||
\begin{tikzpicture}
|
||||
|
||||
\begin{axis}[%
|
||||
width=6.028in,
|
||||
height=4.754in,
|
||||
at={(1.011in,0.642in)},
|
||||
scale only axis,
|
||||
xmin=-1,
|
||||
xmax=500,
|
||||
axis background/.style={fill=white}
|
||||
]
|
||||
\addplot [color=mycolor1, forget plot]
|
||||
table[row sep=crcr]{%
|
||||
0 0\\
|
||||
1 -2.49999498998749e-07\\
|
||||
2 -4.98998000007523e-07\\
|
||||
3 -7.46997511046363e-07\\
|
||||
4 -9.94000040135306e-07\\
|
||||
5 -1.2400075952944e-06\\
|
||||
6 -1.48502218454367e-06\\
|
||||
7 -1.72904581590317e-06\\
|
||||
8 -1.97208049739294e-06\\
|
||||
9 -2.21412823703301e-06\\
|
||||
10 -2.45519104284342e-06\\
|
||||
11 -2.69527092284423e-06\\
|
||||
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|
||||
13 -3.17248993749715e-06\\
|
||||
14 -3.40963308818935e-06\\
|
||||
15 -3.64580134515209e-06\\
|
||||
16 -3.88099671640543e-06\\
|
||||
17 -4.11522120996938e-06\\
|
||||
18 -4.348476833864e-06\\
|
||||
19 -4.58076559610935e-06\\
|
||||
20 -4.81208950472541e-06\\
|
||||
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|
||||
22 -5.27185079314997e-06\\
|
||||
23 -5.50029218899853e-06\\
|
||||
24 -5.72777676329799e-06\\
|
||||
25 -5.95430652406841e-06\\
|
||||
26 -6.1798834793298e-06\\
|
||||
27 -6.40450963710222e-06\\
|
||||
28 -6.6281870054057e-06\\
|
||||
29 -6.85091759226031e-06\\
|
||||
30 -7.07270340568605e-06\\
|
||||
31 -7.29354645370299e-06\\
|
||||
32 -7.51344874433114e-06\\
|
||||
33 -7.73241228559059e-06\\
|
||||
34 -7.95043908550132e-06\\
|
||||
35 -8.16753115208339e-06\\
|
||||
36 -8.38369049335685e-06\\
|
||||
37 -8.59891911734177e-06\\
|
||||
38 -8.81321903205812e-06\\
|
||||
39 -9.02659224552598e-06\\
|
||||
40 -9.2390407657654e-06\\
|
||||
41 -9.45056660079637e-06\\
|
||||
42 -9.66117175863905e-06\\
|
||||
43 -9.87085824731335e-06\\
|
||||
44 -1.00796280748393e-05\\
|
||||
45 -1.02874832492371e-05\\
|
||||
46 -1.04944257785266e-05\\
|
||||
47 -1.0700457670728e-05\\
|
||||
48 -1.09055809338613e-05\\
|
||||
49 -1.11097975759464e-05\\
|
||||
50 -1.13131096050035e-05\\
|
||||
51 -1.15155190290526e-05\\
|
||||
52 -1.17170278561137e-05\\
|
||||
53 -1.19176380942069e-05\\
|
||||
54 -1.21173517513522e-05\\
|
||||
55 -1.23161708355696e-05\\
|
||||
56 -1.25140973548793e-05\\
|
||||
57 -1.27111333173011e-05\\
|
||||
58 -1.29072807308553e-05\\
|
||||
59 -1.31025416035617e-05\\
|
||||
60 -1.32969179434405e-05\\
|
||||
61 -1.34904117585117e-05\\
|
||||
62 -1.36830250567953e-05\\
|
||||
63 -1.38747598463113e-05\\
|
||||
64 -1.40656181350799e-05\\
|
||||
65 -1.42556019311211e-05\\
|
||||
66 -1.44447132424548e-05\\
|
||||
67 -1.46329540771011e-05\\
|
||||
68 -1.48203264430801e-05\\
|
||||
69 -1.50068323484119e-05\\
|
||||
70 -1.51924738011164e-05\\
|
||||
71 -1.53772528092136e-05\\
|
||||
72 -1.55611713807237e-05\\
|
||||
73 -1.57442315236667e-05\\
|
||||
74 -1.59264352460625e-05\\
|
||||
75 -1.61077845559314e-05\\
|
||||
76 -1.62882814612932e-05\\
|
||||
77 -1.6467927970168e-05\\
|
||||
78 -1.66467260905761e-05\\
|
||||
79 -1.6824677830537e-05\\
|
||||
80 -1.70017851980713e-05\\
|
||||
81 -1.71780502011986e-05\\
|
||||
82 -1.73534748479392e-05\\
|
||||
83 -1.75280611463132e-05\\
|
||||
84 -1.77018111043402e-05\\
|
||||
85 -1.78747267300409e-05\\
|
||||
86 -1.80468100314348e-05\\
|
||||
87 -1.82180630165421e-05\\
|
||||
88 -1.8388487693383e-05\\
|
||||
89 -1.85580860699773e-05\\
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||||
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|
||||
};
|
||||
\end{axis}
|
||||
\end{tikzpicture}%
|
||||
Loading…
Reference in New Issue