{"id":10569,"date":"2013-10-14T16:57:00","date_gmt":"2013-10-14T16:57:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=10569"},"modified":"2013-10-14T16:57:00","modified_gmt":"2013-10-14T16:57:00","slug":"%ec%88%98%ec%b9%98%ed%95%b4%ec%84%9d-16-monte-carlo-integration","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=10569","title":{"rendered":"\uc218\uce58\ud574\uc11d 16 – Monte Carlo integration"},"content":{"rendered":"
\n
\n

\n \uc801\ubd84\uc744 \uc218\ud589\ud558\ub294\ub370 \uc5ec\ub7ec\uac00\uc9c0 \ubc29\ubc95\uc774 \uc788\uc9c0\ub9cc, \uc5b4\ub5bb\uac8c \ud574\uc57c \ud560\uc9c0 \uc815\ub9d0 \ubaa8\ub974\uaca0\ub2e4\uba74 \ubaac\ud14c \uce74\ub97c\ub85c \ubc29\ubc95\uc774 \uc788\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \ubaac\ud14c \uce74\ub97c\ub85c \ubc29\ubc95\uc740 \ub2e8\uc21c\ud788 \uba74\uc801\uc744 \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc778\ub370 \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n 1. \ub09c\uc218 (x, y)\ub97c \uc0dd\uc131\ud55c\ub2e4.\n <\/p>\n

\n 2. f(x)>y\uc774\uba74 \uce74\uc6b4\ud2b8\ub97c +1\ud55c\ub2e4.\n <\/p>\n

\n 3. N\ubc88 \ubc18\ubcf5\ud55c \ud6c4\n <\/p>\n

\n 4. \uce74\uc6b4\ud2b8\ub97c N\uc73c\ub85c \ub098\ub204\uba74 \uc801\ubd84\uac12\uc774\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n x\uc758 \ubc94\uc704\ub294 \uc801\ubd84 \uad6c\uac04, y\uc758 \ubc94\uc704\ub294 f(x)\uac00 \ud574\ub2f9 \uc801\ubd84 \uad6c\uac04\uc5d0\uc11c \uac16\uac8c \ub418\ub294 \ucd5c\ub300\uac12\uacfc 0 \uc0ac\uc774\uc758 \uc601\uc5ed\uc774\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \uc798 \ubcf4\uba74 \uc54c\uaca0\uc9c0\ub9cc, y\uac00 f(x)\uc640 0\uc73c\ub85c \ub458\ub7ec\uc2f8\uc778 \uad6c\uac04\uc5d0, \uc784\uc758\ub85c \uc810\uc744 \ubfcc\ub9ac\ub294 \uacfc\uc815\uc774\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \uc810\uc744 \ub2e4 \ubfcc\ub9b0 \ud6c4, \ubfcc\ub9b0 \uc218 \uc911\uc5d0 \uba87\uac1c\ub098 \uad6c\uac04 \uc548\uc5d0 \ub4e4\uc5b4\uac14\ub294\uc9c0 \uac2f\uc218\ub97c \uc13c\ub2e4. \uadf8\ub7fc, \ud574\ub2f9 \ud568\uc218\ub85c \ub458\ub7ec\uc2f8\uc778 \uc601\uc5ed \uc548\uc5d0 \ub4e4\uc5b4\uac08 \ud655\ub960\uc740 \uc601\uc5ed\uc758 \ub113\uc774\uc5d0 \ube44\ub840\ud558\ubbc0\ub85c, \ubfcc\ub9b0 \uc218 \ub300\ube44 \ub4e4\uc5b4\uac04 \uc218\uc758 \ube44\uc728\uc744 \uacc4\uc0b0\ud558\uba74 \ub41c\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \uc2e4\uc81c \ucf54\ub4dc\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.
\n \n<\/p>\n

\n\n<\/p>\n

\n

\n import random as rd
\n
\n import numpy as np
\n
\n import os<\/p>\n

fun = lambda x:np.sqrt(1.-x*x)
\n
\n xA = 0. # x\uc758 \uad6c\uac04 \uc2dc\uc791
\n
\n xB = 1. # y\uc758 \uad6c\uac04 \ub05d
\n
\n yA = 0. # f(x)\uc758 \ucd5c\uc18c\uac12
\n
\n yB = 2. # f(x)\uc758 \ucd5c\ub300\uac12\ubcf4\ub2e4 \ud070 \uc784\uc758\uc758 \uac12. \ud074\uc218\ub85d \uc815\ud655\ud574\uc9c0\uace0 \uc791\uc744\uc218\ub85d \ube68\ub77c\uc9c4\ub2e4. f(x)\uc758 \ucd5c\ub300\uac12\ubcf4\ub2e4 \uac19\uc9c0 \uc54a\uace0 \ub354 \ud070 \uc218\ub97c \ub123\uc5b4\uc57c \ud55c\ub2e4.
\n
\n AREA = np.abs((xA-xB)*(yA-yB)) # \uad6c\uac04\uc73c\ub85c \ub458\ub7ec\uc2f8\uc778 \uc601\uc5ed\uc758 \ub113\uc774.<\/p>\n

rd.seed(os.times())
\n \n<\/p>\n

\n it = 1000
\n \n<\/p>\n

\n savefile = open(“circle.txt”, “w”)
\n \n<\/p>\n

\n
\n
\n counted = 0
\n <\/span>
\n
\n<\/b>\n<\/p>\n

\n
\n
\n for i in range (it):
\n <\/span>
\n
\n
\n if fun(rd.uniform(xA, xB)) > rd.uniform(yA, yB): counted+=1
\n <\/span>
\n<\/b>\n<\/p>\n

\n
\n print str(it)+” iteration, “+str(
\n
\n
\n AREA*float(counted)\/(float(it))
\n <\/span>
\n<\/b>
\n )+” is integration result.”)
\n <\/span>
\n\n<\/p>\n<\/div>\n

\n\n<\/p>\n

\n \ube68\uac04\uc0c9\uc73c\ub85c \uc0c9\uce60\ud55c \ubd80\ubd84\uc774 “\ud575\uc2ec\ucf54\ub4dc”\uc774\ub2e4. \ub108\ubb34 \uc9e7\uc740\uac70 \uc544\ub2c8\ub0d0\uace0 \ubb3c\uc5b4\ubcfc\uc218\ub3c4 \uc788\uc9c0\ub9cc, \uc9c4\uc9dc\ub85c \uc800\uac8c \ub05d\uc774\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \uc5ec\uae30\uc11c, \ud568\uc218 \uc548\uc5d0 \ub4e4\uc5b4\uac04 \uacbd\uc6b0\uc758 \uc218\ub97c \ubc18\ubcf5\ud55c \ud69f\uc218\ub85c \ub098\ub220\uc900 \ub2e4\uc74c \uc65c \uba74\uc801\uc744 \uacf1\ud574\uc8fc\ub294 \uac78\uae4c? \uc0dd\uac01\ud574 \ubd05\uc2dc\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n
\n
\n<\/span>\n<\/p>\n<\/p>\n

\n 0\ubd80\ud130 1\uae4c\uc9c0 Sqrt(1-x*x)\ub97c \uc801\ubd84\ud55c \uacb0\uacfc. \uac00\ub85c\ucd95\uc740 \ubc18\ubcf5 \ud69f\uc218\uc778\ub370, \ubc31\ub9cc\ubc88\uc815\ub3c4 \ubc18\ubcf5\ud55c \uac83\uae4c\uc9c0 \uadf8\ub838\ub2e4. \uc798 \ubcf4\uba74 \uc815\ud655\ud788 pi\/4\uc5d0 \uc218\ub834\ud558\ub294 \uac83\uc744 \uad00\ucc30\ud560 \uc218 \uc788\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \uc544\ubb34\uc0dd\uac01\uc5c6\uc774 \uc9dc\ub3c4 \uc798 \uad74\ub7ec\uac00\ub294 \uad49\uc7a5\ud788 \uc544\ub984\ub2e4\uc6b4 \uc54c\uace0\ub9ac\uc998\uc774\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \ubb38\uc81c\ub294 f(x)\uac00 \uc74c\uc218\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc544\ubb34\uc0dd\uac01\uc5c6\uc774 \uc9dc\uba74 \uc548\ub418\uace0 \uc0dd\uac01\uc740 \ud55c\ubc88 \ud574\uc918\uc57c \ud55c\ub2e4\ub294 \uc810.\n <\/p>\n

\n \uc784\uc758\uc758 N\ucc28\uc6d0\uc5d0\uc11c \uc218\ud589\ud558\ub294 \ub2e4\uc911\uc801\ubd84\uc778 \uacbd\uc6b0\uc5d0\ub294 \ub09c\uc218\ub97c \uc0dd\uc131\ud558\ub294 \uad6c\uac04\uc744 “\uc798” \uc7a1\uac70\ub098, \ub610\ub294! \uadf8\ub0e5 “\ucda9\ubd84\ud788 \ud070” \ucd08\uc9c1\ub2e4\uba74\uccb4(hyper-rectangular)\uc5d0 \ud574\ub2f9\ud558\ub294 \ub09c\uc218\ub97c \uc0dd\uc131\ud55c \ud6c4 \uac2f\uc218\ub97c \uc140\uae4c \ub9d0\uae4c \uce74\uc6b4\ud2b8\ud558\ub294 \ud310\uc815 \ub8e8\ud2f4\uc5d0 f(x)\ubcf4\ub2e4 \uc791\uc544\uc57c \ud55c\ub2e4\ub294 \uc870\uac74 \ubfd0\ub9cc \uc544\ub2c8\ub77c “\ub0b4\uac00 \uc6d0\ud558\ub294 \uad6c\uac04 \uc548\uc5d0 \ub4e4\uc5b4\uac00\uc57c \ud568”\uae4c\uc9c0 \uc870\uac74\uc744 \ub123\uc73c\uba74 \ub41c\ub2e4. \ubb3c\ub860 \uadf8\uac8c \uadf8\uac70\uaca0\uc9c0\ub9cc, \uc5ec\uae30\uc11c\ub294 \ub2e8\uc21c\ud788 “\uc548\uc5d0 \uc788\ub294\uac00 \uc5c6\ub294\uac00”\ub9cc \ud310\ub2e8\ud558\uba74 \ub418\uae30 \ub54c\ubb38\uc5d0 \uadf8\ub0e5 \ub2e4\uc911\uc801\ubd84\ubcf4\ub2e4\ub294 \uc27d\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n \ub2e4\uc2dc\ub9d0\ud574\uc11c,
\n
\n
\n \ub0b4\uac00 \uc5b4\ub514\uc5d0\uc11c \ubb58 \uc801\ubd84\ud558\ub294\uc9c0\ub9cc \uc54c\uace0 \uc788\uc73c\uba74
\n <\/span>
\n<\/b>
\n \uc218\uce58\uc801\uc778 \ud574\ub97c \uad6c\ud560 \uc218 \uc788\ub2e4\ub294 \ub73b\uc774\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n …\n <\/p>\n

\n\n<\/p>\n

\n \uc5ec\ub2f4
\n
\n (=\uac1c\ub4dc\ub9bd)
\n <\/strike>
\n \uc778\ub370.\n <\/p>\n

\n\n<\/p>\n

\n \uc778\uc0dd\uc740 \ub0b4\uac00 \uc5b4\ub514\uc11c \ubb58 \ud574\uc57c \ud558\ub294\uc9c0 \uc54c\uc9c0\ub3c4 \ubabb\ud560 \ubfd0\ub9cc \uc544\ub2c8\ub77c, Monte carlo \ubc29\ubc95\uc744 \uc4f4\ub2f5\uc2dc\uace0 \ub3c4\ubc15\ud558\ub2e4\uac04 \ub9dd\ud55c\ub2e4. \uc218\uce58\ud574\uc11d\uc801 \uc778\uc0dd\uc740 \uc218\uce58\uc2a4\ub7ec\uc6b4 \uc778\uc0dd\uc73c\ub85c \uadc0\uacb0\ub41c\ub2e4.
\n \n<\/p>\n

\n
\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\uc801\ubd84\uc744 \uc218\ud589\ud558\ub294\ub370 \uc5ec\ub7ec\uac00\uc9c0 \ubc29\ubc95\uc774 \uc788\uc9c0\ub9cc, \uc5b4\ub5bb\uac8c \ud574\uc57c \ud560\uc9c0 \uc815\ub9d0 \ubaa8\ub974\uaca0\ub2e4\uba74 \ubaac\ud14c \uce74\ub97c\ub85c \ubc29\ubc95\uc774 \uc788\ub2e4. \ubaac\ud14c \uce74\ub97c\ub85c \ubc29\ubc95\uc740 \ub2e8\uc21c\ud788 \uba74\uc801\uc744 \uacc4\uc0b0\ud558\ub294 \ubc29\ubc95\uc778\ub370 \uc54c\uace0\ub9ac\uc998\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. 1. \ub09c\uc218 (x, y)\ub97c \uc0dd\uc131\ud55c\ub2e4. 2. f(x)>y\uc774\uba74 \uce74\uc6b4\ud2b8\ub97c +1\ud55c\ub2e4. 3. N\ubc88 \ubc18\ubcf5\ud55c \ud6c4 4. \uce74\uc6b4\ud2b8\ub97c N\uc73c\ub85c \ub098\ub204\uba74 \uc801\ubd84\uac12\uc774\ub2e4. x\uc758 \ubc94\uc704\ub294 \uc801\ubd84 \uad6c\uac04, y\uc758 \ubc94\uc704\ub294 f(x)\uac00 \ud574\ub2f9 \uc801\ubd84 \uad6c\uac04\uc5d0\uc11c \uac16\uac8c \ub418\ub294 \ucd5c\ub300\uac12\uacfc […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-10569","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-2Kt","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/10569","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10569"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/10569\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10569"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}