{"id":10535,"date":"2013-09-02T12:54:00","date_gmt":"2013-09-02T12:54:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=10535"},"modified":"2013-09-02T12:54:00","modified_gmt":"2013-09-02T12:54:00","slug":"%ec%88%98%ec%b9%98%ed%95%b4%ec%84%9d1-%eb%af%b8%eb%b6%84%ea%b3%bc-%ec%a0%81%eb%b6%84","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=10535","title":{"rendered":"\uc218\uce58\ud574\uc11d1 – \ubbf8\ubd84\uacfc \uc801\ubd84"},"content":{"rendered":"
\n
\n

\n\n<\/p>\n

\n
\n
\n\"\"
\n lecture_1.py
\n <\/a>
\n<\/span>\n<\/p>\n

\n\n<\/p>\n

\n # Elementary Numerical analysis 1
\n
\n # based on Python
\n
\n # (C) 2013. Keehwan Nam, Dept. of physics, KAIST.
\n
\n # snowall@gmail.com \/ snowall@kaist.ac.kr<\/p>\n

# Differentiation
\n
\n # \ud14c\uc77c\ub7ec \uc815\ub9ac\uc640 \ud14c\uc77c\ub7ec \uc804\uac1c\ub97c \uc801\uadf9 \uc0ac\uc6a9\ud558\uba74 \ub41c\ub2e4.
\n
\n # \uc218\uce58\uc801\uc73c\ub85c \ubbf8\ubd84\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4
\n
\n # df\/dx = (f(x+h) – f(x))\/h
\n
\n # \uc774 \uacbd\uc6b0 \uc624\ucc28\uac00 h\uc758 \uc81c\uacf1\uc5d0 \ube44\ub840\ud55c\ub2e4. 2\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc774\ub2e4.<\/p>\n

# \uc624\ucc28\ub97c \uc904\uc774\uace0 \uc2f6\uc740 \uacbd\uc6b0 \ub300\uce6d\uc131\uc744 \uc774\uc6a9\ud574\uc11c \uc624\ucc28\ub97c \uc904\uc77c \uc218 \uc788\ub2e4.
\n
\n # df\/dx = (f(x+h)-f(x))\/h-(f(x-h)-f(x))\/h = (f(x+h)-f(x-h))\/2h
\n
\n # \uc774 \uacbd\uc6b0 \uc624\ucc28\uac00 h\uc758 \uc138\uc81c\uacf1\uc5d0 \ube44\ub840\ud55c\ub2e4. 3\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc774\ub2e4.<\/p>\n

# \ub354 \uc904\uc774\uace0 \uc2f6\ub2e4\uba74 \uc704\uc758 3\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc744 5\uc810\uc73c\ub85c \ud655\uc7a5\ud560 \uc218 \uc788\ub2e4.
\n
\n # df\/dx = (f(x+2h)+f(x+h)-f(x-h)-f(x-2h))\/6h
\n
\n # \ud558\uc9c0\ub9cc \uc774\ub798\ubd10\uc57c \uc624\ucc28\ub294 \uadf8\ub0e5 h\uc758 \uc138\uc81c\uacf1\uc5d0 \ube44\ub840\ud558\uac8c \ub41c\ub2e4.<\/p>\n

# \uba38\ub9ac\ub97c \uc368 \ubcf4\uba74 5\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.
\n
\n # df\/dx = (-f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h))\/12h
\n
\n # \uc774\ub807\uac8c \ud558\uba74 \uc624\ucc28\uac00 h\uc758 4\uc81c\uacf1\uc5d0 \ube44\ub840\ud558\uac8c \ub41c\ub2e4.<\/p>\n

# 2\ucc28 \uc774\uc0c1\uc758 \ubbf8\ubd84\uc744 \uacc4\uc0b0\ud574\uc57c \ud55c\ub2e4\uba74, 1\ucc28 \ubbf8\ubd84\uc744 \ubc18\ubcf5\uc801\uc73c\ub85c \uacc4\uc0b0\ud560 \uc218\ub3c4 \uc788\uace0, \ub610\ub294 \uc9c1\uc811 2\ucc28 \ub3c4\ud568\uc218\ub97c \uc5bb\uc744 \uc218\ub3c4 \uc788\ub2e4.
\n
\n # d2f\/dx2 = 2(f(x+h)-2f(x)+f(x-h))\/(h*h)<\/p>\n

# \uc774\uc640 \uac19\uc774 n\ucc28 \ub3c4\ud568\uc218\ub97c \uc9c1\uc811 \uacc4\uc0b0\ud558\ub294 \uacf5\uc2dd\uc740 \ud14c\uc77c\ub7ec \uc804\uac1c\uc5d0 \uc758\ud558\uc5ec \uc190\uc27d\uac8c \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\n

# \uc2e4\uc81c \uad6c\ud604\uc740?<\/p>\n

# \ud30c\uc774\uc36c\uc774\ub77c\uba74, \uc218\uce58\uac00 \ub9ac\uc2a4\ud2b8\ub85c \uc8fc\uc5b4\uc838 \uc788\uc744 \uac83\uc774\ub2e4.
\n
\n f = numpy.array([x1, x2, x3, x4, x5])<\/p>\n

h = 1.0e-2 # \ubbf8\ubd84\uc5d0\uc11c \uc0ac\uc6a9\ud55c h\uac12\uc774 \ub41c\ub2e4.<\/p>\n

# \uccab\ubc88\uc9f8\ub85c, 2\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc744 \uc5bb\uc5b4\ubcf4\uc790.<\/p>\n

df = (f[1:]-f[:-1])\/h
\n
\n # \uc774 \uacf5\uc2dd\uc774 \uc65c \uc791\ub3d9\ud558\ub294\uc9c0\ub294 \ucc28\uadfc\ucc28\uadfc \uc0dd\uac01\ud574 \ubcf4\uba74 \ub41c\ub2e4.<\/p>\n

# \ub9c8\ucc2c\uac00\uc9c0\ub85c, 3\uc810 \ubbf8\ubd84\uacf5\uc2dd\ub3c4 \ub611\uac19\uc774 \uc5bb\uc744 \uc218 \uc788\ub2e4.
\n
\n df = (f[2:]-f[:-2])\/(2*h)<\/p>\n

# 5\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc740 \uc9c1\uc811 \uace0\ubbfc\ud574 \ubcf4\uc790.
\n
\n # \ud558\uc9c0\ub9cc, \ud56d\uc0c1 \ub9ac\uc2a4\ud2b8\ub85c\ub9cc \uc8fc\uc5b4\uc838 \uc788\uc744\ub9ac\uac00 \uc5c6\ub2e4. \ud654\uc77c\uc5d0\uc11c \uc9c1\uc811 \uac12\uc744 \ud55c\uc904\uc529 \uc77d\uc5b4\uc624\uba74\uc11c \uacc4\uc0b0\ud574\uc57c \ud558\ub294 \uacbd\uc6b0\ub3c4 \uc788\uc744 \uac83\uc774\ub2e4.
\n
\n # \ubb3c\ub860 \ud654\uc77c\uc744 \ub9ac\uc2a4\ud2b8\uc5d0 \uc9d1\uc5b4\ub123\uace0\ub098\uc11c \uc704\uc758 \ubc29\ubc95\uc744 \uc4f0\uba74 \ub418\uc9c0\ub9cc,
\n
\n # \ud654\uc77c\uc774 \uba54\ubaa8\ub9ac\uc5d0 \uc548 \ub4e4\uc5b4\uac00\ub294, \uac00\ub839 \uc218\uc2ed GB\uc6a9\ub7c9\uc758 \ub370\uc774\ud130\ub97c \ubbf8\ubd84\ud574\uc57c \ud55c\ub2e4\uba74 \uadf8\uac74 \uadf8\uac70\ub300\ub85c \ub9c9\ub9c9\ud558\ub9ac\ub77c\uace0 \ubcf8\ub2e4.<\/p>\n

data = open(“mydata.txt”, “r”)
\n
\n f = [data.readline(), data.readline(), data.readline()]
\n
\n df = []
\n
\n while data.EoF():
\n
\n df.append((f[0]-f[2])\/(2.*h))
\n
\n f.append(data.readline())
\n
\n f=f[1:]<\/p>\n

# data.EoF()\ub294 \ud30c\uc77c\uc758 \ub05d\uc778\uc9c0 \uc544\ub2cc\uc9c0 \ud310\ub2e8\ud558\ub294 \ud568\uc218\uc774\ub2e4. (\uad6c\ud604\uc740 \uc140\ud504!)
\n
\n # \uc774\uac8c \uc65c \uc791\ub3d9\ud558\ub294\uc9c0\ub294 \uc9c1\uc811 \uc0dd\uac01\ud574 \ubcf4\uace0, 5\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc73c\ub85c \ubc14\uafb8\ub824\uba74 \uc5b4\ub5bb\uac8c \ud574\uc57c \ud560\uc9c0 \uc0dd\uac01\ud574 \ubcf4\uc790. \ub610\ub294 2\ucc28\ub3c4\ud568\uc218 \uacc4\uc0b0\uc774\ub77c\uba74?
\n
\n # df.append\ub85c \ub9ac\uc2a4\ud2b8\uc5d0 \uc9d1\uc5b4\ub123\ub294 \uac83\uc774 \uba54\ubaa8\ub9ac\ub97c \uc7a1\uc544\uba39\uc744 \uac83 \uac19\ub2e4\uba74, df\ub97c \ud30c\uc77c\ub85c \uc5f4\uc5b4\uc11c df.writeline\ud568\uc218\ub97c \uc0ac\uc6a9\ud574\ub3c4 \ub41c\ub2e4.
\n
\n # \ub2e4\ub978 \ud504\ub85c\uadf8\ub798\ubc0d \uc5b8\uc5b4\ub77c\uba74 \uad6c\uccb4\uc801\uc73c\ub85c\ub294 \ub2e4\ub974\uac8c \uad6c\ud604\ud574\uc57c \ud560 \uac83\uc774\ub2e4. \uc790\uc2e0\uc774 \uc0ac\uc6a9\ud558\ub294 \uc5b8\uc5b4\uc5d0\uc11c\ub294 \uc5b4\ub5bb\uac8c \uad6c\ud604\ud560 \uc218 \uc788\uc744\uae4c?<\/p>\n

# \ud30c\uc774\uc36c\uc758 scpiy \ubaa8\ub4c8\uc5d0\uc11c \ubbf8\ubd84\uc744 \uc81c\uacf5\ud558\ub294\ub370, scipy.misc.derivative(func, x0, dx=1.0, n=1, args=(), order=3) \ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uba74 \ub41c\ub2e4.
\n
\n # \uc774 \ud568\uc218\ub294 func\ub85c \uc8fc\uc5b4\uc9c4 \ud568\uc218\uac00 x0\uc704\uce58\uc5d0\uc11c \uc8fc\uc5b4\uc9c4 dx\ub85c \ubbf8\ubd84\ud55c n\ucc28 “\ubbf8\ubd84\uacc4\uc218” \uac12\uc744 \uc54c\ub824\uc900\ub2e4. order\ub294 3\uc810\uacf5\uc2dd\uc778\uac00 5\uc810\uacf5\uc2dd\uc778\uac00 \ub4f1\ub4f1\uc774\ub2e4. ‘\ub2f9\uc5f0\ud788’ \ud640\uc218\ub9cc \ub123\uc5b4\uc57c \ud55c\ub2e4.
\n
\n # \ub0b4\uac00 \uc815\uc758\ud55c \ud568\uc218\uac00 \uc218\ub97c \ub123\uc73c\uba74 \uc218\uac00 \ub098\uc624\ub294 \ud568\uc218\ub77c\uba74, \uc704\uc758 \ud568\uc218\ub85c \uc8fc\uc5b4\uc9c4 \uc810\uc5d0\uc11c\uc758 \ubbf8\ubd84\uacc4\uc218\ub97c \uc54c\uc544\ub0bc \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \ud574\uc11d\uc801\uc778 \ub3c4\ud568\uc218\ub97c \uc54c\ub824\uc8fc\uc9c0\ub294 \uc54a\ub294\ub2e4.<\/p>\n

\n # Integration<\/p>\n

# \uc6a9\uc5b4\ub97c \uba3c\uc800 \uc54c\uace0 \uac00\uc790.
\n
\n # Quadrature \ub610\ub294 Numerical quadrature\ub294 \uc218\uce58\ud574\uc11d\uc5d0\uc11c \ub9d0\ud558\ub294 \uc218\uce58 \uc801\ubd84\uc744 \ub73b\ud55c\ub2e4. 1\ucc28\uc6d0 \uc774\uc0c1\uc758 \uace0\ucc28\uc6d0 \uc218\uce58\uc801\ubd84\uc744 \ud3ec\ud568\ud558\uae30\ub294 \ud558\uc9c0\ub9cc, 1\ucc28\uc6d0 \uc218\uce58\uc801\ubd84\uc758 \ub73b\uc774 \uac15\ud558\ub2e4.
\n
\n # Cubature\ub294 1\ucc28\uc6d0 \uc774\uc0c1\uc758 \uace0\ucc28\uc6d0 \uc218\uce58\uc801\ubd84\uc744 \ub300\uccb4\ub85c \ub73b\ud55c\ub2e4.<\/p>\n

# 1\ucc28\uc6d0 \uc801\ubd84\uc744 \uba3c\uc800 \ub17c\uc758\ud574 \ubcf4\uc790.<\/p>\n

# \uac00\uc7a5 \uac04\ub2e8\ud558\uac8c\ub294 \uc0ac\uac01\ud615\uc73c\ub85c \uadfc\uc0ac\ud560 \uc218 \uc788\ub2e4. \uc6d0\ub798 \uc801\ubd84\uc740 \uc5f0\uc18d \ud568\uc218\ub97c \uc798\uac8c \uc370\uc5b4\uc11c \uac01\uac01\uc758 \ub113\uc774\ub97c \uad6c\ud55c \ud6c4, \ub354 \ub9ce\uc740 \uc870\uac01\uc73c\ub85c \ub354 \uc798\uac8c \uc370\uc5b4\uac00\uba70 \uadf9\ud55c\uc744 \uad6c\ud558\ub294 \uacfc\uc815\uc774\ub2e4.
\n
\n # \ub530\ub77c\uc11c \ucef4\ud4e8\ud130\uc5d0\uac8c \uc218\uce58\uc801\uc73c\ub85c \uc801\ubd84\uc744 \uacc4\uc0b0\uc744 \uc2dc\ud0a8\ub2e4\uba74, \ucda9\ubd84\ud788 \ub9ce\uc740 \uc870\uac01\uc73c\ub85c \uc798\uac8c \uc370\uc5b4\uc11c \uac01\uac01\uc758 \ub113\uc774\ub97c \uad6c\ud55c \ud6c4 \ub2e4 \ub354\ud558\ub3c4\ub85d \ud558\uba74 \ub41c\ub2e4.
\n
\n # \uac00\uc7a5 \uac04\ub2e8\ud558\uac8c \uc0ac\uac01\ud615\uc73c\ub85c \uadfc\uc0ac\ud55c\ub2e4\uba74, i\ubc88\uc7ac \ud568\uc218\uac12\uc744 f[i]\ub77c \ud55c\ub2e4\uba74
\n
\n # F = sum(f[i], i=0 to N)*(b-a)\/N
\n
\n # \ubb3c\ub860 \uac01 \uc870\uac01\uc740 N\ub4f1\ubd84\ud588\ub2e4\uace0 \uac00\uc815\ud588\ub2e4. \uc870\uac01\uc758 \uae38\uc774\uac00 \uad6c\uac04\ub9c8\ub2e4 \ub2e4\ub978 \uacbd\uc6b0\ub77c\uba74 \uace8\uce58\uc544\ud30c\uc9c0\ubbc0\ub85c \uadf8\ub7ec\uc9c0 \ub9d0\uc790.
\n
\n # \uc704\uc758 \ucf54\ub4dc\ub294 \ud30c\uc774\uc36c\uc73c\ub85c \uac04\ub2e8\ud788 \uad6c\ud604\ud560 \uc218 \uc788\ub2e4.<\/p>\n

f = [f1, f2, f3, f4, ,f5] # f\ub294 \ud568\uc218\uac12\ub4e4\uc744 \uc218\uce58\uc801\uc73c\ub85c \uc800\uc7a5\ud558\uace0 \uc788\ub294 \ub9ac\uc2a4\ud2b8\uc774\ub2e4.
\n
\n F=0
\n
\n for i in f:
\n
\n F+=i
\n
\n F\/=h # h\ub294 \uad6c\uac04\uc758 \uae38\uc774\uc774\ub2e4. h=(b-a)\/N \uc815\ub3c4\ub85c \uc815\uc758\ud558\uba74 \ub420 \ub4ef.
\n
\n # \ub300\ucda9 \uc774\ub807\uac8c \uc4f0\uba74 \ub420 \uac83\uc774\ub2e4. \ub9cc\uc57d \uc870\uae08 \ub354 \uc9e7\uac8c \uc4f0\uace0 \uc2f6\ub2e4\uba74 reduce\uc640 lambda\ub97c \uc4f8 \uc218 \uc788\ub2e4. \uc774 \ub450 \uad6c\ubb38\uc774 \ubb54\uc9c0\uc5d0 \ub300\ud574\uc11c\ub294 \uc790\uc2b5\ud574\ubcf4\uc790.<\/p>\n

F = reduce(lambda x, y:x+y, f)*h<\/p>\n

# \uc704\uc758 \uad6c\ubb38\uc774 \uc801\ubd84\uc2dd\uc774\ub2e4. \uc774\uac78 midpoint rule \uc774\ub77c\uace0 \ud55c\ub2e4.<\/p>\n

# \uc0ac\uac01\ud615\uc73c\ub85c \uc801\ubd84\ud558\ub294 \uac83\ubcf4\ub2e4, \uc544\ubb34\ub798\ub3c4 \uc0ac\ub2e4\ub9ac\uaf34\ub85c \ub098\ub204\ub294 \uac83\uc774 \uc870\uae08 \ub354 \uc815\ud655\ud558\uc9c0 \uc54a\uc744\uae4c? \ud558\ub294 \ub9c8\uc74c\uc5d0 \ub9cc\ub4e0 \uacf5\uc2dd\uc774 \uc0ac\ub2e4\ub9ac\uaf34 \uaddc\uce59\uc774\ub2e4. Trapezoidal rule (trapezium rule)<\/p>\n

F = reduce(lambda x, y:x+y, f)*h – 0.5*(f[0]+f[-1])*h<\/p>\n

# \uc704\uc758 \uad6c\ubb38\uc774 \uc0ac\ub2e4\ub9ac\uaf34 \uc801\ubd84\uc5d0 \ud574\ub2f9\ud55c\ub2e4. \ubcc4 \ucc28\uc774 \uc5c6\uc5b4 \ubcf4\uc774\ub294\ub370 \uc544\uc8fc \uc870\uae08 \ub354 \uc815\ud655\ud558\ub2e4. \uc65c\uadf8\ub7f0\uc9c0\ub294 \uc5b4\ub835\uc9c0 \uc54a\uc73c\ub2c8 \uc9c1\uc811 \uc0dd\uac01\ud574 \ubcf4\uc790.
\n
\n # \uc774 \uacbd\uc6b0 \uc624\ucc28\ub294 \ub300\ub7b5 \uad6c\uac04\uc758 \ud06c\uae30\uc778 h\uc758 \uc81c\uacf1\uc5d0 \ube44\ub840\ud55c\ub2e4.<\/p>\n

# \ubcf4\ub2e4 \uc815\ud655\ud55c \uadfc\uc0ac\uc2dd\uc740 Simpson’s rule\uc774 \uc81c\uacf5\ud55c\ub2e4. \uc0ac\ub2e4\ub9ac\uaf34 \uaddc\uce59\uc5d0\uc11c \uc2ec\uc2a8 \uaddc\uce59\uc73c\ub85c \uc9c4\ud654\ud558\ub294 \uac83\uc740 \ubbf8\ubd84\uc5d0\uc11c 2\uc810 \uacf5\uc2dd\uc744 3\uc810 \uacf5\uc2dd\uc73c\ub85c \ubc14\uafb8\ub294 \uacfc\uc815\uacfc \uc720\uc0ac\ud558\ub2e4.
\n
\n # \uc989, \uc0ac\ub2e4\ub9ac\uaf34 \uaddc\uce59\uc740 2\uc810\uc744 \uc774\uc6a9\ud574\uc11c \uadf8 \uc0ac\uc774\uc758 \uba74\uc801\uc744 \uadfc\uc0ac\ud588\uc9c0\ub9cc, \uc2ec\uc2a8 \uaddc\uce59\uc740 3\uc810\uc744 \uc774\uc6a9\ud574\uc11c \uadf8 \uc0ac\uc774\uc758 \uba74\uc801\uc744 \uadfc\uc0ac\ud55c\ub2e4.
\n
\n # \uc989, 3\uc810\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 2\ucc28\uace1\uc120\uc774 \uc6d0\ub798 \uc8fc\uc5b4\uc9c4 \uace1\uc120\ubcf4\ub2e4 \uc704\uc778 \uad6c\uac04\uacfc \uc544\ub798\uc778 \uad6c\uac04\uc774 \uc788\uac8c \ub418\ub294\ub370, \ub118\uce58\ub294 \ubd80\ubd84\uacfc \ubaa8\uc790\ub77c\ub294 \ubd80\ubd84\uc774 \uc0c1\uc1c4\ub418\uc5b4 \ubcf4\ub2e4 \uc815\ud655\ud55c \uadfc\uc0ac\uac12\uc744 \uc5bb\ub294\ub2e4. \uace1\uc120\uc758 \uadfc\uc0ac\ub294 \ud2c0\ub9ac\uac8c \ub418\uc9c0\ub9cc, \uc801\ubd84\uac12\uc740 \uc815\ud655\ud574\uc9c4\ub2e4\ub294 \uac83\uc774\ub2e4.
\n
\n # \uc2ec\uc2a8 \uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.
\n
\n # F=(f(a)+4f((a+b)\/2)+f(b))*(b-a)\/6
\n
\n # \ub531 3\uc810, \uc989 a, b, (a+b)\/2\uc758 3\uad70\ub370 \uac12\uc744 \uc54c\uace0 \uc788\uc744 \ub54c \uadf8 \uc0ac\uc774\uc758 \uba74\uc801\uc740 \uc704\uc640 \uac19\uc774 \uadfc\uc0ac\ub41c\ub2e4. \uc774 \uacbd\uc6b0 \uc624\ucc28\ub294 \uad6c\uac04\uc758 \ud06c\uae30\uc778 b-a\uc758 5\uc81c\uacf1\uc5d0 \ube44\ub840\ud55c\ub2e4.
\n
\n # \ud30c\uc774\uc36c\uc73c\ub85c \uad6c\ud604\ud55c\ub2e4\uba74 \uc5b4\ub5bb\uac8c \ub420\uae4c?<\/p>\n

# \uac00\uc7a5 \uac04\ub2e8\ud558\uac8c \uad6c\ud604\ud55c\ub2e4\uba74 \ub2e4\uc74c\uacfc \uac19\uc744 \uac83\uc774\ub2e4.
\n
\n f = [f1, f2, f3]
\n
\n F = (f[0]+4*f[1]+f[2])*h\/6<\/p>\n

# \ud558\uc9c0\ub9cc \uc774\ub7f0 \uacbd\uc6b0\ub294 \uc810\uc774 \uc815\ub9d0 3\uac1c\ubc16\uc5d0 \uc5c6\ub294 \uacbd\uc6b0\uc774\ub2e4. \ub9cc\uc57d \uadf8\ubcf4\ub2e4 \ub9ce\ub2e4\uba74? \uc77c\ub2e8 \uc815\ud655\ud788 \ud640\uc218\uac1c \uc788\ub2e4\uace0 \ud558\uc790.
\n
\n f = [f1, f2, f3, f4, f5] # \ub9ac\uc2a4\ud2b8\ub294 \ub354 \uae38\uc5b4\uc9c8 \uc218\ub3c4 \uc788\ub2e4.
\n
\n F = (2.*reduce(lambda x, y: x+y, map(lambda x:x[0]+x[1]+x[1],f[:-1].reshape(len(f)\/2,2)))-f[0]+f[-1])*h\/6
\n
\n
\n
\n # \uc774 \ucf54\ub4dc\ub294 \uac04\ub2e8\ud574 \ubcf4\uc5ec\ub3c4 \uc790\uadf8\ub9c8\uce58 3\uac1c\uc758 \ud30c\uc774\uc36c \uae30\ub2a5\uc774 \ud569\uccd0\uc9c4 \ucf64\ube44\ub124\uc774\uc158\uc774\ub2e4.
\n <\/span>
\n<\/a>
\n
\n # \ud640\uc218\uac1c\ub9cc\ud07c \uc788\uc744 \ub54c\ub294 \uc704\uc758 \ucf54\ub4dc\ub97c \uc4f0\uba74 \ub41c\ub2e4. \uc65c \ub418\ub294\uc9c0\ub294 \ub2e4\uc2dc \uc798 \uc0dd\uac01\ud574 \ubcf4\ub3c4\ub85d \ud558\uc790. \ud30c\uc774\uc36c \uacf5\ubd80 \uacb8 \uc544\uc774\ud050\ud14c\uc2a4\ud2b8\ub77c\uace0 \ud558\uc790. (\ub098\ub3c4 \ud14c\uc2a4\ud2b8 \uc548\ud574\ubd04.)
\n
\n # \uc9dd\uc218\uac1c\uc77c \ub54c\ub294 \uc5b4\ub5bb\uac8c \ub420\uae4c? \uc9dc\ud22c\ub9ac \ubd80\ubd84\uc758 \uc624\ucc28\ub97c \uc5b4\ub5bb\uac8c \uc815\ub9ac\ud560 \uc218 \uc788\uc744\uc9c0\ub294 \uac01\uc790 \uc0dd\uac01\ud574 \ubcf4\uc790.<\/p>\n

# \ud30c\uc774\uc36c\uc5d0\uc11c \uad6c\ud604\ub41c \uc801\ubd84\uc740 scipy\uc5d0\uc11c \uc81c\uacf5\ud55c\ub2e4.
\n
\n # scipy.integrate(f, a, b)\ub294 \uc8fc\uc5b4\uc9c4 \ud568\uc218 f\ub97c a\uc5d0\uc11c b\uae4c\uc9c0 \uc801\ubd84\ud574\uc900\ub2e4. \ub2e4\uc911\uc801\ubd84\ub3c4 \ub2e4\ub8f0 \uc218 \uc788\ub2e4.<\/p>\n

# 1\ucc28\uc6d0 \uc801\ubd84\uc758 \uacbd\uc6b0 \uc704\uc758 \ucf54\ub4dc\ub85c\ub9cc \uc801\ubd84\ud558\ub354\ub77c\ub3c4 \ud574\ubcfc\ub9cc\ud558\ub2e4. \ubb38\uc81c\ub294 \ub2e4\ucc28\uc6d0 \uc801\ubd84\uc740 \uc801\ubd84 \uad6c\uac04\uc744 (a, b)\ucc98\ub7fc \uc27d\uac8c \ucabc\uac1c\uc904 \uc218 \uc5c6\ub2e4\ub294 \uac83\uc774\ub2e4.
\n
\n # \ubb3c\ub860 \uc798 \ucabc\uac1c\uc11c \ub2e4\uc911 \ubc18\ubcf5\ubb38\uc744 \ub3cc\ub9ac\uba74 \ub41c\ub2e4. \ub2f9\uc5f0\ud788 \ub41c\ub2e4. \ub9cc\uc57d \ud568\uc218\uac00 \uc218\uce58\uc801\uc73c\ub85c, \uc989 \ubaa8\ub4e0 \uc704\uce58\uc5d0\uc11c\uc758 \ud568\uc218\uac12\uc774 ‘\uc9c4\uc9dc \uac12’\uc73c\ub85c \uc8fc\uc5b4\uc838 \uc788\ub2e4\uba74 \ub2e4\uc911\ubc18\ubcf5\ubb38\uc744 \ub3cc\ub824\uc11c \uc801\ubd84\ud574\uc57c \ud560 \uac83\uc774\ub2e4.
\n
\n # \ud558\uc9c0\ub9cc, \ub9cc\uc57d \uace0\ucc28\uc6d0\uc5d0\uc11c \uc815\uc758\ub41c \ub9e4\uc6b0 \uc774\uc0c1\ud55c \ud568\uc218\uac00 \uc788\ub294\ub370, \uc774 \ud568\uc218\uc758 \ud568\uc218\uac12\uc740 \uad6c\ud560 \uc218 \uc788\uc9c0\ub9cc \ud568\uc218\uac12\uc774 \ub2e4 \uc8fc\uc5b4\uc9c4\uac8c \uc544\ub2c8\ub77c \uadf8\ub0e5 \ud568\uc218\ub9cc \uc8fc\uc5b4\uc838 \uc788\ub2e4\uba74? \uadf8\ub9ac\uace0 \uadf8 \ud574\uc11d\uc801\uc778 \uc801\ubd84\uc740 \uad6c\ud560 \uc218 \uc5c6\ub294 \uacbd\uc6b0\ub77c\uba74?
\n
\n # \uc774\ub54c\ub294 \ud655\ub960\uc801 \ubc29\ubc95\uc744 \ud1b5\ud574\uc11c \uad6c\ud560 \uc218 \uc788\ub294\ub370 \uadf8\uac83\uc774 \ubc14\ub85c Monte-carlo integration\uc774\ub2e4.
\n
\n # \ub2e4\ucc28\uc6d0 \ub2e4\uc911\uc801\ubd84 \ubc0f MC\ub294 \ub2e4\ub978 \uae30\ud68c\uc5d0 \uc124\uba85\ud558\ub3c4\ub85d \ud558\uaca0\ub2e4.\n <\/p>\n

\n\n<\/p>\n

\n —\n <\/p>\n

\n Quadratic\uc740 “\uc0ac\uac01\ud615\uc758”\ub77c\ub294 \ub73b\uc744 \ub2f4\uace0 \uc788\ub294\ub370, \uadf8\ub798\uc11c “\uc81c\uacf1”\uc774\ub77c\ub294 \ub73b\ub3c4 \uc788\ub2e4. \uc77c\ubc18\uc801\uc73c\ub85c \uc0ac\uac01\ud615\uc740 2\ucc28\uc6d0 \ud3c9\uba74\uc5d0\uc11c \uc815\uc758\ub41c \ub3c4\ud615\uc774\uace0, 1\ucc28\uc6d0\uc5d0\uc11c 1\ucc28\uc6d0\uc73c\ub85c \uac00\ub294 \ud568\uc218\ub294 \ubcf4\ud1b5 \uc9c1\uc0ac\uac01\ud615\uc73c\ub85c \uadfc\uc0ac\ud574\uc11c \uc801\ubd84\ud558\uac8c \ub418\ubbc0\ub85c quadrature\ub294 2\ucc28\uc6d0 \uc801\ubd84\uc758 \ub73b\uc774 \uac15\ud558\ub2e4. Cube\ub294 \uc815\uc721\uba74\uccb4\ub97c \ub73b\ud558\uace0, Cubic\uc740 \uadf8\ub798\uc11c \uc138\uc81c\uacf1\uc774\ub77c\ub294 \ub73b\uc774 \uc788\ub2e4. \uac70\uae30\uc11c \ub098\uc628 Cubature\ub294 3\ucc28\uc6d0 \uc801\ubd84\uc758 \ub73b\uc774 \uac15\ud558\ub2e4. 3\ucc28\uc6d0 \uc774\uc0c1\uc5d0\ub3c4 \uac01 \ucc28\uc6d0\ub9c8\ub2e4 \ub77c\ud2f4\uc5b4 \uc5b4\uc6d0\uc744 \uac16\ub294 \ud615\uc6a9\uc0ac\ub4e4\uc774 \uc788\uaca0\uc9c0\ub9cc \uadf8\ub0e5 Cubature\ub77c\uace0 \ubd80\ub974\ub294 \ub4ef. Curvature\ub294 “\uace1\ub960”\uc774\ub77c\ub294 \ub73b\uc73c\ub85c cubature\uc640\ub294 \uc544\ubb34 \uad00\ub828 \uc5c6\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":"

lecture_1.py # Elementary Numerical analysis 1 # based on Python # (C) 2013. Keehwan Nam, Dept. of physics, KAIST. # snowall@gmail.com \/ snowall@kaist.ac.kr # Differentiation # \ud14c\uc77c\ub7ec \uc815\ub9ac\uc640 \ud14c\uc77c\ub7ec \uc804\uac1c\ub97c \uc801\uadf9 \uc0ac\uc6a9\ud558\uba74 \ub41c\ub2e4. # \uc218\uce58\uc801\uc73c\ub85c \ubbf8\ubd84\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4 # df\/dx = (f(x+h) – f(x))\/h # \uc774 \uacbd\uc6b0 \uc624\ucc28\uac00 h\uc758 \uc81c\uacf1\uc5d0 \ube44\ub840\ud55c\ub2e4. 2\uc810 \ubbf8\ubd84\uacf5\uc2dd\uc774\ub2e4. # […]<\/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-10535","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-2JV","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/10535","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=10535"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/10535\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10535"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}