疎な転置推移確率行列

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1 B E05( Tue) : Time-stamp: Fri 16:18 JST hig ( ) E05 B(2019) 1 / 11

2 x = 0,..., m 1 m. p(t), p(x, t) 1 double p [m] = { 1. 0, 0. 0,...., 0. 0 } ; /. m. / 2 / {p ( 0, t ), p ( 1, t ), p ( 2, t ),..., p (m 1, t )} / M = ( p 00 p 01 p 10 p 11 ) = ( ) 1 double M[ ] [ m]= { { 0. 1, 0. 3 }, 2 { 0. 9, 0. 7 } } ; / 2 / {{p 00, p 01 }, {p 10, p 11 }} q = M p q x = y M xy p y. 1 p [ ] p ( x, 0 ) ; 2 p ; 3 f o r ( t ){ 4 pn=m p ; / / 5 p=pn ; 6 p ; 7 } compscib_2019/p/markov01/src/markov01sample.c ( ) E05 B(2019) 2 / 11

3 1 / 2 3 Time stamp : F r i 0 9 : 1 8 JST h i g 4 / 5 #d e f i n e CRT SECURE NO WARNINGS / V i s u a l C++ 6 #i n c l u d e <s t d i o. h> 7 8 / m / 9 #d e f i n e NS i n t m u l t i p l y t r a n s ( double pn [ ], double p [ ] ) ; 12 i n t p r i n t d i s t ( double p [ ], i n t t, i n t m) ; i n t main ( ) { 15 i n t t, tmax ; 16 i n t x ; 17 double p [ NS ] ; / p ( t ) / 18 double pn [ NS ] ; / p ( t +1) / 19 i n t m=ns ; / / s c a n f ( %d, &tmax ) ; 23 p r i n t f ( #T=%d\n, tmax ) ; ( ) E05 B(2019) 3 / 11

4 24 25 / / 26 t =0; p [ 0 ] = 1. 0 ; p [ 1 ] = 0. 0 ; p [ 2 ] = 0. 0 ; 27 p r i n t d i s t ( p, t,m) ; f o r ( t =0; t<tmax ; t++){ 30 m u l t i p l y t r a n s ( pn, p ) ; / / 31 f o r ( x =0;x<m; x++){ 32 p [ x]=pn [ x ] ; / / 33 } 34 p r i n t d i s t ( p, t +1,m) ; 35 } 36 r e t u r n 0 ; 37 } / p M M p q. / 40 i n t m u l t i p l y t r a n s ( double q [ ], double p [ ] ) { 41 i n t x, y ; 42 i n t m=ns ; 43 / / 44 double M[ ] [ NS] = {{0.5, 0. 5, 0. 0 }, 45 { 0. 5, 0. 5, 0. 0 }, 46 { 0. 0, 0. 0, 1. 0 } } ; 47 f o r ( x =0;x<m; x++){ ( ) E05 B(2019) 4 / 11

5 48 q [ x ]=0; 49 f o r ( y =0;y<m; y++){ 50 q [ x]+=m[ x ] [ y ] p [ y ] ; 51 } 52 } 53 r e t u r n 1 ; 54 } / t p 1 / 57 i n t p r i n t d i s t ( double p [ ], i n t t, i n t m){ 58 i n t x ; 59 p r i n t f ( %d,, t ) ; 60 f o r ( x =0;x<m; x++){ 61 p r i n t f ( %f,, p [ x ] ) ; 62 } 63 p r i n t f ( \n ) ; 64 r e t u r n 0 ; 65 } ( ) E05 B(2019) 5 / 11

6 Quiz( ) m = 3, S = {x} = {0, 1, 2}. ) t = 0, 1, 2,... p(t) =. ( p(0,t) p(1,t) p(2,t), ( ) double p[3]. 1 p[], E[(X(t) + 1) 2 ] double expect(double p[], int m). 2 p[], X(t) > 0 double ratio(double p[], int m). ( ) E05 B(2019) 6 / 11

7 ( B) I 2 3 ( )..,.,... Gmail t000000@mail.ryukoku.ac.jp. ( )PC 1.. Driver Windows,. Navigator,. ( ) E05 B(2019) 7 / 11

8 ( B) II,..,, TA.,,,,. : Gmail. Google Drive.. Moodle,. ( ) E05 B(2019) 8 / 11

9 ( B) III Moodle 1:,, Moodle. Windows, Moodle /. Moodle 2:..,,. ( ) E05 B(2019) 9 / 11

10 PC Visual Studio Visual Studio Community Edition. https: // ( ) E05 B(2019) 10 / 11

11 + Learn Math Moodle ryukoku.ac.jp/moodle Moodle App for ios/android URL https: //learn.math.ryukoku.ac. jp/moodle. (PC ) Math (1-507/1-542) ( ) E05 B(2019) 11 / 11

マルコフ連鎖の時間発展の数値計算

マルコフ連鎖の時間発展の数値計算 B L07(206-05-2 Mon : Time-stamp: 206-05-2 Mon 8:4 JST hig http://hig.net ( L07 B(206 / 20 L05-Q TA Prob and Sol:, {, 2}. M = ( 2 2 2.. 2 p(0 = ( 0 p(t. p(0 = 2 ( p(t. ( L07 B(206 2 / 20 M λ, λ 2, u, u