fortranfunction2.qxd
|
|
|
- ゆきさ すみだ
- 5 years ago
- Views:
Transcription
1 Fortran Numerical Library Function Catalog
2 IMSL TM Fortran Numerical Library Function Catalog IMSL Fortran IMSL Java TM C 12 IMSL Math / Library IMSL Math / Library Special Functions
3 IMSL TM Fortran Numerical Library Function Catalog IMSL Stat / Library
4 IMSL FORTRAN - 4 -
5 IMSL TM Fortran Numerical Library Function Catalog IMSL Fortran F77 F90 IMSL Fortran IMSL Fortran 100% IMSL Fortran Fortran Fortran IMSL Fortran Fortran IMSL Fortran IMSL Fortran IMSL Fortran F77 IMSL FORTRAN 77 SMP/OpenMP IMSL Fortran (SMP) Fourier SMP IMSL Fortran BLAS BLAS - 5 -
6 IMSL TM Fortran Numerical Library Function Catalog MPI IMSL Fortran MPI MPI IMSL Fortran MPI MPI IMSL Fortran IMSL Fortran IMSL Fortran - 6 -
7 IMSL TM Fortran Numerical Library Function Catalog IMSL 30 IMSL IMSL Fortran Windows NT/98/2000/XP Linux UNIX IMSL IMSL Fortran IMSL VNI IMSL IMSL Q&A VNI IMSL Fortran CPU - 7 -
8 IMSL TM Fortran Numerical Library Function Catalog IMSL Fortran Hermite 3 2 Gauss Adams-Gear Runge-Kutta 1 2 Fourier Laplace (BLAS) CPU - 8 -
9 IMSL TM Fortran Numerical Library Function Catalog IMSL Fortran 12 psi Pochhammer Fresnel Bessel Bessel Kelvin Kelvin Airy Airy Weierstrass P Jacobi 2 Mathieu Mathieu - 9 -
10 IMSL TM Fortran Numerical Library Function Catalog 12 Wilcoxon 2 Shapiro-Wilk - Yates lattice split-plot strip-plot split-split plot strip-split plot Wilcoxon Cochran 2 Kolmogorov/ Smirnov ARMA GARCH (Generalized Autoregressive Conditional Heteroscedasticity) kalman K-means 2 2 Cox Kaplan-Meier
11 IMSL TM Fortran Numerical Library Function Catalog 2 2 Poisson Faure
12 IMSL TM Fortran Numerical Library Function Catalog IMSL --- C JAVA IMSL C IMSL C ( CNL ) C C++ CNL IMSL Fortran 1970 IMSL CNL C CNL JMSL: JAVA JMSL Java 100 Java Java JNL Java JMSL IMSL Java JMSL Java JMSL JMSL 100 Java Java JMSL JMSL Java PC Java
13 IMSL Math / Library
14 IMSL Math / Library
15 IMSL Math / Library
16 IMSL Math / Library
17 IMSL Math / Library
18 IMSL Math / Library
19 IMSL Math / Library
20 IMSL Math / Library α
21 λ l l l l IMSL Math / Library
22 IMSL Math / Library
23 l l λ λ λ l λ λ λ l λ λ IMSL Math / Library
24 IMSL Math / Library
25 IMSL Math / Library
26 IMSL Math / Library
27 IMSL Math / Library
28 IMSL Math / Library
29 IMSL Math / Library
30 IMSL Math / Library
31 IMSL Math / Library
32 IMSL Math / Library
33 IMSL Math / Library
34 IMSL Math / Library
35 IMSL Math / Library
36 IMSL Math / Library A A + αxy T A A + αxx A A +α xy + αyx T A A + αxx A A +α xy T + αyx T T C αab + βc, C αa B + βc T T T C αab + βc, C αa B + βc T T T C α AB + βc C α BA + βc C α AB + βc C α BA + βc
37 IMSL Math / Library T C α AA + βc T C α A A + βc T C α AA + βc T C α A A + βc T T C α AB + αba + βc T T C α A B + αb A + βc T T C α AB + αba + βc T T C α A B + αb A + βc
38 IMSL Math / Library
39 IMSL Math / Library
40 IMSL Math / Library
41 T A USV = IMSL Math / Library
42 IMSL Math / Library
43 IMSL Math / Library
44 b a + IMSL Math / Library
45 IMSL Math / Library Special Functions
46 IMSL Math / Library Special Functions
47 IMSL Math / Library Special Functions
48 IMSL Math / Library Special Functions
49 IMSL Math / Library Special Functions
50 IMSL Math / Library Special Functions
51 IMSL Math / Library Special Functions
52 IMSL Math / Library Special Functions
53 IMSL Math / Library Special Functions
54 IMSL Math / Library Special Functions
55 IMSL Stat / Library
56 IMSL Stat / Library
57 IMSL Stat / Library
58 IMSL Stat / Library
59 IMSL Stat / Library
60 IMSL Stat / Library
61 IMSL Stat / Library
62 IMSL Stat / Library
63 IMSL Stat / Library
64 IMSL Stat / Library
65 IMSL Stat / Library
66 IMSL Stat / Library
67 IMSL Stat / Library
68 IMSL Stat / Library
69 IMSL Stat / Library
70 IMSL Stat / Library
71 IMSL Stat / Library
72 IMSL Stat / Library
73 IMSL Stat / Library
74 IMSL Stat / Library
75 IMSL Stat / Library
76 IMSL Stat / Library
77 IMSL Stat / Library
imslfunction1.qxd
VERSION 5.5 C Numerical Library Function Catalog IMSL TM C Numerical Library Function Catalog IMSL C 3 6 7 IMSL Java TM Fortran 8 IMSL C Math / Library 9 10 10 12 13 13 14 15 15 21 22 22 IMSL C / Stat
CNL社内製本用.PDF
VERSION 6.0 C Numerical Library Function Catalog IMSL TM C IMSL C Math / Library IMSL C / Stat / Library 1 IMSL TM C IMSL C IMSL C IMSL C IMSL C IMSL C IMSL C C IMSL C UNIX/Linux Windows 3 IMSL C IMSL
II
II 16 16.0 2 1 15 x α 16 x n 1 17 (x α) 2 16.1 16.1.1 2 x P (x) P (x) = 3x 3 4x + 4 369 Q(x) = x 4 ax + b ( ) 1 P (x) x Q(x) x P (x) x P (x) x = a P (a) P (x) = x 3 7x + 4 P (2) = 2 3 7 2 + 4 = 8 14 +
1 911 9001030 9:00 A B C D E F G H I J K L M 1A0900 1B0900 1C0900 1D0900 1E0900 1F0900 1G0900 1H0900 1I0900 1J0900 1K0900 1L0900 1M0900 9:15 1A0915 1B0915 1C0915 1D0915 1E0915 1F0915 1G0915 1H0915 1I0915
-1-1 1 1 1 1 12 31 2 2 3 4
2007 -1-1 1 1 1 1 12 31 2 2 3 4 -2-5 6 CPU 3 Windows98 1 -3-2. 3. -4-4 2 5 1 1 1 -5- 50000 50000 50000 50000 50000 50000 50000 50000 50000 50000-6- -7-1 Windows 2 -8-1 2 3 4 - - 100,000 200,000 500,000
, 1. x 2 1 = (x 1)(x + 1) x 3 1 = (x 1)(x 2 + x + 1). a 2 b 2 = (a b)(a + b) a 3 b 3 = (a b)(a 2 + ab + b 2 ) 2 2, 2.. x a b b 2. b {( 2 a } b )2 1 =
x n 1 1.,,.,. 2..... 4 = 2 2 12 = 2 2 3 6 = 2 3 14 = 2 7 8 = 2 2 2 15 = 3 5 9 = 3 3 16 = 2 2 2 2 10 = 2 5 18 = 2 3 3 2, 3, 5, 7, 11, 13, 17, 19.,, 2,.,.,.,?.,,. 1 , 1. x 2 1 = (x 1)(x + 1) x 3 1 = (x 1)(x
untitled
A = QΛQ T A n n Λ Q A = XΛX 1 A n n Λ X GPGPU A 3 T Q T AQ = T (Q: ) T u i = λ i u i T {λ i } {u i } QR MR 3 v i = Q u i A {v i } A n = 9000 Quad Core Xeon 2 LAPACK (4/3) n 3 O(n 2 ) O(n 3 ) A {v i }
1
005 11 http://www.hyuki.com/girl/ http://www.hyuki.com/story/tetora.html http://www.hyuki.com/ Hiroshi Yuki c 005, All rights reserved. 1 1 3 (a + b)(a b) = a b (x + y)(x y) = x y a b x y a b x y 4 5 6
研修コーナー
l l l l l l l l l l l α α β l µ l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
総合薬学講座 生物統計の基礎
2013 10 22 ( ) 2013 10 22 1 / 40 p.682 1. 2. 3 2 t Mann Whitney U ). 4 χ 2. 5. 6 Dunnett Tukey. 7. 8 Kaplan Meier.. U. ( ) 2013 10 22 2 / 40 1 93 ( 20 ) 230. a t b c χ 2 d 1.0 +1.0 e, b ( ) e ( ) ( ) 2013
−g”U›ß™ö‡Æ…X…y…N…g…‰
1 / 74 ( ) 2019 3 8 URL: http://www.math.kyoto-u.ac.jp/ ichiro/ 2 / 74 Contents 1 Pearson 2 3 Doob h- 4 (I) 5 (II) 6 (III-1) - 7 (III-2-a) 8 (III-2-b) - 9 (III-3) Pearson 3 / 74 Pearson Definition 1 ρ
d dt A B C = A B C d dt x = Ax, A 0 B 0 C 0 = mm 0 mm 0 mm AP = PΛ P AP = Λ P A = ΛP P d dt x = P Ax d dt (P x) = Λ(P x) d dt P x =
3 MATLAB Runge-Kutta Butcher 3. Taylor Taylor y(x 0 + h) = y(x 0 ) + h y (x 0 ) + h! y (x 0 ) + Taylor 3. Euler, Runge-Kutta Adams Implicit Euler, Implicit Runge-Kutta Gear y n+ y n (n+ ) y n+ y n+ y n+
_0212_68<5A66><4EBA><79D1>_<6821><4E86><FF08><30C8><30F3><30DC><306A><3057><FF09>.pdf
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
numb.dvi
11 Poisson kanenko@mbkniftycom alexeikanenko@docomonejp http://wwwkanenkocom/ , u = f, ( u = u+f u t, u = f t ) 1 D R 2 L 2 (D) := {f(x,y) f(x,y) 2 dxdy < )} D D f,g L 2 (D) (f,g) := f(x,y)g(x,y)dxdy (L
2 1 Introduction (1.1.2) Logistic ث Malthus (1.1.3) (( ) ث)( ) α = ( ) ( + ) [Verhulst 1845] 0 ( ) ( + ) lim ( ) = 0 t (1.1.4) (( ) ث)( ) α = ( ) Logi
![2 1 Introduction (1.1.2) Logistic ث Malthus (1.1.3) (( ) ث)( ) α = ( ) ( + ) [Verhulst 1845] 0 ( ) ( + ) lim ( ) = 0 t (1.1.4) (( ) ث)( ) α = ( ) Logi](/thumbs/81/82814896.jpg "2 1 Introduction (1.1.2) Logistic ث Malthus (1.1.3) (( ) ث)( ) α = ( ) ( + ) [Verhulst 1845] 0 ( ) ( + ) lim ( ) = 0 t (1.1.4) (( ) ث)( ) α = ( ) Logi")
1 1 Introduction 1.1 ( ) ( ) Malthus ( ) (1.1.1) ( ) α = ( ) ( + ) 0 ( ) ( + ) lim ( ) = 0 t ( ) α = ( ) αt م = ( ) ( ) = ( 0 ) 0 (1.1.2) αt م 0 = ( ) (1.1.1) ( ) ( α + (1 = ( + ) = 0 1 ( ( ) 2... ) geometric
漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト
https://www.hmg-gen.com/tuusin.html https://www.hmg-gen.com/tuusin1.html 1 2 OK 3 4 {a n } (1) a 1 = 1, a n+1 a n = 2 (2) a 1 = 3, a n+1 a n = 2n a n a n+1 a n = ( ) a n+1 a n = ( ) a n+1 a n {a n } 1,
untitled
A = QΛQ T A n n Λ Q A = XΛX 1 A n n Λ X GPGPU A 3 T Q T AQ = T (Q: ) T u i = λ i u i T {λ i } {u i } QR MR 3 v i = Q u i A {v i } A n = 9000 Quad Core Xeon 2 LAPACK (4/3) n 3 O(n 2 ) O(n 3 ) A {v i }
untitled
20 7 1 22 7 1 1 2 3 7 8 9 10 11 13 14 15 17 18 19 21 22 - 1 - - 2 - - 3 - - 4 - 50 200 50 200-5 - 50 200 50 200 50 200 - 6 - - 7 - () - 8 - (XY) - 9 - 112-10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 -
untitled
19 1 19 19 3 8 1 19 1 61 2 479 1965 64 1237 148 1272 58 183 X 1 X 2 12 2 15 A B 5 18 B 29 X 1 12 10 31 A 1 58 Y B 14 1 25 3 31 1 5 5 15 Y B 1 232 Y B 1 4235 14 11 8 5350 2409 X 1 15 10 10 B Y Y 2 X 1 X
xyr x y r x y r u u
xyr x y r x y r u u y a b u a b a b c d e f g u a b c d e g u u e e f yx a b a b a b c a b c a b a b c a b a b c a b c a b c a u xy a b u a b c d a b c d u ar ar a xy u a b c a b c a b p a b a b c a
ax 2 + bx + c = n 8 (n ) a n x n + a n 1 x n a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 4
20 20.0 ( ) 8 y = ax 2 + bx + c 443 ax 2 + bx + c = 0 20.1 20.1.1 n 8 (n ) a n x n + a n 1 x n 1 + + a 1 x + a 0 = 0 ( a n, a n 1,, a 1, a 0 a n 0) n n ( ) ( ) ax 3 + bx 2 + cx + d = 0 444 ( a, b, c, d
: 1g99p038-8
16 17 : 1g99p038-8 1 3 1.1....................................... 4 1................................... 5 1.3.................................. 5 6.1..................................... 7....................................
untitled
351 351 351 351 13.0 0.0 25.8 1.0 0.0 6.3 92.9 0.0 80.5 0.0 1.5 15.9 0.0 3.5 13.1 0.0 30.0 54.8 18.0 0.0 27.5 1.0 0.0 2.5 94.7 0.0 91.7 0.0 1.3 14.7 0.0 3.8 14.4 0.0 25.0 50.5 16.0 0.0 27.5 2.0 0.0 2.5
Macdonald, ,,, Macdonald. Macdonald,,,,,.,, Gauss,,.,, Lauricella A, B, C, D, Gelfand, A,., Heckman Opdam.,,,.,,., intersection,. Macdona
Macdonald, 2015.9.1 9.2.,,, Macdonald. Macdonald,,,,,.,, Gauss,,.,, Lauricella A, B, C, D, Gelfand, A,., Heckman Opdam.,,,.,,., intersection,. Macdonald,, q., Heckman Opdam q,, Macdonald., 1 ,,. Macdonald,
Bessel ( 06/11/21) Bessel 1 ( ) 1.1 0, 1,..., n n J 0 (x), J 1 (x),..., J n (x) I 0 (x), I 1 (x),..., I n (x) Miller (Miller algorithm) Bess
Bessel 5 3 11 ( 6/11/1) Bessel 1 ( ) 1.1, 1,..., n n J (x), J 1 (x),..., J n (x) I (x), I 1 (x),..., I n (x) Miller (Miller algorithm) Bessel (6 ) ( ) [1] n n d j J n (x), d j I n (x) Deuflhard j= j=.1
平成20年5月 協会創立50年の歩み 海の安全と環境保全を目指して 友國八郎 海上保安庁 長官 岩崎貞二 日本船主協会 会長 前川弘幸 JF全国漁業協同組合連合会 代表理事会長 服部郁弘 日本船長協会 会長 森本靖之 日本船舶機関士協会 会長 大内博文 航海訓練所 練習船船長 竹本孝弘 第二管区海上保安本部長 梅田宜弘
![Œ{Ł¶/1ŒÊ −ªfiª„¾ [ 1…y†[…W ]](/thumbs/50/26134150.jpg "Œ{Ł¶/1ŒÊ −ªfiª„¾ [ 1…y†[…W ]")
1 (bit ) ( ) PC WS CPU IEEE754 standard ( 24bit) ( 53bit)
GNU MP BNCpack tkouya@cs.sist.ac.jp 2002 9 20 ( ) Linux Conference 2002 1 1 (bit ) ( ) PC WS CPU IEEE754 standard ( 24bit) ( 53bit) 10 2 2 3 4 5768:9:; = %? @BADCEGFH-I:JLKNMNOQP R )TSVU!" # %$ & " #
a n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552
3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n
( ) a C n ( R n ) R a R C n. a C n (or R n ) a 0 2. α C( R ) a C n αa = α a 3. a, b C n a + b a + b ( ) p 8..2 (p ) a = [a a n ] T C n p n a
![( ) a C n ( R n ) R a R C n. a C n (or R n ) a 0 2. α C( R ) a C n αa = α a 3. a, b C n a + b a + b ( ) p 8..2 (p ) a = [a a n ] T C n p n a](/thumbs/91/106692724.jpg "( ) a C n ( R n ) R a R C n. a C n (or R n ) a 0 2. α C( R ) a C n αa = α a 3. a, b C n a + b a + b ( ) p 8..2 (p ) a = [a a n ] T C n p n a")
9 8 m n mn N.J.Nigham, Accuracy and Stability of Numerical Algorithms 2nd ed., (SIAM) x x = x2 + y 2 = x + y = max( x, y ) x y x () (norm) (condition number) 8. R C a, b C a b 0 a, b a = a 0 0 0 n C n
第1章 微分方程式と近似解法
April 12, 2018 1 / 52 1.1 ( ) 2 / 52 1.2 1.1 1.1: 3 / 52 1.3 Poisson Poisson Poisson 1 d {2, 3} 4 / 52 1 1.3.1 1 u,b b(t,x) u(t,x) x=0 1.1: 1 a x=l 1.1 1 (0, t T ) (0, l) 1 a b : (0, t T ) (0, l) R, u
ad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign(
I n n A AX = I, YA = I () n XY A () X = IX = (YA)X = Y(AX) = YI = Y X Y () XY A A AB AB BA (AB)(B A ) = A(BB )A = AA = I (BA)(A B ) = B(AA )B = BB = I (AB) = B A (BA) = A B A B A = B = 5 5 A B AB BA A
ネットショップ・オーナー２ ユーザーマニュアル
1 1-1 1-2 1-3 1-4 1 1-5 2 2-1 A C 2-2 A 2 C D E F G H I 2-3 2-4 2 C D E E A 3 3-1 A 3 A A 3 3 3 3-2 3-3 3-4 3 C 4 4-1 A A 4 B B C D C D E F G 4 H I J K L 4-2 4 C D E B D C A C B D 4 E F B E C 4-3 4
EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D
ありがとうございました
- 1 - - 2 - - 3 - - 4 - - 5 - 1 2 AB C A B C - 6 - - 7 - - 8 - 10 1 3 1 10 400 8 9-9 - 2600 1 119 26.44 63 50 15 325.37 131.99 457.36-10 - 5 977 1688 1805 200 7 80-11 - - 12 - - 13 - - 14 - 2-1 - 15 -
EPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D
公務員人件費のシミュレーション分析
47 50 (a) (b) (c) (7) 11 10 2018 20 2028 16 17 18 19 20 21 22 20 90.1 9.9 20 87.2 12.8 2018 10 17 6.916.0 7.87.4 40.511.6 23 0.0% 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2.0% 4.0% 6.0% 8.0%
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 A B (A/B) 1 1,185 17,801 6.66% 2 943 26,598 3.55% 3 3,779 112,231 3.37% 4 8,174 246,350 3.32% 5 671 22,775 2.95% 6 2,606 89,705 2.91% 7 738 25,700 2.87% 8 1,134
橡hashik-f.PDF
1 1 1 11 12 13 2 2 21 22 3 3 3 4 4 8 22 10 23 10 11 11 24 12 12 13 25 14 15 16 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 144 142 140 140 29.7 70.0 0.7 22.1 16.4 13.6 9.3 5.0 2.9 0.0
198
197 198 199 200 201 202 A B C D E F G H I J K L 203 204 205 A B 206 A B C D E F 207 208 209 210 211 212 213 214 215 A B 216 217 218 219 220 221 222 223 224 225 226 227 228 229 A B C D 230 231 232 233 A
1
1 2 3 4 5 (2,433 ) 4,026 2710 243.3 2728 402.6 6 402.6 402.6 243.3 7 8 20.5 11.5 1.51 0.50.5 1.5 9 10 11 12 13 100 99 4 97 14 A AB A 12 14.615/100 1.096/1000 B B 1.096/1000 300 A1.5 B1.25 24 4,182,500
05[ ]戸田(責)村.indd
![05[ ]戸田(責)村.indd](/thumbs/91/106164845.jpg "05[ ]戸田(責)村.indd")
147 2 62 4 3.2.1.16 3.2.1.17 148 63 1 3.2.1.F 3.2.1.H 3.1.1.77 1.5.13 1 3.1.1.05 2 3 4 3.2.1.20 3.2.1.22 3.2.1.24 3.2.1.D 3.2.1.E 3.2.1.18 3.2.1.19 2 149 3.2.1.23 3.2.1.G 3.1.1.77 3.2.1.16 570 565 1 2
/9/ ) 1) 1 2 2) 4) ) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x ) x 2 8x + 10 = 0
1. 2018/9/ ) 1) 8 9) 2) 6 14) + 14 ) 1 4 8a 8b) 2 a + b) 4) 2 : 7 = x 8) : x ) x ) + 1 2 ) + 2 6) x + 1)x + ) 15 2. 2018/9/ ) 1) 1 2 2) 4) 2 + 6 5) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x 2 15 12
koji07-01.dvi
2007 I II III 1, 2, 3, 4, 5, 6, 7 5 10 19 (!) 1938 70 21? 1 1 2 1 2 2 1! 4, 5 1? 50 1 2 1 1 2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 3 1, 2 1, 3? 2 1 3 1 2 1 1, 2 2, 3? 2 1 3 2 3 2 k,l m, n k,l m, n kn > ml...?
JMSL 3.0 FC_日_ .doc
V E R S I O N 3. 0 JMSL Numerical Library Function Catalog JMSL Numerical Library Function Catalog Java 4 7 IMSLC C# Fortran 8 com.imsl Package 9 com.imsl.math Package 10 10 10 10 11 11 11 12 12 12 12
WINET情報
WINETCONTENTS 1 2 3 Q&A Q A 4 Q A 5 Q A 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 No. 10. 1. 11. 2. 12. 3. 4. 13. 5. 14. 6. 7. 15. 8. 9. 16. 33 17. 33. 34. 35. 18. 19. 36.
> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3
13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >
情報理論 第5回 情報量とエントロピー
5 () ( ) ( ) ( ) p(a) a I(a) p(a) p(a) I(a) p(a) I(a) (2) (self information) p(a) = I(a) = 0 I(a) = 0 I(a) a I(a) = log 2 p(a) = log 2 p(a) bit 2 (log 2 ) (3) I(a) 7 6 5 4 3 2 0 0.5 p(a) p(a) = /2 I(a)
s s U s L e A = P A l l + dl dε = dl l l
P (ε) A o B s= P A s B o Y l o s Y l e = l l 0.% o 0. s e s B 1 s (e) s Y s s U s L e A = P A l l + dl dε = dl l l ε = dε = l dl o + l lo l = log l o + l =log(1+ e) l o Β F Α E YA C Ο D ε YF B YA A YA
p12.dvi
301 12 (2) : 1 (1) dx dt = f(x,t) ( (t 0,t 1,...,t N ) ) h k = t k+1 t k. h k k h. x(t k ) x k. : 2 (2) :1. step. 1 : explicit( ) : ξ k+1 = ξ k +h k Ψ(t k,ξ k,h k ) implicit( ) : ξ k+1 = ξ k +h k Ψ(t k,t
II III II 1 III ( ) [2] [3] [1] 1 1:
![II III II 1 III ( ) [2] [3] [1] 1 1:](/thumbs/103/160503680.jpg "II III II 1 III ( ) [2] [3] [1] 1 1:")
2015 4 16 1. II III II 1 III () [2] [3] 2013 11 18 [1] 1 1: [5] [6] () [7] [1] [1] 1998 4 2008 8 2014 8 6 [1] [1] 2 3 4 5 2. 2.1. t Dt L DF t A t (2.1) A t = Dt L + Dt F (2.1) 3 2 1 2008 9 2008 8 2008
C による数値計算法入門 ( 第 2 版 ) 新装版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 新装版 1 刷発行時のものです.
C による数値計算法入門 ( 第 2 版 ) 新装版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009383 このサンプルページの内容は, 新装版 1 刷発行時のものです. i 2 22 2 13 ( ) 2 (1) ANSI (2) 2 (3) Web http://www.morikita.co.jp/books/mid/009383
limit&derivative
- - 7 )................................................................................ 5.................................. 7.. e ).......................... 9 )..........................................
VI VI.21 W 1,..., W r V W 1,..., W r W W r = {v v r v i W i (1 i r)} V = W W r V W 1,..., W r V W 1,..., W r V = W 1 W
3 30 5 VI VI. W,..., W r V W,..., W r W + + W r = {v + + v r v W ( r)} V = W + + W r V W,..., W r V W,..., W r V = W W r () V = W W r () W (W + + W + W + + W r ) = {0} () dm V = dm W + + dm W r VI. f n
09 8 9 3 Chebyshev 5................................. 5........................................ 5.3............................. 6.4....................................... 8.4...................................
2 36 41 41 42 44 44 1 2 16 17 18 19 20 25 26 27 28 29 4 4.12 32 4.2 4.2.1 36 4.2.2 41 4.2.3 41 4.2.4 42 4.3 4.3.1 44 4.3.2 44 31 1 32 33 < 2 x 1 x x 2 < x 1 x1x 2 x1x 2 34 36 4.2 (1) (4) (1)
2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 1, 2 1, 3? , 2 2, 3? k, l m, n k, l m, n kn > ml...? 2 m, n n m
2009 IA I 22, 23, 24, 25, 26, 27 4 21 1 1 2 1! 4, 5 1? 50 1 2 1 1 2 1 4 2 2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 1, 2 1, 3? 2 1 3 1 2 1 1, 2 2, 3? 2 1 3 2 3 2 k, l m, n k, l m, n kn > ml...? 2 m, n n m 3 2
7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
.1 A cos 2π 3 sin 2π 3 sin 2π 3 cos 2π 3 T ra 2 deta T ra 2 deta T ra 2 deta a + d 2 ad bc a 2 + d 2 + ad + bc A 3 a b a 2 + bc ba + d c d ca + d bc +
.1 n.1 1 A T ra A A a b c d A 2 a b a b c d c d a 2 + bc ab + bd ac + cd bc + d 2 a 2 + bc ba + d ca + d bc + d 2 A a + d b c T ra A T ra A 2 A 2 A A 2 A 2 A n A A n cos 2π sin 2π n n A k sin 2π cos 2π
R R 16 ( 3 )
(017 ) 9 4 7 ( ) ( 3 ) ( 010 ) 1 (P3) 1 11 (P4) 1 1 (P4) 1 (P15) 1 (P16) (P0) 3 (P18) 3 4 (P3) 4 3 4 31 1 5 3 5 4 6 5 9 51 9 5 9 6 9 61 9 6 α β 9 63 û 11 64 R 1 65 13 66 14 7 14 71 15 7 R R 16 http://wwwecoosaka-uacjp/~tazak/class/017
2014-11.key
2014-11 1 2 3 4 5 7 8 9 10 11 12 PC 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 45 46 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68