Contents 1 Scilab
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1 Scilab (Shuji Yoshikawa) December 18, 2017
2 Contents 1 Scilab
3 , For While (break) (continue) if... end if... else... end if... elseif... else... end select
4 Chapter 1 Scilab 1.1,.,..,. 1.2 (1) (2) Scipad Ctrl + L..sce..sci (MATLAB.m] ). (3) > exec(.sci,-1) ( 3 ). 1.3.,,,,,,. MATLAB _. MATLAB pi, Scilab pi,. 3
5 1.4, ; 1.5 π i e (Not a Number), pi i e inf nan t f 1.6 +, -, *, / a b a^b 1.7 Scilab. (==) == ( =) ~= <=, >=, <, >,, &, (not P) ~P 1.8 a dx b dx dx = 1 a:dx:b a:b :0.1:2 1, 1.1, 1.2,..., 2.0 1:2:20 1, 3, 5,..., 19 ( 20 ) (dx ) 5:-1:3 5, 4, 3 1:3 1, 2, 3 4
6 a = 1:0.1:1.3 a = [ ]., --> a = 1:0.1:1.3; a(3) --> ans = 1.2., a b n linespace(x,y,n) 10 x 10 y n logspace(x,y,n) 1.9. MATLAB Scilab.. ( )a n ( n ) a(n) D MATLAB 6e //. MATLAB MATLAB. log x, log 10 x, log 2 x sin x, cos x, tan x arcsin x, arccos x, arctan x sinh x, cosh x, tanh x sinh 1 x, cosh 1 x, tanh 1 x x, x, signx ( ) log(x), log10(x), log2(x) sin(x), cos(x), tan(x) asin(x), acos(x), atan(x) sinh(x), cosh(x), tanh(x) asinh(x), acosh(x), atanh(x) sqrt(x), abs(x), sign(x) ceil(x), (floor(x)) round(x),, real(x), imag(x), 1.13 > ^ > *, / > +, - 5
7 Chapter 2. [1]. 2.1 x = (1, 2, 3) x = [1 2 3] x = [1,2,3] 1 x = 2 [1;2;3] 3, ;. x = [1 2 3]. A = [1 2 3; 4 5 6; 7 8 9] A = A = [1,2,3;4,5,6;7,8,9] OK : X=[1 2 3]; Y=[4 5 6]; A=[X;Y] 2: A=
8 2.3 n m zeros(n,m) n m 1 ( ) ones(n,m) eye(m,m) X diag(x) m. diag(x,m) rand(n,m, uniform ) rand(n,m, normal ) MATLAB eye(m), Scilab 1. MATLAB Scilab : A=zeros(2,3) A= : B=ones(3,2) B= : C=eye(2,4) C= : X=1:3; D=diag(X) D= : E=diag(X,-1), F=diag(X,+1) E= F=
9 , - *.* : A=[1 2; 3 4]; B=[0 2; 3 0]; C=A+B, D=A*B, E=A.*B 2: C= : D= : E= (, yen) / ( )./ , \ /., AB = C B = A 1 C B=A\C, AB = C A = CB 1 A=C/B., ( ) ^ (.^),, &, ~, ==, >=.,. A = (1, 2) B = (3, 4) A B, A B, A*B. 1: A=[1 2]; B=[0 2]; A*B 2: ans = 4 kron(a,b) 8
10 a a 1n b b 1t A =....., B =....., lm nt a m1... a mn b l1... b lt a 11 B... a 1n B kron(a, B) = a m1 B... a mn B : X=[1 2; 4 9]; sqrt(x) 2: ans= C Java for, MATLAB for., for, ( ). 2.6 length(a) ( ) size(a, m) m m = 1 ( ), m = 2 ( ) and(a, m) m F, m = 1 ( ), m = 2 ( ). or(a, m) m F, m = 1 ( ), m = 2 ( ). find(a) : A=[0 0 3; 0 0 0]; length(a), size(a), size(a,1), size(a,2) 2: ans= 9
11 6 3: ans= : ans= 2. 5: ans= (and) 1: A=[1 2 0; 3 2 1]; a1=and(a), a2=and(a,1), a3=and(a,2) 2: a1= F 3: a2= T T F 4: a3= F T (or) 1: A=[0 0 3; 0 0 0]; a1=or(a), a2=or(a,1), a3=or(a,2) 2: a1= T 3: a2= F F T 4: a3= T F : A=[ ; ; ]; find(a) 2: ans=
12 2.7 (rank) Cholesky LU QR. inv(a) pinv(a) det(a) trace(a) orth(a) rank(a) spec(a) sqrtm(a) expm(a) logm(a) chol(a) lu(a,m) qr(a,m) 2.8 A (m, n)- A m- ( ) A n- ( ). m. ( ) n- l.... A(m,n) A(m,:) A(:,n) A(:, n:n+1) diag : A=[ ; ; ]; A(1,4), diag(a), B=A(1,:), C=A(:,2) 2: ans= 4. 3: ans= : B= : C= 0. 11
13 : A=[ ; ; ]; Y=[1 3]; D=A(:, 2:4), E=A(Y,:) 2: D= : E= A (m, n)- x. A(m,n) 0. Y A. [A;Y] X A. [A X] : A=[1 2 3; 4 5 6]; A(3,4)=7 2: A= : A=[1 2 3; 4 5 6]; B=[7 7 7]; C=[8;8], D=[A;B], E=[A C] 2: D= : E=
14 2.10 A X. matrix. X m n A matrix. X=A(:) X = matrix(a,length(a),1) A = matrix(x,m,n) : A=[1 2 ; 4 5]; X1=A(:), X2=matrix(A,4,1) 2: X1= : X2= : X=1:12; A=matrix(X,2,6) 2: A= [] : A=[1 2 3; 4 5 6]; A(:,2)=[] 2: A=
15 1: A=[1 2 3; 4 5 6]; A(1,:)=[] 2: A= : A=[1 2 3; 4 5 6], A(:,[1 3])=[] 2: A= A. A. tril(a) triu(a) : A=[1 2 3; 4 5 6; 7 8 9]; B=tril(A), C=tril(A) 2: B= : C= [1], meshgrid,. 14
16 Chapter 3,., : function = ( ) 2: 3: endfunction,.sci,,, 1: exec(.sci,-1),... FunctEx1.sci 1: function out = AverageSum(X) 2: N = length(x); 3: S = sum(x); 4: Avr = S./N; 5: out = [Avr S]; 6: endfunction, 15
17 1: exec( 1: N=10; 2: X=1:N; 3: Y=AverageSum(X) --> Y = ,,.. Scilab,.,,( )..., 1: function ( ) 2: 3: endfunction., 1: function = () 2: 3: endfunction. 1: function 2: 3: endfunction.,., global. FunctEx1.sci 1: function AverageSum2 ( ) 2: global X AVR S 2: N = length(x); 16
18 3: S = sum(x); 4: AVR = S./N; 6: endfunction Main.sce 1. global X ARV S 2. N=10; X=1:N; 3. AverageSum2; 4. AVR, S --> AVR = 5.5 S= , Sum2 Sum2(X,Y) X+Y, Sum2(X) sum(x)., argn. argn(1) argn(2) argn(). FunctEx1.sci 1: function S = Sum2(X,Y) 2: if argn(2)==1 3: S= sum(x); 4: else 5: S= X+Y; 6: end 7: endfunction 3.2,. deff( = ( ),[ ( ) ]),,.. 17
19 1: deff( A=Ave2(X),[ N=length(X) ; A=sum(X)/N ] 18
20 Chapter 4 [1]. 4.1, For, 1: for 2: 3: end 1: for, end. 1: x=0; 2: for I=1:10 3: x=x+i; 4: end 5: x 6: --> x= 45 1: x=0; 2: for I=1:10, x=x+i; end 3: x 4: --> x= 45 19
21 4.1.2 While, 1: while 2: 3: end 1: while ; end. 1: x=0; I=0; 2: while I<10 3: I=I+1; x=x+i; 4: end 5: x 6: --> x= 45 1: x=0; I=0; 2: while I<10; I=I+1; x=x+i; end 3: x 4: --> x= (break) (continue) (1) break. 20, : tic() 2: while toc()<20 3: X=fix(rand()*10000); 4: if X == : X, break 6: end 7: end 20
22 rand() 0 1. fix. 20, X = 2013 break., break. (2) continue., 20, 2013,. 1: tic() 2: while toc()<20 3: X=fix(rand()*10000); 4: if X ~= : continue 6: end 7: X 8: end , continue, 8 end. 2013, 7, X., continue, if... end, 1: if 2: 3: end T, F.. 1: if, end. 1: x=2; 2: if x>0 21
23 3: disp( x is positive ); 4: end 5: --> x is positive if... else... end., 1: if 2: 1 3: else 4: 2 3: end T 1, F if... elseif... else... end., 1: if 1 2: 1 3: elseif 2 4: 2 5: else 6: 3 3: end 1 T 1, F 2. 2 T 2, F 3.. elseif elseif,, select select, 1: select (Y) 2: case $1$(A1) 3: : case $n-1$(a2) 22
24 5: $n-1$ 6: else 7: $n$ 8: end select case (Y = A1 1, Y = A2 2 ),., else. case, end.. 1: X=0; 2: select sign(x) 3: case 1 4: disp( X is positive ) 5: case -1 6: disp( X is negative ) 7: else 8: disp( X is zero ) 9: end 10: --> X is zero 23
25 Chapter [1]( ) ,, toc(). tic, toc. tic() 1: x=0; 2: tic() 3: for I=1:10 4: x=x+i; 5: end 6: T1=toc() 7: x 8: --> T1= : --> x= , while, for, sum., f(n x) n,, f(0:\delta x: N). [1][P91] 24
26 5.1.3 N a[n] = sin(n x),, a = zeros(1,n).,. Scilab MATLAB C JAVA. 25
27 Chapter 6 [1]. 6.1, Java,,,. 1: X=1:5, Y=X.^3 2: Fid = mopen( ex6201.txt, w ) 3: mfprintf(fid, %2d%5d\n, X, Y ); 4: mfclose(fid) --> X= Y= , 3, %2d%5d\n,,.. ex6201.txt
28 mopen w ( ) ( ) \%2d%5d\n,,.. 0 r r+ w w+ a a+ -, : \%5.2f +, : \%+5.2f : \%05.2f 10 d e E c e E f g( ) G( ) 8 ( ) o x, X ( ) 6.2 1: Fid = mopen( ex6201.txt, r ) 2: mfscanf(%inf, Fid, %d%d ); 3: mclose(fid); 4: N, [X Y] s u \n \t \b \r \f \ \ \f 27
29 --> N= 2. ans = %inf. %d%d.,. 28
30 References [1], Scilab,, [2], Scilab,, [3], Scilab, CQ, [4], Scilab,,
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[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
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[ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =
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arctan arctan arctan arctan 2 2000 π = 3 + 8 = 3.25 ( ) 2 8 650 π = 4 = 3.6049 9 550 π = 3 3 30 π = 3.622 264 π = 3.459 3 + 0 7 = 3.4085 < π < 3 + 7 = 3.4286 380 π = 3 + 77 250 = 3.46 5 3.45926 < π < 3.45927
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Chap10.dvi
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no35.dvi
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Microsoft PowerPoint - it2_octave_text1.ppt
数値計算ソフトウェア 背景 機械技術者は様々な力学現象を扱う. この現象を表わす解が要求された場合, 先ずは解析解 ( 厳密解 を求める. しかし, 一般には困難である. 解析解が得られない場合には, 工学的に許容される数値近似解を求めることになる. 目標様々な数値計算を行ない, 汎用数値計算ソフトウェアを活用できるようにする. 1 数値計算数値近似解 行列演算 非線型方程式 常微分方程式 統計解析
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128 ビット 4 倍精度と 160 ビット拡張 4 倍精度演算プログラムの作成 平山弘神奈川工科大学自動車システム開発工学科 hirayama@sd.kanagawa-it.ac.jp 工学院大学新宿校舎 28 階第 4 会議室 2013 年 3 月 8 日 ( 金 ) なぜ 4 倍精度か 4 倍精度程度の精度では 多倍長計算はあまり速くない 精度の小さい計算の方が計算精度が大きい計算より需要は多い
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数学の基礎訓練I
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Excel ではじめる数値解析 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, 初版 1 刷発行時のものです.
Excel ではじめる数値解析 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/009631 このサンプルページの内容は, 初版 1 刷発行時のものです. Excel URL http://www.morikita.co.jp/books/mid/009631 i Microsoft Windows
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di-problem.dvi
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I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si
I 8 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No. : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin.
II 1 3 2 5 3 7 4 8 5 11 6 13 7 16 8 18 2 1 1. x 2 + xy x y (1 lim (x,y (1,1 x 1 x 3 + y 3 (2 lim (x,y (, x 2 + y 2 x 2 (3 lim (x,y (, x 2 + y 2 xy (4 lim (x,y (, x 2 + y 2 x y (5 lim (x,y (, x + y x 3y
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1 26 ( ) ( ) 1 4 I II III A B C (120 ) ( ) 1, 5 7 I II III A B C (120 ) 1 (1) 0 x π 0 y π 3 sin x sin y = 3, 3 cos x + cos y = 1 (2) a b c a +
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sin cos No. sine, cosine : trigonometric function π : π = 3.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd cos = cos : even.
08 No. : No. : No.3 : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No.0 : No. : sin cos No. sine, cosine : trigonometric function π : π = 3.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin
I No. sin cos sine, cosine : trigonometric function π : π =.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd cos = cos : even.
I 0 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No.0 : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd
II 2 3.,, A(B + C) = AB + AC, (A + B)C = AC + BC. 4. m m A, m m B,, m m B, AB = BA, A,, I. 5. m m A, m n B, AB = B, A I E, 4 4 I, J, K
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