1 MATLAB MATLAB Octave Octave Octave
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- あかり いなおか
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1 Octave ( )
2 1 MATLAB MATLAB Octave Octave Octave (+), (-) (*) (.*) (ˆ.ˆ) (/), (\) M Octave file load Open Close i
3 Octave. WebPage 1 Scilab MATLAB Octave file. Octave,MATLAB SciLab.RLab.,Yorick, ( ) 1 ponpoko/math/mathindex.html 1
4 1 MATLAB 1.1 MATLAB,The MathWorks,Inc. MAT- LAB. MATLAB C,Toolbox Simulink MATLABR2006a 2,R2006a R(elease),2006( ),a( ). MATLAB,, MATLAB., MAT- LAB. MATLAB Octave RLaB SciLab Yorick., C,,., C,,. Octave MATLAB,MATLAB., MATLAB,gnuplot Octave,. RLaB MATLAB. Octave, MATLAB, Octave. SciLab MATLAB Octave, 2
5 . MATLAB.,SciLab MATLAB Simulink SCICOS, SCICOS., SciLab.,,. yorick, MATLAB,yorick C,,MATLAB.,,,. MATLAB, Octave,,., MATLAB.MATLAB., MATLAB MATLAB 5.2,. 3
6 2 Octave 2.1 Octave,MATLABR2006a.Octave readline Emacs., Octave,.,,Emacs TeXmacs. TeXmacs Maxima,,, Octave TeXmacs Octave.,Octave. TeXmacs,Maxima Macaulay TeXmacs : TeXmacs,.,Maxima 4
7 ,MATLAB,.,,. 2.2 Octave Octave. help. Help,.,m,MATLAB Octave M-file. MATLAB/Octave M-file.,M,help. help MATLAB.,Octave help M-file, help -i.,, help -i ode Octave,.,help -i,texinfo info. Web Browser.,Octave, less Texinfo GNU. MATLAB, MATLAB help.,. 5
8 3 Octave Octave.Octave.,,MATLAB/Octave. 3.1 Octave C., , 1+2*3-4^2.,Octave,.,Octave 3.3. Octave ;.. octave:1> 1+1; octave:2> 1+1 2,,,,.,,, abc "efg".,matlab/octave (= ). (,) ([])...,["123","abc"]., []., ;. SciLab,MATLAB,Octave.. 6
9 octave:20> [1,2,3;4,5,6] octave:21> [1,2,3] octave:22> [1;2;3] MATLAB/Octave., ",", ";".,";" ":". ":"., a i j a(i,j). i,j 1.,a(1,2)=1.,a a(1,2)=1, a 1 2.,1 2 a(1,2) 1.,a(3,2)=10,,a 3 2,..,a m n,a(i,j) a((j-1)*m+i)., a. a, a,a 7
10 .,..,,,, Octave, Octave,,Octave (,for,if ).,x i 1,1x x+y., =. == C. a = octave:4> a a = octave:5> c=pi c = octave:6> s=a^2*pi s = ,Octave MATLAB π, e i,.matlab Octave, ( ) pi,e, i,.,.,for,, i, i i,. octave:1> pi pi = octave:2> i i = 0 + 1i octave:3> e e = octave:4> i*i 8
11 -1 octave:5> a=1+i; octave:6> b=1-i;a*b 2 octave:7>,matlab Octave i,e,pi (, ). who.,type,. i pi. octave:1> who octave:2> type i i is a builtin function octave:3> i=2 i = 2 octave:4> i*i 4 octave:5> type i i is a user-defined variable 2 octave:6> type pi pi is a builtin function octave:7> pi=10 pi = 10 octave:8> i=sqrt(-1) i = 0 + 1i octave:9> pi=acos(-1) pi = octave:10> who *** local user variables: i pi octave:11> type pi pi is a user-defined variable
12 octave:12> for i=1:10 > i*2; > end; octave:13> i i = 10 octave:14> type i i is a user-defined variable 10, who, i pi,,who i pi., type,. for,i 10.,i,for, 1,2,3,,ii., eps. (Ocatve eps=2.2204e-16,, ),,while eps.,matlab/octave.c, MATLAB/Octave.neko.name.. octave:1> neko.namae=" " neko = { namae = } octave:2> neko.weight="5kg" neko = { namae = weight = 5kg } 10
13 octave:3> neko.age=2 neko = { age = 2 namae = weight = 5kg } neko.,,., neko,.octave is struct,struct elements. octave:4> neko neko = { age = 2 namae = weight = 5kg } octave:5> is_struct(neko) 1 octave:6> struct_elements(neko) age namae weight octave:7> is struct 1, 0. MATLAB/Octave 1,0.,MAT- LAB,.,. 11
14 3.3 MATLAB,Octave C.,1+2*3+4^5+6/7,Octave/MATLAB ,.. MATLAB/Octave.,,. MATLAB/Octave (+) A+B,a+b,A+b, (-) A-B,a-b,A-b, (*) A*B,a*b,a*B, (ˆ) aˆb,aˆb,aˆb (/) A/B,a/b,A/b,. A/B=A*Bˆ(-1) (\) A \ B,a \ b,a \ B A \,. B=Aˆ(-1)*B (.*) A.*B,a.*b,a.*B, (.ˆ) A.ˆB,a.ˆb,A.ˆb, a.ˆb (./) A./B,a./b,a./B (/), (.\ ) A.\ B,a.\ b,a.\ B, A.\ b (\), ( ) A,,FORTRAN ** ^. 12
15 ,. A B. octave:1> A=[1,2;3,1] A = octave:2> B=[5,1;2,1] B = (+), (-) octave:3> A octave:4> A octave:5> A+B ,,,,. 13
16 3.3.2 (*) (.*) octave:9> A*B octave:10> A.*B , *.*,,,., *.,.*., A=(A ij ) B=(B ij ),A.*B=(A ij B ij )..*.. 14
17 3.3.3 (ˆ.ˆ) octave:29> A.^ octave:30> 2^A ˆ (/), (\) octave:15> A/B octave:16> A\B octave:17> A*B^(-1)
18 octave:18> A^(-1)*B octave:19> 2\B octave:20> A/ ,A/B=A*Bˆ(-1),A \ B=Aˆ(-1)*B.,,,,B \ 2 2/A.,, ** ^. octave:10> [1,2,3].**[2,3,1] octave:11> [1,2,3].^[2,3,1] octave:12> 16
19 3.4 MATLAB/Octave..,., size. length,.,,. octave:23> a=[1 2 3;4 5 6] a = octave:24> a(1,2) 2 octave:25> a(4) 5 octave:26> a(3) 2 octave:27> size(a) 2 3 octave:28> length(a) 3 MATLAB/Octave., a i a(i), A i j A(i,j).MATLAB/Octave,C,1.,MATLAB., i j( i) a(i:j)., a i j a(i,:) a(:,j). 17
20 . octave:32> a=[1:4;5:8;8:11] a = octave:33> b=a(2,:) b = octave:34> c=a(:,2) c = a(2,:) a ( ).,a(:,2).,matlab Octave, ":". ":",,. octave:37> a=rand(4,4) a = octave:38> b=zeros(4,4) 18
21 b = octave:39> b(:,2)=a(:,4) b = ,a(:,1), ":",. octave:39> a a = octave:40> c=zeros(2,2) c = octave:41> c(:,2)=a(:,2) error: a(i, j) = x: x must be a scalar or the number of elements in i must error: match the number of rows in x and the number of elements in j must error: match the number of columns in x error: assignment failed, or no method for matrix = matrix error: evaluating assignment expression near line 41, column 7 octave:41> a(:,2)=a(:,2) 19
22 error: a(i, j) = x: x must be a scalar or the number of elements in i must error: match the number of rows in x and the number of elements in j must error: match the number of columns in x error: assignment failed, or no method for matrix = matrix error: evaluating assignment expression near line 41, column 7 octave:41> a=a(:,4) a = ":"., ":".,.,. octave:43> d=zeros(10,2) d = octave:44> a a =
23 octave:45> d([7:10],1)=a(:,1) d = , ":",,., :,.,[ : : ]. 1:5 1:1:5, 1.,1:2:6,6, [1 3 5]. octave:111>bb=[0:0.1:0.5] bb = , for,.,for.. octave:116> t1=time;for i=1:100; bb(i,i)=0.01*i;end;t2=time;t2-t octave:117> t1=time;dd=[1:100];t2=time;t2-t e-05,for., for. 21
24 3.5,., diag.diag.,,. 1 0 eye. octave:118> diag([1,2]) octave:119> diag([1,2],1) octave:120> diag([1,2],2) octave:121> diag([1,2],-2)
25 octave:122> a=rand(3,3) a = octave:123> diag(a) octave:124> eye(3,2) octave:125> eye(2,3)
26 3.6 Octave MATLAB.,.Octave. a n x n + a n 1 x n a 1 x + a 0 [a n, a n 1,, a 1, a0], 1., conv,deconv, polyval. octave:2> conv([1,2],[1,-2]) octave:3> conv([1,2,2,1],[1,-2]) octave:4> aa = [aa,bb]=deconv([1,3,3,1],[1,1,1]) 1 2 bb = -1 octave:5> polyval([1,2,3,4],2) 26, conv([1,2],[1,-2]) (x + 2) (x 2). [1,0,-4], x 2 x 0 4,, x 2 4.deconv x 3 + 3x 2 + 3x + 1 x 2 + x + 1. x 3 + 3x 2 + 3x + 1 = (x 2 + x + 1) (x + 2) 1.,,.,Octave., Maxima, 24
27 .,,. 3.7 M- Octave,,MATLABR2006a. MATLAB/Octave.m (M-file). M-file, M-file path, M-file.. function [z]=nekoneko(x,y) if length(x)>length(y) z=x; else z=x./y; end; nekoneko.m. nekoneko.m textttoctave Octave. nekoneko(4,3).octave,. octave:1> nekoneko(4,3) octave:2> Octave,M-file., end. Octave.,> Octave. octave:1> function [z]=nekoneko(x,y) > if length(x)==length(y) > z=x./y; > else if length(x)>length(y) 25
28 > z=x; > else > z=y; > end > end > end octave:2> nekoneko([1:3],[3:-1:1]) octave:3> nekoneko([1:3],[3:-1:0]) octave:4> nekoneko([1:5],[3:-1:0]) type.. octave:6> type nekoneko nekoneko is a user-defined function: function z = nekoneko (x, y) if length (x) == length (y) z = x./ y; else if length (x) > length (y) z = x; else z = y; endif endif endfunction octave:7> 26
29 ,type M-file,. who. octave:8> who *** currently compiled functions: length nekoneko *** local user variables: aa bb octave:9> type aa aa is a user-defined variable [ 1, 2, 3 ] octave:10>,who type., π.,who. help, help M-file.M-file %. nekoneko.m,help. % nekoneko % % help % (^^)v % function [z]=nekoneko(x,y) if length(x)>length(y) z=x; else z=x./y; end; nekoneko.m,. 27
30 octave:1> help nekoneko nekoneko is the user-defined function from the file /home/yokota/webpage/math/books/source/octave/nekoneko.m nekoneko help (^^)v Additional help for built-in functions, operators, and variables is available in the on-line version of the manual. Use the command help -i <topic> to search the manual index. Help and information about Octave is also available on the WWW at and via the mailing list. octave:2> 3.8 Octave,system exec. MATLAB!, ;. Octave! not,matlab Octave. exec Octave,system, Octave, system. system.,system.. x1. 28
31 #!/bin/sh ls -l awk {print $5} >x1,system mike. function x = mike () system ("tama"); load ("x1"); x = sum (x1); endfunction mike tama system, x1,.,system tama path., system("/usr/bin/tama").,system, system("tama mike") "., pochi x1. tama $1. #!/bin/sh ls -l $1 awk {print $5} >x1 pochi,mike kuro. function x = kuro (wrd) evl=["pochi ",wrd]; system (evl); load ("x1"); x = sum (x1); endfunction kuro evl.,wrd /usr,/usr, evl pochi word /usr pochi /usr. system ( evl " ) x1.,system, Octave,Octave,.,Octave cd,ls pwd. UNIX. 29
32 4 4.1 MATLAB Octave LAPACK.,.,MATLAB,.,,. Octave +, -,.*, / ˆ., ˆ., aˆ2 aˆ0.5 a.*a sqrt(a)., rand ,a.*a,a.ˆ2.,. (Pentium 3 1GHz SuSE 9.3 PC).,,. octave:9> t1=time;a.*a;t2=time;t2-t octave:10> t1=time;a.^2;t2=time;t2-t octave:11> t1=time;exp(2*log(a));t2=time;t2-t octave:12> t1=time;a.*a.*a.*a.*a.*a.*a.*a.*a.*a.*a.*a;t2=time;t2-t octave:13> t1=time;a.^12;t2=time;t2-t octave:14> t1=time;exp(12*log(a));t2=time;t2-t , 20 30
33 .,,,,,,., octave:15> t1=time;a.*a.*a.*a.*a.*a.*a.*a.*a;t2=time;t2-t octave:16> t1=time;b=a.*a.*a;b=b.*b.*b;t2=time;t2-t octave:17> t1=time;b=a.^9;t2=time;t2-t octave:18> t1=time;exp(9*log(a));t2=time;t2-t ,., 1.5. Octave.,, log.,,,.,.,matlab for. MATLAB,,.,,.,,. 31
34 4.2 MATLAB,., for loop,.,matlab.,. 2, find.,octave MATLAB 1, 0., for. octave:66> x=[1:5,5:-1:1] x = octave:67> x== octave:68> y=find(x==2) y = 2 9 octave:69> x(y) 2 2 2,C, 2.,. 32
35 octave:83> x=[1:5,5:-1:1] x = octave:84> y=find(x>3) y = octave:85> z=x>3 z = octave:86> z.*x find 0. Octave (i,j), x(find(x>3)). find(x>3) x > 3. m n (i,j) m n m(j 1) + i. octave:5> aa=rand(5); octave:6> bb=aa>0.5 bb =
36 octave:7> find(bb) octave:8>aa(find(bb)) error: single index only valid for row or column vector error: evaluating index expression near line 8, column 1 octave:8> 0.5 aa,. MATLAB,y=x(x>;3) find.., 3 2. octave:89> x=[1:5,5:-1:1] x = octave:90> y=find(x>3) y =
37 octave:91> for i=x(y) > 2*i > end ,MATLAB for.,,. octave:1> x=[1:5,5:-1:1] x = octave:2> z=zeros(size(x)); octave:3> z(x>3)=2*x(x>3) z = x 0 2,x < 0 1, for,. octave:10> (x>=0)*2+(x<0)*(-1); octave:11> tmp=(x>=0); octave:12> tmp*2+(1-tmp)*(-1). Pentium 3 1GHz PC. octave:105> x=rand(100000,1); octave:106> t1=time;(x>=0.5)*2+(x<0.5)*(-1);t2=time;t2-t octave:107> t1=time;tmp=(x>=0.5);tmp*2+(1-tmp)*(-1);t2=time;t2-t
38 octave:108> t1=time;tmp=(x>=0.5);tmp*2+tmp-1;t2=time;t2-t octave:109> x;t1=time;for i1=[1:length(x)] > if x(i1)>=0.5; x(i1)=x(i1)*2; else x(i1)=-x(i1); > end;end;t2=time;t2-t x 0.5 x , 1.,., for,. 400.,, for., for,.,,matlab Octave any all.any 1, 0.,all 1, 0.,. octave:1> a=rand(4,5)-rand(4,5) a = octave:2> if any(a(:,1)>0) > lst=find(a(:,1)>0); > b=exp(a(lst,1)); > end; octave:3> b b = any,., any 36
39 . 1 1 all. octave:11> all(a(:,1)==a(:,3)) 0 octave:12> a(:,1)=a(:,3); octave:13> all(a(:,1)==a(:,3)) 1 octave:14>,for. 37
40 5 5.1 Octave gnuplot.,gnuplot., Matlab,,Octave,,.,.,plot. plot plot( Y,, ) plot( X, Y,, ),plot Y,,.,m n A,plot,A n.,x 1 n,y, X.,X Y.,X Y,., grid. grid, on off.on,off.,hold. hold grid, "on" "off".on,off,. 38
41 X,Y,Z,xlabel, ylabel,zlabel.,,title..,. octave:1> a1=[0:0.05:1]*2*pi; octave:2> b1=sin(a1); octave:3> plot(b1); octave:4> plot(a1,b1); octave:5> xlabel("x") octave:6> ylabel("y") octave:7> title("sine curve"); octave:8> grid("on"); octave:9> hold("on"); octave:10> c1=cos(a1); octave:11> plot(a1,c1); octave:12> title("red:sin, green:cos"); octave:13> hold("off"); octave:14> plot(a1,b1,a1,c1); octave:15> X=[a1;a1]; octave:16> Y=[b1;c1]; octave:17> plot(x,y); octave:18> plot(x,y );. b1, 5.1,X. 5.1: (Y ) 39
42 , a1 b1, 5.2, a1 X, b1 Y. 5.2:,xlabel ylabel X Y,title, 5.3.,xlabel,,. 5.3:, grid( on ) :,.,hold, plot,,plot 40
43 . plot,plot(a1,b1,a1,c1) X Y,X=[a1;a1] Y=[b1;c1] X Y plot(x,y ) : plot(x,y ),plot(x,y),plot, 5.6,. 5.6: plot(x,y) 41
44 6 Octave file,octave.,,,. 6.1 load, load.. neko,. neko neko. load neko. octave:1> load neko octave:2> neko neko = ,,. octave:3> load neko warning: load: local variable name neko exists. warning: use load -force to overwrite 42
45 error: load: unable to load variable neko error: evaluating index expression near line 3, column 1,.Octave,.,.,load -force., load force neko. octave:3> load -force neko octave:4> neko neko = ,.,neko,neko.matrix,. octave:5>load neko.matrix warning: load: local variable name neko exists. warning: use load -force to overwrite error: load: unable to load variable neko error: evaluating index expression near line 5, column 1 octave:5> load -force neko.matrix octave:6> who *** local user variables: neko octave:7>.,,neko.matrix neko.,load -force,. who.neko. 43
46 neko. who.,. save.save who,,,. octave:1> a=rand(4,4); octave:2> b=rand(3,1); octave:3> save neko a octave:4> save test octave:5> who *** local user variables: a b, a,b rand save neko a, a neko, save test,who test., neko test. neko # Created by Octave , Thu May 10 08:21: # name: a # type: matrix # rows: 4 # columns:
47 test # Created by Octave , Thu May 10 08:21: # name: a # type: matrix # rows: 4 # columns: # name: b # type: matrix # rows: 3 # columns: ,save,,,who.,save -append., test c,. octave:6> c=[1,2,3]; octave:7> save -append test c,c test. # Created by Octave , Thu May 10 08:21: # name: a # type: matrix # rows: 4 # columns:
48 # name: b # type: matrix # rows: 3 # columns: # name: c # type: matrix # rows: 1 # columns: load,,.,test test a c. octave:8> save test octave:9> save test a c octave:10> save a c test. # Created by Octave , Thu May 10 08:29: # name: a # type: matrix # rows: 4 # columns: # name: c # type: matrix # rows: 1 # columns: 3 46
49 1 2 3,save load. octave:1> load test octave:2> who *** local user variables: a c octave:3> a a = octave:4> c c = octave:5>,. MATLAB Octave. C,C.,.,Octave,MATLAB. MATLAB,Octave. 47
50 6.1.1 Open Close Open fopen. fopne id = fopen(, ), neko test/neko.dat.,fopen. fopen 1. r 2. w 3. a 4. r+. 5. w+. 6. a+.. fopen. id,., -1,., close C fclocse,fclose(id)..,.,,frewind. fgets,fputs,fscanf, C., C. MATLAB,Octave,..MATLAB,.,,,,,fgets stream,stream sscanf.. 48
51 6.2 fgets,fscanf.,octave fscanf MATLAB,,C-flag C fscanf.,matlab,octave, MATLAB,,, fgets stream, stream sscanf,... neko.txt ,1 2 3,. 1 2,3. ( neko.txt ) Octave,fgets. octave:43> fid=fopen( neko.txt, r ); octave:44> L1=fgets(fid) L1 = octave:45> L2=fgets(fid) L2 = octave:46> L3=fgets(fid) L3 =,1 2 3,. octave:47> frewind(fid) 0 octave:48> L4=fgets(fid) L4 = 1 2 3,,fopen, r., r r+., 49
52 w w+,,. fgets.,, frewind.,fgets., L1.,L1. octave:56> L1+L1 error: invalid conversion from string to real matrix error: invalid conversion from string to real matrix error: evaluating assignment expression near line 56, column 3 octave:56> size(l1) 1 6 octave:57> L1 L1 = 1 2 3, fgets,fgets.,. C sscanf. sscanf %d %f %s, L1=1 2 3 L2=3 2 1 sscanf. 50
53 octave:51> a11=sscanf(l1, %d ) a11 = octave:52> a12=sscanf(l1, %s ) a12 = 123 octave:53> a12=sscanf(l1, %f ) a12 = octave:54> a11=sscanf(l1, %d ) a11 = octave:55> a12=sscanf(l2, %d ) a12 = octave:56> a11+a ,d,Octave., MAT- LAB. Octave 51
54 . Octave MATLAB,.,fgets,sscanf.,L3.L3,, tama. # No. Flag Value 1 t 10 2 f t 20 4 f -20,sscanf,.,MATLAB., tama, sscanf ( %d ) ( %s ). octave:73> fid2=fopen( tama, r ) fid2 = 3 octave:74> tama1=fgets(fid) tama1 = # No. Flag Value octave:75> tama2=fgets(fid) tama2 = 1 t 10 octave:76> tama3=fgets(fid) tama3 = 2 f -10 octave:77> tama4=fgets(fid) tama4 = 3 t 20 octave:78> tama5=fgets(fid) tama5 = 4 f -20 octave:79> st1=sscanf(tama1, %d ) st1 = [](0x1) octave:80> st1=sscanf(tama2, %d ) 52
55 st1 = 1 octave:81> st1=sscanf(tama3, %d ) st1 = 2 octave:82> st1=sscanf(tama4, %d ) st1 = 3 octave:83> st1=sscanf(tama5, %d ) st1 = 4 octave:84> st1=sscanf(tama1, %s ) st1 = #No.FlagValue octave:85> st1=sscanf(tama2, %s ) st1 = 1t10 octave:86> st1=sscanf(tama3, %s ) st1 = 2f-10 octave:87> st1=sscanf(tama4, %s ) st1 = 3t20 octave:88> st1=sscanf(tama5, %s ) st1 = 4f-20,sscanf., %d, flag,flag No..,.,,.,2 f -10 2f-10. MATLAB sscanf,fscanf.,octave sscanf C C. octave:94> [s1,s2,s3,s4]=sscanf(tama1, %s %s %s %s, C ) s1 = # s2 = No. s3 = Flag s4 = Value octave:95> [n1,flg,n3]=sscanf(tama2, %d %s %d, C ) n1 = 1 53
56 flg = t n3 = 10 Octave, C sscanf fscanf, C MATLAB.,,,. octave:96> find(tama2== t tama2== f ) 7 octave:97> n1=sscanf(tama2(1:6), %d ) n1 = 1 octave:98> n2=sscanf(tama2(8:length(tama2)), %d ) n2 = 10 octave:99> flg=sscanf(tama2(7), %s ) flg = t, find tama2 t f,., Octave/MATLAB. #.,, #., Octave MATLAB,,.,,. Octave MATLAB C,.,MATLAB Octave,,. Octave. octave:102> [neko.n1(1),neko.flg(1),neko.n2(1)]=sscanf(tama2, %d %s %d, C ) neko.n1 = 1 neko.flg = t 54
57 neko.n2 = 10 octave:103> [neko.n1(2),neko.flg(2),neko.n2(2)]=sscanf(tama3, %d %s %d, C ) neko.n1 = 2 neko.flg = f neko.n2 = -10 sscanf neko.n1,neko.flg,neko.n2.. MATLAB Octave.,,,,Octave, is struct, struct elements.,matlab,.,. octave:104> neko neko = { n2 = flg = t f n1 = } 1 2 octave:107> is_struct(neko) 1 55
58 octave:108> octave:109> struct_elements(neko) n2 flg n1 MATLAB,, fgets sscanf,. 6.3 fopen,,,.,, w.,,,,.,, a,.,,. function [err]=appenddata(fname,mv,flg) err = 0; %. vfname=[fname,.vdt ]; % flg==0, %. if flg==0 vfp = fopen(vfname, w ); else vfp = fopen(vfname, a ); end; % [m,n]=size(mv); if m>0 if flg==0 fprintf(vfp, %d,mv(1,:)); 56
59 fprintf(vfp, \n ); end; for k=[2:m] fprintf(vfp, %22.15e,mv(k,:)); fprintf(vfp, \n ); end; else err=1; end; fclose(vfp);,.vdt.,, 2, mv. fprintf %22.15e, C FORTRAN., %. Octave, C,MATLAB, C C.,,.,MATLAB,MATLAB,.,Octave MATLAB. 57
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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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