建模竞赛中常用数学软件

是英文MATrixLABoratory(矩阵) 新墨西哥大学计算机科学系的CleveMoler教授设计，之后由Little、Moler、Steve、Bangert合作，于1984年成立了MathWorks公司，并把正式推 4.0版本【window版本】【仿R2012a2012b

help基本数值类型(class函数的使用－class(x)84无符号818无符号162无符号324无符号6480~有符号81有符号162-有符号324 有符号648-8~

字符串结构（struct:与C语言类似a{1,1}=[123;456];

例：a={[1234;567例：c=[123;456];d=mat2cell(c);例：e=[123;456];f=num2cell(ehelp 或docπ∞值，无限大(一个不定的数(0/0i或 InfNaN特殊使用办法：；：；…数据的输出（save;（矩阵运算加+减-乘*除xa=bax=b幂^ 示A=

,B=b1,X

b x 22 2 2AX=BX=A-1BX=A\Y={y1,y},C2YA=CY=CA-1Y=C/特别A2a11

+2 + +2 式式加++减--乘*除幂^A=

,B

b12 22 22 a a 22a

a

a

a2A.B=

特别A.2

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a a

help示示模 ceilremfix向0取整roundfloorsignmod（fiplrdiagfipudtrilfipdimtriu取整数：int8(1.4)=1;int8(-1.5)=-差分运算：diff([1231256X=[2X=[284;739];ans234ans23ans23C=[C,I]=ans=2ans=254535 help<>例& | ~ aa ind=find(X)ind=find(X,k)ind=find(X,k,'first')ind=find(X,k,'last')[row,col]=find(X,...)[row,col,v]=find(X, xy- Fopenfclosefscanf,fprintffread,fwriteC 数据举方式1load函数从文本文件 5load方式2：利用xlsread函数从excel文件 件data.xlsx，其数据如下：表 女男男男[ndata,text,alldata]=xlsread('data.xlsx')% ndatatext'''alldata'''[[[[[[[[forforindex=program:whilewhileexpressionk=

hilbert=zeros(k,k);%Preallocatematrixform=1:k %break forn=hilbert(m,n)=1/(m+n-1);n=

nFactorial=whilenFactorial<1.0e100n=n+1;nFactorial=nFactorial*n;ifexpressionelseifA= %Two-dimensionalB=rand(3,4,5);%Three-dimensionalarrayifisequal(size(A,2),size(B,2))C=[A;warning('AandBarenotthesamesize.');C=[];switchcasecase:mynumber=input('Enteraswitchmynumbercase-1casecase命令M文件（命令

函数Mfunctiony=myfun(x)fori=1:N提示functionfunctiony=subroutine1(x)functiony=subroutine2(x)x=[123;45functionm=findmfunctiony=objfun(m)%目标函数y=(quadl(@(t)t.^m.*cos(t),0,m)-N(1)).^2+…%其它定义函数方法（使用方便）%举例f1=@(x)sum(x.^2);%定义自变量为x的 f2=@(x,y)sin(x).*cos(y);%定义自变量为x、y的 a=[123];b=[34v1=f1(a)%调用f1函数v2=f2(a,b)%调用f2函数v1=14v2=- v3=function_handle y=[345;67arrayfun1z(xyexp(-x2y2在[-10,10]*[-10,10]的图形。[x0,y0]=meshgrid(-z0=arrayfun(@(x,y)z(x,y),x0,y0);z(x,y在网格点（x0,y0）的值z0例2f(x

sin

(1-t23dt在[04p0fun_int=@(t)(1-t.^2).^(2/3);%定义 Value=@(x)(integral(fun_int,0,sin(x)));%定义变上限 例3：利用fsolvef(te-atsin2tb|ta= b=，

holdongridon;x=arrayfun(@(k)fsolve(f(0.1,0.5),x0(k)),1:5);%求出[-

YI=YI='nearest'-nearestneighbor'linear'-linear'spline'-cubicspline -cubic x=0:10;y=xx=yy=spline(x,y,xx);注：pp=spline(x,y)….返回分段多项式的表示=2001.2-==2001.2-==2001.2-2001.2-

'nearest'-nearestneighbor'linear'-bilinear -bicubic'spline'-splinef=@(x,y,z,t)t.*exp(-x.^2-y.^2-v=[xi,yi,zi,ti]=ndgrid(-1:0.05:1,-1:0.08:1,-...vi=vq=vq=vq=griddata(...,w=w=x=rand(100,1)*4-y=rand(100,1)*4-z=x.*exp(-x.^2-y.^2);ti=-2:.25:2;[xq,yq]=meshgrid(ti,ti);zq=griddata(x,y,z,xq,yq);mesh(xq,yq,zq),holdplot3(x,y,z,'o'),holdoff

021

0 0 set(gca,'XTick',[-2-101set(gca,'YTick',[-2-101,,xi,i=1:nyi,i,a)=(y－f(x,,a)=(y－f(x,a,an

,ak2

ai 非线性拟合（拟合函数的选择f(x)= +g(x)=Ax+1+ F=xdata=[0.91.513.819.824.128.235.260.374.6ydata=[455.2428.6124.167.343.228.113.1-0.4-1.3-x0=[100;-10];%Startingguess[x,resnorm]=lsqcurvefit(F,x0,xdata,ydata)xdata=[0.91.513.819.824.128.235.260.374.6ydata=[455.2428.6124.167.343.228.113.1-0.4-1.3-F=@(x)x(1)*exp(x(2).*xdata)-ydata;x0=[100;-10];%Startingguess[x,resnorm]=lsqnonlin(F,x0) fitobject=fit([x,y],z,fitType)fitobject=fit(...,Name,Value,...)fitobject=fit(x,y,libname,options)fitobject=fit(...,'problem',vals)fitobject=fit(x,y,fitType,...,'Weight',Weights)[fitobject,gof]=fit(...)[cfun,gof,output]=doc [t0,tfx0options=odeset;options.RelTol=1e-functionXdot=funname(t,x)function[f,g,h]=myfun(x)ifnargout>1

ifnargout>2options=optimset(' DFP7BFGS52minf(x)ax2bx2，其中ab

2x-

-e-x1= -x1+2x2

-e- =minf(x,x)=(2x-x-e-x1)2+(-x+2x -e-x2 F=@(x)(2*x(1)-x(2)-exp(-x(1)))^2+(-x(1)+2*x(2)-exp(- x0=[-5;-5];minf(x)=10x3+xx2+x

22

-x-10£x2x2+12x2+12+xx2+123x2+x2+x2-15= 非线性约束描述（

x1£0,x2£0,x3£function[c,ceq]=c(1)=sqrt(x(1)^2+x(2)^2)-x(3)-10;%不等式约束 0（含两个c(2)=sqrt(x(1)^2+x(2)^2)+x(3)-ceq=x(1)^2+x(2)^2+x(3)^2-15;%等式约束 0（含一个F=@(x)10*x(1)^3+x(1)*x(2)^2+x(3)*(x(1)^2+x(2)^2);%目标函数描述x0=[-1,-2,-3];%初始值ub=zeros(3,1);%上界向量opts=optimset('Tolfun',1.0e-14,'TolX',1.0e-14,'Algorithm','interior-[x,fval,exitflag,output]=fmincon(F,x0,[], ,nvars,A,b,Aeq,beq A,b,Aeq,beq,LB,UB,nonlcon：线性与非线性约束参数，其含义与前面介绍的相同minf(x)=100(x2-x)2+(1-x xx+x- 2+210£x£11functiony=simple_fitness(x)y=100*(x(1)^2-x(2))^2+(1-c=[1.5+x(1)*x(2)+x(1)-x(2);-x(1)*x(2)+ceq LB=[0UB=[1

%Upperx= fval=minf(x)=(x-0.2)2+(x-1.7)2+(x- s.t.x2x3fun@(x)(x(10.2)^2+(x(2)-1.7)^2(x(3)-5.1)^2; x=ga(fun,3,[],[],[],[],[],[],[],[23])%variables2and3arex Ras(x20x2x2-10(cos2pxcos2px 点 f=@(x)20+x(1)^2+x(2)^2-10*(cos(2*pi*x(1))+cos(2*pi*x(2)));%适应度函数nvars=2; %Numberofvariablesoptions=gaoptimset(options,'PopulationSize',500);%optionss=gaoptimset(options,' options=gaoptimset(options,'Popinitrange',[-5,-5;-5,5]);options=gaoptimset(options,'CrossoverFraction',0.85);%options=gaoptimset(options,'MigrationFraction',0.15);%options=gaoptimset(options,'Generations',500);options=gaoptimset(options,'Tolfun',1.0e-10);[x,Fval,exitFlag,Output]=ga(f,nvars,options)

%x= 1.0e-03* Fval exitFlag %%多起点算法（例）x0=[0.0063-0.00340.2542];ms=MultiStart('TolX',1.0e-10,'MaxTime',50);%opts=o