Matlab 實(shí)驗(yàn)程序 匯總40

MATLAB數(shù)學(xué)實(shí)驗(yàn)程序(2011-12-18)ex1.單位圓的正多邊形逼近alpha=linspace(0,2*pi,13);x=sin(alpha);y=cos(alpha);I2=1:2:13;I1=1:4:13;x1=x(I1);y1=y(I1);x2=x(I2);y2=y(I2);plot(x1,y1,x2,y2,x,y)axisoffex2拋射曲線的最大射程計(jì)算v0=100;g=9.8;alpha=pi/4;T=2*v0*sin(alpha)/g;t=linspace(0,T,17);x=v0*t*cos(alpha);y=vO*t*sin(alpha)-g*t42/2;plot(x,y,x,y,'r*')xmax=x(end)ex3.巴拿馬草帽.圖形[x,y]=meshgrid(-8:0.5:8);r=sqrt(x.A2+y.A2)+eps;z=sin(r)./r;mesh(x,y,z)colormap([1,0,0])axisoffex4.三葉玫瑰線實(shí)驗(yàn)theta=linspace(0,2*pi,10000);n=3;r=cos(n*theta);figure(1)polar(theta,r,'k')x=r.*cos(theta);y=r.*sin(theta);figure(2)comet(x,y)ex5.拋射曲線簇繪圖程序alpha=linspace(0.1,pi/2,20);v0=100;g=9.8;Taim=2*v0*sin(alpha)/g;T=(0:16)'*Taim/16;X=v0*T*diag(cos(alpha));Y=v0*T*diag(sin(alpha))-g*T.A2/2;%計(jì)算正十二邊形頂點(diǎn)坐標(biāo)%提取正三邊形坐標(biāo)%提取正六邊形坐標(biāo)%設(shè)定初速度%計(jì)算飛行時(shí)間%設(shè)定飛行時(shí)刻%計(jì)算坐標(biāo)點(diǎn)%顯示最遠(yuǎn)射程%創(chuàng)建網(wǎng)格點(diǎn)矩陣%計(jì)算網(wǎng)格點(diǎn)到原點(diǎn)距離%計(jì)算二元函數(shù)值%二元函數(shù)繪圖%設(shè)置紅色%去掉坐標(biāo)架%創(chuàng)建區(qū)間［0，2］上離散點(diǎn)%設(shè)置三葉玫瑰線參數(shù)%計(jì)算玫瑰線坐標(biāo)數(shù)據(jù)%創(chuàng)建第一個(gè)圖形窗%極坐標(biāo)繪圖%直角坐標(biāo)轉(zhuǎn)換%創(chuàng)建第二個(gè)圖形窗口%用慧星繪圖做動(dòng)態(tài)模擬%創(chuàng)建20個(gè)發(fā)射角數(shù)據(jù)的行向量%計(jì)算對應(yīng)的飛行時(shí)間%計(jì)算飛行時(shí)刻矩陣T%對角矩陣右乘飛行時(shí)刻矩陣%%創(chuàng)建網(wǎng)格點(diǎn)%設(shè)置復(fù)數(shù)自變量%計(jì)算復(fù)變函數(shù)值%分離實(shí)部和虛部plot(X,Y,'r')ex6.黎曼曲面繪圖程序[r,theta]=meshgrid(s,t);z=r.*exp(i*theta);f=sqrt(r).*exp(i*theta/2);x=real(z);y=imag(z);figure(1),mesh(x,y,real(f)),axisofffigure(2),mesh(x,y,imag(f)),axisoffpk=P(ki,:);L0=a;forkj=1:3L=L0;II=pk(kj);L(II)=[];pk=P(ki,:);L0=a;forkj=1:3L=L0;II=pk(kj);L(II)=[];A(ki,kj)=prod(L);L0(II)=b(II);endcolormap([001]),view(AZ,20)M(:,k)=getframe;AZ=AZ+15;endt=linspace(-pi/4,pi/4,50);ro=sqrt(cos(2*t));x=ro.*cos(t);y=ro.*sin(t);X=[0.6;1]*x;Y=[0.6;1]*y;Z=[0;1]*ones(1,50);mesh(X,Y,Z),holdoncolormap([000])view(17,-12),axisofffill3(0.6*x,0.6*y,zeros(1,50),'c')exp7.寶石切割問題實(shí)驗(yàn)程序P=perms(l:3);a=[19,14,12];b=[5,4,2];forki=1:6endQ=A*[1;1;1];disp([P,2*Q])exp8馬鞍面動(dòng)態(tài)旋轉(zhuǎn)幀播放程序M=moviein(16);[x,y]=meshgrid(-6:.5:6);z=x.A2-y.A2;mesh(x,y,z),axisoffAZ=-30;fork=1:24movie(M,2)ex9.飛機(jī)機(jī)翼圖仿真程序%創(chuàng)建全排歹【I操作數(shù)%設(shè)置石料數(shù)據(jù)%提取操作數(shù)%模擬切割%計(jì)算單次切割面積%計(jì)算每種操作切割面積%創(chuàng)建馬鞍面坐標(biāo)數(shù)據(jù)%馬鞍面繪圖

%設(shè)置初始方位角%旋轉(zhuǎn)圖形%幀設(shè)計(jì)%方位解增加15。%幀播放%設(shè)置50個(gè)點(diǎn)%計(jì)算雙紐線坐標(biāo)%直角坐標(biāo)轉(zhuǎn)換%XY坐標(biāo)擴(kuò)充矩陣%Z坐標(biāo)矩陣%設(shè)置黑色%設(shè)置視角、去坐標(biāo)架%底面填充Y(k,2:k-1)=Y(k-1,1:k-2)+Y(k-1,2:k-1);endY(k,2:k-1)=Y(k-1,1:k-2)+Y(k-1,2:k-1);endex13.正方形旋轉(zhuǎn)實(shí)驗(yàn)程序%輸入正整數(shù)%n不等于l%求n/2的余數(shù)%第一種操作%第二種操作exlO.角谷猜想或3n+l問題的周期計(jì)算n=input('inputn:=');N=n;T=l;whilen~=lr=rem(n,2);ifr==0

n=n/2;elsen=3*n+l;endN=[N,n];T=T+l;endT,NExll.騎摩托問題模擬程序A=0;B=l00;va=l0;vb=8;vc=60;f=l;k=0;while(B-A)>0.2iff==ltk=(B-A)/(vb+vc);elsetk=(B-A)/(vc+va);endA=A+va*tk;B=B-vb*tk;f=-f;k=k+1;endk,A,Bex12.楊輝三角形計(jì)算程序functionY=young(n)ifnargin==0,n=3;endY=eye(n);Y(:,1)=ones(n,1);fork=3:n%計(jì)算C和B相遇時(shí)間%計(jì)算C和A相遇時(shí)間%根據(jù)相遇時(shí)間計(jì)算位移%將矩陣第一列和對角元置為1%根據(jù)前一行計(jì)算當(dāng)前行數(shù)據(jù)xy=[-1-1;1-1;11;-11;-1-1];A=[cos(pi/24)—sin(pi/24);sin(pi/24)cos(pi/24)];%創(chuàng)建正交矩陣x=xy(:,1);y=xy(:,2); %提取坐標(biāo)數(shù)據(jù)%畫線并暫停一秒%旋轉(zhuǎn)并壓縮%畫線并暫停一秒%旋轉(zhuǎn)并壓縮fork=1:24xy=.89*xy*A';x=xy(:,1);y=xy(:,2);line(x,y),pause(1)endex14.中國農(nóng)歷年與十二生肖functionyears(year)%輸入年份year%輸出天干地支農(nóng)歷年生肖屬相

ifnargin==0,year=2011;endS1='甲乙丙丁戊己庚辛壬癸ifnargin==0,year=2011;endS1='甲乙丙丁戊己庚辛壬癸'；S2='子丑寅卯辰巳午未申酉戍亥';S='鼠?；⑼谬埳唏R羊猴雞狗豬'；k1=mod(year-4,10)+1；k2=mod(year-4,12)+1;s1=S1(k1);s2=S2(k2);s=S(k2);X=[S1,'..';S2;S]disp([int2str(year)，年是',sl,s2,'年,%創(chuàng)建天干字符串?dāng)?shù)組%創(chuàng)建地支字符串?dāng)?shù)組%創(chuàng)建十二生肖字符串?dāng)?shù)組%年份除10的余數(shù)%準(zhǔn)確定位%輸出天干地支十二生肖表','屬相：’,s])ex15.生日與十二星座模擬functionAries(x)%輸入生日格式[mm,dd]data=[1,19;2,18;3,20;4,20;5,20;6,21;7,23;8,23;9,23;10,24;11,22;12,22];Const=['水瓶';'雙魚';'白羊';'金牛';'雙子';'巨蟹';'獅子';'處女';'天秤';'天蝎';'射手';'魔蝎'];P=data(:,1);Q=data(:,2);p=x(1);q=x(2);II=find(P<=p&p<P+1);ifq<Q(II),II=II-1;endifII==0,II=12;endzodiac=Const'disp(['你輸入的生日屬于:',Const(II,:),座'])Ex16科赫曲線繪圖程序n=1;p=[00;100];A=[cos(pi/3)-sin(pi/3);sin(pi/3)cos(pi/3)]; %創(chuàng)建正交矩陣fork=1:5j=1;fori=1:nq1=p(i,:);q2=p(i+1,:);fori=1:nq1=p(i,:);q2=p(i+1,:);d=(q2-q1)/3;r(j,:)=q1;r(j+1,:)=q1+d;r(j+2,:)=q1+d+d*A';r(j+3,:)=q1+2*d;j=j+4;%提取線段起點(diǎn)%提取線段終點(diǎn)%計(jì)算第一個(gè)插入點(diǎn)%計(jì)算第二個(gè)插入點(diǎn)%計(jì)算第三個(gè)插入點(diǎn)endn=4*n;p=[];p=[r;q2];%整合分形曲線的數(shù)據(jù)endx=p(:,1);y=p(:,2);plot(x,y)%分離出坐標(biāo)數(shù)據(jù)ex17?endn=4*n;p=[];p=[r;q2];%整合分形曲線的數(shù)據(jù)endx=p(:,1);y=p(:,2);plot(x,y)%分離出坐標(biāo)數(shù)據(jù)ex17?北京到紐約飛行航程計(jì)算程序city=[40,116;31,122;36,140;37,-123;41,-76];R=6400+10;theta=city(:,1)*pi/180;fai=city(:,2)*pi/180;x=R*cos(theta).*cos(fai);y=R*cos(theta).*sin(fai);%五城市經(jīng)緯度%飛行高度設(shè)置%提取緯度數(shù)據(jù)%提取經(jīng)度數(shù)據(jù)%球坐標(biāo)變換%城市坐標(biāo)%城市坐標(biāo)%計(jì)算距離矩陣op=[x,y,z];formatbankDmatrix=R*acos(op*op7R^2)Ex18.北京到紐約飛行模擬實(shí)驗(yàn)程序functionflytravel()city=[40,116;31,122;36,140;37,-123;41,-76];figure(1),sphere(24),colormap([111])axisoff,holdonp1=city(1,:);p2=city(5,:);skyway(p1,p2)figure(2),sphere(24),colormap([1,1,1])axisoff,holdonfork=1:4p1=city(k,:);p2=city(k+1,:);skyway(p1,p2)endfunctionskyway(p1,p2)city=[p1;p2]*pi/180;theta=city(:,1);fai=city(:,2);x=cos(theta).*cos(fai);y=cos(theta).*sin(fai);z=sin(theta);t=linspace(0,1,20);xt=(1-t)*x(1)+t*x(2);yt=(1-t)*y(1)+t*y(2);zt=(1-t)*z(1)+t*z(2);r=sqrt(xt.*xt+yt.*yt+zt.*zt);xt=xt./r;yt=yt./r;zt=zt./r;plot3(x,y,z,'ro',xt,yt,zt,'b','linewidth',2)exl9?牟合方蓋體積計(jì)算與繪圖程序symsxyRy0=sqrt(RA2-xA2);V=8*int(int('sqrt((RA2-xA2))',y,0,y0),x,0,R)V0=subs(V,R,l)r=linspace(0,l,20);t=linspace(0,2*pi,80);u=r'*cos(t);v=r'*sin(t);w=sqrt(1+eps-u.A2);meshz(u,v,w),colormap([0,0,l])axisoffview(-46,52)colormap([0,0,0])ex20?左矩形公式計(jì)算及繪圖程序

functionS=interg(h)ifnargin==0,h=.5;endf=inline('x.A3./(exp(x)-l)');x=eps:h:5-h;y=f(x);n=length(x);X(l:3:3*n)=x;X(2:3:3*n)=x;X(3:3:3*n)=[x(2:n),5];Y(2:3:3*n)=y;Y(3:3:3*n)=y;X=[X,5];Y=[Y,0];t=eps:0.l:l0;u=f(t);plot(X,Y,'k',t,u,'k','LineWidth',l)S=sum(y)*h;Ex2l.探月衛(wèi)星初始軌道的最大速度計(jì)算程序h=200;H=5l000;R=6378;a=(h+H+2*R)/2;c=(H-h)/2;el=c/a;b=sqrt(a*a-c*c);T=l6*3600;Sl=a*b*pi/T;symse2th=200;H=5l000;R=6378;a=(h+H+2*R)/2;c=(H-h)/2;el=c/a;b=sqrt(a*a-c*c);T=l6*3600;Sl=a*b*pi/T;symse2tf=sqrt(1-e2*cos(t)人2);ft=subs(f,e2,el*el);S=int(ft,0,pi/2);L=4*a*double(S)V=L/TVmax=2*S1/(R+h)Ex22.探月衛(wèi)星的周期計(jì)算程序R=6378;h=[200,600,600,600,600];%輸入重要數(shù)據(jù)%計(jì)算長半軸和半焦距%計(jì)算離心率和短半軸%定義兩個(gè)符號變量%定義符號表達(dá)式%替換離心率數(shù)據(jù)%計(jì)算積分%符號數(shù)據(jù)轉(zhuǎn)換為數(shù)值%計(jì)算平均速度H=[51000,51000,71000,128000,370000];a=(h+H+2*R)/2;c=(H-h)/2;E2=(c./a).人2;b=sqrt(a.*a-c.*c);Vmax=linspace(10.3,10.9,5);bar(Vmax,'c')S=a.*b.*pi;Times=2*S./Vmax./(R+h)/3600Ex23.探月衛(wèi)星軌道模擬程序functionsatel1()R=6378;h=[200,600,600,600,600];H=[51000,51000,71000,128000,370000];a=(h+H+2*R)/2;c=(H-h)/2;b=sqrt(a.*a-c.*c);t=linspace(-pi,pi,500);x=a'*cos(t);y=b'*sin(t);s=c-c(1);s(2)=-s(2);S=s'*ones(size(t));x=S+x;X=x';Y=y';figure(1),plot(X,Y,'k',-c(1),0,'ob')X=reshape(X,2500,1);Y=reshape(Y,2500,1);figure(2),comet(X,Y)ex24.小行星軌道模擬程序x=[4.5596;5.0816;5.5546;5.9636;6.2756];y=[0.8145;1.3685;1.9895;2.6925;3.5265];A=[x.A2,2*x.*y,y.A2,2*x,2*y];b=-[1;1;1;1;1];ak=A\b;C=[ak(1),ak(2);ak(2),ak(3)];X=-C\[ak(4);ak(5)];x0=X(1);y0=X(2);X=[X;1];D=[ak(1),ak(2),ak(4);ak(2),ak(3),ak(5);ak(4),ak(5),1];F=X'*D*X;[Ud]=eig(C);a=sqrt(-F/d(1,1));b=sqrt(-F/d(2,2));t=2*pi*(0:5000)/5000;u=a*cos(t);v=b*sin(t);V=U*[u;v];x1=V(1,:)+x0;y1=V(2,:)+y0;plot(x1,y1,x,y,'*',x0,y0,'rO'),holdonx2=[x1,x1,x1];y2=[y1,y1,y1];comet(x2,y2)disp([x0,y0])disp([a,b])ex25.汽車租賃業(yè)務(wù)的矩陣特征向量應(yīng)用程序X=[120;150];p=0.1;q=0.12;A=[1-p,q;p1-q];Cars=X;fork=1:6X=A*X;Cars=[Cars,X];endCarsfigure(1),bar(Cars(1,:))figure(2),bar(Cars(2,:))alpha=[q;p];R=alpha/sum(alpha);X0=R*270;Taxs=X0;fork=1:6X0=A*X0;Taxs=[Taxs,X0];endTaxsfigure(3),bar(Taxs(1,:))figure(4),bar(Taxs(2,:))ex26.汽車緊急剎車滑行距離的數(shù)據(jù)擬合R1=1.609;R2=0.3048;x=[2025303540455055606570];

y=[202841537293118149y=[202841537293118149P2=polyfit(x,y,2);

y2=polyval(P2,x);Rest2=sum((y-y2).人2)figure(1),plot(x,y,'*',x,y2)P3=polyfit(x,y,3);y3=polyval(P3,x);Rest3=sum((y-y3).人2)figure(2),plot(x,y,'ok',x,y3,'k')V=[20,30,40,60,80,100,120]./Rl;S=polyval(P3,V);[x;y][V*R1;S*R2]ex27.兩船相遇的隨機(jī)模擬實(shí)驗(yàn)程序1266];%二次多項(xiàng)式擬合%計(jì)算二次擬合多項(xiàng)式在數(shù)據(jù)點(diǎn)處的值%計(jì)算二次擬合多項(xiàng)式的殘差平方和%三次多項(xiàng)式擬合%計(jì)算三次擬合多項(xiàng)式在數(shù)據(jù)點(diǎn)處的值%計(jì)算三次擬合多項(xiàng)式的殘差平方和%將公里數(shù)轉(zhuǎn)換為英里數(shù)%使用三次多項(xiàng)式計(jì)算剎車距離%顯示公里數(shù)和剎車距離function[P,Fn]=shipmeet(N)ifnargin==0,N=10000;endS1=0.5*22*22;S2=0.5*23*23;P=1-(S1+S2)/(24*24);data=24*rand(N,2);X=data(:,1);Y=data(:,2);II=find(X-1<=Y&Y<=X+2);Fn=length(II)/N;plot(X(II),Y(II),'.')ex28.平面多邊形填充和定積分蒙特卡羅計(jì)算實(shí)驗(yàn)x1=0:.01:1;y1=sqrt(x1);x2=1:-.01:0;y2=x2.A2;fill([x1,x2],[y1,y2],'r')N=10000;fork=1:6data=rand(N,2);x=data(:,1);y=data(:,2);II=find(y<=sqrt(x)&y>=x.A2);M=length(II);S(k)=M/N;endSsymsuf=sqrt(u)-uA2;Si=int(f,u,0,1)Ex29.維維安尼繪圖及體積計(jì)算程序r=linspace(0,1,20);alfa=linspace(0,2*pi,30);X=1+r'*cos(alfa);Y=r'*sin(alfa);Z=sqrt(4.01-X.A2-Y.A2);meshz(X,Y,Z),axisoffcolormap([0,0,1])view(133,16)symsxy;f=sqrt(4-xA2-yA2);y1=-sqrt(2*x-xA2);y2=sqrt(2*x-xA2);S1=int(f,y,y1,y2);S2=int(S1,x,0,2)Ex30.維維安尼體積計(jì)算蒙特卡羅實(shí)驗(yàn)function[V,error]=MonteC(L)ifnargin==0,L=7;endfork=1:LS(k)=viviani;endV=mean(S);error=V-(8/3*pi-32/9);hist(S,7)functionV=viviani(n)ifnargin==0,n=10000;endP=rand(n,3);X=2*P(:,1);Y=2*P(:,2)-1;Z=2*P(:,3);II=find((X-1).A2+Y.A2<=1&Z<=sqrt(4-X.A2-Y.A2));V=8*length(II)/n;Ex31.維維安尼體動(dòng)態(tài)積切割演示程序functionvivia0[X,Y,Z]=sphere(36);colormap([000])mesh(X,Y,Z),axisoffview(150,24)holdont=linspace(0,2*pi,36);xt=.5*cos(t)+.5;yt=.5*sin(t);x=[xt;xt];y=[yt;yt];z=[-1;1.1]*ones(1,36);II=31:36;fork=30:-1:1II=[k,II];mesh(x(:,II),y(:,II),z(:,II)),pause(.5)endzt=sqrt(l+eps-xt42-yt.A2);plot3([xt,xt],[yt,yt],[zt,-zt],'k')ex32.貸款與還貸問題模擬程序fun=inline('100*1.1A(x+1)-300*(1.1Ax-1)');x0=fzero(fun,5);x0+1p=1.1;S=100;k=1;S=S*p;pay=S;whileS>0k=k+1;S=S*p;S=S-30;pay=[pay,S];endpayex33.梯子問題的數(shù)學(xué)模型求解程序fun=inline('3./sin(alpha)+2./cos(alpha)');figure(1)fplot(fun,[pi/6,2*pi/5]),holdon[x0,y0]=fminbnd(fun,0,pi/2)plot(x0,y0,'o')fun1=inline('(1+2./x).*sqrt(x.A2+9)');figure(2)fplot(fun1,[2,4]),holdon[x1,y1]=fminbnd(fun1,2,4)plot(x1,y1,'o')ex34.單位根實(shí)驗(yàn)functionR=myroots(n)ifnargin==0,n=3;endt=linspace(0,2*pi,40);x=cos(t);y=sin(t);P(1)=1;P(n+1)=1;R=roots(P);X=real(R);Y=imag(R);plot(x,y,X,Y,'ro')ex35?常微分方程向量場模擬程序[x,y]=meshgrid(0:.25:6,0:.05:2);k=y.*(1-y);d=sqrt(1+k.A2);px=1./d;py=k./d;quiver(x,y,px,py),holdonu=dsolve('Du=u*(1-u)','u(0)=.2');v=dsolve('Dv=v*(1-v)','v(0)=1.8');ezplot(u,[0,6])ezplot(v,[0,6])axis([0,6.3,-.04,2.01])ex36.追擊問題的模擬實(shí)驗(yàn)程序function[T,Lp,Lq]=chase(dt)ifnargin==0,dt=1;endV1=1;V2=2*V1;P=[100,0];Q=[0,0];e=[-1,0];d=100;k=1;whiled>0.5P(k+1,:)=P(k,:)+V2*dt*e;Q(k+1,2)=Q(k,2)+V1*dt;e=Q(k+1,:)-P(k+1,:);d=norm(e);e=e/d;k=k+1;endu=Q(:,1);v=Q(:,2);x=P(:,1);y=P(:,2);plot(x,y,'ro',u,v,'b.')T=k*dt;Lp=k*V2*dt;Lq=k*V1*dt;Ex37.渡船航線模擬實(shí)驗(yàn)程序function[distance,times]=route(v)ifnargin==0,v=0.5;endB=[0,100];V=1;dt=1;x=v;y=V;distance=sqrt(x^2+(100-y)人2);P=[x,y];times=1;whiledistance>0.5x=x+dt*(v-V