matlab典型例题.doc

例2.1 muw0=1.785; a=0.03368; b=0.000221; t=0:20:80; muw=muw0./(1+a*t+b*t.2)例2.2 数值数组和字符串的转换 a=1:5; b=num2str(a); a*2ans = 2 4 6 8 10 b*2ans =98 64 64 100 64 64 102 64 64 104 64 64 106例2.9比较左除和右除求解恰定方程 rand(seed,12); a=rand(100)+1.e8; x=ones(100,1); b=a*x; cond(a)ans = 5.0482e+011 tic;x1=b/a;t1=toct1 = 0.4711 er1=norm(x-x1)er1 = 139.8326 re1=norm(a*x1-b)/norm(b)re1 = 4.3095e-009 tic;x1=ab;t1=toct1 = 0.0231 tic;x1=ab;t1=toct1 = 0.0011 er2=norm(x-x1)er2 = 1.5893e-004 re1=norm(a*x1-b)/norm(b)re1 = 4.5257e-016例2.14：计算矩阵的指数 b=magic(3); expm(b)ans = 1.0e+006 * 1.0898 1.0896 1.0897 1.0896 1.0897 1.0897 1.0896 1.0897 1.0897例2.18：特征值条件数 a=-149 -50 -154;537 180 546; -27 -9 -25a = -149 -50 -154 537 180 546 -27 -9 -25 V,D,s=condeig(a)V = 0.3162 -0.4041 -0.1391 -0.9487 0.9091 0.9740 -0.0000 0.1010 -0.1789D = 1.0000 0 0 0 2.0000 0 0 0 3.0000例2.41 5阶多项式在【0,2pi】最小二乘拟合 x=0:pi/20:pi/2; y=sin(x); a=polyfit(x,y,5); x1=0:pi/30:pi*2; y1=sin(x1); y2=a(1)*x1.5+a(2)*x1.4+a(3)*x1.3+a(4)*x1.2+a(5)*x1+a(6); plot(x1,y1,b-,x1,y2,r*) legend(原曲线,拟合曲线) axis(0,7,-1.2,4)例3.7 gradient绘制矢量图 x=0:pi/20:pi/2; y=sin(x); a=polyfit(x,y,5); x1=0:pi/30:pi*2; y1=sin(x1); y2=a(1)*x1.5+a(2)*x1.4+a(3)*x1.3+a(4)*x1.2+a(5)*x1+a(6); plot(x1,y1,b-,x1,y2,r*) legend(原曲线,拟合曲线) axis(0,7,-1.2,4) x,y=meshgrid(-2:.2:2,-2:.2:2); z=x.*exp(-x.2-y.2); px,py=gradient(z,.2,.2); contour(z), hold on quiver(px,py) hold off例 基本绘图命令 rand(100,1);plot(y)例4.1 绘制如图 x=1:0.1*pi:2*pi; y=sin(x); z=cos(x); plot(x,y,-k,x,z,-.rd)例4.5 绘制如图 x=1:10; y=rand(10,1); bar(x,y); x=0:0.1*pi:2*pi; y=x.*sin(x); feather(x,y)例4.6 绘制如图 lim=0,2*pi,-1,1; fplot(sin(x),cos(x),lim)例4.7绘图如下 x=2,4,6,8; pie(x,math,english,chinese,music)例4.9 绘图如下三维螺旋线 x=0:pi/50:10*pi; y=sin(x); x=0:pi/50:10*pi; y=sin(x); z=cos(x); plot3(x,y,z);例4.10 绘图如下。矩阵三维图 x,y=meshgrid(-2:0.1:2,-2:0.1:2); z=x.*exp(-x.2-y.2); plot3(x,y,z)例4.13绘图如下 X,Y=meshgrid(-4:0.5:4); Z=sqrt(X.2+Y.2); meshc(Z)例4.19 绘制柱面图 x=0:pi/20:pi*3; r=5+cos(x); a,b,c=cylinder(r,30); mesh(a,b,c)例4.20 地球表面气温分布示意图 a,b,c=sphere(40); t=abs(c); surf(a,b,c,t); axis(equal) axis(square) colormap(hot)例4.24坐标标注函数应用示意图 x=1:0.1*pi:2*pi; y=sin(x); plot(x,y) xlabel(x(0-2pi),fontweight,bold); ylabel(y=sin(x),fontweight,bold); title(正弦函数,fontsize,12,fontweight,bold,fontname,隶书)例4.30 同一张图绘制几个三角函数 x=0:0.1*pi:2*pi; y=sin(x); z=cos(x); plot(x,y,-*) hold on plot(x,z,-o) plot(x,y+z,-h) legend(sin(x),cos(x),sin(x)+cos(x),0) hold off例4.31 4个子图中绘制不同的三角函数图 x=0:0.1*pi:2*pi; subplot(2,2,1); plot(x,sin(x),-*); title(sin(x); subplot(2,2,2); plot(x,cos(x),-o); title(cos(x); subplot(2,2,3); plot(x,sin(x).*cos(x),-x); title(sin(x)*cos(x); subplot(2,2,4); plot(x,sin(x)+cos(x),-h); title(sin(x)+cos(x);例7.3正弦曲线插值示例 x=0:0.1:10; y=sin(x); xi=0:.25:10; yi=interp1(x,y,xi); plot(x,y,o,xi,yi)例7.7 x 0.5 1.0 2.0 2.5 3.0 y 1.75 2.45 3.81 4.80 8.00 8.60 y=span1,x,x2，最小二乘法拟合 x=0.5 1.0 1.5 2.0 2.5 3.0; y=1.75 2.45 3.81 4.80 8.00 8.60; a=polyfit(x,y,2)a = 0.4900 1.2501 0.8560 x1=0.5:0.05:3.0; y1=a(3)+a(2)*x1+a(1)*x1.2; plot(x,y,*) hold on plot(x1,y1,-r)例7.8最小二乘法求y=a+b*x2的经验公式Xi 19 25 31 38 44Yi 19.0 32.3 49.0 73.3 98.8 x=19 25 31 38 44; y=19.0 32.3 49.0 73.3 98.8; x1=x.2x1 = 361 625 961 1444 1936 x1=ones(5,1),x1x1 = 1 361 1 625 1 961 1 1444 1 1936 ab=x1yab = 0.5937 0.0506 x0=19:0.2:44; y0=ab(1)+ab(2)*x0.2; clf plot(x,y,o) hold on plot(x0,y0,-r)例7.10求积分function y=fun(t)y=exp(-0.5*t).*sin(t+pi/6); d=pi/1000; t=0:d:3*pi; nt=length(t); y=fun(t); sc=cumsum(y)*d; scf=sc(nt)scf = 0.9016 z=trapz(y)*dz = 0.9008例7.12用Newton-cotes公式求积分Fun.mfunction f=fun(x)f=exp(-x/2);quad8(fun,1,3,1e-10)例 微分函数 x=sym(x); diff(sin(x2) ans = 2*x*cos(x2)例题7-44 273-274页fun.mfunction f=fun(x,y)f=-2*y+2*x.2+2*x; x,y=ode23(fun,0,0.5,1); xans = Columns 1 through 7 0 0.0400 0.0900 0.1400 0.1900 0.2400 0.2900 Columns 8 through 12 0.3400 0.3900 0.4400 0.4900 0.5000 yans = Columns 1 through 7 1.0000 0.9247 0.8434 0.7754 0.7199 0.6764 0.6440 Columns 8 through 120.6222 0.6105 0.6084 0.6154 0.6179例题7-45tic;p1=flops;x,y=ode23(fun,0,0.5,1);p2=flops;t=toc;p=p2-p1; bj例题7-46function f=f(x,y)f=-2 1;988 -999*y+2*sin(x);999*(cos(x)-sin(x); ode23(f,0,10,2,3); a=-2 1;998 -999; %求方程的刚性比 b1=max(abs(real(eig(a); b2=min(abs(real(eig(a); s=b1/b2s = 1000例7-17/18 246页 a=0.4096, 0.1234, 0.3678, 0.2943;0.2246, 0.3872, 0.4015, 0.1129;0.3645, 0.1920, 0.3781, 0.0643;0.1784, 0.4002, 0.2786, 0.3927; aa = 0.4096 0.1234 0.3678 0.2943 0.2246 0.3872 0.4015 0.1129 0.3645 0.1920 0.3781 0.0643 0.1784 0.4002 0.2786 0.3927 b=0.4043 0.1550 0.4240 -0.2557; x=abx = -0.1819 -1.6630 2.2172 -0.4467265页，例7-39 （非线性方程组的符号解法）g.mfunction y=g(x)y(1)=0.7*sin(x(1)+0.2*cos(x(2);y(2)=0.7*cos(x(1)-0.2*sin(x(2); x0=0.5 0.5; fsolve(g,x0)No solution found.fsolve stopped because the problem appears regular as measured by the gradient,but the vector of function values is not near zero as measured by thedefault value of the function tolerance.ans = -0.0493 1.5215307页，例9-21 x=0.236 0.238 0.248 0.245 0.243; 0.257 0.253 0.255 0.254 0.261; 0.258 0.264 0.259 0.267 0.262; anova1(x)ans = 1.3431e-005308页，例9-22 a=58.2000 56.2000 65.3000;52.6000 41.2000 60.8000;49.1000 54.1000 51.6000;42.80