数学实验练习作业.doc

1. 试分别生成 5 阶的单位阵、8 阶均匀分布的随机矩阵及其下三角矩阵 A=ones(5)B=rand(8)C=tril(B)A = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 B = 0.8909 0.8143 0.3517 0.3804 0.5688 0.1656 0.2290 0.1067 0.9593 0.2435 0.8308 0.5678 0.4694 0.6020 0.9133 0.9619 0.5472 0.9293 0.5853 0.0759 0.0119 0.2630 0.1524 0.0046 0.1386 0.3500 0.5497 0.0540 0.3371 0.6541 0.8258 0.7749 0.1493 0.1966 0.9172 0.5308 0.1622 0.6892 0.5383 0.8173 0.2575 0.2511 0.2858 0.7792 0.7943 0.7482 0.9961 0.8687 0.8407 0.6160 0.7572 0.9340 0.3112 0.4505 0.0782 0.0844 0.2543 0.4733 0.7537 0.1299 0.5285 0.0838 0.4427 0.3998 C = 0.8909 0 0 0 0 0 0 0 0.9593 0.2435 0 0 0 0 0 0 0.5472 0.9293 0.5853 0 0 0 0 0 0.1386 0.3500 0.5497 0.0540 0 0 0 0 0.1493 0.1966 0.9172 0.5308 0.1622 0 0 0 0.2575 0.2511 0.2858 0.7792 0.7943 0.7482 0 0 0.8407 0.6160 0.7572 0.9340 0.3112 0.4505 0.0782 0 0.2543 0.4733 0.7537 0.1299 0.5285 0.0838 0.4427 0.39982. 生产列向量 x=1, 3, 5, 7, 9, , 29x=1, 3, 5, 7, 9, 11, 13 , 15, 17, 19, 21, 23, 25, 27, 29;A=reshape(x,15,1) A = 1 3 5 7 9 11 13 15 17 19 21 23 25 27 293. 生成以 x 的前 5 个元素为对角线的矩阵 A x=1, 3, 5, 7, 9; A=diag(x) A = 1 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 7 0 0 0 0 0 94. 生成一个与 A 同阶的正态分布的随机矩阵 BB=randn(5)B = -0.2725 -0.3538 0.0335 0.0229 -0.9792 1.0984 -0.8236 -1.3337 -0.2620 -1.1564 -0.2779 -1.5771 1.1275 -1.7502 -0.5336 0.7015 0.5080 0.3502 -0.2857 -2.0026 -2.0518 0.2820 -0.2991 -0.8314 0.96425. 输出 A 与 B 的 kronecker 乘积矩阵 C x=1, 3, 5, 7, 9; A=diag(x) ; B=randn(5); C=kron(A,B)6. 生成由 B 与其同阶魔方矩阵点乘得到的矩阵 D X=1:2:29;X=X;E=X(1:5);A=diag(E);K=size(A);B=randn(K);C=kron(A,B);F=size(B);G=magic(F);D=B.*GD = -23.1488 24.9382 -0.1952 6.6085 2.7484 10.4657 -5.5882 -1.5232 21.3777 -16.4763 -3.3948 7.5640 -3.9404 9.3383 20.8829 -3.3489 7.9217 0.4379 -4.4040 0.9212 6.0806 -1.2216 1.2823 1.2504 1.21667. 生成由 D 的第 2、4、5 行和第4、1 列组成的子矩阵 EX=1:2:29;X=X;E=X(1:5);A=diag(E);K=size(A);B=randn(K);C=kron(A,B);F=size(B);G=magic(F);D=B.*G;E=D(2,4,5,4,1)E = 13.0722 -3.5866 -0.6091 -2.6116 0.3649 4.87768. 求出矩阵 E 的最大元素a=max(max(E)a= 13.07229、教材第 53 页，1、2、3、4、51. 按顺序进行如下操作：（1） 产生一个5阶魔术方阵A，并计算A与inv(A);A=magic(5)Ainv(A) l1A = 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9ans = 17 23 4 10 11 24 5 6 12 18 1 7 13 19 25 8 14 20 21 2 15 16 22 3 9ans = -0.0049 0.0512 -0.0354 0.0012 0.0034 0.0431 -0.0373 -0.0046 0.0127 0.0015 -0.0303 0.0031 0.0031 0.0031 0.0364 0.0047 -0.0065 0.0108 0.0435 -0.0370 0.0028 0.0050 0.0415 -0.0450 0.0111（2） 求A的特征值；A=magic(5);eig(A) l2ans = 65.0000 -21.2768 -13.1263 21.2768 13.1263（3） 计算A的各列的总和与平均值；A=magic(5);B=sum(A)C=mean(A) l3B = 65 65 65 65 65C = 13 13 13 13 13（4） 计算A的各行的总和与平均值；A=magic(5);D=sum(A)E=mean(A) l4D = 65 65 65 65 65E = 13 13 13 13 13（5） 若b=1 2 3 4 5,求方程组Ax=b的解；A=magic(5);b=1,2,3,4,5;x=Ab l5x = 0.0128 0.0128 0.1795 0.0128 0.01282. 产生行向量S=1.0,1.2,1.4,20,并计算S*S与S*S,你有何”发现”?S=1.0:0.2;20;S*SS*S l6ans = 400ans = 4003. 设,.求C=A*B-B*A,你有何发现？A=1 2;3 4;B=5 5;0 5;C=A*B-B*A l7C = -15 -15 0 154. 设矩阵，.求C=A*B-B*A,你有何发现？A=1 2;3 4;B=5 0;0 5;C=A*B-B*A l8C = 0 0 0 05. 如何建立如下的矩阵?；2004*eye(10) l9ans =Columns 1 through 72004 0 0 0 0 0 0 0 2004 0 0 0 0 0 0 0 2004 0 0 0 0 0 0 0 2004 0 0 0 0 0 0 0 2004 0 0 0 0 0 0 0 2004 0 0 0 0 0 0 0 2004 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 8 through 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2004 0 0 0 2004 0 0 0 2004 ； 10*(ones(10)-eye(10) l10ans = 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0 10 10 10 10 10 10 10 10 10 10 0； ones(10)+2003*eye(10) l11ans = Columns 1 through 8 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 2004 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Columns 9 through 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2004 1 1 2004 20*eye(10)-10*ones(10) l12ans = 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 10 diag(10:10:100)+tril(ones(10)-eye(10) l13ans =10 0 0 0 0 0 0 0 0 0 1 20 0 0 0 0 0 0 0 0 1 1 30 0 0 0 0 0 0 0 1 1 1 40 0 0 0 0 0 0 1 1 1 1 50 0 0 0 0 0 1 1 1 1 1 60 0 0 0 0 1 1 1 1 1 1 70 0 0 0 1 1 1 1 1 1 1 80 0 0 1 1 1 1 1 1 1 1 90 0 1 1 1 1 1 1 1 1 1 100H=hilb(11);H(1:10,2:11) l14ans = Columns 1 through 9 0.5000 0.3333 0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.3333 0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.2500 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.2000 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.1667 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.1429 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.1000 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.0556 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.0556 0.0526 Column 10 0.0909 0.0833 0.0769 0.0714 0.0667 0.0625 0.0588 0.0556 0.0526 0.05002004*eye(5)+diag(20:10:50,1) l15ans = 2004 20 0 0 0 0 2004 30 0 0 0 0 2004 40 0 0 0 0 2004 50 0 0 0 0 20041. 做出圆环面和球面的组合图形。 ezsurf(5+2*cos(u)*cos(v),(5+2*cos(u)*sin(v),2*sin(u),0,2*pi,0,2*pi); hold on; ezsurf(2*cos(u).*cos(v),2*cos(u).*sin(v),2*sin(u),0,2*pi,0,pi) ;axis equal; shiyan1 2. 墨西哥帽子及其剪裁图形 subplot(2,2,1) a,b=meshgrid(-8:.3:8); c=sqrt(a.2+b.2)+eps; z=sin(c)./c; mesh(a,b,z) axis square hold on subplot(2,2,2) a,b=meshgrid(-8:.3:8); c=sqrt(a.2+b.2)+eps; z=sin(c)./c; mesh(a,b,z) i=find(a.2+b.2=64); z1=z;z1(i)=NaN; mesh(a,b,z1); axis square hold on subplot(2,2,3) a,b=meshgrid(-11:.3:11); c=sqrt(a.2+b.2)+eps; z=sin(c)./c; mesh(a,b,z) axis square hold on subplot(2,2,4) a,b=meshgrid(-11:.2:11); c=sqrt(a.2+b.2)+eps; z=(sin(c)-c)./c; mesh(a,b,z) i=find(a.2+b.2=121); z1=z;z1(i)=NaN; mesh(a,b,z1); axis square hold on shiyan23. 画出球面、椭球面、双叶双曲面、单叶双曲面。 subplot(2,2,1)u=0:pi/60:2*pi;v=0:pi/60:pi;U,V=meshgrid(u,v);X=3*sin(V).*cos(U);Y=3*sin(V).*sin(U);Z=3*cos(V);surf(X,Y,Z);axis equalhold onsubplot(2,2,2)u=0:pi/60:2*pi;v=0:pi/60:pi;U,V=meshgrid(u,v);X=2*sin(V).*cos(U);Y=3*sin(V).*sin(U);Z=4*cos(V);surf(X,Y,Z);axis equalhold onsubplot(2,2,3)ezsurf(3*sec(u)*cos(v),4*sec(u)*sin(v),5*tan(u), -pi/2,pi/2,0,2*pi);axis autohold onsubplot(2,2,4)ezsurf(3*tan(u)*cos(v), 4*tan(u)*sin(v),5*sec(u),-pi/2,3*pi/2,0,2*pi);axis auto hold on shiyan3 4.若要求田螺线的一条轴截面的曲边是一条抛物线：试重新设计田螺线的参数方程，并画出该田螺线。t=0:0.1:60;x=5*t.*cos(t);y=4*t.*sin(t);z=5*(t.2);plot3(x,y,-z)axis auto shiyan4 5.绘制马鞍面x,y=meshgrid(-25:25,-25:25);z=x.2/9-y.2/4;meshz(x,y,z)colormap(gray)title(马鞍面)grid off shiyan56.绘制黎曼函数图形。n=input(Enter n,negative quits:); x=;y=;k=1; for i=2:n; for j=1:i-1; if gcd(i,j)=1 x(k)=j/i; y(k)=1/i; k=k+1; end end end plot(x,y,.b); axis(0,1,0,1) shiyan6Enter n,negative quits:506.绘制下列曲线的的图形（散点图与折线图）：。x=-1:0.05:2;y=(x.3-x.2-x+1).(1/3);subplot(1,2,1)plot(x,y,.);subplot(1,2,2) plot(x,y,-)l167.绘制下列曲面的图形：（提示：曲面由两部分构成）。x,y=meshgrid(-10:0.5:10);z1=sqrt(x.2+2*y.2);z2=-sqrt(x.2+2*y.2);surf(x,y,z1)hold onsurf(x,y,z2)l178.在同一个图形上做下列两个函数的图像：（1）（2）。x=0:0.1*pi:2*pi;plot(x,(sin(x).2,-,x,(cos(x).2,-) 9. 利用 plot 函数在一个坐标系下绘制以下函数的图形： 。 x=0:0.1*pi:2*pi;plot(x,sin(x),*-k,x,cos(x),s-r,x,sin(2*x),o:b)1.试用 surf 绘制椭球面、单叶和双叶双曲面。subplot(2,2,1)u=0:pi/60:pi;v=0:pi/60:2*pi;U,V=meshgrid(u,v);a=3;b=3;c=2;X=a*sin(U).*cos(V);Y=b*sin(U).*sin(V);Z=c*cos(U);surf(X,Y,Z)axis equalhold onsubplot(2,2,2)u=-pi/2:pi/60:pi/2;v=0:pi/60:2*pi;U,V=meshgrid(u,v);a=4;b=3;c=2;X=a*sec(U).*cos(V);Y=b*sec(U).*cos(V);Z=c*tan(U);surf(X,Y,Z)axis equalhold onsubplot(2,2,3)u=-pi/2:pi/30:3*pi/2;v=0:pi/30:2*pi;U,V=meshgrid(u,v);a=4;b=4;c=5;X=a*tan(U).*cos(V);Y=b*tan(U).*sin(V);Z=c*sec(U);surf(X,Y,Z)axis equal2.试用 plot3 绘制三类螺线。 subplot(2,2,1)t=0:0.5:100;a=3;b=5;x=a*cos(t);y=a*sin(t);z=b*t;plot3(x,y,z)title(圆柱螺线)hold onsubplot(2,2,2)t=0:0.5:100;a=2;b=2;c=2;x=a*t.*cos(t);y=b*t.*sin(t);z=c*t;plot3(x,y,z)title(圆锥螺线)hold onsubplot(2,2,3)t=0:0.5:100;a=2;b=2;c=1/3;x=a*t.*cos(t);y=b*t.*sin(t);z=c*t.2;plot3(x,y,z)title(抛物螺线)1. 编写一个使用循环计算n!的函数。（factor2.m ） function f=factor2(n)y=1; for i=1:n y=y*i;endf=y; 2. 编写一个函数，要求实现以下功能：（factor3.m）（1） 当输入一个参数时，计算它的阶乘。（2） 当输入两个参数时，计算他们的阶乘的和。（3） 当输入参数超过三个时，输入错误信息，并返回。 function f=factor3(a) n=length(a); if n=1 y=1; for i=1:a y=y*i; end f=y; elseif n=2 x1=1; x2=1; for c=1:a(1); x1=x1*c; end for d=1:a(2) x2=x2*d; end y=x1+x2; f=y; else input(erro) return end符号运算一上机作业1. 指出下面的 M1，M2，M3 分别是