matlab精选习题.doc

exp(1)ans = 2.7183 log(1)ans = 0 log(13)ans = 2.5649 log10(10)ans = 1 log2(2)ans = 1 sqrt(-4)ans = 0 + 2.0000i abs(-2)ans = 2 imag(3+5i)ans = 5 real(3+5i)ans = 3 conj(3+5i)ans = 3.0000 - 5.0000i round(1.499)ans = 1 round(-1.499) %四舍五入ans = -1 fix(1.72) %朝0取整ans = 1 ceil(1.72) %朝无穷取整ans = 2 rem(10,3) %求余ans = 1 lcm(3,7) %最小公倍数ans = 21 gcd(4,8) %最大公约数ans = 4 length(1 2 0;3 4 5)ans = 3 size(1 2 0;3 4 5)ans = 2 3 find(1 2 0;0 1 4)ans = 1 3 4 6 eye(3,5)ans = 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 zeros(2)ans = 0 0 0 0 ones(4,3)ans = 1 1 1 1 1 1 1 1 1 1 1 1 ans = rand(3,2) %产生随机矩阵ans = 0.8147 0.9134 0.9058 0.6324 0.1270 0.0975 linspace(1,2,10) %1to2,10个点ans = 1.0000 1.1111 1.2222 1.3333 1.4444 1.5556 1.6667 1.7778 1.8889 2.0000 magic(3) %产生魔方矩阵ans = 8 1 6 3 5 7 4 9 2 det(magic(3) %求行列式ans = -360 a=1 2 3;4 5 6;7 8 9a = 1 2 3 4 5 6 7 8 9 diag(a) %提取主对角向量ans = 1 5 9 V,D=eig(a) %求特征值和特征向量V = -0.2320 -0.7858 0.4082 -0.5253 -0.0868 -0.8165 -0.8187 0.6123 0.4082D = 16.1168 0 0 0 -1.1168 0 0 0 -0.0000 rank(a) %求秩ans = 2 A=2 -1 3;1 2 1;2 4 3;L, U=lu(A) %三角分解 L = 1.0000 0 0 0.5000 0.5000 1.0000 1.0000 1.0000 0U = 2.0000 -1.0000 3.0000 0 5.0000 0 0 0 -0.5000 inv(a) %求逆矩阵Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.541976e-018. ans = 1.0e+016 * -0.4504 0.9007 -0.4504 0.9007 -1.8014 0.9007 -0.4504 0.9007 -0.4504 a=1:10;reshape(a,2,5)ans = 1 3 5 7 9 2 4 6 8 10 A=1 -34 -80 0 0 %(x-1)(x+34)(x+80)(x-0)(x-0)A = 1 -34 -80 0 0 PA=poly(A) %（求多项式展开式的系数向量）PA = 1 113 2606 -2720 0 0 poly2str(PA,x) %写成多项式形式，以x为变量ans = x5 + 113 x4 + 2606 x3 - 2720 x2 polyval(PA,1) %多项式代指计算ans = 0 polyder(PA) %多项式求导ans = 5 452 7818 -5440 0 p=conv(1 -4,conv(1 5,1 -6 9) px=poly2str(p,x)x=roots(p)p = 1 -5 -17 129 -180px = x4 - 5 x3 - 17 x2 + 129 x - 180x = -5.0000 4.0000 3.0000 3.0000 clearsum=0;for i=1:100 sum=sum+i;endsumsum = 5050 clearsum=0; i=0;while i clearsum=0;for i=1:5 pdr=1; for k=1:i pdr=pdr*k; end sum=sum+pdr;endsumsum = 153 clearchicken=1;while 1 If rem(100-chicken*2, 4)=0&(chicken+(100-chicken*2)/4)=36 break; end chicken=chicken+1;endchickenrabbit=(100-2*chicken)/4chicken = 22rabbit = 14 %由指令A=rand(3,5)生成二维数组A，试求该数组中所有大于0.5的元素的位置。（12分） A=rand(3,5)A = 0.2785 0.9649 0.9572 0.1419 0.7922 0.5469 0.1576 0.4854 0.4218 0.9595 0.9575 0.9706 0.8003 0.9157 0.6557 B=(A0.5) %水仙花数for m=100:999 m1=fix(m/100); m2=rem(fix(m/10),10); m3=rem(m,10); if m=m13+m23+m33 disp(m) endend 153 370 371 407 ch=ABc123d4e56Fg9;subch=ch(1:5) revch=ch(end:-1:1) k=find(ch=a&ch %m文件%阶乘function f=factor(n)if n%编写程序实现f(n)=f(n-1)+f(n-2)（f(1)=1和f(2)=2）函数function f=fab(n) if (n=1) f = 1; elseif (n=2) f =2; else f = fab(n-1) + fab(n-2); endEndprice=input(请输入商品价格);switch fix(price/100) case 0,1 %价格小于200 rate=0; case 2,3,4 %价格大于等于200但小于500 rate=3/100; case num2cell(5:9) %价格大于等于500但小于1000 rate=5/100; case num2cell(10:24) %价格大于等于1000但小于2500 rate=8/100; case num2cell(25:49) %价格大于等于2500但小于5000 rate=10/100; otherwise %价格大于等于5000 rate=14/100;endprice=price*(1-rate) %输出商品实际销售价格 %A 是一个維度mn的矩阵. 写一段程序, 算出A中有多少个零元素（10分）A=input(请输入一个矩阵)m,n= size(A);sig=0;for i=1:m for j=1:n if A(i,j)=0 sig = sig+1; end end sigend请输入一个矩阵4 5 0 2 1 0A = 4 5 0 2 1 0sig = 2%向量. 写一段程序, 找出A中的最小元素（10分）A= input (请输入一个向量)m,n=size(A)min =A(1,n);for i=1:n if A(1,i)%Fibonacci数组的元素满足Fibonacci 规则： ，；且。现要求该数组中第一个大于10000的元素。a(1)=1;a(2)=1;i=2;while a(i)用for循环指令来寻求Fibonacc数组中第一个大于10000的元素。n=100;a=ones(1,n);for i=3:n a(i)=a(i-1)+a(i-2); if a(i)=10000 a(i), break; end;end,i %学生的成绩管理，用来演示switch结构的应用。clear;for i=1:10;ai=89+i;bi=79+i;ci=69+i;di=59+i;end;c=d,c;Name= Jack,Marry,Peter, Rose, Tom;Mark=72,83,56,94,100;Rank=cell(1,5);S=struct(Name,Name,Marks,Mark,Rank,Rank);for i=1:5 switch S(i).Marks case 100 S(i).Rank=满分; case a S(i).Rank= 优秀; case b S(i).Rank= 良好; case c S(i).Rank= 及格; otherwise S(i).Rank=不及格; endenddisp(学生姓名 , 得分 , 等级);disp( )for i=1:5; disp(S(i).Name,blanks(6),num2str(S(i).Marks),blanks(6),S(i).Rank);end; 学生姓名 得分 等级 Jack 72 及格Marry 83 良好Peter 56 不及格 Rose 94 优秀 Tom 100 满分 %matlab 魔方矩阵的程序设计function M = magic(n)%MAGIC Magic square.% MAGIC(N) is an N-by-N matrix constructed from the integers% 1 through N2 with equal row, column, and diagonal sums.% Produces valid magic squares for all N 0 except N = 2. % Copyright 1984-2002 The MathWorks, Inc. % $Revision: 5.15 $ $Date: 2002/04/15 03:44:23 $ % Historically, MATLABs magic was a built-in function.% This M-file uses a new algorithm to generate the same matrices. n = floor(real(double(n(1); % Odd order.if mod(n,2) = 1 J,I = meshgrid(1:n); A = mod(I+J-(n+3)/2,n); B = mod(I+2*J-2,n); M = n*A + B + 1; % Doubly even order.elseif mod(n,4) = 0 J,I = meshgrid(1:n); K = fix(mod(I,4)/2) = fix(mod(J,4)/2); M = reshape(1:n*n,n,n); M(K) = n*n+1 - M(K); % Singly even order.else p = n/2; M = magic(p); M = M M+2*p2; M+3*p2 M+p2; if n = 2, return, end i = (1:p); k = (n-2)/4; j = 1:k (n-k+2):n; M(i; i+p,j) = M(i+p; i,j); i = k+1; j = 1 i; M(i; i+p,j) = M(i+p; i,j);end%产生一个1x10的随机矩阵，大小位于（-5 5），并且按照从大到小的顺序排列好！（注：要程序和运行结果的截屏）a=10*rand(1,10)-5;b=sort(a,descend)cleart=0:0.1:10;y1=sin(t);y2=cos(t);plot(t,y1,r,t,y2,b-);x=1.7*pi;1.6*pi;y=-0.3; 0.7;s=sin(t);cos(t);text(x, y, s);指定位置加标注title(正弦和余弦曲线);标题legend(正弦,余弦)%添加图例注解xlabel(时间)x坐标名ylabel(正弦&余弦)y坐标名grid on%添加网格axis square%将图形设置为正方形%plot3绘制的三维曲线图cleart=0:pi/50:10*pi;plot3(t,sin(t),cos(t),r:)grid onz=peaks(40);mesh(z);% 网格线 figure%产生新的图形窗口surf(z); %着色表面图%（1）极坐标绘制 0，2内 y=cost+sint的图形，要求用点线，颜色为红色，并加上横纵坐标的标识，在空白处加上函数的表达式，打开网格。（7分）（2）绘制矩阵A=1 2 3；0 2 7 的饼图，并让 3 和2 分离出来。并给图形加上标题。（7分）t=0:pi/10:2*pi; y=cos(t)+sin(t); plot(t,y,r:) grid on xlabel(independent variable T) ylabel(Dependent Variable Y) text(1.5,0.3, y=cos(t)+sin(t) x=1 2 3;0 2 7; explode=0 1 1; 0 0 0; pie(x,explode) title(矩阵A=1 2 3；0 2 7 的饼图)%在同一图上分别用红色实线和绿色虚线绘制y1=sin(x)和y2=cos(x)在区间0，4*pi的曲线，并用星号*标出两条曲线的交点以及建立图例。clfx=0:pi/200:2*pi;y1=sin(x);y2=cos(x);zz=x(find(abs(y1-y2)%分别在同一图形窗的不同子图绘制y=sin(t)sin(9t)和y=sin(t)sin(9t)及其包络线。t=(0:pi/100:pi);y1=sin(t)*1,-1;y2=sin(t).*sin(9*t);t3=pi*(0:9)/9;y3=sin(t3).*sin(9*t3);subplot(1,2,1)plot(t,y1,r:,t,y2,b,t3,y3,bo)subplot(1,2,2)plot(t,y2,b)axis(0,pi,-1,1)%设y=cos0.5+(3sinx)/(1+x2)把x=02间分为101点，画出以x为横坐标，y为纵坐标的曲线；x=linspace(0,2*pi,101);y=cos(0.5+3.*sin(x)./(1+x.*x);plot(x,y)%f(x)=x5-4x4+3x2-2x+6.取x=-2,8之间函数的值（取100个点），画出曲线，看它有几个零点。（提示：用polyval 函数）p=1 -4 3 -2 6;x=linspace(-2,8,100);y=polyval(p,x);plot(x,y);axis(-2,8, -200,2300);为了便于观察，在y=0处画直线，图如下所示：与y=0直线交点有两个，有两个实根。（2）用roots函数求此多项式的根 a=roots(p)a =3.0000 ,1.6956 , -0.3478 + 1.0289i , -0.3478 - 1.0289i在-10，10；-10，10范围内画出函数的三维图形。 X,Y=meshgrid(-10 : 0.5 :10);a=sqrt(X.2+Y.2) +eps;Z=sin(a)./a;mesh(X,Y,Z);将一个屏幕分4幅，选择合适的步长在右上幅与左下幅绘制出下列函数的图形。（10分）（曲线图）； （曲面图）。答： subplot(2,2,2)ezplot(cos(x)(1/2),-pi/2 pi/2) ylabel(y) subplot(2,2,3) x=-2:0.5:2; y=-4:1:4;ezsurfc(x2/22+y2/42)clear f1 = sym(1/(a-b) ); f2 = sym(2*a/(a+b) ); f3 = sym( (a+1)*(b-1)* (a-b) ); f1+f2%符号和ans =1/(a-b)+2*a/(a+b) f1*f3 %符号积ans = (a+1)*(b-1) f1/f3 %符号商ans = 1/(a-b)2/(a+1)/(b-1)clear f1 =sym(exp(x)+x)*(x+2); f2 = sym(a3-1); f3 = sym(1/a4+2/a3+3/a2+4/a+5); f4 = sym(sin(x)2+cos(x)2); collect(f1)ans = x2+(exp(x)+2)*x+2*exp(x)expand(f1)ans = exp(x)*x+2*exp(x)+x2+2*xfactor(f2)ans = (a-1)*(a2+a+1) m,n=numden(f3)%m为分子，n为分母m =1+2*a+3*a2+4*a3+5*a4n =