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1、师资培训暨教学研讨会师资培训暨教学研讨会5050MATLAB基础基础西安电子科技大学西安电子科技大学 杨威杨威2009.42009.4例例1 1 已知矩阵已知矩阵：，计算：计算：C=AC=AB B，D=AD=A（A AB B）解：在解：在MATLABMATLAB的的M M文件编辑器中建立文件编辑器中建立m01.mm01.m文件文件A=9,3,2;6,5,6;6,6,0B=3,3,6;3,4,8;5,8,6C=A+BD=A*(A-B)在在MATLABMATLAB的命令窗口中输入：的命令窗口中输入：m01m01 变量名是以字母开头，后接字母、数字或变量名是以字母开头，后接字母、数字或下划线的字符序
2、列下划线的字符序列七、七、MATLABMATLAB的变量的变量 变量名区分字母的大小写变量名区分字母的大小写 MATLABMATLAB提提供供的的标标准准函函数数名名以以及及命命令令名名一一般般用小写字母用小写字母 MATLAB MATLAB将所有变量均存成将所有变量均存成doubledouble形式，形式，不需经过变量声明不需经过变量声明pi pi 圆周率圆周率八、八、MATLABMATLAB的常量的常量i i，j j 虚数单位虚数单位inf inf 无穷大无穷大Nan Nan 表示不确定的数表示不确定的数例例2 2 计算计算 的值。的值。解：在解：在MATLABMATLAB命令窗口输入：命
3、令窗口输入：x=(1+cos(23*pi/180)/(4+sqrt(5)-6*i)x=(1+cos(23*pi/180)/(4+sqrt(5)-6*i)九、产生特殊矩阵的函数：九、产生特殊矩阵的函数：zeros zeros 创建零矩阵创建零矩阵 ones ones 创建全创建全1 1矩阵矩阵eye eye 创建单位矩阵创建单位矩阵randrand（randnrandn）创建随机矩阵创建随机矩阵round round 四舍五入运算四舍五入运算length(A)length(A)矩阵的长度矩阵的长度size(A)size(A)矩阵的尺寸矩阵的尺寸例例3 3 分别建立以下矩阵：分别建立以下矩阵：E
4、E：5 5阶单位矩阵；阶单位矩阵；A A：6363全全1 1矩阵；矩阵；O O：与矩阵：与矩阵A A同型的零矩阵；同型的零矩阵；B B：随机的：随机的5656整数矩阵整数矩阵解：在解：在MATLABMATLAB的的M M文件编辑器中建立文件编辑器中建立m03.mm03.m文件，文件，E=eye(5)A=ones(6,3)O=zeros(size(A)B=round(10*randn(5,6)在在MATLABMATLAB的命令窗口中输入：的命令窗口中输入：m03m03十、冒号表达式十、冒号表达式冒号表达式的一般格式：冒号表达式的一般格式：e1:e2:e3 e1:e2:e3函数函数linspace
5、(a,b,n)linspace(a,b,n)例例5 5 创建行向量创建行向量x x，在，在0 0到到2*pi2*pi间等间距取间等间距取100100个值个值解：在解：在MATLABMATLAB命令窗口输入：命令窗口输入：x=linspace(0,2*pi,100)x=linspace(0,2*pi,100)例例4 4 创建行向量创建行向量y=2,4,6,y=2,4,6,，100100解：在解：在MATLABMATLAB命令窗口输入：命令窗口输入：y=2:2:100y=2:2:100十一、基本数学函数十一、基本数学函数三角函数三角函数 sin,cos,tan,sin,cos,tan,指数函数指数
6、函数 exp,log,sqrt,exp,log,sqrt,复数运算复数运算 abs,angle,real,conj,abs,angle,real,conj,舍入函数舍入函数 round,fix,floor,mod,round,fix,floor,mod,离散函数离散函数 factor,gcd,lcm,primes,factor,gcd,lcm,primes,例例6 6 生成生成10001000内的质数表内的质数表解：在解：在MATLABMATLAB命令窗口输入：命令窗口输入：primes(1000)primes(1000)A(5,3)=68 A(5,3)=68 把矩阵把矩阵A A的第的第5 5
7、行第行第3 3列元素赋值列元素赋值6868十二、矩阵的拆分十二、矩阵的拆分A(:,3)=A(:,1)A(:,3)=A(:,1)把矩阵把矩阵A A的第的第1 1列赋值到第列赋值到第3 3列列A(i,:)=A(i,:)=删除矩阵删除矩阵A A的第的第i i行行A(1:3,:)=A(4:6,:)A(1:3,:)=A(4:6,:)把矩阵把矩阵A A的第的第4,5,64,5,6行赋值到第行赋值到第1,2,31,2,3行行解：解：m07.mA=round(10*rand(3)B=A;B(:,2)=A(:,3);B(:,3)=A(:,2)E=1,0,0;0,0,1;0,1,0A*E-B例例7 7 随机生成随
8、机生成3 3阶方阵阶方阵A A，交换，交换A A的第的第2 2列和第列和第3 3列，得列，得到矩阵到矩阵B B，演算，演算AE(2,3)AE(2,3)B B例例8 8 随机生成随机生成5 5阶方阵，构造其伴随矩阵阶方阵，构造其伴随矩阵解：解：m08.m%构造矩阵构造矩阵A的伴随矩阵的伴随矩阵A=round(10*randn(5);fori=1:5forj=1:5T=A;%把矩阵把矩阵A赋给矩阵赋给矩阵TT(i,:)=;%删去矩阵删去矩阵T的第的第i行行T(:,j)=;%删去矩阵删去矩阵T的第的第j列列%此时，此时，|T|为矩阵为矩阵A元素元素aij的余子式的余子式AA(j,i)=(-1)(i+
9、j)*det(T);%算出算出aij的代数余子式的代数余子式%并放入矩阵并放入矩阵AA的第的第j行、第行、第i列列%当循环结束，矩阵当循环结束，矩阵AA即为即为A的伴随矩阵的伴随矩阵endend 关系符号关系符号意义意义=小于小于小于等于小于等于大于大于大于等于大于等于等于等于不等于不等于十三、关系运算十三、关系运算 例例9 9 创建创建5 5阶随机方阵阶随机方阵A A，其元素为，其元素为0,100,10区间上区间上的随机整数。分析的随机整数。分析A A是否为奇异阵。重复是否为奇异阵。重复10001000次，次，统计出奇异阵的总数。统计出奇异阵的总数。解：解：m09.ms=0;fori=1:1
10、0000A=round(100*rand(5);if(det(A)=0)s=s+1;endends例例10 10 创建随机创建随机5 5阶矩阵阶矩阵A A，然后找出其最大值，及最，然后找出其最大值，及最大值所在位置。大值所在位置。解解:m10.m:m10.m文件文件A=round(10*randn(5)Amax=max(max(A)m,n=find(A=Amax)十四、输入和输出十四、输入和输出例例11 11 求一元二次方程求一元二次方程 ax ax2 2+bx+c=0+bx+c=0 的根。的根。解：解：m11.mm11.ma=input(a=?);a=input(a=?);b=input(b
11、=?);b=input(b=?);c=input(c=?);c=input(c=?);d=b*b-4*a*c;d=b*b-4*a*c;disp(disp(一元二次方程的根为：一元二次方程的根为：););x1=(-b+sqrt(d)/(2*a)x1=(-b+sqrt(d)/(2*a)x2=(-b-sqrt(d)/(2*a)x2=(-b-sqrt(d)/(2*a)十五、数值运算与基本作图十五、数值运算与基本作图例例12下表给出了平面坐标系中五个点的坐标。下表给出了平面坐标系中五个点的坐标。X01234Y-270210-75（1）请过这五个点作一个四次多项式函数）请过这五个点作一个四次多项式函数p4
12、(x)，并求并求p4(5)。（2）请根据这五个点，拟合一个二次多项式函数，）请根据这五个点，拟合一个二次多项式函数，并绘制多项式函数曲线及已知的五个点。并绘制多项式函数曲线及已知的五个点。解：解：m12.mm12.m%插值、拟合与绘图插值、拟合与绘图clearcloseallx=0;1;2;3;4;y=-27;0;21;0;-75;p=polyfit(x,y,4);xi=linspace(-1,9.5,100);yi=polyval(p,xi);x0=5;y0=polyval(p,x0);subplot(1,2,1);plot(xi,yi,x,y,o,x0,y0,*);axissquare;a
13、xis(-19-400100)gridon;p=polyfit(x,y,2)xi=linspace(-1,5,100);yi=polyval(p,xi);subplot(1,2,2);plot(xi,yi,x,y,o);axissquare;axis(-15-15050)gridon;例例13 13 求函数求函数y yx x3sin(x)3sin(x)在区间在区间0,200,20上的最小上的最小二乘二乘6 6次（次（1010次）多项式。次）多项式。解：解：m13.mm13.mx=linspace(0,20,100);y=x+3*sin(x);p=polyfit(x,y,6);yi=polyva
14、l(p,x);plot(x,y,k:,x,yi,r-);例例14 14 求下面求下面5 5次多项式函数的零点。次多项式函数的零点。p p5 5(x)=x(x)=x5 5-8x-8x4 4-48x-48x3 3+230 x+230 x2 2+575x-750+575x-750解：解：m14.mm14.mp=1,-8,-48,230,575,-750r=roots(p)x=linspace(-6,11,100);y=polyval(p,x);plot(x,y);gridon;例例15 15 用三维曲面图表现函数用三维曲面图表现函数z=sin(y)cos(x)。解：解：m15.mx,y=meshgr
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29、PgSjVnYq!t*w-A1D4G8JbMeQhTlWoZr%u(x+B2E5H9KcOfRiUmXp#s&v)z0C3F7IaLdPgSkVnYq$t*w-A1D5G8JbNeQhTlWo#r%u(y+B2E6H9LcOfRjUmXp!s&w)z0C4F7IaMdPgSkVnZq$t*x-A1D5G8KbNeQiTlWo#r%v(y+B3E6H9LcOgRjUmYp!s&w)z1C4F7JaMdPhSkWnZq$u*x-A2D5H8KbNfQiTlXo#s%v(y0B3E6I9LcOgRjVmYp!t&w)z1C4G7eQiTlWo#r%v(y+B3E6H9LcOgRjUmYp!s&w)z
30、1C4F7JaMdPhSkWnZq$u*x-A2D5G8KbNfQiTlXo#r%v(y0B3E6I9LcOgRjVmYp!t&w)z1C4G7JaMePhSkWnZr$u*x+A2D5H8KcNfQiUlXo#s%v)y0B3F6I9LdOgRjVmYq!t&w-z1C4G7JbMePhTkWnZr$u(x+A2E5H8KcNfRiUlXp#s%v)y0C3F6IaLdOgSjVnYq!t*w-z1D4G8JbMeQhTkWoZr%u(x+B2E5H9KcNfRiUmXp#s&v)y0C3F7IaLdPgSjVnYq$t*w-A1D4G8JbNeQhTlWoZr%u(y+B2E6H9KcOfRjUmXp!s&v)z0C4F7IaMdPgSkVnYq$t*x-A5H9KcNfRiUmXp#s&v)y0C3F7IaLdPgSjVnYq$t*w-A1D4G8JbNeQhTlWoZr%u(y+B2E6H9KcOfRjUmXp!s&v)z0C3F7IaMdPgSkVnYq$t*x-A1D5G8JbNeQiTlWo#r%u(y+B3E6H9LcOfRjUmYp!s&w)z0C4F7JaMdPhSkVnZq$u*x-A2D5G8KbNeQiTlXo#r%v(y+B3E6I9LcOgRjUmYp!结束语结束语谢谢大家聆听！谢谢大家聆听！32