Matlab实验一.docx

1、Matlab实验一电子信息工程学系实验报告 成 绩：课程名称：Matlab 指导教师（签名）：实验项目名称：数值运算实验 实验时间： 班级：测控102 姓名： 学号： 1 实验目的（1）学习MATLAB语言的基本矩阵运算（2）学习MATLAB语言的点运算（3）学习复杂运算2 实验内容在下面的实验操作中，认真记录每项操作的作用和目的。（1） 基本矩阵运算1） 创建数值矩阵a=1 2 3;4 5 6;7 8 9; 观察a a = 0 1 0 0 0 1 -6 -11 -6 a(3,2) ans = -11 a(:,1) ans = 0 0 -6 键入t=0:10;u=0:0.1:10; 观察矩阵变

2、量t、u的值。t t = 0 1 2 3 4 5 6 7 8 9 10 u u = Columns 1 through 9 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 Columns 10 through 18 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 Columns 19 through 27 1.8000 1.9000 2.0000 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 Columns 28

3、 through 36 2.7000 2.8000 2.9000 3.0000 3.1000 3.2000 3.3000 3.4000 3.5000 Columns 37 through 45 3.6000 3.7000 3.8000 3.9000 4.0000 4.1000 4.2000 4.3000 4.4000 Columns 46 through 54 4.5000 4.6000 4.7000 4.8000 4.9000 5.0000 5.1000 5.2000 5.3000 Columns 55 through 63 5.4000 5.5000 5.6000 5.7000 5.800

4、0 5.9000 6.0000 6.1000 6.2000 Columns 64 through 72 6.3000 6.4000 6.5000 6.6000 6.7000 6.8000 6.9000 7.0000 7.1000 Columns 73 through 81 7.2000 7.3000 7.4000 7.5000 7.6000 7.7000 7.8000 7.9000 8.0000 Columns 82 through 90 8.1000 8.2000 8.3000 8.4000 8.5000 8.6000 8.7000 8.8000 8.9000 Columns 91 thro

5、ugh 99 9.0000 9.1000 9.2000 9.3000 9.4000 9.5000 9.6000 9.7000 9.8000 Columns 100 through 101 9.9000 10.0000 键入a(:,3)=2;3;4;观察矩阵a的变化。a a = 0 1 0 0 0 1 -6 -11 -6 键入b=1 1+2i;3+4i 3; 观察复数矩阵。b b = 1.0000 1.0000 + 2.0000i 3.0000 + 4.0000i 3.0000 2） 创建特殊矩阵键入a=ones(3,3);b=zeros(2,2);c=eye(4);magic(4); 观察特殊

6、矩阵。a a = 0 1 0 0 0 1-6 -11 -6 b b = 1.0000 1.0000 + 2.0000i 3.0000 + 4.0000i 3.0000 c c = 1 1 0 0 1 1 magic(4) ans = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 3） 练习矩阵运算a=0 1 0;0 0 1;-6 -11 -6;b=1 2;3 4;5 6;c=1 1 0;0 1 1; 作矩阵乘运算v1=c*av2=a*bv3=c*a*bv4=b*cv5=c*b v1 = 0 1 1 -6 -11 -5v2 = 3 4 5 6 -69 -92v3

7、= 8 10 -64 -86v4 = 1 3 2 3 7 4 5 11 6v5 = 4 6 8 10 矩阵乘方运算a2ans = 0 0 1 -6 -11 -636 60 25a(1/2) ans = 0.0000 + 0.4894i -0.0000 - 0.5588i -0.0000 - 0.0482i 0.0000 + 0.2891i 0.0000 + 1.0195i -0.0000 - 0.2696i 0.0000 + 1.6179i 0.0000 + 3.2553i 0.0000 + 2.6374i 矩阵加减运算a1=a+b*ca2=c*b-a(1:2,1:2)a3=a(1:2,2:3

8、)+c*b a1 = 1 4 2 3 7 5 -1 0 0a2 = 4 5 8 10a3 = 5 6 8 11 矩阵右除ar=c/a ar = -0.8333 -1.0000 -0.1667 1.0000 1.0000 0 矩阵左除al=ab al = -5.6667 -8.6667 1.0000 2.0000 3.0000 4.0000 4） 练习矩阵特征运算完成以下特征运算inv(a) ans = -1.8333 -1.0000 -0.1667 1.0000 0 0 0 1.0000 0 tril(a) ans = 0 0 0 0 0 0 -6 -11 -6 rank(a) ans = 3

9、 （2） MATLAB语言的点运算1） 练习点乘与点除a1=1 2;3 4;a2=0.2*a1; 观察a1 a2 ans = 1.0000 2.0000 0.2000 0.4000 3.0000 4.0000 0.6000 0.8000 a1.*a2 a1./a2 ans = 0.2000 0.8000 5.0000 5.0000 1.8000 3.2000 5.0000 5.0000 (2) 由点运算完成标量函数运算与作图正余弦函数的点运算t=0:2*pi/180:2*pi; y1=sin(t);y2=cos(t); y=y1.*y2 y = Columns 1 through 9 0 0.

10、0349 0.0696 0.1040 0.1378 0.1710 0.2034 0.2347 0.2650 Columns 10 through 18 0.2939 0.3214 0.3473 0.3716 0.3940 0.4145 0.4330 0.4494 0.4636 Columns 19 through 27 0.4755 0.4851 0.4924 0.4973 0.4997 0.4997 0.4973 0.4924 0.4851 Columns 28 through 36 0.4755 0.4636 0.4494 0.4330 0.4145 0.3940 0.3716 0.347

11、3 0.3214 Columns 37 through 45 0.2939 0.2650 0.2347 0.2034 0.1710 0.1378 0.1040 0.0696 0.0349 Columns 46 through 54 0.0000 -0.0349 -0.0696 -0.1040 -0.1378 -0.1710 -0.2034 -0.2347 -0.2650 Columns 55 through 63 -0.2939 -0.3214 -0.3473 -0.3716 -0.3940 -0.4145 -0.4330 -0.4494 -0.4636 Columns 64 through

12、72 -0.4755 -0.4851 -0.4924 -0.4973 -0.4997 -0.4997 -0.4973 -0.4924 -0.4851 Columns 73 through 81 -0.4755 -0.4636 -0.4494 -0.4330 -0.4145 -0.3940 -0.3716 -0.3473 -0.3214 Columns 82 through 90 -0.2939 -0.2650 -0.2347 -0.2034 -0.1710 -0.1378 -0.1040 -0.0696 -0.0349 Columns 91 through 99 -0.0000 0.0349

13、0.0696 0.1040 0.1378 0.1710 0.2034 0.2347 0.2650 Columns 100 through 108 0.2939 0.3214 0.3473 0.3716 0.3940 0.4145 0.4330 0.4494 0.4636 Columns 109 through 117 0.4755 0.4851 0.4924 0.4973 0.4997 0.4997 0.4973 0.4924 0.4851 Columns 118 through 126 0.4755 0.4636 0.4494 0.4330 0.4145 0.3940 0.3716 0.34

14、73 0.3214 Columns 127 through 135 0.2939 0.2650 0.2347 0.2034 0.1710 0.1378 0.1040 0.0696 0.0349 Columns 136 through 144 0.0000 -0.0349 -0.0696 -0.1040 -0.1378 -0.1710 -0.2034 -0.2347 -0.2650 Columns 145 through 153 -0.2939 -0.3214 -0.3473 -0.3716 -0.3940 -0.4145 -0.4330 -0.4494 -0.4636 Columns 154

15、through 162 -0.4755 -0.4851 -0.4924 -0.4973 -0.4997 -0.4997 -0.4973 -0.4924 -0.4851 Columns 163 through 171 -0.4755 -0.4636 -0.4494 -0.4330 -0.4145 -0.3940 -0.3716 -0.3473 -0.3214 Columns 172 through 180 -0.2939 -0.2650 -0.2347 -0.2034 -0.1710 -0.1378 -0.1040 -0.0696 -0.0349 Column 181 -0.0000 plot(

16、t,y y y2) 复变函数的点运算。w=0.1:0.1:2;g1=(1+0.5*w*i)/(1-0.5*w*i); g1 g1 = 0.4719 + 0.7728i g2=(1+0.5*w*i)./(1-0.5*w*i); g2 g2 = Columns 1 through 4 0.9950 + 0.0998i 0.9802 + 0.1980i 0.9560 + 0.2934i 0.9231 + 0.3846i Columns 5 through 8 0.8824 + 0.4706i 0.8349 + 0.5505i 0.7817 + 0.6236i 0.7241 + 0.6897i Col

17、umns 9 through 12 0.6632 + 0.7484i 0.6000 + 0.8000i 0.5355 + 0.8445i 0.4706 + 0.8824i Columns 13 through 16 0.4060 + 0.9139i 0.3423 + 0.9396i 0.2800 + 0.9600i 0.2195 + 0.9756i Columns 17 through 20 0.1611 + 0.9869i 0.1050 + 0.9945i 0.0512 + 0.9987i 0 + 1.0000i plot(g2);xlabel(real g2(w);ylabel(inag

18、g2(w) axis(square) (3) 多项式运算1) 建立多项式向量ap=1 2 2 1;b=-1 -2 -3; bp=poly(b) bp = 1 6 11 6 2) 练习多项式乘与求根p=conv(ap,bp) p = 1 8 25 41 40 23 6 roots(p) ans = -3.0000 -2.0000 -0.5000 + 0.8660i -0.5000 - 0.8660i -1.0000 + 0.0000i -1.0000 - 0.0000i 3) 练习多项式运算a=1 2 3 4;b=1 -1;c=a+zeros(1,length(a)-length(b) b; poly2str(c,x) ans = x3 + 2 x2 + 4 x + 3 polyvalm(a,3) ans = 58 (4) 代数方程组1）恰定方程组a=1 2;2 3;b=8;13; 方法1：逆矩阵求解X=inv(a)*b X = 2 3 方法2：矩阵左除求解X=ab X = 2 3 实 验 心 得：