Matlab实验一.docx
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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=[123;456;789];
观察
a
a=
010
001
-6-11-6
a(3,2)
ans=
-11
a(:
1)
ans=
0
0
-6
键入
t=0:
10;
u=0:
0.1:
10;
观察矩阵变量t、u的值。
t
t=
012345678910
u
u=
Columns1through9
00.10000.20000.30000.40000.50000.60000.70000.8000
Columns10through18
0.90001.00001.10001.20001.30001.40001.50001.60001.7000
Columns19through27
1.80001.90002.00002.10002.20002.30002.40002.50002.6000
Columns28through36
2.70002.80002.90003.00003.10003.20003.30003.40003.5000
Columns37through45
3.60003.70003.80003.90004.00004.10004.20004.30004.4000
Columns46through54
4.50004.60004.70004.80004.90005.00005.10005.20005.3000
Columns55through63
5.40005.50005.60005.70005.80005.90006.00006.10006.2000
Columns64through72
6.30006.40006.50006.60006.70006.80006.90007.00007.1000
Columns73through81
7.20007.30007.40007.50007.60007.70007.80007.90008.0000
Columns82through90
8.10008.20008.30008.40008.50008.60008.70008.80008.9000
Columns91through99
9.00009.10009.20009.30009.40009.50009.60009.70009.8000
Columns100through101
9.900010.0000
键入
a(:
3)=[2;3;4];
观察矩阵a的变化。
a
a=
010
001
-6-11-6
键入
b=[11+2i;3+4i3];
观察复数矩阵。
b
b=
1.00001.0000+2.0000i
3.0000+4.0000i3.0000
2)创建特殊矩阵
键入
a=ones(3,3);
b=zeros(2,2);
c=eye(4);
magic(4);
观察特殊矩阵。
a
a=
010
001
-6-11-6
b
b=
1.00001.0000+2.0000i
3.0000+4.0000i3.0000
c
c=
110
011
magic(4)
ans=
162313
511108
97612
414151
3)练习矩阵运算
a=[010;001;-6-11-6];
b=[12;34;56];
c=[110;011];
作矩阵乘运算
v1=c*a
v2=a*b
v3=c*a*b
v4=b*c
v5=c*b
v1=
011
-6-11-5
v2=
34
56
-69-92
v3=
810
-64-86
v4=
132
374
5116
v5=
46
810
矩阵乘方运算
a^2
ans=
001
-6-11-6
366025
a^(1/2)
ans=
0.0000+0.4894i-0.0000-0.5588i-0.0000-0.0482i
0.0000+0.2891i0.0000+1.0195i-0.0000-0.2696i
0.0000+1.6179i0.0000+3.2553i0.0000+2.6374i
矩阵加减运算
a1=a+b*c
a2=c*b-a(1:
2,1:
2)
a3=a(1:
2,2:
3)+c*b
a1=
142
375
-100
a2=
45
810
a3=
56
811
矩阵右除
ar=c/a
ar=
-0.8333-1.0000-0.1667
1.00001.00000
矩阵左除
al=a\b
al=
-5.6667-8.6667
1.00002.0000
3.00004.0000
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
1.000000
01.00000
tril(a)
ans=
000
000
-6-11-6
rank(a)
ans=
3
(2)MATLAB语言的点运算
1)练习点乘与点除
a1=[12;34];
a2=0.2*a1;
观察
[a1a2]
ans=
1.00002.00000.20000.4000
3.00004.00000.60000.8000
[a1.*a2a1./a2]
ans=
0.20000.80005.00005.0000
1.80003.20005.00005.0000
(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=
Columns1through9
00.03490.06960.10400.13780.17100.20340.23470.2650
Columns10through18
0.29390.32140.34730.37160.39400.41450.43300.44940.4636
Columns19through27
0.47550.48510.49240.49730.49970.49970.49730.49240.4851
Columns28through36
0.47550.46360.44940.43300.41450.39400.37160.34730.3214
Columns37through45
0.29390.26500.23470.20340.17100.13780.10400.06960.0349
Columns46through54
0.0000-0.0349-0.0696-0.1040-0.1378-0.1710-0.2034-0.2347-0.2650
Columns55through63
-0.2939-0.3214-0.3473-0.3716-0.3940-0.4145-0.4330-0.4494-0.4636
Columns64through72
-0.4755-0.4851-0.4924-0.4973-0.4997-0.4997-0.4973-0.4924-0.4851
Columns73through81
-0.4755-0.4636-0.4494-0.4330-0.4145-0.3940-0.3716-0.3473-0.3214
Columns82through90
-0.2939-0.2650-0.2347-0.2034-0.1710-0.1378-0.1040-0.0696-0.0349
Columns91through99
-0.00000.03490.06960.10400.13780.17100.20340.23470.2650
Columns100through108
0.29390.32140.34730.37160.39400.41450.43300.44940.4636
Columns109through117
0.47550.48510.49240.49730.49970.49970.49730.49240.4851
Columns118through126
0.47550.46360.44940.43300.41450.39400.37160.34730.3214
Columns127through135
0.29390.26500.23470.20340.17100.13780.10400.06960.0349
Columns136through144
0.0000-0.0349-0.0696-0.1040-0.1378-0.1710-0.2034-0.2347-0.2650
Columns145through153
-0.2939-0.3214-0.3473-0.3716-0.3940-0.4145-0.4330-0.4494-0.4636
Columns154through162
-0.4755-0.4851-0.4924-0.4973-0.4997-0.4997-0.4973-0.4924-0.4851
Columns163through171
-0.4755-0.4636-0.4494-0.4330-0.4145-0.3940-0.3716-0.3473-0.3214
Columns172through180
-0.2939-0.2650-0.2347-0.2034-0.1710-0.1378-0.1040-0.0696-0.0349
Column181
-0.0000
plot(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=
Columns1through4
0.9950+0.0998i0.9802+0.1980i0.9560+0.2934i0.9231+0.3846i
Columns5through8
0.8824+0.4706i0.8349+0.5505i0.7817+0.6236i0.7241+0.6897i
Columns9through12
0.6632+0.7484i0.6000+0.8000i0.5355+0.8445i0.4706+0.8824i
Columns13through16
0.4060+0.9139i0.3423+0.9396i0.2800+0.9600i0.2195+0.9756i
Columns17through20
0.1611+0.9869i0.1050+0.9945i0.0512+0.9987i0+1.0000i
plot(g2);xlabel('realg2(w)');ylabel('inagg2(w)')
axis('square')
(3)多项式运算
1)建立多项式向量
ap=[1221];
b=[-1-2-3];
bp=poly(b)
bp=
16116
2)练习多项式乘与求根
p=conv(ap,bp)
p=
18254140236
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=[1234];
b=[1-1];
c=a+[zeros(1,length(a)-length(b))b];
poly2str(c,'x')
ans=
x^3+2x^2+4x+3
polyvalm(a,3)
ans=
58
(4)代数方程组
1)恰定方程组
a=[12;23];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=a\b
X=
2
3
实验心得: