实验二 MATLAB语言基础

1、 实验二 MATLAB语言基础1、 实验目的基本掌握MATLAB向量、矩阵、数组的生成及其基本运算（区分数组运算和矩阵运算)、常用的数学函数。交接字符串的操作。2、 实验内容(1) 向量的生成和运算。(2) 矩阵的创建、引用和运算。(3) 多维数组的创建及运算。(4) 字符串的操作。三、实验步骤1.向量的生成和运算1) 向量的生成直接输入法：A = 2 3 4 5 6 B=1;2;3;4;5 B = 1 2 3 4 5 冒号生成发： A=1:2:10 ,B=1:10 ,C=10:-1:1 A = 1 3 5 7 9 B = 1 2 3 4 5 6 7 8 9 10 C = 10 9 8 7 6

2、 5 4 3 2 1 函数法：Linspace( )是线性等分函数，logspace( )是对数等分函数。 A=linspace(1,10) ,B=linspace(1,30,10)A = Columns 1 through 9 1.0000 1.0909 1.1818 1.2727 1.3636 1.4545 1.5455 1.6364 1.7273 Columns 10 through 18 1.8182 1.9091 2.0000 2.0909 2.1818 2.2727 2.3636 2.4545 2.5455 Columns 19 through 27 2.6364 2.7273 2

3、.8182 2.9091 3.0000 3.0909 3.1818 3.2727 3.3636 Columns 28 through 36 3.4545 3.5455 3.6364 3.7273 3.8182 3.9091 4.0000 4.0909 4.1818 Columns 37 through 45 4.2727 4.3636 4.4545 4.5455 4.6364 4.7273 4.8182 4.9091 5.0000 Columns 46 through 54 5.0909 5.1818 5.2727 5.3636 5.4545 5.5455 5.6364 5.7273 5.81

4、82 Columns 55 through 63 5.9091 6.0000 6.0909 6.1818 6.2727 6.3636 6.4545 6.5455 6.6364 Columns 64 through 72 6.7273 6.8182 6.9091 7.0000 7.0909 7.1818 7.2727 7.3636 7.4545 Columns 73 through 81 7.5455 7.6364 7.7273 7.8182 7.9091 8.0000 8.0909 8.1818 8.2727 Columns 82 through 90 8.3636 8.4545 8.5455

5、 8.6364 8.7273 8.8182 8.9091 9.0000 9.0909 Columns 91 through 99 9.1818 9.2727 9.3636 9.4545 9.5455 9.6364 9.7273 9.8182 9.9091 Column 100 10.0000 B = Columns 1 through 9 1.0000 4.2222 7.4444 10.6667 13.8889 17.1111 20.3333 23.5556 26.7778 Column 10 30.0000 A=logspace(0,4,5)A = 1 10 100 1000 10000练习

6、： 使用logspace( )创建1-4的有10个元素的行向量。答案： A=logspace(1,10,4*pi)A = 1.0e+010 * Columns 1 through 9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0035 Columns 10 through 12 0.0231 0.1520 1.00002) 向量的运算维数相同的行向量只见可以相加减，维数相同的列向量也可以相加减，标量可以与向量直接相乘除。 A=1 2 3 4 5, B=3:7, A = 1 2 3 4 5 B = 3 4 5 6 7 AT

7、=A, BT=B, AT = 1 2 3 4 5 BT = 3 4 5 6 7 E1=A+B, E2=A-B E1 = 4 6 8 10 12E2 = -2 -2 -2 -2 -2 F=AT-BT, F = -2 -2 -2 -2 -2 G1=3*A, G2=B/3, G1 = 3 6 9 12 15 G2 = 1.0000 1.3333 1.6667 2.0000 2.3333 向量的点积与叉积运算。 A=ones(1,10);B=(1:10); BT=B; E1=dot(A,B) E1 = 55 E2=A*BT E2 = 55 clear A=1:3,B=3:5, A = 1 2 3 B

8、= 3 4 5 E=cross(A,B) E =-2 4 -22. 矩阵的创建、引用和运算 1) 矩阵的创建和引用 矩阵是由元素构成的矩阵结构，行向量和列向量是矩阵的特殊形式。 直接输入法： A=1 2 3;4 5 6 A = 1 2 3 4 5 6 B= 1 4 7 2 5 8 3 6 9 B = 1 4 7 2 5 8 3 6 9 A(1)ans = 1 A(4:end)ans = 5 3 6 B(:,1)ans = 1 2 3 B(:)ans = 1 2 3 4 5 6 7 8 9 B(5)ans = 5抽取法 clear A=1 2 3 4;5 6 7 8;9 10 11 12;13

9、14 15 16A = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 B=A(1:3,2:3)B = 2 3 6 7 10 11 C=A(1 3,2 4)C = 2 4 10 12 A(1 3;2 4)ans = 1 9 5 13 函数法： A=ones(3,4)A = 1 1 1 1 1 1 1 1 1 1 1 1 B=zero(3)? Undefined function or method zero for input arguments of type double. B=zeros(3)B = 0 0 0 0 0 0 0 0 0 C=eyes(3,2)

10、? Undefined function or method eyes for input arguments of type double. C=eye(3,2)C = 1 0 0 1 0 0 D=magic(3)D = 8 1 6 3 5 7 4 9 2拼接法 clear A=ones(3,4)A = 1 1 1 1 1 1 1 1 1 1 1 1 B=zeros(3)B = 0 0 0 0 0 0 0 0 0 C=eye(4)C = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 D=A BD = 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0

11、 0 0 F=A;CF = 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1拼接函数和变形函数法： clear A=0 1;1 1A = 0 1 1 1 B=2*ones(2)B = 2 2 2 2 cat (1,A,B,A)ans = 0 1 1 1 2 2 2 2 0 1 1 1 cat (2 A,B,A)? cat (2 A,B,A)Error: Unexpected MATLAB expression. cat(2,A,B,A)ans = 0 1 2 2 0 1 1 1 2 2 1 1 repmat(A,2,2)ans =

12、0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 repmat(A,2)ans = 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1练习：使用函数法、拼接法、拼接函数法和变形函数法，按照要求创建以下矩阵：A为 的全1矩阵、B为的0矩阵/C为的单位矩阵、D为的魔方阵、E由C 和D纵向拼接而成，F抽取E的2-5行元素生成、G由经变形为的矩阵而得、 以为子矩阵用复制函数(repmat)生成的大矩阵H。答案： A=ones(3,4)A = 1 1 1 1 1 1 1 1 1 1 1 1 B=zeros(3,3)B = 0 0 0 0 0 0 0 0 0 C=eye(3)C

13、= 1 0 0 0 1 0 0 0 1 D=magic(3)D = 8 1 6 3 5 7 4 9 2 E=C;DE = 1 0 0 0 1 0 0 0 1 8 1 6 3 5 7 4 9 2 F=(2:5,:)? F=(2:5,:)Error: Expression or statement is incorrect-possibly unbalanced (, , or . F=E(2:5,:)F = 0 1 0 0 0 1 8 1 6 3 5 7 G=respace(E,3,4)? Undefined command/function respace. G=respace(F,3,4)?

14、 Undefined command/function respace. G=reshape(F,3,4)G = 0 3 1 1 0 1 5 6 8 0 0 7 H=repmat(G,2,2)H = 0 3 1 1 0 3 1 1 0 1 5 6 0 1 5 6 8 0 0 7 8 0 0 7 0 3 1 1 0 3 1 1 0 1 5 6 0 1 5 6 8 0 0 7 8 0 0 72) 矩阵的运算 矩阵的加减、数乘与乘法 已知矩阵： A=1 2 3 -1,A = 1 2 3 -1 B=-1 0 1 2B = -1 0 1 2 A+Bans = 0 2 4 1 2*Aans = 2 4 6

15、 -2 2*A-3*Bans = 5 4 3 -8 A*Bans = 1 4-4 -2 矩阵的逆矩阵 format rat;A=1 0 1;2 1 2;0 4 6A = 1 0 1 2 1 2 0 4 6 A1=inv(A)A1 = -1/3 2/3 -1/6 -2 1 0 4/3 -2/3 1/6 A*A1ans = 1 0 0 0 1 0 0 0 1 矩阵的除法 a=1 2 1;3 1 4;2 2 1,b=1 1 2,d=ba = 1 2 1 3 1 4 2 2 1 b = 1 1 2 d = 1 1 2 c1=b*inv(a),c2=b/ac1 = 6/7 3/7 -4/7 c2 = 6

16、/7 3/7 -4/7 c3=inv(a)*d, c4=abc3 = 1 2/7 -4/7 ? Error using = mldivideMatrix dimensions must agree. c3=inv(a)*d, c4=adc3 = 1 2/7 -4/7 c4 = 1 2/7 -4/7 练习： 按下列要求求出各种的矩阵运算的值 求矩阵的秩、特征值和特征向量、 矩阵的乘幂与开方； 矩阵的指数与对数 矩阵的提取与翻转答案： A=6 3 4 3 -2 5 7 -4 8 -1 -3 -7A = 6 3 4 3 -2 5 7 -4 8 -1 -3 -7 B=rank(A)B = 3 rb=r

17、ank(A)rb = 3 X,Lamda=eig(A)? Error using = eigMatrix must be square. X,Lamda=eigs(A)? Error using = eigsA must be a square matrix or a function which computes A*x. C=6 3 4 -2 5 7 8 -1 -3C = 6 3 4 -2 5 7 8 -1 -3 X,Lamda=eigs(C)X = 0.8013 -0.1094 -0.1606 0.3638 -0.6564 0.8669 0.4749 0.7464 -0.4719Lamd

18、a = 9.7326 0 0 0 -3.2928 0 0 0 1.5602 X,Lamda=eig(C)X = 0.8013 -0.1094 -0.1606 0.3638 -0.6564 0.8669 0.4749 0.7464 -0.4719Lamda = 9.7326 0 0 0 -3.2928 0 0 0 1.5602 X,Lamda=eig(C)X = 0.8013 -0.1094 -0.1606 0.3638 -0.6564 0.8669 0.4749 0.7464 -0.4719Lamda = 9.7326 0 0 0 -3.2928 0 0 0 1.5602 D=A2? Erro

19、r using = mpowerMatrix must be square. D=C2D = 62 29 33 34 12 6 26 22 34 E=sqrtm(C)E = 2.2447 + 0.2706i 0.6974 - 0.1400i 0.9422 - 0.3494i -0.5815 + 1.6244i 2.1005 - 0.8405i 1.7620 - 2.0970i 1.9719 - 1.8471i -0.3017 + 0.9557i 0.0236 + 2.3845i F=expm(C)F = 1.0e+004 * 1.0653 0.5415 0.6323 0.4830 0.2465

20、 0.2876 0.6316 0.3206 0.3745 G=logm(C)Warning: Principal matrix logarithm is not defined for A with nonpositive real eigenvalues. A non-principal matrix logarithm is returned. In funm at 153 In logm at 27G = 1.7129 + 0.4686i 0.5305 - 0.2425i 0.5429 - 0.6049i 1.1938 + 2.8123i 0.3658 - 1.4552i -0.5514

21、 - 3.6305i -0.0748 - 3.1978i 0.7419 + 1.6546i 1.8333 + 4.1282i H=fliplr(C)H = 4 3 6 7 5 -2 -3 -1 8 I=triu(C)I = 6 3 4 0 5 7 0 0 -3 J=tril(C)J = 6 0 0 -2 5 0 8 -1 -3 K=diag(C)K = 6 5-33. 多维数组的创建及运算1） 多维数组的创建 A1=1,2,3;4 5 6;7,8,9;A2=reshape(10:18,3,3)A2 = 10 13 16 11 14 17 12 15 18 T1(:,:,1)=ones(3);T

22、1(:,:,2)=zeros(3)T1(:,:,1) = 1 1 1 1 1 1 1 1 1T1(:,:,2) = 0 0 0 0 0 0 0 0 0 T2=ones(3,3,2)T2(:,:,1) = 1 1 1 1 1 1 1 1 1T2(:,:,2) = 1 1 1 1 1 1 1 1 1 T3=cat(3,A1,A2),T4=repmat(A1,1,1,2)T3(:,:,1) = 1 2 3 4 5 6 7 8 9T3(:,:,2) = 10 13 16 11 14 17 12 15 18T4(:,:,1) = 1 2 3 4 5 6 7 8 9T4(:,:,2) = 1 2 3 4 5 6 7 8 92） 多维数组的创建 数组运算用小圆点加在运算符的前面表示，以区分矩阵的运算。特点是两个数组相对应的元素进行运算。 A=1:6;B=ones(1,6); C1=A+B,C2=A-BC1 = 2 3 4 5 6 7C2 = 0 1 2 3 4 5 C3=A.*B,C4=B./A,C5=A.BC3 =