matlab实验报告二.docx

Matlab实验报告实验2 数值数组及运算一、 实验目的（1） 掌握一维数组、二维数组、多项式和高维数组的创建（2） 掌握对数组操作的常用函数二、 实验内容使用冒号运算符创建下面各表达式对应的向量。 x=logspace(1,3,3); x=10.1:3x = 10 100 1000 x=logspace(1,3,5)x = 1.0e+003 * 0.0100 0.0316 0.1000 0.3162 1.0000利用MATLAB内置函数计算下面的值 cosh(5)ans = 74.2099 sinh(-2)ans = -3.6269 (exp(5)+exp(-5)/2ans = 74.2099 help erf ERF Error function. Y = ERF(X) is the error function for each element of X. X must be real. The error function is defined as: erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(-t2) dt. Class support for input X: float: double, single See also erfc, erfcx, erfinv. Overloaded functions or methods (ones with the same name in other directories) help sym/erf.m Reference page in Help browser doc erf erf(1.2)ans = 0.9103利用linspace函数创建下面表达式的对应向量 x=0:10; x=linspace(0,10,11)x = 0 1 2 3 4 5 6 7 8 9 10 x=0:0.2:10; x=linspace(0,10,51)x = Columns 1 through 16 0 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 1.8000 2.0000 2.2000 2.4000 2.6000 2.8000 3.0000 Columns 17 through 32 3.2000 3.4000 3.6000 3.8000 4.0000 4.2000 4.4000 4.6000 4.8000 5.0000 5.2000 5.4000 5.6000 5.8000 6.0000 6.2000 Columns 33 through 48 6.4000 6.6000 6.8000 7.0000 7.2000 7.4000 7.6000 7.8000 8.0000 8.2000 8.4000 8.6000 8.8000 9.0000 9.2000 9.4000 Columns 49 through 51 9.6000 9.8000 10.0000 x=-12:12; x=linspace(-12,12,25)x = -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 x=10:-1:1; x=linspace(10,1,10)x = 10 9 8 7 6 5 4 3 2 1 x=10 9 8 7x = 10 9 8 7 x=10 9 8 7;y=1 2 3 4; z=x-y; zz = 9 7 5 3计算 A=1 2 3 3;2 3 5 7;1 3 5 7;3 2 3 9;1 8 9 4; B=1+4i 4 3 6 7;2 3 3 5 5;2 6+7i 5 3 4;1 8 9 4 3; C=A*B; CC = 1.0e+002 * 0.1400 + 0.0400i 0.5200 + 0.2100i 0.5100 0.3700 0.3800 0.2500 + 0.0800i 1.0300 + 0.3500i 1.0300 0.7000 0.7000 0.2400 + 0.0400i 0.9900 + 0.3500i 1.0000 0.6400 0.6300 0.2200 + 0.1200i 1.0800 + 0.2100i 1.1100 0.7300 0.7000 0.3900 + 0.0400i 1.1400 + 0.6300i 1.0800 0.8900 0.9500 D=C(4:5,3:5); DD = 111 73 70 108 89 95 A=1 2 3 3;2 3 5 7;1 3 5 7;3 2 3 9;1 8 9 4; A=1 2 3 3;2 3 5 7;1 3 5 7;3 2 3 9;1 8 9 4A = 1 2 3 3 2 3 5 7 1 3 5 7 3 2 3 9 1 8 9 4 A=4 12 20;12 45 78;20 78 136; B=1 2 3;4 5 6;7 8 0; I=1 0 0;0 1 0;0 0 1; A+5*Bans = 9 22 35 32 70 108 55 118 136 A-B+Ians = 4 10 17 8 41 72 13 70 137 A.*Bans = 4 24 60 48 225 468 140 624 0 A*Bans = 192 228 84 738 873 306 1284 1518 528 A.Bans = 1.0e+015 * 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 1.3701 0.0000 ABWarning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.328379e-018.ans = 1.0e+015 * 0.0000 -0.0000 3.6192 -0.0000 0.0000 -7.2384 0.0000 -0.0000 3.6192 A/Bans = 9.3333 -1.3333 0.0000 40.0000 -7.0000 0.0000 70.6667 -12.6667 0.0000 A(find(A50)&(A B(find(B5)ans = 7 8 6 A=1 2 NaN Inf -Inf 5 NaNA = 1 2 NaN Inf -Inf 5 NaN isnan(A)ans = 0 0 1 0 0 0 1 isfinite(A)ans = 1 1 0 0 0 1 0 isinf(A)ans = 0 0 0 1 1 0 0 any(A)ans = 1 all(A)ans = 1求出以下矩阵的逆矩阵 A=1 -5 -2;3 4 -9;-7 2 6A = 1 -5 -2 3 4 -9 -7 2 6 B=sin(1) sin(-5) sin(-2);sin(3) sin(4) sin(9); sin(-7) sin(2) sin(6)B = 0.8415 0.9589 -0.9093 0.1411 -0.7568 0.4121 -0.6570 0.9093 -0.2794 inv(A)ans = -0.1673 -0.1036 -0.2112 -0.1793 0.0319 -0.0120 -0.1355 -0.1315 -0.0757 inv(B)ans = 6.8645 23.4969 12.3171 9.7255 35.0011 19.9746 15.5090 58.6555 32.4631 A=1 2 3;4 5 6;7 8 9; B=flipud(A)B = 7 8 9 4 5 6 1 2 3 u=1 2 3; v=4 5 6; A=u;vA = 1 2 3 4 5 6用两行语句实现从C中引用列向量 C=11 5;5 1;18 7; s=C(:,1)s = 11 5 18 t=C(:,2)t = 5 1 7使用diag函数和冒号运算符创建下面矩阵 diag(1:1:4)ans = 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 diag(4:-1:1)ans = 4 0 0 0 0 3 0 0 0 0 2 0 0 0 0 1 diag(1:6:19)ans = 1 0 0 0 0 7 0 0 0 0 13 0 0 0 0 19使用diag函数创建nxn对称三对角阵 a=2 2 2 2; b=-1 -1 -1; D=diag(a)+diag(b,-1)+diag(b,1)D = 2 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2创建矩阵 e=eye(3); E=fliplr(e)E = 0 0 1 0 1 0 1 0 0 a=2*eye(5)-ones(5)a = 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 b=tril(a)b = 1 0 0 0 0 -1 1 0 0 0 -1 -1 1 0 0 -1 -1 -1 1 0 -1 -1 -1 -1 1 b(:,5)=1b = 1 0 0 0 1 -1 1 0 0 1 -1 -1 1 0 1 -1 -1 -1 1 1 -1 -1 -1 -1 1使用rehape函数和冒号运算符创建矩阵 reshape(2:2:24,3,4)ans = 2 8 14 20 4 10 16 22 6 12 18 24 reshape(-5:1:6,2,6)ans = -5 -3 -1 1 3 5 -4 -2 0 2 4 6（a）找出每个矩阵各列中绝对值最大的元素（b）找出每个矩阵各行中绝对值最大的元素 c=C(:,1)c = 11 2 1 max(real(c)ans = 11 d=C(:,2)d = -4 2 11 max(real(d)ans = 11 e=C(1,:)e = 11 -4 max(real(e)ans = 11 f=C(2,:)f = 2 2 max(real(f)ans = 2 c=D(:,1)c = 13 2 13 max(real(c)ans = 13 d=D(:,2)d = -6 2 23 max(real(d)ans = 23 e=D(1,:)e = 13 -6 max(real(e)ans = 13 f=D(2,:)f = 2 2 max(real(f)ans = 2 c=E(:,1)c = 4.5000 -3.0000 -0.7500 max(real(c)ans = 4.5000 d=E(:,2)d = 1.0000 1.0000 1.7500 max(real(d)ans = 1.7500 e=E(1,:)e = 4.5000 1.0000 max(real(e)ans = 4.5000 f=E(2,:)f = -3 1 max(real(f)ans = 1思考下面的程序 A=ones(3,2); B=2*ones(2,3); A*B; A(2,3)=2; A*B;? Error using = mtimesInner matrix dimensions must agree. A*B? Error using = mtimesInner matrix dimensions must agree. u=0:3; v=(3:-1:0); w=u.*v;? Error using = timesMatrix dimensions must agree. clear all A=ones(3,3); A(k,k)? Undefined function or variable k. A(i,i)? Subscript indices must either be real positive integers or logicals.定义多项式 a=1 -12 25 6; p=poly2sym(a) p = x3-12*x2+25*x+6 x(2)求下面矩阵的特征多项式 D=2 -1 0 0;-1 2 -1 0;0 -1 2 -1;0 0 -1 2; PA=