Matlab实验内容.docx
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Matlab实验内容.docx
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Matlab实验内容
Matlab实验内容
第1章
1.用help命令可以查询到自己的工作目录。
输入help命令:
help<函数名>
2.MATLAB的主要优点:
通过例1-1至例1-4的验证,MATLAB的优点是MATLAB以矩阵作为数据操作的基本单位,使得矩阵运算变得非常简捷,方便,高效。
还提供了丰富的数值计算函数。
MATLAB绘图十分方便,只需输入绘图命令,MATLAB便可自动绘出图形。
3.INV(X)istheinverseofthesquarematrixX。
AwarningmessageisprintedifXisbadlyscaledornearlysingular.PLOT(X,Y)plotsvectorYversusvectorX.IfXorYisamatrix,thenthevectorisplottedversustherowsorcolumnsofthematrix,whicheverlineup.IfXisascalarandYisavector,length(Y)disconnectedpointsareplotted.PLOT(Y)plotsthecolumnsofYversustheirindex.IfYiscomplex,PLOT(Y)isequivalenttoPLOT(real(Y),imag(Y)).InallotherusesofPLOT,theimaginarypartisignored.Forvectors,MAX(X)isthelargestelementinX.Formatrices,
MAX(X)isarowvectorcontainingthemaximumelementfromeachcolumn.ForN-Darrays,MAX(X)operatesalongthefirstnon-singletondimension.[Y,I]=MAX(X)returnstheindicesofthemaximumvaluesinvectorI.Ifthevaluesalongthefirstnon-singletondimensioncontainmorethanonemaximalelement,theindexofthefirstoneisreturned.ROUND(X)roundstheelementsofXtothenearestintegers.MAX(X,Y)returnsanarraythesamesizeasXandYwiththelargestelementstakenfromXorY.Eitheronecanbeascalar。
[Y,I]=MAX(X,[],DIM)operatesalongthedimensionDIM.Whencomplex,themagnitudeMAX(ABS(X))isused,andtheangleANGLE(X)isignored.NaN'sareignoredwhencomputingthemaximum.
4.sinx是以步长为∏/10,起始值为0,终止值为2∏的正弦函数。
5.MATLAB是一种用于数值计算、可视化及编程的高级语言和交互式环境。
使用MATLAB,可以分析数据,开发算法,创建模型和应用程序。
借助其语言、工具和内置数学函数,您可以探求多种方法,比电子表格或传统编程语言(如C/C++或Java™)更快地求取结果。
第2章
1.
(1)w=sqrt
(2)*(1+0.34245*10^(-6))
w=1.4142
(2)a=3.5;
b=5;
c=-9.8;
x=(2*pi*a+(b+c)/(pi+a*b*c)-exp
(2))/(tan(b+c)+a)
x=0.9829
(3)a=3.32;
b=-7.9;
y=2*pi*a^2*((1-pi/4)*b-(0.8333-pi/4)*a)
y=-128.4271
(4)t=[2,1-3i;5,-0.65];
z=0.5*exp(2*t)*log(t+sqrt(1+t*t))
z=
1.0e+004*
0.0048+0.0002i0.0048-0.0034i
1.58992.0090-1.3580i
2.
(1)A+6B=[47,23,-10;12,37,26;-15,73,7;]
A^2-B+I=[18,-216,18;23,533,110;22,868,526]
(2)A*B=[14,14,16;-10,51,21;125,328,180]
A.*B=[-8,15,4;0,35,24;-9,122,0]
B*A=[-11,0,-15;7,228,533,-1,28]
(3)A/B=[1.2234,-0.925,2.9787;-0.9468,2.3511,-0.9574;4.6170,3.8723,13.8936]
B\A=[-0.5106,-8.6170,-1.1277;0.7340,17.5745,1.8085;-0.8830,-21.2128,0.4043]
(4)[A,B]=[-1,5,-4,8,3,-1;0,7,8,2,5,3;3,61,7,-3,2,0]
[A([1,3],:
);B^2]=[-1,5,4;3,6,7;73,37,1;17,7,3;-20,1,9]
3.
(1)A=[2310-0.7780;41-45655;325032;6-9.54543.14]
A=
23.000010.0000-0.77800
41.0000-45.000065.00005.0000
32.00005.0000032.0000
6.0000-9.540054.00003.1400
B=A(1:
3,:
)
B=
23.000010.0000-0.77800
41.0000-45.000065.00005.0000
32.00005.0000032.0000
C=A(:
1:
2)
C=
23.000010.0000
41.0000-45.0000
32.00005.0000
6.0000-9.5400
D=A(2:
4,3:
4)
D=
65.00005.0000
032.0000
54.00003.1400
E=B*C
E=
1.0e+003*
0.9141-0.2239
1.20802.7123
1.1330-0.2103
(2)E ans= 01 00 01 E&D ans= 11 01 11 E|D ans= 11 11 11 ~D ans= 00 10 00 ~E ans= 00 00 00 4.H=hilb(5); P=pascal(5); Hh=det(H) Hh=3.7493e-012 Hp=det(P) Hp=1 Th=cond(H) Th=4.7661e+005 Tp=cond(P) Tp=8.5175e+003 条件数越趋近于1,矩阵的性能越好,所以帕斯卡矩阵性能更好。 5.A=[-29,6,18;20,5,12;-8,8,5] A= -29618 20512 -885 [V,D]=eig(A) V= 0.71300.28030.2733 -0.6084-0.78670.8725 0.34870.55010.4050 D= -25.316900 0-10.51820 0016.8351 V为A的特征向量,D为A的特征值。 它们之间满足A*V=V*D 第3章 1. n=input(‘请输入一个三位数: ’); a=fix(n/100); b=fix((n-a*100)/10); c=n-a*100-b*10; d=c*100+b*10+a 2. (1) n=input('请输入成绩'); switchn casenum2cell(90: 100) p='A'; casenum2cell(80: 89) p='B'; casenum2cell(70: 79) p='C'; casenum2cell(60: 69) p='D'; otherwise p='E'; end price=p (2)n=input('请输入成绩'); ifn>=90&n<=100 p='A'; elseifn>=80&n<=89 p='B'; elseifn>=70&n<=79 p='C'; elseifn>=60&n<=69 p='D'; else p='E'; end price=p (3)try n; catch price='error' end 3. (1)方法一: n=[1,5,56,4,3,476,45,6,3,76,45,6,4,3,6,4,23,76,908,6]; a=n (1); b=n (1); form=2: 20 ifn(m)>a a=n(m); elseifn(m) b=n(m); end end max=a min=b (2)方法二: n=[1,5,56,4,3,476,45,6,3,76,45,6,4,3,6,4,23,76,908,6]; min=min(n) max=max(n) 4. b=[-3.0: 0.1: 3.0]; forn=1: 61 a=b(n); y(n)=(exp(0.3*a)-exp(-0.3*a))/2*sin(a+0.3)+log((0.3+a)/2); end y 5. y1=0; y2=1; n=input('请输入n的值: '); fori=1: n y1=y1+1/i^2; y2=y2*((4*i*i)/((2*i-1)*(2*i+1))); end y1 y2 6. A=[1,1,1,1,1,1;2,2,2,2,2,2;3,3,3,3,3,3;4,4,4,4,4,4;5,5,5,5,5,5;6,6,6,6,6,6]; n=input('请输入n的值: '); ifn<=5&n>=0 disp(A([n],: )); elseifn<0 disp(lasterr); elsedisp(A([6],: )); disp(lasterr); end 7. (1) f=[]; forn=1: 40 f(n)=n+10*log(n^2+5); end y=f(40)/(f(30)+f(20)) (2) f=[];a=0; forn=1: 40 f(n)=a+n*(n+1); a=f(n); end y=f(40)/(f(30)+f(20)) 8. y=0; m=input('输入m的值: '); n=input('输入n值: '); fori=1: n y=y+i^m; end y **************************************************** functions=shi8_1(n,m) s=0; fori=1: n s=s+i^m; end **************************************************** shi8_1(100,1)+shi8_1(50,2)+shi8_1(10,1/2) 第4章 1. (1) x=-10: 0.05: 10; y=x-x.^3./6; plot(x,y) (2) x=-10: 0.5: 10; ezplot('x^2+2*y^2-64',[-8,8]); gridon; 2. t=-pi: pi/10: pi; y=1./(1+exp(-t)); subplot(2,2,1);bar(t,y); title('条形图(t,y)'); axis([-pi,pi,0,1]); subplot(2,2,2); stairs(t,y,'b'); title('阶梯图(t,y)'); axis([-pi,pi,0,1]); subplot(2,2,3); stem(t,y,'k'); title('杆图(t,y)'); axis([-pi,pi,0,1]); subplot(2,2,4); loglog(t,y,'y'); title('对数坐标图(t,y)'); 3. (1) t=0: pi/50: 2*pi; r=5.*cos(t)+4; polar(t,r); title('\rho=5*cos\theta+4'); (2) t=-pi/3: pi/50: pi/3; r=5.*((sin(t)).^2)./cos(t); polar(t,r); 4. (1) t=0: pi/50: 2*pi; x=exp(-t./20).*cos(t); y=exp(-t./20).*sin(t); z=t; plot3(x,y,z); gridon; (2) [x,y]=meshgrid(-5: 5); z=zeros(11)+5; mesh(x,y,z); shadinginterp; 5 [x,y,z]=sphere(20); surf(x,y,z); axisoff; shadinginterp; m=moviein(20); fori=1: 20 axis([-i,i,-i,i,-i,i]) m(: i)=getframe; end movie(m,4); 第5章 1. A=randn(10,5) x=mean(A) y=std(A) Max=max(max(A)) Min=min(min(A)) Sumhang=sum(A,2) SumA=sum(Sumhang) B=sort(A); C=sort(B,2,'descend'); C 2. (1) a=0: 15: 90; b=a./180.*pi; s=sin(b) c=0: 15: 75; d=c./180.*pi; t=tan(d) e=input('请输入想计算的值: '); S=sin(e/180*pi) T=tan(e/180*pi) S1=interp1(a,s,e,'spline') T1=interp1(c,t,e,'spline') P1=polyfit(a,s,5); P2=polyfit(c,t,5); S2=polyval(P1,e) T2=polyval(P2,e) (2) n=[1,9,16,25,36,49,64,81,100]; N=sqrt(n); x=input('jisuanzhi: '); interp1(n,N,x,'cubic') 3. N=64; T=5; t=linspace(0,T,N); h=exp(-t); dt=t (2)-t (1); f=1/dt; X=fft(t); F=X(1: N/2+1); f=f*(0: N/2)/N; plot(f,abs(F),'-*') 4. P=[2,-3,0,5,13]; Q=[1,5,8]; p=polyder(P) q=polyder(P,Q) [a,b]=polyder(P,Q) 5. P1=[1,2,4,0,5]; P2=[0,1,2]; P3=[1,2,3]; P=P1+conv(P2,P3) X=roots(P) A=[-1,1.2,-1.4;0.75,2,3.5;0,5,2.5]; p=polyval(P,A) 第6章 1. (1) A=[1/2,1/3,1/4;1/3,1/4,1/5;1/4,1/5,1/6]; B=[0.95,0.67,0.52]'; X=A\B X= 1.2000 0.6000 0.6000 (2) C=[0.95,0.67,0.53]'; X=A\C X= 3.0000 -6.6000 6.6000 b3变大后,X1,X3明显增大,X2符号改变了,且绝对值仍然等于X3的绝对值。 (3) cond(A) ans= 1.3533e+003 2. (1)(M文件) functionfx=funx(x) fx=x^41+x^3+1; x=fzero('funx',-1) x= -0.9525 (2)(M文件) functionfx=funx2(x) fx=x-sin(x)/x; x2=fzero('funx2',0.5) x2= 0.8767 (3)functionq=fun3(p) x=p (1); y=p (2); z=p(3); q (1)=sin(x)+y^2+log(z)-7; q (2)=3*x+2^y-z^3+1; q(3)=x+y+z-5; options=optimset('Display','off'); x=fsolve(@fun3,[1,1,1]',options) x= 0.5991 2.3959 2.0050 q=fun3(x) q= 1.0e-010* 0.22130.38040.0009 3. (1)functionyp=fun4(t,y) yp=-(1.2+sin(10*t))*y; t0=0; tf=5; y0=1; [t,y]=ode23(@fun4,[t0,tf],y0); tf=5; y0=1; [t,y]=ode23(@fun4,[t0,tf],y0); t' ans= Columns1through9 00.06670.13750.20030.26950.35280.43620.50330.5663 Columns10through18 0.63690.69130.74570.80810.87380.95911.02771.09631.1600 Columns19through27 1.22461.30821.37141.43471.50011.58421.65301.72191.7858 Columns28through36 1.85011.93191.99532.05872.12362.20532.27452.34382.4080 Columns37through45 2.47192.55012.61402.67792.74192.81932.90462.96853.0323 Columns46through54 3.09593.17213.23643.30073.36423.43953.53283.59653.6602 Columns55through63 3.72383.79983.86423.92863.99204.06714.14084.21444.2800 Columns64through72 4.34324.41594.48124.54654.60944.68124.75674.83224.8990 Columns73through74 4.96205.0000 y' ans= Columns1through9 1.00000.90350.78220.68230.59840.54020.51820.51060.4976 Columns10through18 0.46560.42800.38440.33550.29360.25950.24690.24210.2382 Columns19through27 0.22900.20540.18190.15850.13870.12250.11640.11400.1122 Columns28through36 0.10800.09740.08640.07530.06580.05810.05490.05370.0529 Columns37through45 0.05110.04660.04150.03610.03160.02780.02580.02530.0249 Columns46through54 0.02410.02210.01970.01720.01500.01320.01220.01190.0117 Columns55through63 0.01140.01040.00930.00810.00710.00620.00580.00560.0055 Columns64through72 0.00540.00500.00450.00390.00340.00300.00270.00260.0026 Columns73through74 0.00250.0025 (2) functionyp=funb(t,y) yp=cos(t)-y/(1+t^2); t0=0; tf=5; y0=1;[t,y]=ode23('funb',[t0,tf],y0); t' ans= Columns1through9 00.50000.80161.10331.40771.75372.23012.52152.8129 Columns10through18 2.97273.13263.30013.50913.75494.03754.36374.75845.0000 y' ans= Columns1through9 1.00001.01461.03631.04501.01620.91570.64510.41220.1437 Columns10through18 -0.0122-0.1699-0.3330-0.5273-0.7327-0.9233-1.0649-1.1040-1.0534 4. functionfx=mymin(x)
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