MATLAB作业

第一次作业

1.shortProblems

%标量变量生成

a=10

b=2.5*(10^23)

c=2+3*i

d=exp(j*2*pi/3)

%向量生成

aVec=[3.14 15 9 26]

bVec=[2.71 8 28 182]'

cVec=5:-0.2:-5

dVec=logspace(0,1,101)

eVec='Hello'

%矩阵变量

aMat=2*ones(9,9)

B=[1 2 3 4 5 4 3 2 1];

bMat=diag(B)

C=[1:100];

cMat=reshape(C,10,10)

dMat=NaN*ones(3,3)

E=[13 -22 -1 10 5 -87];

eMat=reshape(E,2,3)

F=-3+fix(3*rand(1,15));

fMat=reshape(F,5,3)

%标量方程

x=1/(1+exp(-(a-15)/6))

y=(sqrt(a)+b^(1/21))^pi

z=log(real((c+d)*(c-d))*sin(a*pi/3))/(c*conj(c))

%向量方程计算

xVec=1/(2.*pi.*(2.5.^2))*exp((-cVec.^2)./(2.*(2.5.^2))) yVec=sqrt((aVec'.^2)+bVec.^2)

zVec=log10(1./dVec)

%矩阵运算

xMat=(aV ec*bVec)*(aMat^2)

yMat=bVec*aVec

zMat=det(cMat)*((aMat*bMat)')

%一般运算及元素索引

cSum=sum(cMat)

eMean=mean(eMat,2)

eMat(1,:)=[1 1 1]

cSub=cMat(2:9,2:9)

lin=1:20;

lin(2:2:end)=-lin(2:2:end)

r=rand(1,5)

r(find(r<0.5))=0

2.twoLinePlot

figure;

t=0:pi/100:2*pi;

plot(t,sin(t));

hold on;

plot(t,cos(t),'r:');

xlabel('Time(s)');

ylabel('Function value');

title('Sin and Cos');

legend('sin','cos','location','NorthEast'); xlim([0 2*pi]);

ylim([-1.4 1.4]);

3.calculateGrades

R=xlsread('testdata.xls');

ans=R(1:5,:)

grades=R(:,2:end);

ans=mean(grades)

meanGrades=nanmean(grades)

meanMatrix=repmat(meanGrades,size(grades,1),1) curvedGrades=3.5*(grades./meanMatrix);

ans=nanmean(curvedGrades)

curvedGrades(find(curvedGrades>5))=5;

totalGrade=(ceil(nanmean(curvedGrades')))'

letters='FDCBA';

for k=1:length(totalGrades)

switch totalGrades(k)

case 1

Grades(k)=letters(1);

case 2

Grades(k)=letters(2);

case 3

Grades(k)=letters(3);

case 4

Grades(k)=letters(4);

case 5

Grades(k)=letters(5);

end

end

disp(['Grades:',letterGrades]);

4.encrypt

original='This is my top secret message!';

encodeouter=randperm(length(original));

encoded=original(encodeouter);

temp=[encodeouter;1:length(original)]';

temp=sortrows(temp)

decodeouter=temp(:,2);

decoded=encoded(decodeouter);

disp(['Original: ' original]);

disp(['Encoded : ' encoded]);

disp(['Decoded : ' decoded]);

correct=strcmp(original,decoded);

disp(['Decoded correctly (1 true;0 false): ' num2str(correct)]);

5.throwBall

clear all;

h=1.5;

g=9.8;

v=4;

a=45;

t=linspace(0,1,1000);

x_t=v*cos(a*pi/180)*t;

plot(t,x_t,'r');

hold on;

t=linspace(0,1,1000);

y_t=h+v*sin(a*pi/180)*t-1/2*g*t.^2;

plot(t,y_t);

t0=min(find(y_t<=0));

x0=x_t(t0);

disp(x0);

xlabel('时间轴');

ylabel('函数');

title('抛球模型');

legend('x(t)','y(t)');

disp(['小球在',num2str(x0),'处撞到地面']);

hold on;

plot([0 max(x_t)],[0 0],'k--');

第二次作业

1.semilog plot：

x=1:5;

y=[15 25 55 115 144];

h=semilogy(x,y,'--rs','MarkerFaceColor','g','MarkerEdgeColor','k','LineWidth',2); xlabel('years');

ylabel('number of students');

title('growth trend');

xlim([0 6]);

2.bar graph：

y=rand(5,1);

bar(y,'r');

x=0:0.1:1;

title('Bar graph of 5 random values');

3.插入和面绘制：

z0=rand(5);

[x0,y0]=meshgrid(1:5,1:5);

[x1,y1]=meshgrid(1:0.1:5,1:0.1:5);

z1=interp2(x0,y0,z0,x1,y1);

surf(z1);

colormap(hsv);

shading interp;

hold on;

contour(z1);

% caxis([0 1]);

colorbar;

4.使用find：

function ind=findNearest(x,desiredVal)

[m,n]=size(x);

A=abs(x-desiredVal);

min_a=min(A);

B=reshape(A,m,n);

[ind]=find(B==min_a)

x=input('input x:')

desiredVal=input('input desiredVal:')

ind=findNearest(x,desiredVal);

5.循环和流程控制

function loopTest(n)

for n=1:n

if (mod(n,2)==0)&(mod(n,3)==0)

disp([num2str(n),'is divisible by 2 AND 3']) elseif mod(n,2)==0

disp([num2str(n),'is divisible by 2'])

elseif mod(n,3)==0

disp([num2str(n),'is divisible by 3'])

else

disp([num2str(n),'is NOT divisible by 2 AND 3']) end

end

N=input('input n:');

loopTest(n);

6.平滑器：

function smoothed=rectFilt(x,width)

if rem(width,2)==0;

width=width+1;

disp('width must be odd!');

end

for n=1:length(x);

if n<(width+1)/2;

smoothed(n)=mean(x(n:2*n-1));

elseif n>length(x)-(width-1)/2;

smoothed(n)=mean(x(n-4:n));

else

smoothed(n)=mean(x(n-(width-1)/2:n+(width-1)/2));

end

end

x=xlsread('noisyData.xls');

width=11;

smoothed=rectFilt(x,width);

plot(x,'b--','Linewidth',2.5);

hold on;

plot(smoothed,'r-','Linewidth',2.5);

xlabel('lndex');

ylabel('Data value');

title('Smoothing Demonstration');

legend('Original Data','Smoothed');

7.绘制圆的函数

color=['b','k','g','y','r'];

r=[1,4,7,10,13];

center=[0,0];

for i=1:5

[x,y]=getCircle(center,r(i));

plot(x,y,color(i),'Linewidth',5);

hold on

end

axis([-16 16 -13 13]);

function[x,y]=getCircle(center,r)

t=linspace(-2*pi,2*pi,5000);

x=cos(t).*r+center(1);

y=sin(t).*r+center(2);

color=['b','k','g','y','r'];

center=[-1 0;0 0;1 0;-0.5 -0.5;0.5 -0.5]; for i=1:5

[x,y]=getCircle(center(i,:),0.5);

plot(x,y,color(i),'Linewidth',5);

hold on

end

set(gca,'xtick',[-1.5:0.5:1.5]);

set(gca,'ytick',[-1.4:0.2:1.0]);

axis([-1.5 1.5 -1.4 1.0]);

第三次作业

1.线性方程求解：

A=[3,6,4;1,5,0;0,7,7];

B=[1;2;3];

X=A\B

2.数值积分：

x=0:0.001:5;

y=exp(-x./3).*x;

trapz(x,y)

3.矩阵求逆：

A=[1,2;3,4];

B=inv(A);

C=A*B

4.多项式拟合：

x=xlsread('randomDatax.xls');

y=xlsread('randomDatay.xls');

plot(x,y,'.k');

hold on;

a='bgrym';

for n=1:5

x1=x;

y1=y;

[p,S,mu]=polyfit(x1,y1,n);

[y1,delta]=polyval(p,x1,S,mu);

plot(x1,y1,a(n),'linewidth',2);

hold on;

end

xlabel('x');

ylabel('y');

title('Plynomial fits to random data');

legend('Original','Order 1','Order 2','Order 3','Order 4','Order 5',4);

5.神经脉冲传导过程Hodgkin-Huxley方程仿真

function dy=HHODEfun(t,y)

%n,m,h,v

C=1;

Gk=36;

Gna=120;

Gl=0.3;

Ek=-72;

Ena=55;

El=-49.4;

an=alphan(y(4));

bn=betan(y(4));

am=alpham(y(4));

bm=betam(y(4));

ah=alphah(y(4));

bh=betah(y(4));

dy=zeros(4,1);

dy(1)=(1-y(1))*an-y(1)*bn;

dy(2)=(1-y(2))*am-y(2)*bm;

dy(3)=(1-y(3))*ah-y(3)*bh;

dy(4)=-1/C*(Gk*y(1)^4*(y(4)-Ek)+Gna*y(2)^3*y(3)*(y(4)-Ena)+Gl*(y(4)-El));

for i=1:10

[t,x]=ode45(@HHODEfun,0:0.001:20,[x(end,1) x(end,2) x(end,3) x(end,4)+i]);

if max(x(:,4))>0

plot(t,x(:,4),'r','lineWidth',2);

else

plot(t,x(:,4),'k','lineWidth',2);

end

hold on;

end

xlabel('Time(ms)');

ylabel('Transmembrane Voltage (mV)');

title('Threshold Behavior');

[t,x]=ode45(@HHODEfun,0:0.001:20,[0.5 0.5 0.5 -60]); plot(t,x(:,4))

xlabel('Time(ms)');

ylabel('Transmembrane Voltage (mV)');

title('Approaching Steady State');

%%

6.Julia分形集：

function julia(zMax,c,k,v)

d=linspace(-zMax,zMax,v);

A=ones(v,1)*d+i*(ones(v,1)*d)';

B=zeros(v,v);

for n=1:k

B=B+(abs(A)<=2);

A=A.*A+ones(v,v).*c;

end

imagesc(0.1*atan(B))

hold off;

axis xy;

第四次作业

1.随机变量生成：

R=2+sqrt(5)*randn(1,500)

mean(R)

std(R)

2.硬币投掷试验：

r=rand(10000,1);

r=round(r);

count=1:length(r);

headProb=cumsum(r)./count';

figure

plot(count,headProb,'k','linewidth',1.5);

hold on;

plot([1 length(r)],[.5 .5],'r--');

title('Sample Probability of Heads in n flips of a simulated coin'); xlabel('Number of coin flips');

ylabel('Probability of heads');

legend('Sample Probability','Fair coin');

hold off;

3.cell练习：

c=cell(3,3);

c{1,1}='Joe';

c{2,1}='Sarah';

c{3,1}='Pat';

c{1,2}='Smith';

c{2,2}='Brown';

c{3,2}='Jackson';

c{1,3}=30000;

c{2,3}=150000;

c{3,3}=120000;

disp(c)

c{2,2}='Meyers';

disp(c)

c{3,3}=c{3,3}+50000;

disp(c)

4.使用structs：

function displayDir

a=dir;

for n=1:length(a)

if ~a(n).isdir

disp(['File ' a(n).name ' contains ' num2str(a(n).bytes) ' bytes.']); end

end

5.Handels使用：

x=linspace(0,2*pi,100);

y=sin(x);

figure;

plot(x,y,'r');

xlim([0 2*pi]);

set(gca,'xtick',[0 pi 2*pi],'xticklabel',{'0','1','2'});

set(gca,'ytick',[-1:0.5:1]);

grid on;

set(gca,'ycolor','g')

set(gca,'xcolor','c');

set(gca,'color','k');

set(gcf,'color',[.3 .3 .3]);

title('One sine wave from 0 to 2\pi','fontsize',14,'fontweight','bold','color','w') xlabel('X values (in terms of \pi)','fontsize',12,'color','c');

ylabel('Sin(X)','fontsize',12,'color','g')

6.图片读取与绘制：

x=imread('12110015.jpg');

subplot(2,2,1),imshow(x);

a=x(:,:,1);

aa=x(:,:,2);

aaa=x(:,:,3);

r=cat(3,a,zeros(size(a)),zeros(size(a)));

subplot(2,2,2),imzgesc(r);

g=cat(3,zeros(size(aa)),aa,zeros(size(aa)));

subplot(2,2,3),imagesc(g);

b=cat(3,zeros(size(aaa)),zeros(size(aaa)),aaa);

subplot(2,2,4),imagesc(b);

7.动画模拟Brown运动：

function brown2D(N)

figure;

axis square

axis([-1 1 -1 1]);

x=zeros(N,1);

y=zeros(N,1);

h=plot(x,y,'.k');

for n=1:1000

x=x+randn(size(x))*.005;

y=y+randn(size(y))*.005;

set(h,'xdata',x,'ydata',y);

axis([-1 1 -1 1])

pause(0.01);

end

8.Julia分形集动画制作

function juliaAnimation(zMax,c,N)

res=500;

temp=linspace(-zMax,zMax,res);

[R,I]=meshgrid(temp,temp);

Z=R+1i*I;

M=N*ones(size(Z));

figure

for n=1:N

Z=Z.^2+c;

inds=find(abs(Z)>2);

M(inds)=n;

Z(inds)=nan;

imagesc(temp,temp,atan(0.1*M)); axis xy

drawnow

end