国立台湾大学_郭彦甫老师_MATLAB课程练习

国立台湾大学_郭彦甫老师_MATLAB课程课程链接
【Bilibili链接】

【最近在自学郭彦甫老师MATLAB的相关课程，课程中有些许小练习在此记录下来，如果各位也学习了老师的相关课程，或是有更好的方法，欢迎交流】

01 Array_Operation

• 1.Calculate:

• cos( sqrt((1+2+3+4)³/5) )
• sin( sqrt() ) + ln( tan(1) ) )
• 2^3.5×1.7
• ^sin(10)

cos( sqrt((1+2+3+4)^3/5) )
sin( sqrt(pi) + log( tan(1) ))
2^(3.5*1.7)
exp(sin(10))

• 2.Calculate:

3/13 +4/14 +5/15=

format long
3/13 +4/14 +5/15
format rat
3/13 +4/14 +5/15

• 3.Change the following elements in the matrix:

A=[1 21 6;5 17 9;31 2 7];
A(1,2)=76;A(3,2)=0;
A([1:2],[2:3])=0;

• 4.try the expression:

A=[1 0 0;5 0 0;31 0 7];
>A(3,:)
>A(3,:) = [ ]

>>A(3,:)
ans =
      31              0              7
>>A(3,:)=[]
A =
       1              0              0       
       5              0              0   

• 5.Create matrices A, B, C, and D and concatenate them into F:

A=[1 2;3 4];B=[9 9;9 9];
C=[5 6 7 8];D=[-2 -1 0 1];
F=[A B;C;D]

02 Structured_Programming_&_Function

• 1.Use while loop to calculate the summation of the series 1+2+3+…+999

n=1;
s=0;
while n<=999
     s=s+n;
     n=n+1;
end
disp(s)

• 2.Use structured programming to:

1.Find the entries in matrix A that are negative
2.Store these entries’ position in a matrix B
3.Change the values of these entries to zero
A =[0 −1 4;9 −14 25;−34 49 64]

A=[0 -1 4;9 -14 25;-34 49 64];
[x, y]=size(A);
B=zeros(x,y);
for i=1:x
    for j=1:y
        B(i,j)=A(i,j);
        if B(i,j)<0
            B(i,j)=0;
        end
    end
end
disp([A;B]);

• 3.Exercise:

Write a function that asks for a temperature in degrees Fahrenheit
• Compute the equivalent temperature in degrees Celsius
• Show the converted temperature in degrees Celsius
• The script should keep running until no number is provided to convert

function test()
H=input('→→请求输入温度（华氏度）：');
while ~isempty(H)
    C=(H-32).*(5/9);
    disp(['转化为摄氏度为：',num2str(C)]);
    test();
    break;
end

03 Data_Structure_&_File_Access

• 1.Write a script that inverts any given string

s1=‘I like the letter E’

s2=‘E rettel eht ekil I’

s1=input('请输入待转换的字符串：','s');
n=length(s1);
s2=zeros(1,n);
for i=1:n
    s2(i)=s1(n-i+1);
end
disp(['转换前：',s1]);		%%s2=(end:-1:1);
disp(['转换后：',s2]);		%%s2=reverse(s1);

• 2.Create a cell array B that has the following structure

B={'This is the first cell' [5+j*6 4+j*5];...
    [1 2 3;4 5 6;7 8 9] {'Tim','Chris'}}

B{1,1}='This is the first cell'
B{1,2}=[5+j*6 4+j*5];
B{2,1}=[1 2 3;4 5 6;7 8 9];
B{2,2}='Tim','Chris';

• 3.How do we write both the text and number into an Excel file?

data=xlsread('example1.xlsx');
z=mean(data')';
xlswrite('example1.xlsx',z,1,'E2:E4');%%写数值内容
xlswrite('example1.xlsx',{'AVERAGE'},1,'E1');%%写标题

std_1=sqrt(sum((data-z).^2))./length(data);
xlswrite('example1.xlsx',std_1',1,'F2:F4');
xlswrite('example1.xlsx',{'标准差'},1,'F1');

[numeric, title_01]=xlsread('example1.xlsx');
numeric_cell=num2cell(numeric);
title_01(2:4,2:6)=numeric_cell(1:3,1:5);
xlswrite('example1.xlsx',title_01,1,"n1:s4");

04 Basic_Plotting

• 1.Plot 1

•Plot as a black line and as a series of red circles for the range t = 1 to 2 in one figure：
= ² and = sin(2)
•Label each axis, and add title and legend

t=linspace(1,2);
h=plot(t,t.^2,'k-',t,sin(2*pi*t),'ro');
title('Mini Assignment #1');
legend('t^2','sin(2\pit)','location','northwest');
xlabel('Time (ms)');        %%x坐标标签
ylabel('f(t)');      %%y坐标标签

• 2.Plot 2

t=linspace(1,2);
h=plot(t,t.^2,'k-',t,sin(2*pi*t),'ro');
title('Mini Assignment #1');
legend('t^2','sin(2\pit)','location','northwest');
xlabel('Time (ms)');        %%x坐标标签
ylabel('f(t)');      %%y坐标标签

set(gca,'FontSize',16)
set(h(1),'LineWidth',2);
set(h(2),'MarkerEdgeColor','r','MarkerFaceColor','b','LineWidth',1);

05 Advanced_Plotting

• 1.Stack the horizontal bar chart

x = [1 2 5 4 8];
y = [x;1:5];
subplot(1,3,1);
bar(y,'stacked');title('Stacked');
subplot(1,3,2);
barh(y);title('Horizontal');
subplot(1,3,3);
barh(y,'stacked');

• 2.Separate all the pieces in the pie chart

a = [10 5 20 30];
subplot(2,3,1); pie(a);title('饼图');
subplot(2,3,2); pie(a, [0,0,0,1]);title('饼图散');
subplot(2,3,3); pie3(a, [0,0,0,1]);title('饼图立体');
subplot(2,3,4); pie(a);
subplot(2,3,5); pie(a, [1,1,1,1]);
subplot(2,3,6); pie3(a, [1,1,1,1]);

• 3.Plot a hexagon on a polar chart

theta=linspace(0,2*pi,7);
r=ones(1,length(theta));        %%1行n列
h=polar(theta,r,'r-');
set(h,'LineWidth',1)

• 4.Exercise

• Plot a function: () = sin(²/4)
• Add the points sampled at 5 Hz using stem()

t1=0:0.01:10;
y1=sin(pi.*t1.^2./4);
plot(t1,y1,'b');hold on;
t2=0:0.2:10;
y2=sin(pi.*t2.^2./4);
stem(t2,y2,'r');hold off;

• 5.Plot a wait sign

t =[0:pi/2:2*pi]; x = cos(t);y=sin(t);
h=fill(x,y,'y'); axis square off;
set(h,'LineWidth',3);
text(0,0,'WAIT','Color', 'K','FontSize', 66, ...
    'FontWeight','bold','HorizontalAlignment', 'center');

• 6.‘Gold’, ‘Silver’ and 'Bronze

G = [46 38 29 24 13]; S = [29 27 17 26 8];
B = [29 23 19 32 7]; h = bar(1:5, [G' S' B']);
set(h(1),'FaceColor',[hex2dec('FF')/255 hex2dec('FF')/255 hex2dec('00')/255])
set(h(2),'FaceColor',[hex2dec('cc')/255 hex2dec('cc')/255 hex2dec('cc')/255])
set(h(3),'FaceColor',[hex2dec('FF')/255 hex2dec('99')/255 hex2dec('00')/255])
get(gca);
set(gca, 'XTickLabel',{'USA','CHN','GBR','RUS','KOR'})
title('Medal count for top 5 countries in 2012 Olympics');
ylabel('Number of medals'); xlabel('Country');
legend('Gold', 'Silver', 'Bronze')

• 7.Create a custom green color map such that the output of the script below looks like:

green=[zeros(255,1)  linspace(0,1,255)' zeros(255,1)];
colormap(green);
colorbar;

• 8.Combine the contour techniques to generate a figure as shown below

x = -3.5:0.2:3.5; y = -3.5:0.2:3.5;
[X,Y] = meshgrid(x,y); Z = X.*exp(-X.^2-Y.^2);
% subplot(1,3,1); contour(Z,[-.45:.05:.45]); axis square;
% subplot(1,3,2); [C,h] = contour(Z);clabel(C,h); axis square;
% subplot(1,3,3); contourf(Z); axis square;
[Ex,el]=contourf(Z,[-.45:.05:.45]);
clabel(Ex,el);

06 Graphical_User_Interface

% --- Executes on slider movement.
function slider1_Callback(hObject, eventdata, handles)
% hObject    handle to slider1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
handles.a=get(handles.slider1,'Value');guidata(hObject, handles);
handles.b=get(handles.slider2,'Value');guidata(hObject, handles);
c=num2str(int16(handles.a+handles.b));
set(handles.text2,'String',['A+B=',c]);
% Hints: get(hObject,'Value') returns position of slider
%        get(hObject,'Min') and get(hObject,'Max') to determine range of slider


% --- Executes on slider movement.
function slider2_Callback(hObject, eventdata, handles)
% hObject    handle to slider2 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
handles.a=get(handles.slider1,'Value');guidata(hObject, handles);
handles.b=get(handles.slider2,'Value');guidata(hObject, handles);
c=num2str(int16(handles.a+handles.b));
set(handles.text2,'String',['A+B=',c]);
% Hints: get(hObject,'Value') returns position of slider
%        get(hObject,'Min') and get(hObject,'Max') to determine range of slider
%%%%其他部分保持默认即可

07 Image_Processing I

• 1.Adjust the “brightness” and “contrast” of rice.png and display it on the screen
  • Plot the histograms of the images before and after the “brightness” and “contrast” adjustment for rice.png

I=imread('rice.png');
J=immultiply(I,0.5);
K=immultiply(I,1.5);
subplot(2,3,1);imshow(I);
subplot(2,3,2);imshow(K);
subplot(2,3,3);imshow(J);
subplot(2,3,4);imhist(I);
subplot(2,3,5);imhist(J);
subplot(2,3,6);imhist(K);

• 2.Write your own equalization function, try it on pout.tif, and display it on the screen

I=imread('pout.tif');
N=double(255/(max(max(I))-min(min(I)))*1.5);
IEQ=immultiply(imsubtract(I,double(min(min(I)))),N);
subplot(2,3,1);imshow(I);title('原图');
subplot(2,3,2);imshow(IEQ);title('自制');
subplot(2,3,3);imshow(histeq(I));title('系统');
subplot(2,3,4);imhist(I);
subplot(2,3,5);imhist(IEQ);
subplot(2,3,6);imhist(histeq(I));

08 Image_Processing II

• 1.Practice 1

• Write a program to convert the image rice.png into a binary image using a threshold
• Do NOT use im2bw()
• Try different threshold values to see if your program works

I=imread('rice.png');
[x,y]=size(I);
I1=zeros(x,y);
thre=sum(sum(I))/(x*y);
thre_1=max(max(I))-min(min(I))*0.5;
for i=1:x
    for j=1:y
        if I(i,j)>(thre+thre_1)*0.5
            I1(i,j)=255;
        end
    end
end
subplot(1,3,1);imshow(I);title('原图');
subplot(1,3,2);imshow(I1);title('自制');
level=graythresh(I);
I2=im2bw(I,level);
subplot(1,3,3);imshow(I2);title('im2bw');

• 2.Practice

• Plot the histogram of grain size
• Identify all the grains in the image by painting them in red

%%%%读取图像并进行二值化
I=imread('rice.png');       %%读取图像
BG=imopen(I,strel('disk',15));      %%生成背景图
I_1=imsubtract(I,BG);       %%图像相减
level=graythresh(I_1);      %%分界线
I_2=im2bw(I_1,level);       %%新的二值化
[labeled,numObjects]=bwlabel(I_2,8);
RGB_label=label2rgb(labeled);
imshow(RGB_label);title('RGB\_label');
[x, y, z]=size(RGB_label);

%%%%Paint red
redim=labeled;
for i=1:x
    for j=1:y
        if redim(i,j)>0
            redim(i,j)=255;
        end
    end
end
gr=zeros(x,y);bl=zeros(x,y);
redim(:,:,2)=gr;
redim(:,:,3)=bl;
figure;imshow(redim);title('Red Painted');

%%%%数米的数量绘制直方图
h=zeros(1,numObjects);
for n=1:numObjects
    for i=1:x
        for j=1:y
            if labeled(i,j)==n
                h(n)=h(n)+1;
            end
        end
    end
end
figure;hist(h,20);title('The Grain Size');

09 Integration_&_Differentiation

• 1.Plot the polynomial and its derivative for −2 ≤ ≤ 1

f(x)=(5x³-7x²+5x+10)(4x²+12x-3)

y1=[5 -7 5 10];
y2=[4 12 -3];
y3=conv(y1,y2);		%%返回向量 u 和 v 的卷积。如果 u 和 v 是多项式系数的向量，对其卷积与将这两个多项式相乘等效
x=linspace(-2,1);
plot(x,polyval(y3,x),'--b','LineWidth',1.6);hold on;
plot(x,polyval(polyder(y3),x),'-r','LineWidth',1.6);hold off;
legend({'f (x)','f''(x)'},'FontSize',12);
set(gca,'FontSize',12);

• 2.Given () = sin(), write a script to find the error of ′(₀) at ₀ = /2 using various ℎ

n=1:7;
x0=pi/2;
for i=1:n
    x=[x0 x0+power(10,-n)];
    y=[sin(x0) sin(x0+power(10,-n))];
    m(n)=diff(y)./diff(x);
end
disp(m);

• 3.Given () = ⁻sin(²/2), plot the approximate derivatives ′ of ℎ = 0.1, 0.01, and 0.001

g = colormap(lines); hold on;
for i=1:3
    x = 0:power(10, -i):2*pi;
    y = exp(-x).*sin(x.^2./2);
    m = diff(y)./diff(x);
    plot(x(1:end-1), m, 'Color', g(i,:));
end
hold off;
set(gca,'XLim', [0, 2*pi]); set(gca,'YLim', [-0.25,0.25]);
set(gca,'FontSize', 18); set(gca,'FontName', '宋体');
set(gca,'XTick', 0:pi/2:2*pi);
set(gca,'XTickLabel', {'0', '\pi/2', '\pi','3\pi/2','2\pi'});
h = legend('h=0.1','h=0.01','h=0.001');
set(h,'FontName', '宋体'); box on;

10 Root_Finding

• 1.Find the roots for:

cos(x) ² − sin(x)² = 0;
cos(x) ² + sin(x)² = 0

syms x;
y1=cos(x).^2-sin(x).^2;
y2=cos(x).^2+sin(x).^2;
solve(y1,x)
solve(y2,x)

• 2.Solve this equation for x using symbolic approach

(x − a)² + (y − b )² = r²

syms x y a b r;     %%不能有逗号
y1=(x-a)^2+(y-b)^2-r^2;
x0=solve(y1)

Find the matrix inverse using symbolic approach [a b;c d]

syms a b c d a1 b1 c1 d1;
y1=a*a1+b*c1-1;
y2=a*b1+b*d1-1;
y3=c*a1+d*c1-1;
y4=c*b1+d*d1-1;
A=solve(y1,y2,y3,y4,a1,b1,c1,d1)

• 3.求偏导

syms x y
y1=exp(x^2)/(x^3-x+3);
y2=(x^2+x*y-1)/(y^3+x+3);
y1p=diff(y1)
y2p=diff(y2)		%%对y求偏导y2p=diff(y2，y)

• 4.求积分

syms x;
y=(x^2-x+1)/(x+3);
z=int(y,[0 10])

• 5.Exercise

% % z1=@(x,y) (2*x-y-exp(-x));
% % z2=@(x,y) (-x+2*y-exp(-y));fsolve不能同时解两个
f=@(x)[2*x(1)-x(2)-exp(-x(1));-x(1)+2*x(2)-exp(-x(2))];
x=fsolve(f,[-5 -5])     %%不会的时候去help吧。fsolve牛顿法斜率、fzero二分法

11 Linear_Equations

• 1.Write a function to solve 1 … 5 for given 1, 2, and 1 … 5

syms R1 R2 R3 R4 R5 V1 V2;
A=[R1 0 0 R4 0;
    0 R2 0 -R4 R5;
    0 0 -R3 0 R5;
    1 -1 0 -1 0;
    0 1 -1 0 -1];
b=[V1 0 V2 0 0];
x=A\b

• 2.Plot the planes in 3D

x=0:40;
y=0:40;
[X,Y]=meshgrid(x,y);
z1=-X-Y;
z2=-X+Y;
z3=-X./3;
hold on;surf(X,Y,z1);
surf(X,Y,z2);
surf(X,Y,z3);grid on;
hold off;
xlabel('这是x轴');ylabel('这是y轴');zlabel('这是z轴');
set(gca,'XLim',[0 40]);
set(gca,'YLim',[0 40]);
set(gca,'ZLim',[-20 20]);		%%这个和老师PPT上的好像不太一样@_@

12 Statistics_&_Data_Analysis

• 1.Find the following properties of the variable x4

1 Mean, median, mode, and quartile
2 Range and interquartile range
3 Variance and standard deviation

load stockreturns;
x4=stocks(:,4);
Mean=mean(x4)
Median=median(x4)
Mode=mode(x4)
Quartile=quantile(x4,0.25)
Range=max(x4)-min(x4)
Variance=var(x4)
Standa_d=std(x4)

• 2.Plot the histograms:

x = [1 3 5 5 5 5 7 9 9 9 10 13 14];
fre=zeros(1,max(x));
for i=1:length(x)
    for j=1:length(fre)
        if x(i)==j
            fre(j)=fre(j)+1;
        end
    end
end
subplot(1,3,1);bar(1:14,fre);xlim([0 15]);
subplot(1,3,2);area(1:14,fre);xlim([0 15]);
subplot(1,3,3);stem(1:14,fre);xlim([0 15]);

• 3.Plot the boxplot of the variable stocks

Find the skewness and kurtosis for each column of the variable stocks

load stockreturns;
boxplot(stocks);
prctile(stocks,[25 50 75]);
y = skewness(stocks);
plot(y)

13 Curve_Fitting_&_Interpolation

• 1.Given the table below

1.Find the 0 and 1 of the regression line
2 Plot the figure

TC=[0.025 0.035 0.050 0.060 0.080];
TE=[20 30 40 50 60];
fit=polyfit(TE,TC,1);
x=[TE(1):0.1:TE(end)];
yfit=fit(1)*x+fit(2);
plot(TE,TC,'ko',x,yfit,'-r','LineWidth',1);grid on;
set(gca,'FontSize',12);
xlabel('Temperature (\circC)');
ylabel('TC Output (mV)');

• 2.Find the 4th, 5th, and 6th-order polynomials

x =[-1.2 -0.5 0.3 0.9 1.8 2.6 3.0 3.5];
y =[-15.6 -8.5 2.2 4.5 6.6 8.2 8.9 10.0];

x =[-1.2 -0.5 0.3 0.9 1.8 2.6 3.0 3.5];
y =[-15.6 -8.5 2.2 4.5 6.6 8.2 8.9 10.0];
figure('Position', [50 50 1500 400]);
for i=4:6
    subplot(1,3,i-3); p = polyfit(x,y,i);
    xfit = x(1):0.1:x(end);
    yfit = polyval(p,xfit);
    plot(x,y,'ro',xfit,yfit);
    set(gca,'FontSize',14);ylim([-17, 11]);
    legend('Data points','Fitted curve','Location','southeast');
end

• 3.Fit the data using the formulation:

= 0 + 1₁ + 2₂ + 3₁² + 4₂² + 5₁₂

load carsmall;
y = MPG;
x1 = Weight;
x2 = Horsepower;
X = [ones(length(x1),1) x1 x2 x1.^2 x2.^2 x1.*x2];
b = regress(y,X);
x1fit = min(x1):100:max(x1);
x2fit = min(x2):10:max(x2);
[X1FIT,X2FIT]=meshgrid(x1fit,x2fit);
YFIT=b(1)+b(2)*X1FIT+b(3)*X2FIT+b(4)*X1FIT.^2+b(5)*X2FIT.^2+b(6)*X1FIT.*X2FIT;
scatter3(x1,x2,y,'filled'); hold on;
surf(X1FIT,X2FIT,YFIT); hold off;
xlabel('Weight');
ylabel('Horsepower');
zlabel('MPG'); view(50,10)

• 4.Fit the data using linear lines and cubic splines

x=[0 0.25 0.50 0.75 1.0 1.25 1.5 1.75 2.0 2.25];
y=[1.2 1.18 1.1 1 0.92 0.8 0.7 0.55 0.35 0];
n=length(x);
xfit=x(1):0.01:x(end);
yfit_1=interp1(x,y,xfit);
yfit_2=spline(x,y,xfit);
hold on;
plot(x,y,'-bo',xfit,yfit_1,'r-','LineWidth',1);
plot(xfit,yfit_2,'g','LineWidth',1);
hold off;
legend('Original','Linear','Spline');