Matlab/Test

% Test 1
% (1)生成一个空矩阵A
A = []
% 对A进行赋值，取值为5行5列的单位矩阵
A = eye(5)
% 将矩阵A存储在硬盘上的Matlab数据文件A.mat中
save A.mat A

%(2) 利用函数xlsread读取硬盘上电子表格
% data.xls中的第一个工作表区域中
% A2:C5的区域的数据(自行敲入)，并赋值给矩阵
% B，然后利用命令保存矩阵B到硬盘上的B.mat文件中。

B =xlsread('data1.xlsx', 1,  'A2:C5')
save B.mat B

% (3) 利用load实现将数据文件A.mat 和 B.mat
% 载入到内存中，然后将A、B两个变量保存到MATLAB数据文件AB.mat中
load A.mat
load B.mat
save AB.mat A B

• Test 3

  • 将大些字母转换为小写的两种方法

    % 创建由数值和大小写字母构成的字符
    str = 'gfAFHSKFHsag354346'
    % 将大写字母转换为小写字母
    str = lower(str) % first
    
    % second
    % upper = find(str >='A' & str <= 'Z');
    % str(upper) = str(upper) + 32;
    % new = char(str)

    % 创建由数值和大小写字母构成的字符
    str = 'gfAFHSKFHsag354346'
    % 将大写字母转换为小写字母
    str = lower(str)
    
    upper = find(str >='0' & str <= '9');
    str(upper) = 0;
    str = char(str);
    % 去掉尾部的空格
    str = deblank(str)
    
    % 在str的前面添加'New strings: '形成一个新的字符串
    add = 'New strings: ';
    newStr = ([add, str])
    % 统计字符串的字符数
    strSize = size(newStr)

• Test 4

  % 1 结构数组
  course=struct('courseName',{'Matlab程序设计','Java程序设计','线性代数','高等数学','大学物理'},'score',{2,2,2,2,2},'degreeOfDifficulty',{'difficult','difficult','difficult','medium','difficult'})
  % 新添教师姓名
  course(1).teacherName = '肖老师';
  course(2).teacherName = '龙老师';
  course(3).teacherName = '全老师';
  course(4).teacherName = '宋老师';
  course(5).teacherName = '王老师';
  % 显示course
  course
  % 删除难易信息
  course(1).degreeOfDifficulty = [];
  course(2).degreeOfDifficulty = [];
  course(3).degreeOfDifficulty = [];
  course(4).degreeOfDifficulty = [];
  course(5).degreeOfDifficulty = [];
  % 显示course
  course
  
  % 2 创建元胞数组
  
  course=cell(6,3);
  % 设置第一栏
  course(1,1)={'courseName'};
  course(1,2)={'score'};
  course(1,3)={'degreeOfDifficulty'};
  
  % 填写courseName信息
  course(2,1)={'Matlab程序设计'};
  course(3,1)={'Java程序设计'};
  course(4,1)={'线性代数'};
  course(5,1)={'高等数学'};
  course(6,1)={'大学物理'};
  
  % 填写score信息
  course(2,2)={2};
  course(3,2)={2};
  course(4,2)={2};
  course(5,2)={2};
  course(6,2)={2};
  
  % 填写degreeOfDifficulty信息
  course(2,3)={'difficult'};
  course(3,3)={'difficult'};
  course(4,3)={'difficult'};
  course(5,3)={'medium'};
  course(6,3)={'difficult'};
  
  % 添加第四个信息教师姓名
  course(1,4)={'teacherName'};
  course(2,4) = {'肖老师'};
  course(3,4)={'龙老师'};
  course(4,4)={'全老师'};
  course(5,4)={'宋老师'};
  course(6,4)={'王老师'};
  
  % 删除难易程度信息
  course(1,3)={[]};
  course(2,3)={[]};
  course(3,3)={[]};
  course(4,3)={[]};
  course(5,3)={[]};
  course(6,3)={[]};
  
  % 显示course
  course

• Test 5

  % 创建系数矩阵
  numbers=[1 -1 1;2 1 1;1 -1 -2];
  
  % 行列式
  A=det(numbers)
  
  % 迹
  B=trace(numbers)
  
  % 秩
  C=rank(numbers)
  
  % 逆
  D=inv(numbers)
  
  % 求解方程组
  b=[1 2 4];
  x=inv(A)*b

• Test 6

  % Test 6
  A =  [-10000:10000];
  num=find(A>1000 & mod(A,17)==0);
  Size=size(A(num))
  All=A(num);
  B=All(end-9:end)

% 简答与编程三 数据可视化
% Test 1
% 分别绘图
% sin(x)
x1=linspace(0,4*pi,2000);
plot(x1,sin(x1))

% cos(x)
x2=linspace(-pi,3*pi,2000);
plot(x2,cos(x2))

% tan(x)
x3=linspace(0,4*pi,2000);
plot(x3,tan(x3))

% 绘制在一幅图中
subplot(131);
plot(x1,sin(x1))
subplot(132);
plot(x2,cos(x2))
subplot(133);
plot(x3,tan(x3))



% Test 2
% sin(x)
x1=linspace(0,4*pi,2000);
plot(x1,sin(x1),'k')
axis auto;
hold on;

% cos(x)
x2=linspace(-pi,3*pi,2000);
plot(x2,cos(x2),'--g*','linewidth',3)
hold on;

% tan(x)
x3=linspace(0,4*pi,2000);
plot(x3,tan(x3),'-.ro','linewidth',2);

% 图例标注
legend('sin(x)','cos(x)','tan(x)','4');

% Test3
x=linspace(-3,3,49);
y=linspace(-3,3,49);
[xx,yy]=meshgrid(x,y); %确定作图的范围
zz=xx.^2/8-yy.^2/3; 

% 使用mesh函数
mesh(xx,yy,zz)

% 使用surf函数
surf(xx,yy,zz)


% Test4

% sin(x)
x1=linspace(0,4*pi,2000);
p1=plot(x1,sin(x1));
hold on;
% cos(x)
x2=linspace(-pi,3*pi,2000);
p2=plot(x2,cos(x2));

% 获取图形句柄并修改曲线属性
h1=findobj(p1);
set(h1,'color','r')
set(h1,'linewidth',2)
h2=findobj(p2);
set(h2,'color','g','linestyle','--')

% 简答与编程五 程序设计
% Test 01
% swith 
score1 = input('Please enter your score1:');
switch score1
    case num2cell(90:100)
        disp('A')
    case num2cell(80:89)
        disp('B')
    case num2cell(70:79)
        disp('C')        
    case num2cell(60:69)
        disp('D')
    case num2cell(0:59)
        disp('E')
    otherwise
        error('Inputting Error!')
end


% if
score2 = input('Please enter your score2:');
if (score2 >= 90 & score2 <= 100)
        disp('A')
elseif (score2 >= 80 & score2 <= 89)
        disp('B')
elseif (score2 >= 70 & score2 <= 79)
       disp('C')        
elseif (score2 >= 60 & score2 <= 69)
        disp('D')
elseif (score2 >= 0 & score2 <= 59)
        disp('E')
else
        error('Inputting Error!')
end

% Test 02 
% 数值计算：计算出0-1000之间所有是4的倍数的整数的和
% for循环
s1=0;
for i = 0:4:1000
    s1=s1+i;
   
end
s1

% while 循环
num=0;
s2=0;
while num<=1000
    s2=s2+num;
    num=num+4;
end
s2
% 不使用循环语句
s3=sum(0:4:1000)
% 显然s1,s2,s3的值都是相等的

% 符号计算
% 计算出 1+1/2^2+1/3^2+...+1/k^2+...的前10项和

% for 循环
s4=0;
for j = 1:10
    s4=s4+1/j^2;
end
s4
% while 循环
s5 = 0;
num1=1;
while num1<=10
    s5=s5+1/num1^2;
    num1=num1+1;
end
s5
% 不使用循环语句
syms  k
s6=symsum(1/k^2,1,10)

% Test  02'!!!!
% for 循环
s1= 0;
for i = 0:10000001;
    s1=s1+0.2^i;
    
end
s1

% while循环
num=0;
s2=0;
while num<=1000000
    s2=s2+0.2^num;
    num=num+1;
end
s2

% 很显然s1和s2是相等的。

% Test 03
function [] = Test(varargin)
% Test 给定不同的输入绘画出不同的图形
% 当没有输入量时，画出单位圆
% 当输入量是大于2的整数N时，绘制正N边形并在图片名中反映显示多边形的真实边数
% 当输入量是"非自然数数"时，给出"出错提示"。
% Author:雷博闻
% Time: 2020/03/25
if nargin == 0
    angle=0:pi/360:2*pi;
figure(1);
plot(1*sin(angle),1*cos(angle));
axis tight
axis equal

elseif nargin ==1
    a = varargin{1};
    if a > 2 & rem(a,1)==0
        pgon=nsidedpoly(a);
        figure(1);
        plot(pgon)
        title(['正',num2str(a),'边形'])
        axis equal
        axis tight

    elseif a<0 | (a>=0 & rem(a,1)~=0)
        error('请输入一个自然数！')
    else
        error('超出范围')
    end
    
end

% Test 04
n=[2:100];
number=0;
tem=0;
sum=0;
for i=1:length(n)-1
        tem=n(i)*n(i+1)-1;
        for j=2:floor(tem/2)
            if rem(tem,j)~=0 
                if j==floor(tem/2)
                    disp([num2str(n(i)),'和',num2str(n(i + 1)),'是一对亲密数'])
                    number=number+1;
                    sum=sum+tem;
                end
            else
                break;
            end
        end
end

number
sum

%  简答与编程5 数值计算
% Test1
function [] =Test
A = [27 6 -1;6 15 2;1 1 54];
b = [85;5;110];

% LU 分解法
[L,U] = lu(A);
X = U\(L\b)

% 雅可比迭代法
[x1,n1]=jacobi(A,b, [0;0;0],1.0e-3)

% G-S迭代法
[x2,n2]=gauseidel(A,b, [0;0;0],1.0e-3)

function [y,n] = jacobi(A,b,x0,ep)
% 雅可比迭代法算法
D = diag(diag(A));
L = -tril(A,-1);
U=-triu(A,1);
B=D\(L+U);
f=D\b;
y=B*x0+f;
n=1;
while norm(y-x0) >= ep
    x0=y;
    y=B*x0+f;
    n=n+1;
end

function [y,n]=gauseidel(A,b,x0,ep)
D = diag(diag(A));
L = -tril(A,-1);
U=-triu(A,1);
B=(D-L)\U;
f=(D-L)\b;
y=B*x0+f;
n=1;
while norm(y-x0) >= ep
    x0=y;
    y=B*x0+f;
    n=n+1;
end

% Test 2


function [] = Test()
% 主函数
% solve 命令求解
syms x
answer=solve(x.^3 - 3*x+1);
vpa(answer)

% 实现逐步搜索法求方程的解
tic
X=StepSearch(-10,10,0.001,0.0001)
toc
% 实现二分法
tic
 [k1,x1,wuca1,yx1]=erfen(-2,-1,0.0001);
 x1
  [k2,x2,wuca2,yx2]=erfen(0,1,0.0001);
  x2
    [k3,x3,wuca3,yx3]=erfen(1,2,0.0001);
    x3
toc

function y = funs(x)

y = x.^3 - 3 * x + 1;


function r=StepSearch(a,b,h,tol)
% 逐步搜索法算法
X=a:h:b;n=(b-a)/h+1;m=0; 
Y=funs(X);
X(n+1)=X(n);Y(n+1)=Y(n);
k=2; 
    while(k<=n)
        sk=Y(k)*Y(k-1);
        if sk<=0
            m=m+1;
            if(abs(Y(k))<abs(Y(k-1)))
                r(m)=X(k);
                k=k+1;
            else
                r(m)=X(k-1);
            end
        else
            xielv=(Y(k+1)-Y(k))* (Y(k)-Y(k-1));
            if (abs(Y(k))<tol)&( xielv<=0)
                m=m+1;r(m)=X(k);
            end
        end
        k=k+1;    
        
    end
    
     
 

function [k,x,wuca,yx]=erfen(a,b,abtol)
     % 二分法算法
     a(1)=a; b(1)=b; 

ya=funs(a(1)); yb=funs(b(1)); %程序中调用的fun.m为函数

if ya* yb>0

disp('注意：ya*yb>0,请重新调整区间端点a和b.'), return
end
max1=-1+ceil((log(b-a)- log(abtol))/log(2)); %ceil是向正方向取整
for k=1:max1+1

    ya=funs(a); b; yb=funs(b); x=(a+b)/2;

yx=funs(x); wuca=abs(b-a)/2; k=k-1;
[k,a,b,x,wuca,ya,yb,yx];

if yx == 0
    a=x;b=x;
elseif yb*yx>0
    b=x;yb=yx;
else
    a=x;ya=yx;
    
end
if b-a<abtol,return,end 
end
k=max1;x;wuca;yx=funs(x);

%  简答与编程5 数值计算
% Test3 
x=linspace(-5,5,10); % 已知数据点的x坐标
y=1./(1+x.^2); % 已知数据点y坐标
x0=linspace(-5,5,10); % 已知数据点x坐标
y0=1./(1+x0.^2); % 已知数据点y坐标
x1=linspace(-5,5,10);
y1=interp1(x,y,x1,'linear'); % 线性插值
y2=interp1(x,y,x1,'spline'); % 三次样条插值
y3=interp1(x,y,x1,'pchip'); % 三次Hermite插值
y4=interp1(x,y,x1,'nearest'); % 最邻近插值

% 作图
figure(1)
plot(x0,y0,'-',x,y,'og',x1,y1,'*r');
legend('被插值曲线','已知离散数据点','线性插值数据点 ','location','NorthWest');
title('interp with linear')
figure(2) 
plot(x0,y0,'-',x,y,'og',x1,y4,'hr');
legend('被插值曲线','已知离散数据点','线性插值数据点 ','location','NorthWest');
title('interp with cubic')
figure(3) 
plot(x0,y0,'-',x,y,'og',x1,y2,'sr');
legend('被插值曲线','已知离散数据点','线性插值数据点 ','location','NorthWest');
title('interp with spline')
figure(4)
plot(x0,y0,'-',x,y,'og',x1,y3,'dr');
legend('被插值曲线','已知离散数据点','线性插值数据点 ','location','NorthWest');
title('interp with pchip')

%  简答与编程5 数值计算
% Test4
x=1.23;
h=[0.1,0.01,0.001,0.0001];
x1=x+h;
x2=x-h;
y = 7.*x.*(sin(3.*x)+cos(3.*x));
y1= 7.*x1.*(sin(3.*x1)+cos(3.*x1));
y2=7.*x2.*(sin(3.*x2)+cos(3.*x2));
yCS=(y1-y2)./(2*h) % 差商数值求导
syms x;
f=7.*x.*(sin(3.*x)+cos(3.*x));
dy=diff(f,x); % 理论导数符号表达式
dyl=eval(subs(dy,x,1.23)) ;% 理论导数
detF=yCS-dyl % 差商求导误差

% Test 05 

h=(exp(1)-1)/20;
x=1:h:exp(1);
y=2.*x.^3.*log(5*x);
z1=sum(y(1:20))*h;
z2=sum(y(2:21)*h);
z=(z1+z2)/2,z3=trapz(y)*h,z3h=trapz(x,y)

简答与编程六 符号计算

%  简答与编程六 符号计算
%  Test 1
% 展开成傅立叶级数
l=1/2;
syms x n;
f=1-x^2;
a0=int(f*cos(0),-l,l)/l
an=int(f*cos(n*pi*x/l),-l,l)/l
bn=int(f*sin(n*pi*x/l),-l,l)/l

% 简答与编程六 符号计算
% Test 2
x = sym('x');
y = sym('y');
z = sym('z');
[xx,yy,zz]=solve(x-y^2+z==10,x+y-5*z==0,2*x-4*y+z==0',x,y,z);

%  Test3
%%输入信号 
t=0:1e-3:20;%时域信号的时间范围 
x=sin(t)+sin(1.5*t+1)+5*cos(0.5*t)+2*randn(size(t));%时域信号x
w=[0:1e-2:2];%想要观察的频率范围
%%预定义 
y=w;
a=w;
j=sqrt(-1);
%%计算频点 
for i=1:length(w)
f=trapz(t,x.*exp(-j*w(i)*t));
y(i)=abs(f);
a(i)=angle(f);
end
%%输出 
subplot(3,1,1),
plot(t,x)
subplot(3,1,2),
plot(w,y)
subplot(3,1,3),
plot(w,a)

% Test 04
% f1

s1=taylor(1/(5+cos(x)),x,5)

% f2
s2=taylor(exp(x* sin(x)),x,12)
% Test 05
% （1）求展开式，并求方程的根。
syms x;
f=(x^2+x)*(x-1);
g=x^2+2*x+1;
a=expand(f+g)
solve(f+g,x)
% (2)求 f(x)/g(x)的商式和余式
p1=sym2poly(f);
p2=sym2poly(g);
[Q,r]=deconv(p1,p2); % 其中Q是商式系数，r是余式系数
Qa=poly2sym(Q) % 商式
ra=poly2sym(r) % 余式
% Test 06
syms x y
f =x*y^2-y^3;
fx1=diff(f,x,1) % 对x的1阶
fx2=diff(f,x,2) % 对x的2阶

fy1=diff(f,y,1) % 对y的1阶
fy2=diff(f,y,2) % 对y的2阶
% Test 07
syms x;
f = (1+x)^(1/x);
a=limit(f,x,0)
% Test 08
% (1)
syms a x;
f1=sin(a*x);
a1=int(f1,0,pi/2)
% (2)
f2=x/log(x);
a2=int(f2,2,3)

% Test09
syms x y z
y1=@(x) sqrt(x);
y2=@(x) x.^2;
z1=@(x,y) sqrt(x.*y);
z2=@(x,y) x.^2.*y;
fun=@(x,y,z) x.^2+y.^2+z.^2;
a=integral3(fun,1,2,y1,y2,z1,z2)

% Test 10
syms x;
g=x^3-6*x^2+11*x-6;
% (1)因式
a1=factor(g)
% (2)嵌套式
a2=horner(g)
simplify(a2)

GUI Test

function varargout = Test03(varargin)

gui_Singleton = 1;
gui_State = struct(‘gui_Name’, mfilename, …
‘gui_Singleton’, gui_Singleton, …
‘gui_OpeningFcn’, @Test03_OpeningFcn, …
‘gui_OutputFcn’, @Test03_OutputFcn, …
‘gui_LayoutFcn’, [] , …
‘gui_Callback’, []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
defaultanswers={‘5’};
answer=inputdlg(‘Enter your grade’,’Enter’,1,defaultanswers,’on’);
answer1=str2num(char(answer));
if answer1 >= 90 && answer1 <= 100
msgbox(“优秀”,’成绩分析’,’none’,’on’)
elseif answer1 >= 80 && answer1 <= 89
msgbox(“良好”,’成绩分析’,’none’,’on’)
elseif answer1 >= 70 && answer1 <= 79
msgbox(“中等”,’成绩分析’,’none’,’on’)
elseif answer1 >= 60 && answer1 <= 69
msgbox(“合格”,’成绩分析’,’help’,’on’)
else
msgbox(“不合格”,’Result’,’warn’,’on’)
end

% — Executes just before Test03 is made visible.
function Test03_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to Test03 (see VARARGIN)

% Choose default command line output for Test03
handles.output = hObject;
ha=axes(‘units’,’normalized’,’pos’,[0 0 1 1]);

uistack(ha,’down’);

ii=imread(‘p1.jpg’);

%设置程序的背景图为p1.jpg

image(ii);

colormap gray

set(ha,’handlevisibility’,’off’,’visible’,’off’);

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes Test03 wait for user response (see UIRESUME)
% uiwait(handles.figure1);

% — Outputs from this function are returned to the command line.
function varargout = Test03_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;

% — Executes during object creation, after setting all properties.
function axes1_CreateFcn(hObject, eventdata, handles)
% hObject handle to axes1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called

% Hint: place code in OpeningFcn to populate axes1

function edit1_Callback(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% Hints: get(hObject,’String’) returns contents of edit1 as text
% str2double(get(hObject,’String’)) returns contents of edit1 as a double

% — Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,’BackgroundColor’), get(0,’defaultUicontrolBackgroundColor’))
set(hObject,’BackgroundColor’,’white’);
end

function varargout = Test04(varargin)
% TEST04 MATLAB code for Test04.fig
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct(‘gui_Name’, mfilename, …
‘gui_Singleton’, gui_Singleton, …
‘gui_OpeningFcn’, @Test04_OpeningFcn, …
‘gui_OutputFcn’, @Test04_OutputFcn, …
‘gui_LayoutFcn’, [] , …
‘gui_Callback’, []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
users={‘123’,’321’;’456’,’789’};% 存储一系列账号和密码
[x,y]=size(users);
prompt={‘请输入账号:’,’请输入密码:’}
name=’输入’;
numlines=1;
defaultanswer={‘000’,’000’};
input=inputdlg(prompt,name,numlines,defaultanswer);
input1=str2num(char(input));
for i=1:x
if input1(1)==str2num(char(users(i,1)))
if input1(2)==str2num(char(users(i,2)))
msgbox(‘欢迎登录本系统’,’Welcome ‘,’none’)
break
else
msgbox(‘输入有误，请重新输入账号和密码’,’出错’,’error’)
break
end
else
msgbox(‘输入有误，请重新输入账号和密码’,’出错’,’error’)
break
end
end

% — Executes just before Test04 is made visible.
function Test04_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to Test04 (see VARARGIN)

% Choose default command line output for Test04
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes Test04 wait for user response (see UIRESUME)
% uiwait(handles.figure1);

% — Outputs from this function are returned to the command line.
function varargout = Test04_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;