matlab学习笔记

cos = 'changqingaas';
cos(8)
% disp(['ans is ', num2str(ans)])
clear; % 若某函数被变量名所覆盖,则调用clear <变量名>可以取消绑定在该函数名上的变量名
cos(8)
% disp(['ans is ', num2str(ans)])

输出：

ans =

    'n'


ans =

   -0.1455

if condition1
	statement1
elseif condition2
	statement2
else 
	statement3
end

switch expression
    case value1
        statement1
    case value2
        statement2
    otherwise 
        statement
end

while expression
	statement
end

for variable = start:increment:end
	commands
end

x = 2; k = 0; error = inf;
error_threshold = 1e-32;

while error > error_threshold

    if k > 100
        break
    end

    x = x - sin(x) / cos(x);
    error = abs(x - pi);
    k = k + 1;
end

clear all	% 清空工作区内存中的变量
close all 	% 关闭之前程序绘制的图像
clc			% 清空之前程序在终端的输出

edit(which('mean.m'))

function [输出变量名] = 函数名(输入变量名) 
% 函数的文档

函数代码

function x = freebody(x0,v0,t)
% calculation of free falling
% x0: initial displacement in m
% v0: initial velocity in m/sec
% t: the elapsed time in sec
% x: the depth of falling in m
x = x0 + v0.*t + 1/2*9.8*t.*t;

freebody(0, 0, 2)			% 得到 19.6000
freebody(0, 0, [0 1 2 3])	% 得到 [0 4.9000 19.6000 44.1000]
freebody(0, 0, [0 1; 2 3])	% 得到 [0 4.9000; 19.6000 44.1000]

function F2C()
while 1
    F_degree = input('tempreature in Fahrenheit: ', 's');
    F_degree = str2num(F_degree);
    if isempty(F_degree)
        return
    end
    C_degree = (F_degree-32)*5/9;
    disp(['tempreature in Celsius: ' num2str(C_degree)])
end

函数句柄 = @(输入变量) 输出变量 

f = @(x) exp(-2*x);
x = 0:0.1:2;
plot(x, f(x));

n = 3;
class(n)	 

n = int8(3);
class(n)	 

ans =
    'double'
ans =
    'int8'

s1 = 'h';
uint16(s1)	% 得到 104

str1 = 'hello';
str2 = 'world';

str3 = [str1 str2];
size(str3)		% 得到 [1 10]

str4 = [str1; str2];
size(str4)		% 得到 [2 5]

str = 'aardvark';
'a' == str				% 得到 [1 1 0 0 0 1 0 0]
str(str == 'a') = 'Z'	% 得到 'ZZrdvZrk'

student.name = 'John Doe';
student.id = 'jdo2@sfu.ca';
student.number = 301073268;
student.grade = [100, 75, 73; ...
                 95, 91, 85.5; ...
                 100, 98, 72];
student

student.name = 'John Doe';
student.id = 'jdo2@sfu.ca';
student.number = 301073268;
student.grade = [100, 75, 73; 95, 91, 85.5; 100, 98, 72];

student

student(2).name = 'Ann Lane';
student(2).id = 'aln4@sfu.ca';
student(2).number = 301078853;
student(2).grade = [95 100 90; 95 82 97; 100 85 100];

student(1) = [] % 删除student列表第一项

A = struct('data', [3 4 7; 8 0 1], ...
'nest', struct('testnum', 'Test 1', ...
'xdata', [4 2 8], ...
'ydata', [7 1 6]));
A(2).data = [9 3 2; 7 6 5];
A(2).nest.testnum = 'Test 2';
A(2).nest.xdata = [3 4 2];
A(2).nest.ydata = [5 0 9];

A

A = { [1 4 3; 0 5 8; 7 2 9]		'Anne Smith' ;...
3+7i		-pi:pi:pi}

A(1,1)={[1 4 3; 0 5 8; 7 2 9]};
A(1,2)={'Anne Smith'};
A(2,1)={3+7i};
A(2,2)={-pi:pi:pi};

A{1,1}=[1 4 3; 0 5 8; 7 2 9];
A{1,2}='Anne Smith';
A{2,1}=3+7i;
A{2,2}=-pi:pi:pi;
A

a = magic(3)

b = num2cell(a)
% 得到
% [8] [1] [6]
% [3] [5] [7]
% [4] [9] [2]

c = mat2cell(a, [1 2], [2, 1])
% 得到
% [1x2 double] [6]
% [2x2 double] [2x1 double]

Score = xlsread('04Score.xlsx')
Score = xlsread('04Score.xlsx', 'B2:D4')
[Score Header] = xlsread('04Score.xlsx')

M = mean(Score);
xlswrite('04Score.xlsx', M, 1, 'E2:E4');
xlswrite('04Score.xlsx', {'Mean'}, 1, 'E1');

plot(x,y,LineSpec)

x=0:0.5:4*pi;
y=sin(x); h=cos(x); w=1./(1+exp(-x)); g=(1/(2*pi*2)^0.5).*exp((-1.*(x-2*pi).^2)./(2*2^2));
plot(x,y,'bd-' ,x,h,'gp:',x,w,'ro-' ,x,g,'c^-');		% 绘制多条图线
legend('sin(x)','cos(x)','Sigmoid','Gauss function');	% 添加图例

x = 0:0.1:2*pi; y1 = sin(x); y2 = exp(-x);
plot(x, y1, '--*', x, y2, ':o');
xlabel('t = 0 to 2\pi');
ylabel('values of sin(t) and e^{-x}')
title('Function Plots of sin(t) and e^{-x}');
legend('sin(t)','e^{-x}');

x = linspace(0,3); y = x.^2.*sin(x); plot(x,y);
line([2,2],[0,2^2*sin(2)]);
str = '$$ \int_{0}^{2} x^2\sin(x) dx $$';
text(0.25,2.5,str,'Interpreter','latex');
annotation('arrow','X',[0.32,0.5],'Y',[0.6,0.4]); 

t = 0:0.1:2*pi; x = 3*cos(t); y = sin(t);
subplot(2, 2, 1); plot(x, y); axis normal
subplot(2, 2, 2); plot(x, y); axis square
subplot(2, 2, 3); plot(x, y); axis equal
subplot(2, 2, 4); plot(x, y); axis equal tight

hold on		% 提起画笔,开始绘制一组图片			
plot(cos(0:pi/20:2*pi));
plot(sin(0:pi/20:2*pi));
hold off	% 放下画笔,该组图片绘制完毕

% 第一张图
set(gca, 'FontSize', 25);

% 第二张图
set(gca, 'XTick', 0:pi/2:2*pi);
set(gca, 'XTickLabel', 0:90:360);

% 第三张图
set(gca, 'FontName', 'symbol');
set(gca, 'XTickLabel', {'0', 'p/2', 'p', '3p/2', '2p'});

h = plot(x,y); 
set(h, 'LineStyle','-.', ...
	'LineWidth', 7.0, ...
	'Color', 'g');

saveas(gcf, 'myfigure.png')

x = logspace(-1,1,100); y = x.^2;

subplot(2,2,1);
plot(x,y);
title('Plot');

subplot(2,2,2);
semilogx(x,y);
title('Semilogx');

subplot(2,2,3);
semilogy(x,y);
title('Semilogy');

subplot(2,2,4);
loglog(x, y);
title('Loglog'); 

set(gca, 'XGrid','on');

x = 0:0.01:20;
y1 = 200*exp(-0.05*x).*sin(x);
y2 = 0.8*exp(-0.5*x).*sin(10*x);
[AX,H1,H2] = plotyy(x,y1,x,y2);
set(get(AX(1),'Ylabel'),'String','Left Y-axis')
set(get(AX(2),'Ylabel'),'String','Right Y-axis')
title('Labeling plotyy');
set(H1,'LineStyle','--'); set(H2,'LineStyle',':');

x = [1 2 5 4 8]; y = [x;1:5];
subplot(1,3,1); bar(x); title('A bargraph of vector x');
subplot(1,3,2); bar(y); title('A bargraph of vector y');
subplot(1,3,3); bar3(y); title('A 3D bargraph');

x = [1 2 5 4 8];
y = [x;1:5];
barh(y);
title('Horizontal');

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

a = [10 5 20 30];
subplot(1,3,1); pie(a);
subplot(1,3,2); pie(a, [0,0,0,1]);
subplot(1,3,3); pie3(a, [0,0,0,1]);

x = linspace(0, 4*pi, 40); y = sin(x);
subplot(1,2,1); stairs(y);
subplot(1,2,2); stem(y);

[x, y] = meshgrid(-3:.2:3,-3:.2:3); z = x.^2 + x.*y + y.^2; 

subplot(1, 2, 1)
surf(x, y, z); 

subplot(1, 2, 2)
imagesc(z);

x = -2:1:2;
y = -2:1:2;
[X,Y] = meshgrid(x,y)
Z = X.^2 + Y.^2

x=0:0.1:3*pi; z1=sin(x); z2=sin(2.*x); z3=sin(3.*x);
y1=zeros(size(x)); y3=ones(size(x)); y2=y3./2;
plot3(x,y1,z1,'r',x,y2,z2,'b',x,y3,z3,'g'); grid on;
xlabel('x-axis'); ylabel('y-axis'); zlabel('z-axis');

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(1,2,1); mesh(X,Y,Z);
subplot(1,2,2); surf(X,Y,Z);

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;

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(1,2,1); meshc(X,Y,Z);
subplot(1,2,2); surfc(X,Y,Z);

v = [0 0 0; 1 0 0 ; 1 1 0; 0 1 0; 0.25 0.25 1; 0.75 0.25 1; 0.75 0.75 1; 0.25 0.75 1];
f = [1 2 3 4; 5 6 7 8; 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8];

subplot(1,2,1); 
patch('Vertices', v, 'Faces', f, 'FaceVertexCData', hsv(6), 'FaceColor', 'flat');
view(3); axis square tight; grid on;

subplot(1,2,2); 
patch('Vertices', v, 'Faces', f, 'FaceVertexCData', hsv(8), 'FaceColor','interp');
view(3); axis square tight; grid on

sphere(50); shading flat;
material shiny;
axis vis3d off;
view(-45,20);

sym(1/3)	% 得到 1/3
1/3			% 得到 0.3333

sin(sym(pi))	% 得到 0
sin(pi)			% 得到 1.2246e-16

syms a		% sym命令只能创建一个符号变量
syms b c d	% syms命令可以创建多个符号变量

syms x y
f = x+y;	% 隐式创建符号变量f
sym f		% 不清空变量f原有的值,即f = x + y

syms x y
f = x+y;	% 隐式创建符号变量f
syms f		% 清空变量f原有的值,即f = f

A = sym('a', [2 5])	% 创建一个2*5的符号变量矩阵
whos

A =
[ a1_1, a1_2, a1_3, a1_4, a1_5]
[ a2_1, a2_2, a2_3, a2_4, a2_5]
 
 
  Name      Size            Bytes  Class    Attributes
  A         2x5               112  sym      

clear all
syms(sym('a', [1 5]))
whos

Name      Size            Bytes  Class    Attributes
a1        1x1                 8  sym                
a2        1x1                 8  sym                
a3        1x1                 8  sym                
a4        1x1                 8  sym                
a5        1x1                 8  sym                

syms x a b c

simplify(sin(x)^2 + cos(x)^2);		% 得到 1
simplify(exp(c*log(sqrt(a+b))));	% 得到 (a + b)^(c/2)

syms x

f = (x ^2- 1)*(x^4 + x^3 + x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1);
expand(f);		% 得到 x^10 - 1

syms x

g = x^3 + 6*x^2 + 11*x + 6;
factor(g);		% 得到 (x + 3)*(x + 2)*(x + 1)

syms x

h = x^5 + x^4 + x^3 + x^2 + x;
horner(h);		% 得到 x*(x*(x*(x*(x + 1) + 1) + 1) + 1)

syms x y

f = x^2*y + 5*x*sqrt(y);
subs(f, x, 3);	% 得到 9*y + 15*y^(1/2)

syms x

eqn = x^3 - 6*x^2 == 6 - 11*x;
solve(eqn);		% 得到 [1 2 3]

syms x y

eqn = [6*x^2 - 6*x^2*y + x*y^2 - x*y + y^3 - y^2 == 0];
solve(eqn, y);	% 得到 [1, 2*x, -3*x]

syms u v

eqns = [2*u + v == 0, u - v == 1];
S = solve(eqns,[u v]);	

S.u;				% 得到 1/3
S.v;				% 得到 -2/3
subs(3*v + u, S);	% 得到 -3/5

syms x;
expr = 1/x;

limit(expr,x,0);			% 得到NaN
limit(expr,x,0,'left');		% 得到-Inf
limit(expr,x,0,'right');	% 得到Inf

syms a b c x;
expr = a*x^2 + b*x + c;

diff(expr, a);		% 得到 x^2
diff(expr, b);		% 得到 x
diff(expr, x);		% 得到 b + 2*a*x
diff(expr, x, 2);	% 得到 2*a

syms x a b
expr = -2*x/(1+x^2)^2;

int(expr, x);			% 得到 1/(x^2 + 1)
int(expr, x, [1, 2]);	% 得到 -0.3
int(expr, x, [1, Inf]);	% 得到 -0.5
int(expr, x, [a, b]);	% 得到 1/(b^2 + 1) - 1/(a^2 + 1)

syms x
int(sin(sinh(x)));	% 一个无解的积分,MATLAB返回 int(sin(sinh(x)),

syms k x

symsum(k^2, k)			% 得到 k^3/3 - k^2/2 + k/6
symsum(k^2, k, [0 10])	% 得到 385
symsum(x^k/factorial(k),k,1,Inf)	% 得到 exp(x) - 1

syms x

taylor(exp(x))	% 得到 x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1
taylor(sin(x))	% 得到 x^5/120 - x^3/6 + x
taylor(cos(x))	% 得到 x^4/24 - x^2/2 + 1

subplot(1, 2, 1)
syms x
f = x^3 - 6*x^2 + 11*x - 6;
fplot(f, x)

subplot(1, 2, 2)
syms t
fplot3(t^2*sin(10*t), t^2*cos(10*t), t)

syms x y
fsurf(x^2 + y^2)

syms x y
eqn = (x^2 + y^2)^4 == (x^2 - y^2)^2;
fimplicit(eqn, [-1 1])

a = [9,-5,3,7]; x = -2:0.01:5;
f = polyval(a,x);
plot(x,f);

p = conv([1 0 1], [2 7])

p = roots([1 -3.5 2.75 2.125 -3.875 1.25])

p = polyder([5 0 -2 0 1]);

p = polyint([5 0 -2 0 1], 3)

f2 = @(x) (1.2*x+x*sin(x)+0.3);
fsolve(f2,0)	% 得到 -0.3500

fun = @(x) [exp(-exp(-(x(1)+x(2))))-x(2)*(1+x(1)^2)...
    x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5]
x0 = [0,0];
x = fsolve(fun,x0)	% 得到[0.3532 0.6061]

x = [1 2 5 2 1];
diff(x);	% 得到 [1 3 -3 -1]
diff(x,1);	% 得到 [1 3 -3 -1]
diff(x,2);	% 得到 [2 -6 2]

x = -2:0.005:2; y = x.^3;
m = diff(y)./diff(x);			% 计算一阶导数
m2 = diff(m)./diff(x(1:end-1));	% 计算二阶导数

plot(x,y,x(1:end-1),m,x(1:end-2),m2);
xlabel('x'); ylabel('y');
legend('f(x) =x^3','f''(x)','f''''(x)', 4);

h = 0.05; x = 0:h:2;


% 使用矩形法计算近似积分
midpoint = (x(1:end-1)+x(2:end))./2;
y = 4*midpoint.^3;
s = sum(h*y)			% 得到 15.9950

% 使用梯形法计算近似积分
trapezoid = (y(1:end-1)+y(2:end))/2;
s = h*sum(trapezoid)	% 得到 15.2246

% 使用抛物线法计算数值积分
s = h/3*(y(1)+2*sum(y(3:2:end-2))+4*sum(y(2:2:end))+y(end))	% 得到 15.8240

f = @(x) 1./(x.^3-2*x-5);
integral(f,0,2)		% 得到 -0.4605

f = @(x,y) y.*sin(x)+x.*cos(y);
integral2(f,pi,2*pi,0,pi)	% 得到 -9.8696

f = @(x,y,z) y.*sin(x)+z.*cos(y);
integral3(f,0,pi,0,1,-1,1)

x = 1:14;
freqy = [1 0 1 0 4 0 1 0 3 1 0 0 1 1];
subplot(1,3,1); bar(x,freqy); xlim([0 15]);
subplot(1,3,2); area(x,freqy); xlim([0 15]);
subplot(1,3,3); stem(x,freqy); xlim([0 15]);

marks = [80 81 81 84 88 92 92 94 96 97];
boxplot(marks) 
% prctile(marks, [25 50 75])	% 得到 [81 90 94]

X = randn([10 3]);		% 构造10*3的矩阵
X(X(:,1)<0, 1) = 0; 	% 将第一列数据右偏
X(X(:,3)>0, 3) = 0;		% 将第二列数据左偏
boxplot(X, {'Right-skewed', 'Symmetric', 'Left-skewed'});
skewness(X);	% 得到 [0.5162 -0.7539 -1.1234]

load examgrades
x = grades(:,1);
y = grades(:,2);
[h,p] = ttest(x,y);

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];

for i = 1:3 % 分别进行一次,二次,三次拟合
    p = polyfit(x, y, i);
    xfit = x(1):0.1:x(end); yfit = polyval(p, xfit);
    subplot(1, 3, i); plot(x, y, 'ro', xfit, yfit);
    legend('Data points', 'Fitted curve', 'Location', 'southeast');
end

load carsmall;
y = MPG; x1 = Weight; x2 = Horsepower;		% 导入数据集
X = [ones(length(x1),1) x1 x2];				% 构建增广X矩阵
b = regress(y,X);							% 进行线性回归

% 下面是绘图语句
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;
scatter3(x1,x2,y,'filled'); hold on;
mesh(X1FIT,X2FIT,YFIT); hold off;
xlabel('Weight'); ylabel('Horsepower'); zlabel('MPG'); view(50,10);

% 构造数据
x = linspace(0, 2*pi, 40); x_m = x; x_m([11:13, 28:30]) = NaN; 
y_m = sin(x_m);
plot(x_m, y_m, 'ro', 'MarkerFaceColor', 'r'); hold on; 	

% 对数据进行线性插值
m_i = ~isnan(x_m);
y_i = interp1(x_m(m_i), y_m(m_i), x);
plot(x,y_i, '-b'); hold on;

% 对数据进行三次样条插值
m_i = ~isnan(x_m);
y_i = spline(x_m(m_i), y_m(m_i), x);
plot(x,y_i, '-g'); 

legend('Original', 'Linear', 'Spline');

% 构建样本点
xx = -2:.5:2; yy = -2:.5:3; [x,y] = meshgrid(xx,yy); 
xx_i = -2:.1:2; yy_i = -2:.1:3; [x_i,y_i] = meshgrid(xx_i,yy_i);
z = x.*exp(-x.^2-y.^2);

% 线性插值
subplot(1, 2, 1); 
z_i = interp2(xx,yy,z,x_i,y_i);
surf(x_i,y_i,z_i); hold on;
plot3(x,y,z+0.01,'ok','MarkerFaceColor','r'); hold on;

% 三次插值
subplot(1, 2, 2); 
z_ic = interp2(xx,yy,z,x_i,y_i, 'spline');
surf(x_i,y_i,z_ic); hold on;
plot3(x,y,z+0.01,'ok','MarkerFaceColor','r'); hold on;