MATLAB 学习笔记

格式化

format()

https://ww2.mathworks.cn/help/matlab/ref/format.html?searchHighlight=format&s_tid=srchtitle_support_results_1_format

format(style)

formate style

矩阵

索引和元素编辑

• 使用()索引

位置索引

线性索引

• 按列索引

逻辑值索引

• 按列输出

删除元素

1
2
3
4
5

A(:,3) = []
A(2,:) = []
	
A(2,2)=[]
% A null assignment can have only one non-colon index.

创建

• sparese()

  S = sparse(A)
  S = sparse(m,n)
  

合并

• [A, B], [A; B]

网格

size & shape

• reshape()

  >> reshape(A,2,3)
  ans =
       1     3     5
       2     4     6
  >> reshape(A,[2],3)
  ans =
       1     3     5
       2     4     6
  

重排

• isempty()

数据类型

数值

• double()

  >> a = double(10.00)
  

显示转换

• class()

  >> class(a)
  ans =
      'double'
  
  >> class(ones(3))
  ans =
      'double'
  

• cast()

  B = cast(A,newclass)
  B = cast(A,"like",p)
  

复数

• x = 2 + 3i
• z = complex(x, y)

• real(), imag()

  zr = real(z)
  zr =
      4.7842    0.8648    1.2616
      2.6130    4.8987    4.3787
      4.4007    1.3572    3.6865
  
  zi = imag(z)
  zi =
     -1.0921   -1.5931   -2.2753
     -0.0941   -2.3898   -3.7538
     -7.1512   -5.2915   -0.5182
  

Inf,NaN

字符

字符串

结构体

创建、引用结构体

Student.name = 'wangx';
Student.sex = 'Male';
Student.height = '170';

Student(2).name = 'zhangsan';
Student(2).sex = 'Male';
Student(2).height = 172;

field1 = 'f1';  value1 = zeros(1,10);
field2 = 'f2';  value2 = {'a', 'b'};
field3 = 'f3';  value3 = {pi, pi.^2};
field4 = 'f4';  value4 = {'fourth'};
s = struct(field1,value1,field2,value2,field3,value3,field4,value4)

元胞

创建元胞

c = {42,rand(5),"abcd"}
c =
  1×3 cell array
    {[42]}    {5×5 double}    {["abcd"]}

C = {1,2,3;
 'text',rand(5,10,2),{11; 22; 33}}
C=_2×3 cell array_
    {[   1]}    {[          2]}    {[     3]}
    {'text'}    {5x10x2 double}    {3x1 cell}

C = cell(n)
C = cell(sz1,...,szN)
C = cell(sz)
D = cell(obj)

访问元胞元素：

例如，假设有一个包含混合数据的 2×3 元胞数组。

C = {'one','two','three'; 
     100,200,rand(3,3)}

C=_2×3 cell array_
    {'one'}    {'two'}    {'three'   }
    {[100]}    {[200]}    {3x3 double}

每个元素都包含在一个元胞内。如果使用标准圆括号对该数组进行索引，得到的结果是一个包含元胞的元胞数组子集。

C2 = C(1:2,1:2)

C2=_2×2 cell array_
    {'one'}    {'two'}
    {[100]}    {[200]}

要向特定元胞读取或写入内容，请用花括号将索引括起来。

R = C{2,3}

R = _3×3_

    0.8147    0.9134    0.2785
    0.9058    0.6324    0.5469
    0.1270    0.0975    0.9575

函数句柄

函数

函数声明

function [y1,...,yN] = myfun(x1,...,xM)
    %code
end

function [y1,...,yN] = myfun(x1,...,xM) 声明名为 myfun 的函数，该函数接受输入 x1,...,xM 并返回输出 y1,...,yN。此声明语句必须是函数的第一个可执行代码行。有效的函数名称以字母字符开头，并且可以包含字母、数字或下划线。

• return

  匿名函数

  h = @(arglist)anonymous_function

  sqr = @(n) n.^2;
  x = sqr(3)
  x =

  9
  

运算和数学

运算符

算数运算

加法

减法

乘法

除法

幂

转置

模除法和舍入

关系运算

逻辑运算

集合运算

离散数学

线性代数

随机数生成

• rand()
X = rand 返回从区间 (0,1) 的均匀分布中得到的随机标量。
  X = rand(n) 返回一个由均匀分布的随机数组成的 n×n 矩阵。
  X = rand([sz1,...,szN]) 返回由随机数组成的 sz1×…×szN 数组，其中 sz1,...,szN 指示每个维度的大小。例如：rand(3,4) 返回一个 3×4 的矩阵。

  X = rand
  X = rand(n)
  X = rand(sz1,...,szN)
  

• randi()
X = randi([imax]) 返回一个介于 1 和 imax 之间的伪随机整数标量。

  X = randi(imax)
  X = randi(imax,n)
  X = randi(imax,sz1,...,szN)
  
  X = randi([imin,imax],___)
  

流程控制

• if, elseif, else

  if `expression`
      `statements`
  elseif `expression`
      `statements`
  else
      `statements`
  end
  

• switch

  switch `switch_expression`
     case `case_expression`
        `statements`
     case `case_expression`
        `statements`
      ...
     otherwise
        `statements`
  end
  

• for

  for v = 1.0:-0.2:0.0
     disp(v)
  end
  
  for v = [1 5 8 17]
     disp(v)
  end
  

• try, catch

  try
     `statements`
  catch `exception`
     `statements`
  end
  

• pause(n)

代数

多项式

MATLAB® 将多项式表示为行向量，其中包含按降幂排序的系数。

 %p(x)=x2−4x+4。
p = [1 -4 4];

 %p(x)=4x5−3x2+2x+33。
p = [4 0 0 -3 2 33];

符号运算

Symbolic Math Toolbox

符号创建

• sym(), syms符号变量

  % 创建符号
  a1Sym = sym(1/3)
  a2Sym = sym(pi)
  bSym = sin(sym(pi))
  sym('1234567 + 1i')
  
  y = sym('y')
  syms x
  syms a b c
  A = sym('a',[1 10])
  
  %符号表达式
  phi = (1 + sqrt(sym(5)))/2;
  f = phi^2 - phi - 1
  
  syms a b c x
  f = a*x^2 + b*x + c
  
  %等式
  eqn = (x^2 + y^2)^4 == (x^2 - y^2)^2;
  

• syms符号函数

  syms f(x,y)
  f(x,y) = x^2*y
      f(x, y) =
      x^2*y
  
  %Find the value of `f` at `(3,2)`.
  f(3,2)
      ans =
      18
  
  %Symbolic functions accept array inputs.
  xVal = 1:5;
  yVal = 3:7;
  f(xVal,yVal)
      ans =
      [ 3, 16, 45, 96, 175]
  %从隐函数生成
  y1 = @(a,b) cos(a) + cos(b); 
  ys1 = sym(y1)；
  

  运算

  多项式

• collect(f)

• factor(f)

  syms x
  g = x^3 + 6*x^2 + 11*x + 6;
  factor(g)
  
  ans =
  [ x + 3, x + 2, x + 1]
  

• expand(f)
• simplify(f)
• subs(f,[x,y,z],[a,b,c])

• coeffs()

  syms x y
  cx = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, x)
  cy = coeffs(x^3 + 2*x^2*y + 3*x*y^2 + 4*y^3, y)
      cx =
      [ 4*y^3, 3*y^2, 2*y, 1]
  
      cy =
      [ x^3, 2*x^2, 3*x, 4]
  

• coeffs(f,x)
• sym2poly(f)
• poly2sym(pl,x)
• [N,D] = numden(A)
• finverse(f)

• compose(f,g)

  微积分

• diff(f,x,y)

• int(f,x,[0,1])
• limit(f,x,0,"left")
• `taylor(f,x,0,’Order’,10)
• symsum(f,k,[0,Inf])

  求解

• solve()

  syms x
  solve(x^3 - 6*x^2 == 6 - 11*x)
  
  solve(x^3 - 6*x^2 + 11*x - 6)
  
  %If you do not specify any variable, you get the solution of an equation for the alphabetically closest to `x` variable.
  syms x y
  solve(6*x^2 - 6*x^2*y + x*y^2 - x*y + y^3 - y^2 == 0, y)
      ans =
          1
        2*x
       -3*x
  
  syms x y z
  [x, y, z] = solve(z == 4*x, x == y, z == x^2 + y^2)
  

• dsolve(ode,[cond])

  syms y(x)
  Dy = diff(y);
  
  ode = diff(y,x,2) == cos(2*x)-y;
  cond1 = y(0) == 1;
  cond2 = Dy(0) == 0;
  
  %Solve `ode` for `y`. Simplify the solution using the `simplify` function.
  
  conds = [cond1 cond2];
  ySol(x) = dsolve(ode,conds);
  ySol = simplify(ySol)
      ySol(x) =
      1 - (8*sin(x/2)^4)/3
  

绘图

• fplot(), fplot3(), fpolarplot()

  syms x
  f = x^3 - 6*x^2 + 11*x - 6;
  fplot(f)
  
  %参数方程
  syms t
  fplot3(t^2*sin(10*t), t^2*cos(10*t), t)
  

• fimplicit()

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

绘图

网格

• meshgrid()

  [X,Y] = meshgrid(x,y)
  [X,Y] = meshgrid(x)
  [X,Y,Z] = meshgrid(x,y,z)
  [X,Y,Z] = meshgrid(x)
  
  %使用均匀间隔的 _x_ 坐标和 _y_ 坐标在区间 [-2,2] 内创建二维网格。
  x = -2:0.25:2;
  y = x;
  [X,Y] = meshgrid(x);
  

在二维网格上计算并绘制函数 f(x,y)=xe−x2−y2。

Get

F = X.*exp(-X.^2-Y.^2);
surf(X,Y,F)

图形对象 figure

• get(h,propName), set(h,propName,Value)

  子图 subplot

  ubplot(m,n,p)
  subplot(m,n,p,’replace’)
  subplot(m,n,p,’align’)
  ax = subplot(___)
  subplot(ax)
  %eg1

  subplot(2,2,1);
  x = linspace(-3.8,3.8);
  y_cos = cos(x);
  plot(x,y_cos);
  title('Subplot 1: Cosine')
  
  subplot(2,2,2);
  y_poly = 1 - x.^2./2 + x.^4./24;
  plot(x,y_poly,'g');
  title('Subplot 2: Polynomial')
  
  subplot(2,2,[3,4]);
  plot(x,y_cos,'b',x,y_poly,'g');
  title('Subplot 3 and 4: Both')
  

  绘图类型

  线图

• plot(), plot3()

  plot(X,Y)
  plot(X,Y,LineSpec)
  
  plot(X1,Y1,...,Xn,Yn)
  plot(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn)
  
  plot(Y)
  plot(Y,LineSpec)
  
  % 指定属性
  figure
  plot(x,y,'--gs',...
      'LineWidth',2,...
      'MarkerSize',10,...
      'MarkerEdgeColor','b',...
      'MarkerFaceColor',[0.5,0.5,0.5])
  

  • Area 属性

  • Line 属性

    p = plot(x,y1,x,y2);
    
    p(1).LineWidth = 2;
    p(2).Marker = '*';
    

  • title

    title(titletext)
    title(titletext,subtitletext)
    title(___,Name,Value)
    
    title(ax1,'Top Plot')
    title(ax2,'Bottom Plot')
    
    t = title(___)
    t.Color = 'red';
    

  • xlabel, ylabel

    xlabel(txt)
    xlabel(target,txt)
    xlabel(___,Name,Value)
    t = xlabel(___)
    

  • xlim, ylim

    xlim(limits)
    xlim(limitmethod)
    xlim(limitmode)
    xl = xlim
    limmethod = xlim("method")
    limmode = xlim("mode")
    ___ = xlim(target,___)
    
    %eg1
        xlim([0 5])
        xlim([0 inf])
        xlim tight
        xlim auto
    
    %eg2
        xl = xlim
        xl = _1×2_
            -3     4
    

  • legend

    legend
    legend(label1,...,labelN)
    legend(labels)
    legend(subset,___)
    legend(target,___)
    
    legend(___,Name,Value)
    
    legend(vsbl)
    legend('off')
    
    lgd = legend(___)
    
    %eg1
        x = linspace(0,pi);
        y1 = cos(x);
        plot(x,y1)
    
        hold on 
        y2 = cos(2*x);
        plot(x,y2)
    
        legend('cos(x)','cos(2x)')
    
        y3 = cos(3*x);
        plot(x,y3,'DisplayName','cos(3x)')
    
    %eg2
        tiledlayout(2,1)
        y1 = rand(3);
        ax1 = nexttile; 
        plot(y1)
    
        y2 = rand(5);
        ax2 = nexttile; 
        plot(y2)
    
        legend(ax1,{'Line 1','Line 2','Line 3'})
    

  • hold on, hold off

  • axis equal
  • grid on, grid off

  • yyaxis

    yyaxis left
    yyaxis right
    yyaxis(ax,___)
    %eg1
        load('accidents.mat','hwydata')
        ind = 1:51;
        drivers = hwydata(:,5);
        pop = hwydata(:,7);
    
        yyaxis left
        scatter(ind,drivers)
        title('Highway Data')
        xlabel('States')
        ylabel('Licensed Drivers (thousands)')
    
        yyaxis right
        scatter(ind,pop)
        ylabel('Vehicle Miles Traveled (millions)')
    

  • text

    x = linspace(-5,5);
    y = x.^3-12*x;
    plot(x,y)
    
    xt = [-2 2];
    yt = [16 -16];
    str = {'local max','local min'};
    text(xt,yt,str)
    

  • colormap

    colormap map
    colormap(map)
    colormap(target,map)
    cmap = colormap(___)
    cmap = colormap
    cmap = colormap(target)
    

• loglog, semilogx, semilogy
• scatter()

• polarplot()

• fplot, fimplicit, fplot3

  • FunctionLine 属性
  • ImplicitFunctionLine 属性

• area

数据分布图

• histogram
• scatter， scatter3
• pie, pie3
• bar, barh, bar3, bar3h
• stem, stem3

等高线图

向量场图

• quiver

  quiver(X,Y,U,V)
  quiver(U,V)
  

曲面图

• surf(), mesh()

  动画

• movie, getframe, drawnow

  movie(M)
  movie(M,n)
  movie(M,n,fps)
  %g1
      h = figure;
      Z = peaks;
      surf(Z)
  
      loops = 40;
      M(loops) = struct('cdata',[],'colormap',[]);
  
      h.Visible = 'off';
      for j = 1:loops
          X = sin(j*pi/10)*Z;
          surf(X,Z)
          drawnow
          M(j) = getframe;
      end
  
      h.Visible = 'on';
      movie(M);
  

图像输出

show

GUI

数据导入

• readtable

  T = readtable("patients.xls");
  T(1:5,1:5)
  
  ans =
  
    5×5 table
  
        LastName        Gender      Age              Location               Height
      ____________    __________    ___    _____________________________    ______
  
      {'Smith'   }    {'Male'  }    38     {'County General Hospital'  }      71  
      {'Johnson' }    {'Male'  }    43     {'VA Hospital'              }      69  
      {'Williams'}    {'Female'}    38     {'St. Mary's Medical Center'}      64  
      {'Jones'   }    {'Female'}    40     {'VA Hospital'              }      67  
      {'Brown'   }    {'Female'}    49     {'County General Hospital'  }      64
  

• readmatrix

  M = readmatrix("basic_matrix.xls")
  
  M = 5×4
  
       6     8     3     1
       5     4     7     3
       1     6     7    10
       4     2     8     2
       2     7     5     9
  

• readcell

  C = readcell("basic_cell.xls")
  
  C = 3×3 cell array
      {[                   1]}    {[    2]}    {[        3]}
      {'hello'               }    {'world'}    {[      NaN]}
      {[10-Oct-2018 10:27:56]}    {[    1]}    {1x1 missing}
  

？？？

• sum()
• 幻方
• 线性方程解法

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