Matlab与Linear Algebra

det(A)就是求A的行列式，这里要求A为方阵
inv（A）求A的逆矩阵
A的伴随矩阵就是det(A)*inv(A)
B=A’ ,” ‘ “是求矩阵转置的意思
rank(A)求A的秩
rref(A)把A化到行最简形
rrefmovie(A)显示rref每一步操作

但要加入下面的代码

function rrefmovie(A,tol)
%RREFMOVIE Movie of the computation of the reduced row echelon form.
%   RREFMOVIE(A) produces the reduced row echelon form of A.
%   RREFMOVIE, by itself, supplies its own 8-by-6 matrix with rank 4.
%   RREFMOVIE(A,tol) uses the given tolerance in the rank tests.

%   Copyright 1984-2004 The MathWorks, Inc.
%   $Revision: 5.12.4.3 $  $Date: 2004/04/10 23:25:44 $

% Sample matrix if none was provided.

commandwindow

Old_Format=get(0,'Format');
if nargin < 1

    A = [ 9     4     1     6    12     7
          4     0     4    15     1    14
          7     0     7     8    10     9
         16     0    16     3    13     2
          0     2    -4     0     0     0
          0     6   -12     0     0     0
          9     0     9     6    12     7
          5     0     5    10     8    11];
end
format rat
more off
clc
home
disp('  Original matrix')
A
disp('Press any key to continue. . .'), pause
[m,n] = size(A);

% Compute the default tolerance if none was provided.
if (nargin < 2), tol = max([m,n])*eps*norm(A,'inf'); end

% Loop over the entire matrix.
i = 1;
j = 1;
k = 0;
while (i <= m) && (j <= n)
   % Find value and index of largest element in the remainder of column j.
   [p,k] = max(abs(A(i:m,j))); k = k+i-1;
   if (p <= tol)
      % The column is negligible, zero it out.
      home
      disp(['  column ' int2str(j) ' is negligible'])
      A(i:m,j) = zeros(m-i+1,1)
      disp('Press any key to continue. . .'), pause
      j = j + 1;
   else
      if i ~= k
         % Swap i-th and k-th rows.
         home
         disp(['  swap rows ' int2str(i) ' and ' int2str(k) blanks(10)])
         A([i k],:) = A([k i],:)
         disp('Press any key to continue. . .'), pause
      end
      % Divide the pivot row by the pivot element.
      home
      disp(['  pivot = A(' int2str(i) ',' int2str(j) ')' blanks(10)])
      A(i,j:n) = A(i,j:n)/A(i,j)
      disp('Press any key to continue. . .'), pause
      home
      % Subtract multiples of the pivot row from all the other rows.
      disp(['  eliminate in column ' int2str(j) blanks(10)])
      A
      disp('Press any key to continue. . .'), pause
      for k = 1:m
         if k ~= i
            home
            disp(' ')
            A(k,j:n) = A(k,j:n) - A(k,j)*A(i,j:n)
         end
      end
      disp('Press any key to continue. . .'), pause
      i = i + 1;
      j = j + 1;
   end
end
%  Restore Format
set(0,'Format',Old_Format)

SEIR模型

save(‘data.mat’,’a’,’b’,’c’) %假如有三个变量’a’, ‘b’, ‘c’，要将它们保存在’data’数据文件中

v = load(‘data.mat’,’a’) %将’data’数据文件中’a’变量读出存到’v’中
画图

subplot(m,n,p)
m,n说明分成几行几列，p说明是第几个（左→右，上↓下）

hold on

Yalmip

介绍

yalmip是由Lofberg开发的一种免费的优化求解工具，其最大特色在于集成许多外部的最优化求解器，形成一种统一的建模求解语言，提供了Matlab的调用API，减少学习者学习成本。

下载 Yalmip 工具箱：

https://yalmip.github.io/
放到toolbox文件夹下
设置路径。选择“添加并包含子文件夹”，将 yalmip 的路径添加进去

测试是否成功：

doc yalmip

yalmiptest

which sdpva

教程

命令

sdpvar:实数变量

intvar：整数变量

binvar：0-1变量

check：可以检查约束条件是否被满足（检查约束条件的余值）

value：可以查看变量或表达式的值

assign: 可以给变量赋值，这个命令调试时很重要

options=sdpsettings(‘solver’,’cplex’); 设置求解方法为调用 CPLEX

optimize(constraints,f,options); Yalmip求解的命令。