function [x,y]=eulerpro(fun,x0,xfinal,y0,n);
if nargin<5,n=50;end 
h=(xfinal-x0)/n;
x(1)=x0;y(1)=y0;
for i=1:n
    x(i+1)=x(i)+h;
    y1=y(i)+h*feval(fun,x(i),y(i));
    y2=y(i)+h*feval(fun,x(i+1),y1);
    y(i+1)=(y1+y2)/2;
end 

function Derivatives(block)

tau = block.DialogPrm(1).Data;
Uc = block.DialogPrm(2).Data; 

if block.CurrentTime <= block.DialogPrm(3).Data
    block.Dwork(3).Data = 0;
else
    block.Dwork(3).Data = 1;
end
    
block.Derivatives.Data = block.Dwork(3).Data * 1/tau * (block.InputPort(1).data^2 / Uc^2 - 1);
%endfunction

function msfunCassie(block)
% smileland作品，免费使用，但请不要删除此句话
% 以下设定参数并不一定全部需要，不需要的注释掉就好
setup(block);

%endfunction

function setup(block)
  %block.CurrentTime 只读对象，调用当前时间

  % 初始化对话框参数，即对话框内给定的初始化参数.
  block.NumDialogPrms     = 2;%给定2个参数
  %block.DialogPrmsTunable = {'Tunable','Nontunable','SimOnlyTunable'};%参数是否可变（此句话可选是否需要，默认不可变）

  %%%%%%%%初始化输入输出端口的属性%%%%%%%
  
  % 初始化输入输出端口个数.
  block.NumInputPorts  = 1;%输入端口个数
  block.NumOutputPorts = 1;%输出端口个数
  
  % 设定输入输出端口时继承还是动态，以指示输入和输出端口从模型继承其已编译属性（尺寸、数据类型、复杂度和采样模式）.
  block.SetPreCompInpPortInfoToDynamic;%设定输入端口为动态
  block.SetPreCompOutPortInfoToDynamic;%设定输出端口为动态

  % 设定输入端口属性.（也可以再Dwork中设定，在PostPropagationSetup子方法中）
  block.InputPort(1).DatatypeID  = 0;  % （-1 inherited；0 double;1 single;2 int8;3 uint8;4 int16;5 uint16;6 int32;7 uint12;8 boolean）
  block.InputPort(1).Complexity  = 'Real';%是否为复数
  
  % 设定输出端口属性.（也可以再Dwork中设定，在PostPropagationSetup子方法中）
  block.OutputPort(1).DatatypeID  = 0; % double
  block.OutputPort(1).Complexity  = 'Real';
  
  block.InputPort(1).Dimensions = 1;%输入口1的维数是1，最高支持到2维
  % block.InputPort(1).DimensionsMode = 'Fixed';%Fixed表示端口维数固定，Variable表示端口维数可变
  block.OutputPort(1).Dimensions = 1;%输出口1的维数是1，最高支持到2维
  % block.OutputPort(1).DimensionsMode = 'Fixed';%Fixed表示端口维数固定，Variable表示端口维数可变
  
  block.InputPort(1).DirectFeedthrough = true;%输入口有无直接馈通（true/false）
  
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
  % 设定有多少连续状态变量.
  block.NumContStates = 1;
  
  % 设定有多少离散状态变量.
  % block.NumDworkDiscStates = 1;

  % 设定采样时间.
  %  [0 0.5]            : 从0.5s开始连续采样
  %  [0.1 0.5]          : 从0.5s开始，每0.1s采样一次
  %  [-1, 0]            : 继承采样频率
  %  [-2, 0]            : 动态变化的采样频率
  block.SampleTimes = [0 0];%连续采样率
  
  %设定离散工作向量个数
  % block.NumDworks = 1;
  
  % -----------------------------------------------------------------
  % Options，若使用TLC则需要以下语句，否则注释掉即可
  % -----------------------------------------------------------------

  % block.SetAccelRunOnTLC(false);
  
  % block.OperatingPointCompliance = 'Default';
  
  % -----------------------------------------------------------------
  % 引用使用的子方法，主要有PostPropagationSetup;InitializeConditions;
  % Start;Outputs;Updates;Derivatives;Terminate.以下子方法仅保留着几个。
  % -----------------------------------------------------------------
  
  %{
  %包含PostPropagationSetup子方法，用于初始化DWork工作向量
  block.RegBlockMethod('PostPropagationSetup', @DoPostPropSetup);
  %}
  
  %包含InitializeConditions子方法，用于初始化状态变量或DWork工作向量的值
  block.RegBlockMethod('InitializeConditions', @InitializeConditions);
  
  %与InitializeConditions子方法功能一致，但只初始化一次，Ini方法每次调用子方法时均会初始化
  % block.RegBlockMethod('Start', @Start);

  %包含输出模块
  block.RegBlockMethod('Outputs', @Outputs);

  %包含离散状态更新模块
  %block.RegBlockMethod('Update', @Update);

  %包含连续状态微分模块
  block.RegBlockMethod('Derivatives', @Derivatives);
  
  %包含终止模块
  %block.RegBlockMethod('Terminate', @Terminate);

  %还有其他模块，仅将最主要的列出，若需要则使用S函数自带模板。
%endfunction

% -------------------------------------------------------------------
% 以下为子方法模块，同样主要有DoPostPropSetup;InitializeConditions;
  % Start;Outputs;Updates;Derivatives;Terminate.以下子方法仅保留这几个。
% -------------------------------------------------------------------
%{
function DoPostPropSetup(block)
  block.NumDworks = 4;
  
  block.Dwork(1).Name            = 'tau';
  block.Dwork(1).Dimensions      = 1;
  block.Dwork(1).DatatypeID      = 0;      % double
  block.Dwork(1).Complexity      = 'Real'; % real
  block.Dwork(1).UsedAsDiscState = false;
  
  block.Dwork(2).Name            = 'Uc';
  block.Dwork(2).Dimensions      = 1;
  block.Dwork(2).DatatypeID      = 0;      % double
  block.Dwork(2).Complexity      = 'Real'; % real
  block.Dwork(2).UsedAsDiscState = false;
  
  block.Dwork(3).Name            = 'step';
  block.Dwork(3).Dimensions      = 1;
  block.Dwork(3).DatatypeID      = 0;      % double
  block.Dwork(3).Complexity      = 'Real'; % real
  block.Dwork(3).UsedAsDiscState = false;
  
  block.Dwork(4).Name            = 'u';
  block.Dwork(4).Dimensions      = 1;
  block.Dwork(4).DatatypeID      = 0;      % double
  block.Dwork(4).Complexity      = 'Real'; % real
  block.Dwork(4).UsedAsDiscState = false;
  
  % Register all tunable parameters as runtime parameters.
  block.AutoRegRuntimePrms;

%endfunction
%}
%

function InitializeConditions(block)

block.ContStates.Data = log(1e-6);
    
%{
function Start(block)

  tau = block.DialogPrm(1).Data;
  Uc = block.DialogPrm(2).Data; 

%}

%{
  function Update(block)
  block.Dwork(1).Data = [];
%}

function Outputs(block)
  
  block.OutputPort(1).Data = block.InputPort(1).data * exp(block.ContStates.Data);
  
  
function Derivatives(block)

tau = block.DialogPrm(1).Data;
Uc = block.DialogPrm(2).Data; 
  
if block.CurrentTime <= 0.02
    step = 0;
else
    step = 1;
end
    
block.Derivatives.Data = step * 1/tau * (block.InputPort(1).data^2 / Uc^2 - 1);
%endfunction

%endfunction
  
%function Terminate(block)

%disp(['Terminating the block with handle ' num2str(block.BlockHandle) '.']);

%endfunction

function msfuntmpl(block)
%MSFUNTMPL A Template for a MATLAB S-Function
%   The MATLAB S-function is written as a MATLAB function with the
%   same name as the S-function. Replace 'msfuntmpl' with the name
%   of your S-function.  

%   Copyright 2003-2018 The MathWorks, Inc.
  
%
% The setup method is used to setup the basic attributes of the
% S-function such as ports, parameters, etc. Do not add any other
% calls to the main body of the function.  
％设置方法用于设置S功能的基本属性，例如端口，参数等。请勿在功能主体上添加其他任何调用。
%   

setup(block);%设置模块
  
%endfunction

% Function: setup ===================================================
% Abstract:
%   Set up the S-function block's basic characteristics such as:%设定基础参数
%   - Input ports%输入端口
%   - Output ports%输出端口
%   - Dialog parameters%对话参数
%   - Options%选项
% 
%   Required         : Yes
%   C MEX counterpart: mdlInitializeSizes
%
function setup(block)

  % Register the parameters.初始化对话框参数
  block.NumDialogPrms     = 1;%初始化三个S函数对话框参数
  block.DialogPrmsTunable = {'Tunable','Nontunable','SimOnlyTunable'};%参数是否可变

  % Register the number of ports.设置输入输出端口数
  block.NumInputPorts  = 1;
  block.NumOutputPorts = 1;
  
  % Set up the port properties to be inherited or dynamic.将端口属性设置为继承或动态。以指示输入和输出端口从模型继承其已编译属性（尺寸，数据类型，复杂度和采样模式）
  block.SetPreCompInpPortInfoToDynamic;%设定输入端口属性为动态
  block.SetPreCompOutPortInfoToDynamic;%设定输出端口属性为动态

  % Override the input port properties.覆盖输入端口属性
  block.InputPort(1).DatatypeID  = 0;  % double
  block.InputPort(1).Complexity  = 'Real';
  
  % Override the output port properties.覆盖输出端口属性
  block.OutputPort(1).DatatypeID  = 0; % double
  block.OutputPort(1).Complexity  = 'Real';

  % Hard-code certain port properties
  block.InputPort(1).Dimensions = 1;
  block.InputPort(1).DirectFeedthrough = false;
  block.OutputPort(1).Dimensioins = 1;
  
  % Set up the continuous states.设定具有连续状态变量个数
  % block.NumContStates = 1;

  % Register the sample times.设定采样时间
  %  [0 offset]            : Continuous sample time连续的采样时间
  %  [positive_num offset] : Discrete sample time离散的采样时间
  %
  %  [-1, 0]               : Inherited sample time继承的采样时间
  %  [-2, 0]               : Variable sample time可变采样时间
  block.SampleTimes = [0.1 0];%设定上面的采样时间，设置为[-1 0]即制定S函数具有继承的采样时间
  
   % -----------------------------------------------------------------
   % Register the methods called during update diagram/compilation.
   % -----------------------------------------------------------------
   
  %
  % PostPropagationSetup:
  %   Functionality    : Set up the work areas and the state variables. You can
  %                      also register run-time methods here.
  %   C MEX counterpart: mdlSetWorkWidths
  %
  block.RegBlockMethod('PostPropagationSetup', @DoPostPropSetup);
  
  % 
  % InitializeConditions:
  %   Functionality    : Call to initialize the state and the work
  %                      area values.
  %   C MEX counterpart: mdlInitializeConditions
  % 
  block.RegBlockMethod('InitializeConditions', @InitializeConditions);
  
  % 
  % Outputs:
  %   Functionality    : Call to generate the block outputs during a
  %                      simulation step.
  %   C MEX counterpart: mdlOutputs
  %
  block.RegBlockMethod('Outputs', @Outputs);
  
  % 
  % Update:
  %   Functionality    : Call to update the discrete states
  %                      during a simulation step.
  %   C MEX counterpart: mdlUpdate
  %
  block.RegBlockMethod('Update', @Update);
  
  % 
  % Derivatives:
  %   Functionality    : Call to update the derivatives of the
  %                      continuous states during a simulation step.
  %   C MEX counterpart: mdlDerivatives
  %
  block.RegBlockMethod('Derivatives', @Derivatives);

 function DoPostPropSetup(block)
  block.NumDworks = 1;
  
  block.Dwork(1).Name            = 'x0';
  block.Dwork(1).Dimensions      = 1;
  block.Dwork(1).DatatypeID      = 0;      % double
  block.Dwork(1).Complexity      = 'Real'; % real
  block.Dwork(1).UsedAsDiscState = true;

  % Register all tunable parameters as runtime parameters.
  block.AutoRegRuntimePrms;

%endfunction

function InitializeConditions(block)

block.Dwork(1).Data = block.DialogPrm(1).Data;
block.ContStates.Data = 1;

%endfunction

function Outputs(block)
  
  block.OutputPort(1).Data = block.Dwork(1).Data;
  
%endfunction

function Update(block)
  
  block.Dwork(1).Data = block.InputPort(1).Data;
  
%endfunction

function Derivatives(block)

block.Derivatives(1).Data = block.InputPort(1).Data;

%endfunction

m1 = imread('阿布罗狄.jpg');
m1 = m1(:,:,1);
m2 = imread('艾欧里亚.jpg');
m2 = m1(:,:,1);

setup(block);%设置模块
  
%endfunction

% Function: setup ===================================================
% Abstract:
%   Set up the S-function block's basic characteristics such as:%设定基础参数
%   - Input ports%输入端口
%   - Output ports%输出端口
%   - Dialog parameters%对话参数
%   - Options%选项
% 
%   Required         : Yes
%   C MEX counterpart: mdlInitializeSizes
%
function setup(block)

  % Register the number of ports.设置输入输出端口数
  block.NumInputPorts  = 2;
  block.NumOutputPorts = 0;
  
  % Set up the port properties to be inherited or dynamic.将端口属性设置为继承或动态。以指示输入和输出端口从模型继承其已编译属性（尺寸，数据类型，复杂度和采样模式）
  block.SetPreCompInpPortInfoToDynamic;%设定输入端口属性为动态

  % Override the input port properties.覆盖输入端口属性
  block.InputPort(1).DatatypeID  = 3;  % uint8
  block.InputPort(1).Complexity  = 'Real';
  block.InputPort(2).DatatypeID  = 3;  % uint8
  block.InputPort(2).Complexity  = 'Real';

  % Hard-code certain port properties
  block.InputPort(1).Dimensions = [375 500];
  block.InputPort(1).DirectFeedthrough = false;
  block.InputPort(2).Dimensions = [375 500];
  block.InputPort(2).DirectFeedthrough = false;
  
  %Register parameters
  block.NumDialogPrms = 0;
  
  % Set up the continuous states.设定具有连续状态变量个数
  % block.NumContStates = 1;

  % Register the sample times.设定采样时间
  %  [0 offset]            : Continuous sample time连续的采样时间
  %  [positive_num offset] : Discrete sample time离散的采样时间
  %
  %  [-1, 0]               : Inherited sample time继承的采样时间
  %  [-2, 0]               : Variable sample time可变采样时间
  block.SampleTimes = [0 0];%设定上面的采样时间，设置为[-1 0]即制定S函数具有继承的采样时间
  
  block.SimStateCompliance = 'DefaultSimState';
  
   % -----------------------------------------------------------------
   % Register the methods called during update diagram/compilation.
   % -----------------------------------------------------------------
   
  %
  % PostPropagationSetup:
  %   Functionality    : Set up the work areas and the state variables. You can
  %                      also register run-time methods here.
  %   C MEX counterpart: mdlSetWorkWidths
  %
 % block.RegBlockMethod('PostPropagationSetup', @DoPostPropSetup);
  
  % 
  % InitializeConditions:
  %   Functionality    : Call to initialize the state and the work
  %                      area values.
  %   C MEX counterpart: mdlInitializeConditions
  % 
%  block.RegBlockMethod('InitializeConditions', @InitializeConditions);
  
  % 
  % Outputs:
  %   Functionality    : Call to generate the block outputs during a
  %                      simulation step.
  %   C MEX counterpart: mdlOutputs
  %
%  block.RegBlockMethod('Outputs', @Outputs);
  
  % 
  % Update:
  %   Functionality    : Call to update the discrete states
  %                      during a simulation step.
  %   C MEX counterpart: mdlUpdate
  %
%  block.RegBlockMethod('Update', @Update);
  
  % 
  % Derivatives:
  %   Functionality    : Call to update the derivatives of the
  %                      continuous states during a simulation step.
  %   C MEX counterpart: mdlDerivatives
  %
%  block.RegBlockMethod('Derivatives', @Derivatives);

  % 
  % Terminate:
  %   Functionality    : Call at the end of a simulation for cleanup.
  %   C MEX counterpart: mdlTerminate
  %
  block.RegBlockMethod('Terminate', @Terminate);
  
  function Terminate(block)

  imshow((block.InputPort(1).data + block.InputPort(2).data) / 2);

  %endfunction