随机游走问题的神奇应用(三)

二维变概率问题的Matlab GUI设计

一.方程的基本形式
二.基本框架的搭建
三.关键函数

一.方程的基本形式

a(P)∂2u∂x2+b(P)∂2u∂y2+c(P)∂u∂x+d(P)∂u∂y+e(P)u(P)=q(P),p∈Du(Q)=f(Q),Q∈Γ=∂Da(P)\frac{\partial ^2u}{\partial x^2}+b(P)\frac{\partial ^2u}{\partial y^2}+c(P)\frac{\partial u}{\partial x}+d(P)\frac{\partial u}{\partial y}+e(P)u(P) = q(P),p\in D\\ u(Q) = f(Q),Q\in\Gamma = \partial D a(P)∂x2∂2u+b(P)∂y2∂2u+c(P)∂x∂u+d(P)∂y∂u+e(P)u(P)=q(P),p∈Du(Q)=f(Q),Q∈Γ=∂D
若a(P),b(P)>0,e(P)≤0a(P),b(P)>0,e(P)\leq 0a(P),b(P)>0,e(P)≤0求u(P),p∈Du(P),p\in Du(P),p∈D的数值解。

解法参考

二.基本框架的搭建

三.关键函数

随机游走函数：

function [uFinal,zeta,FirstPx,FirstPy,u] = possionRandomChangeGUI(xPoint,yPoint,a,b,c ,d ,e,q,f,Constrain,h,N)
%UNTITLED 求a = 1/4;b = 1/8;c = 1/2;d = 1/2;e = 0;q = x+2y+1 在u(L) = 2边界条件
%   [xPoint,yPoint]表示该点坐标,h仿真步长,N仿真次数
u = zeros(1,N);
W = @(x,y)(1-h^2*e(x,y)/(2*(a(x,y)+b(x,y))))^(-1);
Z = @(x,y)(q(x,y)/(a(x,y)+b(x,y)));
for i = 1:NsumV = 0;xValue = xPoint;yValue = yPoint;P = [xValue ,yValue];Ws = 1;%以下是游走过程while(1)if Constrain(xValue,yValue)>0P = [P;xValue,yValue];break;endA = (2*a(xValue,yValue)+h*c(xValue,yValue))/(4*(a(xValue,yValue)+b(xValue,yValue)));B = (2*a(xValue,yValue)-h*c(xValue,yValue))/(4*(a(xValue,yValue)+b(xValue,yValue)));C = (2*b(xValue,yValue)+h*d(xValue,yValue))/(4*(a(xValue,yValue)+b(xValue,yValue)));D = (2*b(xValue,yValue)-h*d(xValue,yValue))/(4*(a(xValue,yValue)+b(xValue,yValue)));randNumber = randsrc(1,1,[[0 1 2 3];[A C B D]]);switch (randNumber)case 0xValue = xValue + h;yValue = yValue;case 1xValue = xValue ;yValue = yValue + h;case 2xValue = xValue - h ;yValue = yValue ;    case 3xValue = xValue;yValue = yValue - h;endP = [P;xValue,yValue];end%以下是画图过程if i == 1FirstPx = P(:,1);FirstPy = P(:,2);end%以下是计算过程[m,n] = size(P);for j = 1:m-1Ws = Ws*W(P(j,1),P(j,2));sumV = sumV + Ws*Z(P(j,1),P(j,2));endzeta(i) = -h^2/2*sumV + Ws*f(P(m,1),P(m,2));u(i) = sum(zeta(1:i))/i;
end
uFinal = u(N);
% xlabel('次数');
% ylabel('进化曲线');
% title('收敛过程');
end

两个按键的回调函数：

% --- Executes on button press in walk.
function walk_Callback(hObject, eventdata, handles)
% hObject    handle to walk (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
af = str2func(get(handles.a,'String'));
bf = str2func(get(handles.b,'String'));
cf = str2func(get(handles.c,'String'));
df = str2func(get(handles.d,'String'));
ef = str2func(get(handles.e,'String'));
qf = str2func(get(handles.q,'String'));
hn = str2num(get(handles.h,'String'));
ff = str2func(get(handles.f,'String'));
Areaf = str2func(get(handles.Area,'String'));
xLP = str2num(get(handles.xL,'String'));
yLP = str2num(get(handles.yL,'String'));
N = str2num(get(handles.N,'String'));
[uFinal,zeta,FirstPx,FirstPy,u] = possionRandomChangeGUI(xLP,yLP,af,bf,cf ,df ,ef,qf,ff,Areaf,hn,N);
set(handles.uxy,'String',num2str(uFinal));
axes(handles.Imag1);
plot(FirstPx,FirstPy,'b.-');
xlabel('x');
ylabel('y');
title('第一次的轨迹');% --- Executes on button press in breakUp.
function breakUp_Callback(hObject, eventdata, handles)
% hObject    handle to breakUp (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
af = str2func(get(handles.a,'String'));
bf = str2func(get(handles.b,'String'));
cf = str2func(get(handles.c,'String'));
df = str2func(get(handles.d,'String'));
ef = str2func(get(handles.e,'String'));
qf = str2func(get(handles.q,'String'));
hn = str2num(get(handles.h,'String'));
ff = str2func(get(handles.f,'String'));
Areaf = str2func(get(handles.Area,'String'));
xLP = str2num(get(handles.xL,'String'));
yLP = str2num(get(handles.yL,'String'));
N = str2num(get(handles.N,'String'));
[uFinal,zeta,FirstPx,FirstPy,u] = possionRandomChangeGUI(xLP,yLP,af,bf,cf ,df ,ef,qf,ff,Areaf,hn,N);
axes(handles.Imag1);
plot(1:N,u,'r-');
xlabel('次数');
ylabel('进化曲线');
title('收敛过程');
set(handles.uxy,'String',num2str(uFinal));

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