现代算法

现代算法/小波分析/xiaobofenxi.m

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+function main()
+clc;clear all;close all;
+%用Mexihat函数作为样本输入和输出
+x=0:0.03:3; %样本输入值
+c=2/(sqrt(3).*pi.^(1/4));
+d=1/sqrt(2);
+u=x/2-1;
+targ=d.*c.*exp(-u.^2/2).*(1-u.^2);  % 目标函数的样本输出值
+eta=0.02;aerfa=0.735; %赋予网络学习速率和动量因子初始值
+%初始化输出层和隐层的连接权wjh和隐层和输出层的连接权.
+%假设小波函数节点数为H,样本数为P,输出节点数为J,输入节点数为I.
+H=15;P=2;I=length(x);J=length(targ);
+b=rand(H,1);a=rand(H,1); %初始化小波参数
+whi=rand(I,H);wjh=rand(H,J); %初始化权系数；
+b1=rand(H,1);b2=rand(J,1);%阈值初始化;
+p=0;
+Err_NetOut=[];%保存的误差；
+flag=1;count=0;
+while flag>0
+flag=0;
+count=count+1;
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+xhp1=0;
+for h=1:H
+    for i=1:I
+        xhp1=xhp1+whi(i,h)*x(i);
+    end
+ixhp(h)=xhp1+b1(h);
+xhp1=0;
+end
+for h=1:H
+oxhp(h)=fai((ixhp(h)-b(h))/a(h));
+end
+ixjp1=0;
+for j=1:J
+  for h=1:H
+      ixjp1=ixjp1+wjh(h,j)*oxhp(h);
+  end
+ixjp(j)=ixjp1+b2(j);
+ixjp1=0;
+end
+for i=1:J
+oxjp(i)=fnn(ixjp(i));
+end
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+wuchayy=1/2*sumsqr(oxjp-targ);
+Err_NetOut=[Err_NetOut wuchayy];%保存每次的误差;
+%求解小波网络运用BP算法，各参数每次学习的调整量
+for j=1:J
+detaj(j)=-(oxjp(j)-targ(j))*oxjp(j)*(1-oxjp(j));
+end
+for j=1:J
+  for h=1:H
+      detawjh(h,j)=eta*detaj(j)*oxhp(h);
+  end
+end
+detab2=eta*detaj;
+sum=0;
+for h=1:H
+  for j=1:J
+      sum=detaj(j)*wjh(h,j)*diffai((ixhp(h)-b(h))/a(h))/a(h)+sum;
+  end
+detah(h)=sum;
+sum=0;
+end
+for h=1:H
+  for i=1:I
+      detawhi(i,h)=eta*detah(h)*x(i);
+  end
+end
+detab1=eta*detah;
+detab=-eta*detah;
+for h=1:H
+detaa(h)=-eta*detah(h)*((ixhp(h)-b(h))/a(h));
+end
+%引入动量因子aerfa，加快收敛速度和阻碍陷入局部极小值.
+wjh=wjh+(1+aerfa)*detawjh;
+whi=whi+(1+aerfa)*detawhi;
+a=a+(1+aerfa)*detaa';
+b=b+(1+aerfa)*detab';
+b1=b1+(1+aerfa)*detab1';
+b2=b2+(1+aerfa)*detab2';
+%本算法采用的是样本逐个处理而不是数据批处理
+p=p+1;
+if p~=P
+flag=flag+1;
+else
+if Err_NetOut(end)>0.008
+flag=flag+1;
+else
+figure;
+plot(Err_NetOut);
+xlabel('网络学习的次数');ylabel('网络输出的误差');
+title('网络学习误差曲线','fontsize',20,'color',[0 1 1],'fontname','隶书');
+end
+end
+if count>6000
+figure(1);
+subplot(1,2,1)
+plot(Err_NetOut,'color','b','linestyle','-','linewidth',2.2,...
+'marker','^','markersize',3.5);
+xlabel('网络学习的次数');ylabel('网络输出的误差');
+title('误差曲线','fontsize',20,'color',[1 1 1],'fontname','隶书');
+subplot(1,2,2)
+handle1=plot(x,targ,'color','r','linestyle','--','linewidth',2.2,...
+'marker','p','markersize',3.5);
+hold on
+handle1=plot(x,oxjp,'color','g','linestyle','-.','linewidth',2.2,...
+    'marker','d','markersize',3.5);
+xlabel('样本输入值');ylabel('样本目标值与网络输出值');
+title('目标值与网络输出值比较','fontsize',20,'color',[1 1 1],'fontname','隶书');
+legend('样本目标值','网络仿真值');
+break;
+end
+end
+function y3=diffai(x)  %子程序
+y3=-1.75*sin(1.75*x).*exp(-x.^2/2)-cos(1.75*x).*exp(-x.^2/2).*x;
+function yl=fai(x)  %子程序
+yl=cos(1.75.*x).*exp(-x.^2/2);
+function y2=fnn(x)  %子程序
+y2=1/(1+exp(-x));

现代算法/模拟退火法/monituihuo.m

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+clear	
+	clc
+	a = 0.99;	% �¶�˥�������IJ���
+	t0 = 97; tf = 3; t = t0;
+	Markov_length = 10000;	% Markov������
+	coordinates = [
+1	 565.0	 575.0;	2	  25.0	 185.0;	3	 345.0	 750.0;	
+4	 945.0	 685.0;	5	 845.0	 655.0;	6	 880.0	 660.0;	
+7	  25.0	 230.0;	8	 525.0	1000.0;	9	 580.0	1175.0;	
+10	 650.0	1130.0;	11	1605.0	 620.0;	12	1220.0	 580.0;	
+13	1465.0	 200.0;	14	1530.0	   5.0;	15	 845.0	 680.0;	
+16	 725.0	 370.0;	17	 145.0	 665.0;	18	 415.0	 635.0;	
+19	 510.0	 875.0;	20	 560.0	 365.0;	21	 300.0	 465.0;	
+22	 520.0	 585.0;	23	 480.0	 415.0;	24	 835.0	 625.0;	
+25	 975.0	 580.0;	26	1215.0	 245.0;	27	1320.0	 315.0;	
+28	1250.0	 400.0;	29	 660.0	 180.0;	30	 410.0	 250.0;	
+31	 420.0	 555.0;	32	 575.0	 665.0;	33	1150.0	1160.0;	
+34	 700.0	 580.0;	35	 685.0	 595.0;	36	 685.0	 610.0;	
+37	 770.0	 610.0;	38	 795.0	 645.0;	39	 720.0	 635.0;	
+40	 760.0	 650.0;	41	 475.0	 960.0;	42	  95.0	 260.0;	
+43	 875.0	 920.0;	44	 700.0	 500.0;	45	 555.0	 815.0;	
+46	 830.0	 485.0;	47	1170.0	  65.0;	48	 830.0	 610.0;	
+49	 605.0	 625.0;	50	 595.0	 360.0;	51	1340.0	 725.0;	
+52	1740.0	 245.0;	
+];
+	coordinates(:,1) = [];
+	amount = size(coordinates,1); 	% ���е���Ŀ
+	% ͨ���������ķ�������������
+	dist_matrix = zeros(amount, amount);
+	coor_x_tmp1 = coordinates(:,1) * ones(1,amount);
+	coor_x_tmp2 = coor_x_tmp1';
+	coor_y_tmp1 = coordinates(:,2) * ones(1,amount);
+	coor_y_tmp2 = coor_y_tmp1';
+	dist_matrix = sqrt((coor_x_tmp1-coor_x_tmp2).^2 + ...
+					(coor_y_tmp1-coor_y_tmp2).^2);
+
+	sol_new = 1:amount;         % ������ʼ��
+% sol_new��ÿ�β������½⣻sol_current�ǵ�ǰ�⣻sol_best����ȴ�е���ý⣻
+	E_current = inf;E_best = inf; 		% E_current�ǵ�ǰ���Ӧ�Ļ�·���룻
+% E_new���½�Ļ�·���룻
+% E_best�����Ž��
+	sol_current = sol_new; sol_best = sol_new;          
+	p = 1;
+
+	while t>=tf
+		for r=1:Markov_length		% Markov������
+			% ��������Ŷ�
+			if (rand < 0.5)	% ��������ǽ�������������������
+				% ������
+				ind1 = 0; ind2 = 0;
+				while (ind1 == ind2)
+					ind1 = ceil(rand.*amount);
+					ind2 = ceil(rand.*amount);
+				end
+				tmp1 = sol_new(ind1);
+				sol_new(ind1) = sol_new(ind2);
+				sol_new(ind2) = tmp1;
+			else
+				% ������
+				ind1 = 0; ind2 = 0; ind3 = 0;
+				while (ind1 == ind2) || (ind1 == ind3) ...
+					|| (ind2 == ind3) || (abs(ind1-ind2) == 1)
+					ind1 = ceil(rand.*amount);
+					ind2 = ceil(rand.*amount);
+					ind3 = ceil(rand.*amount);
+				end
+				tmp1 = ind1;tmp2 = ind2;tmp3 = ind3;
+				% ȷ��ind1 < ind2 < ind3
+				if (ind1 < ind2) && (ind2 < ind3)
+					;
+				elseif (ind1 < ind3) && (ind3 < ind2)
+					ind2 = tmp3;ind3 = tmp2;
+				elseif (ind2 < ind1) && (ind1 < ind3)
+					ind1 = tmp2;ind2 = tmp1;
+				elseif (ind2 < ind3) && (ind3 < ind1) 
+					ind1 = tmp2;ind2 = tmp3; ind3 = tmp1;
+				elseif (ind3 < ind1) && (ind1 < ind2)
+					ind1 = tmp3;ind2 = tmp1; ind3 = tmp2;
+				elseif (ind3 < ind2) && (ind2 < ind1)
+					ind1 = tmp3;ind2 = tmp2; ind3 = tmp1;
+				end
+
+				tmplist1 = sol_new((ind1+1):(ind2-1));
+				sol_new((ind1+1):(ind1+ind3-ind2+1)) = ...
+					sol_new((ind2):(ind3));
+				sol_new((ind1+ind3-ind2+2):ind3) = ...
+					tmplist1;
+			end
+
+			%����Ƿ�����Լ��
+
+			% ����Ŀ�꺯��ֵ�������ܣ�
+			E_new = 0;
+			for i = 1 : (amount-1)
+				E_new = E_new + ...
+					dist_matrix(sol_new(i),sol_new(i+1));
+			end
+			% �����ϴ����һ�����е���һ�����еľ���
+			E_new = E_new + ...
+				dist_matrix(sol_new(amount),sol_new(1));
+
+			if E_new < E_current
+				E_current = E_new;
+				sol_current = sol_new;
+				if E_new < E_best
+% ����ȴ��������õĽⱣ������
+					E_best = E_new;
+					sol_best = sol_new;
+				end
+			else
+				% ���½��Ŀ�꺯��ֵС�ڵ�ǰ��ģ�
+				% �����һ�����ʽ����½�
+				if rand < exp(-(E_new-E_current)./t)
+					E_current = E_new;
+					sol_current = sol_new;
+				else	
+					sol_new = sol_current;
+				end
+			end
+		end
+		t=t.*a;		% ���Ʋ���t���¶ȣ�����Ϊԭ����a��
+	end
+
+	disp('���Ž�Ϊ��')
+	disp(sol_best)
+	disp('��̾��룺')
+	disp(E_best)

现代算法/神经网络/Lecture 2/SIsin.m

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+u=[-1:0.05:1];
+% t=sin(2*pi*u);
+t=0.5+0.5*sin(2*pi*u);
+% try to use different f and training algo.
+net=newff([-1 1],[10 1],{'tansig','purelin'},'trainlm');
+% training param.
+net.trainParam.goal=1e-8;
+net.trainParam.epochs=10000;
+
+[net,tr]=train(net,u,t);
+y=sim(net,u);
+% plot(u,t,'b',u,y,'r');
+% nnd9sdq