covidvaccine.m
8daa7c7f64acmaster

covidvaccine.m
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			function [alpha,alpha_bfgs]=covidvaccine(m)
			d=load("datavdvaccine.csv");
			ld=length(d);
			x=sparse(m,1);
			y=sparse(m,1);
			alpha=sparse(2,1);
			for i=1:m
			x(i)=i;
			y(i)=d(i);%exp(0.1*x(i));
			end
			%Initialization Newton
			alpha(1)=10200;
			alpha(2)=0.032;
			%Initialization BFGS
			alpha_init(1) = 1;
			alpha_init(2) = 0.1;
			for i=1:m
			ystart(i)=alpha(1)exp(alpha(2)x(i));
			end
			%Newton algorithm
			for iter=1:10
			g=zeros(2,1);
			h=zeros(2,2);
			for i=1:m
			eax=exp(alpha(2)*x(i));
			gg=alpha(1)exp(alpha(2)x(i))-y(i);
			g(1)=g(1)+gg*eax;
			g(2)=g(2)+ggalpha(1)x(i)*eax;
			h(1,1)=h(1,1)+???;
			h(1,2)=h(1,2)+???;
			h(2,2)=h(2,2)+???;
			end
			h(2,1)=h(1,2);
			delta=h\g;
			nd=norm(delta)
			ng=norm(g)
			if (nd<1.e-8)
			iter
			break
			end
			alpha=alpha-delta;
			end

			%BFGS algorithm
			alpha_init = full(alpha_init);
			f = @(z) 0.5sum((z(1).exp(z(2)*full(x))-full(y)).^2);
			options = optimoptions('fminunc','Algorithm','quasi-newton');
			options.StepTolerance = 1e-10;

			[alpha_bfgs, fval, exit, output] = fminunc(f,alpha_init,options)

			for i=1:m
			yend(i)=alpha(1)exp(alpha(2)x(i));
			yend_bfgs(i)=alpha_bfgs(1)exp(alpha_bfgs(2)x(i));
			end
			figure
			plot(x,y,'o',x,ystart,x,yend,x,yend_bfgs)
			legend('data','initial','Newton','BFGS')
			figure
			plot(x,y,'o',x,yend,x,yend_bfgs)
			legend('data','Newton','BFGS')
			f(alpha)
			f(alpha_bfgs)
			end