优化这段代码function parafitzzsd1 t=[1964 1985 1992 1997 1999 2004 2007 2020]; y=[1.0625 1.1333 1.4167 1.4407 1.4783 1.4783 1.5455 1.5455]; z=[0.6563 0.7188 0.8438 0.9375 0.8906 0.8125 0.9375 0.9375]; y0=1.0625; % Nonlinear least square estimate using lsqnonlin() k0=[0,0,0]; lb=[0,0,0];ub=[inf,inf,inf]; [k,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin(@Func,k0,lb,ub,[],t,y0); ci = nlparci(k,residual,jacobian); k; % result fprintf('\n Estimated Parameters by Lsqnonlin():\n') fprintf('\t k1 = %.4f ± %.4f\n',k(1),ci(1,2)-k(1)) fprintf('\t k2 = %.4f ± %.4f\n',k(2),ci(2,2)-k(2)) fprintf('\t k3 = %.4f ± %.4f\n',k(3),ci(3,2)-k(3)) fprintf(' The sum of the residual squares is: %.1e\n\n',sum(residual.^2)) % plot of fit results tspan = [1964 2050]; [tt yc] = ode45(@ModelEqs,tspan,y0,[],k); tc=linspace(1964,2050,400); yca = spline(tt,yc,tc); plot(t,y,'ro',tc,yca,'r-'); hold on xlabel('Time'); ylabel('y'); hold off % ======================================= function f1 = Func(k,t,y,y0) % Define objective function tspan =t; [tt yy] = ode45(@ModelEqs,tspan,y0,[],k); yc= spline(tt,yy,t); f1=y-yc; % ================================== function dydt = ModelEqs(t,y,k) dydt =k(1)*y-k(2)*y.^2+k(3)*y*z;

There are a few ways to optimize this code:

1. Vectorization: Instead of using a for loop to solve the ODE, you can use vectorization to solve it for all time points at once. This can significantly speed up the code.

2. Preallocation: Preallocate any arrays that are used in loops to avoid reallocation at each iteration.

3. Use anonymous functions: Instead of defining separate functions for the objective function and the ODE, you can use anonymous functions to define them inline. This can make the code more concise and easier to read.

Here's an optimized version of the code:

% Define data
t = [1964 1985 1992 1997 1999 2004 2007 2020];
y = [1.0625 1.1333 1.4167 1.4407 1.4783 1.4783 1.5455 1.5455];
z = [0.6563 0.7188 0.8438 0.9375 0.8906 0.8125 0.9375 0.9375];
y0 = 1.0625;

% Define objective function and ODE inline
objfun = @(k) y - spline(ode45(@(t,y) k(1)*y - k(2)*y.^2 + k(3)*y.*z, t, y0), t);
odefun = @(t,y,k) k(1)*y - k(2)*y.^2 + k(3)*y.*z;

% Nonlinear least square estimate using lsqnonlin()
k0 = [0, 0, 0];
lb = [0, 0, 0];
ub = [inf, inf, inf];
options = optimoptions('lsqnonlin', 'Display', 'off');
k = lsqnonlin(objfun, k0, lb, ub, options);

% Calculate confidence intervals
J = jacobianest(objfun, k);
ci = nlparci(k, objfun(k), J);

% Display results
fprintf('\n Estimated Parameters by Lsqnonlin():\n')
fprintf('\t k1 = %.4f ± %.4f\n', k(1), ci(1,2)-k(1))
fprintf('\t k2 = %.4f ± %.4f\n', k(2), ci(2,2)-k(2))
fprintf('\t k3 = %.4f ± %.4f\n', k(3), ci(3,2)-k(3))
fprintf('  The sum of the residual squares is: %.1e\n\n', sum(objfun(k).^2))

% Plot of fit results
tspan = [1964  2050];
[tt, yc] = ode45(odefun, tspan, y0, [], k);
tc = linspace(1964, 2050, 400);
yca = spline(tt, yc, tc);
plot(t, y, 'ro', tc, yca, 'r-');
xlabel('Time');
ylabel('y');