matlab指数增长和阻滞增长拟合代码之欧阳文创编

代码：

时间：2021.03.12 创作：欧阳文 t=1:13;

x=[3.04,6.63,11.13,28.43,49.22,87.85,134.11,200.00,208.69,303.03,410.73,580.00,728.57];

c=[0.40,0.97,2.31,4.45,7.63,10.11,19.86,33.44,38.03,75.07,112.08,152.39,226.55];

d=[2.06,2.35,3.17,8.06,15.22,28.82,43.31,54.67,55.83,75.26,102.01,174.05,200.95];

e=[0.54,1.18,1.98,5.06,8.77,15.65,23.89,36.63,37.17,53.98,73.16,123.31,159.78]; %指数增长模型 y=log(x); cc=log(c); dd=log(d); ee=log(e);

a=polyfit(t,y,1); h=polyfit(t,cc,1); i=polyfit(t,dd,1); k=polyfit(t,ee,1); r=a(1);

欧阳文创编

欧阳文创编

r2=h(1); r3=i(1); r4=k(1); x0=exp(a(2)); x1=x0*exp(r*t); c0=exp(h(2)); c1=c0*exp(r2*t); d0=exp(i(2)); d1=d0*exp(r3*t); e0=exp(k(2)); e1=e0*exp(r4*t); %阻滞增长模型

f=@(a,t) a(1)./(1+(a(1)/x(1)-1)*exp(-a(2)*(t-t(1)))); f=@(h,t) h(1)./(1+(h(1)/c(1)-1)*exp(-h(2)*(t-t(1)))); f=@(i,t) i(1)./(1+(i(1)/d(1)-1)*exp(-i(2)*(t-t(1)))); f=@(k,t) k(1)./(1+(k(1)/e(1)-1)*exp(-k(2)*(t-t(1)))); a=lsqcurvefit(f,[800 1],t,x); h=lsqcurvefit(f,[800 1],t,c); i=lsqcurvefit(f,[800 1],t,d); k=lsqcurvefit(f,[800 1],t,e); figure(1); subplot(2,1,1);

欧阳文创编

欧阳文创编

plot(t,x,'o',t,x1,'r:.'); x2=f(a,t);

plot(t,x,'o',t,x1,'r:.',t,x2,'g*--')

legend('原始数据','指数增长模型','阻滞增长模型',2) xlabel 时间段

ylabel 公众号总量（万） title('资讯类'); figure(1)

subplot(2,1,2);

plot(t,c,'o',t,c1,'r:.'); c2=f(h,t);

plot(t,c,'o',t,c1,'r:.',t,c2,'g*--')

legend('原始数据','指数增长模型','阻滞增长模型',2) xlabel 时间段

ylabel 公众号总量（万） title('生活类'); figure(2)

subplot(2,1,1);

plot(t,d,'o',t,d1,'r:.'); d2=f(i,t);

plot(t,d,'o',t,d1,'r:.',t,d2,'g*--')

legend('原始数据','指数增长模型','阻滞增长模型',2)

欧阳文创编

欧阳文创编

xlabel 时间段

ylabel 公众号总量（万） title('娱乐类'); figure(2)

subplot(2,1,2);

plot(t,e,'o',t,e1,'r:.'); e2=f(k,t);

plot(t,e,'o',t,e1,'r:.',t,e2,'g*--')

legend('原始数据','指数增长模型','阻滞增长模型',2) xlabel 时间段

ylabel 公众号总量（万） title('其他');

参数

资讯类

生活类

娱乐类

其他类

公众号总量

6a b

158.1 47.52 811.4 671 1365 301.5

2.45910 9.888105

2254 164

k 0.2461 0.2313 0.166 0.174 0.182

程序代码：

x=[1:2:26]';

y=[3.04,6.63,11.13,28.43,49.22,87.85,134.11,200.00,208.69,303.03,410.73,580.00,728.57]';

b=[2.04,2.14,3.68,10.86,17.60,33.27,47.05,75.26,77.66,88.72,123.48,130.25,141.29]';

c=[0.40,0.97,2.31,4.45,7.63,10.11,19.86,33.44,38.03,75.07,112.08,152.39,226.55]';

欧阳文创编

欧阳文创编

d=[2.06,2.35,3.17,8.06,15.22,28.82,43.31,54.67,55.83,75.26,102.01,174.05,200.95]';

e=[0.54,1.18,1.98,5.06,8.77,15.65,23.89,36.63,37.17,53.98,73.16,123.31,159.78]'; st_ = [500 30 0.2 ];

ft_ = fittype('a0/(1+b0*exp(-k0*(x-1)))',... 'dependent',{'y'},'independent',{'x'},... 'coefficients',{'a0', 'b0','k0'}); cf_ = fit(x,y,ft_,'Startpoint',st_)

plot(cf_,'fit',0.95);hold on,plot(x,y,'ro') f1t_ = fittype('a1/(1+b1*exp(-k1*(x-1)))',... 'dependent',{'b'},'independent',{'x'},... 'coefficients',{'a1', 'b1','k1'}); c1f_ = fit(x,b,f1t_,'Startpoint',st_)

plot(c1f_,'fit',0.95);hold on,plot(x,b,'g*') f2t_ = fittype('a2/(1+b2*exp(-k2*(x-1)))',... 'dependent',{'c'},'independent',{'x'},... 'coefficients',{'a2', 'b2','k2'}); c2f_ = fit(x,c,f2t_,'Startpoint',st_)

plot(c2f_,'fit',0.95);hold on,plot(x,c,'b+') f3t_ = fittype('a3/(1+b3*exp(-k3*(x-1)))',... 'dependent',{'d'},'independent',{'x'},...

欧阳文创编

欧阳文创编

'coefficients',{'a3', 'b3','k3'}); c3f_ = fit(x,d,f3t_,'Startpoint',st_)

plot(c3f_,'fit',0.95);hold on,plot(x,d,'*') f4t_ = fittype('a4/(1+b4*exp(-k4*(x-1)))',... 'dependent',{'e'},'independent',{'x'},... 'coefficients',{'a4', 'b4','k4'}); c4f_ = fit(x,e,f4t_,'Startpoint',st_)

plot(c4f_,'fit',0.95);hold on,plot(x,e,'yo')

时间：2021.03.12 创作：欧阳文 欧阳文创编