Update GM_Verhulst.m

GM_Verhulst.m

+%% Creating symbolic variables a (Development factor) and b (Volume of ash action)
+syms a b;
+c = [a b]';
+
+%% Original series A
+A = [0.240 0.711 2.305 5.403];
+n = length(A);
+
+%% The series B is obtained by cumulative subtraction of the original series A
+for i = 2:n
+    H(i) = A(i) - A(i - 1);
+end
+H(1) = [];
+
+
+%% Immediate neighbourhood mean generation for the original series A
+for i = 2:n
+    C(i) = (A(i) + A(i-1))/2;
+end
+C(1) = [];
+
+%% Constructing the data matrix 
+D = [-C; C.^2];
+Y = H; Y = Y';
+
+%% Calculation of parameters using the least squares method
+% a (Development factor) and b (Volume of ash action)
+c = inv(D*D')*D*Y;
+c = c';
+a = c(1); b = c(2);
+
+%% Get the predicted data
+F = []; F(1) = A(1);
+for i = 2:(n+n)
+    F(i) = (a*A(1))/(b*A(1)+(a - b*A(1))*exp(a*(i-1)));
+end
+
+disp('Forecast data for：');
+F
+
+%% Plotting graphs
+t1 = 0:n-1; 
+t2 = 0:2*n-1;
+plot(t1, A, 'bo'); hold on;
+plot(t2, F, 'b');
+xlabel('Uniform sampling at each point of time/2h'); ylabel('Bacterial culture absorbance/OD600');
+legend('Actual quantity','Forecast quantity');
+title('S type growth curve of Escherichia coli culture');
+grid on;